CivilFEM 2026

5.1. General Concepts

5.1.1. Forces and Moments Sign Criteria

The following figure illustrates the sign criteria for forces and moments. The direction shown in the figure represents the positive direction of the force/moment.

T_x	Axial force in X direction
T_y	Axial force in Y direction
T_xy	Shear force in XY plane
M_x	Bending moment about Y axis (XZ plane)
M_y	Bending moment about X axis (YZ plane)
M_xy	Torsional moment XY
N_x	Shear force in X
N_y	Shear force in Y

5.1.2. Reinforcement Directions

Three type of reinforcements are considered for concrete shells:

· Axial+Bending reinforcement.

· Out of plane shear reinforcement.

· In-plane shear reinforcement.

Note: Some design methods or codes consider in-plane shear together with axial+bending. In these cases, a single group of reinforcement is provided that covers these actions.

The following diagrams show the different reinforcements along with the axis on which they are defined.

Armadura 1.png

Armadura 2.png

Armadura 3.png

The interaction diagram is a curve in space that contains the forces and moments (axial load, bending moment) corresponding to the shell ultimate strength states. In CivilFEM the ultimate strength states are determined through the pivots diagram.

A pivot is a strain limit associated with a material and its position in the shell vertex. If the strain in a section’s pivot exceeds the limit for that pivot, the shell vertex is considered cracked. Thus, pivots establish the positions of the strain plane. So, in an ultimate strength state, the strain plane supports at least one pivot of the shell vertex.

In CivilFEM pivots are defined as material properties and these properties (pivots) are extrapolated to all the points through the thickness of the shell vertex, accounting for the particular material of each point (concrete or reinforcement). Therefore, for the section’s strain plane determination, the following pivots and their corresponding material properties will be considered:

A Pivot	EPSmax. Maximum allowable strain in tension at any point of the shell vertex (the largest value of the maximum strains allowable for each point of the section in case there are different materials in the section).
B Pivot	EPSmin. Maximum allowable strain in compression at any point of the section (the largest value of the maximum strains allowable for each point of the section).
C Pivot	EPSint. Maximum allowable strain in compression at the interior points of the section.

Navier’s hypothesis is assumed for the determination of the strains plane. The strains plane is defined according to the following equation:

e (z) = e_g + K·z EQN.1

where:

e (z)	Strain of a point of the shell vertex. Depends on its z location.
e_g	Strain in the center of the section (center of gravity).
K	Curvature.

Diagram Construction Process

CivilFEM uses the elements (e_g,K) to determine the strains plane (ultimate strength plane) of the shell vertex. The process is composed of the following steps:

1. Values of e_g are chosen arbitrarily within the valid range:

EPSmin (B pivot ) < e_g< EPSmax (A pivot)

If there is no A pivot, (no reinforcement steel or if the ACI, AS3600 or BS8110 codes are used) there is no tension limit, and this is considered as infinite.

2. Two extreme admissible strains (EPSmin and EPSmax) are defined (different strains for different materials)

3. For each point of the shell vertex, the minimum ultimate strength curvature (K) is calculated.

4. The K curvature adopted will be the minimum of all the curvatures of the shell vertex points, according to the condition K ³ 0.

5. From the obtained K curvature and e_g (strain imposed at the center of gravity) the deformation corresponding to each of the shell vertex points e(z), is determined using EQN.1.

6. From the e(z) strain, the stress corresponding to each point of the shell vertex (s_p) is calculated. With this method, the stress distribution inside the shell vertex will be determined.

7. The ultimate axial force and bending moment is obtained by integrating the resulting stresses.

Note: For the design process, two components of forces and moments will be calculated: the component relative to the fixed points (corresponding to the concrete) and the component relative to the scalable points (corresponding to the bending reinforcement). The final forces and moments will be equal to the sum of the forces and moments of both components. The forces and moments due to the component for scalable points will be multiplied by the reinforcement factor (w).

(F, M)_real = (F, M)_fixed + w·(F, M)_scalable

Steps 1 to 7 are repeated, adjusting the e_g value and calculating the corresponding ultimate axial force and bending moment. Therefore, each value of e_g represents a point in the interaction diagram of the shell vertex.

5.1.4. Axial + Bending Check and Design

5.1.4.2 Calculation Hypothesis

The checking procedure only verifies the shell vertex strength requirements; thus, requirements relating to the serviceability conditions, minimum reinforcement amounts or reinforcement distribution for each code and structural type will not be considered.

It is assumed that plane sections will remain plane. The longitudinal strain of concrete and steel will be proportional to the distance from the neutral axis.

5.1.4.2 Criterion Definition

Checking of elements with regards to axial force and bending moment is performed as follows:

1. Acting forces and moments on the shell vertex (F, M) are obtained from the CivilFEM results file (file .RCF).

2. To construct the interaction diagram of the shell vertex, the ultimate strain state is determined such that the ultimate forces and moments are homothetic to the acting forces and moments with respect to the diagram center.

3. The strength criterion of the shell vertex is defined as the ratio between two distances. As shown above, the distance to the “center” of the diagram (point A of the figure) from the point representing the acting forces and moments (point P of the figure) is labeled as d₁ and the distance to the center from the point representing the homothetic ultimate forces and moments (point B) is d₂.

If the criterion is less than 1.00, the forces and moments acting on the shell vertex will be inferior to its ultimate strength, and the shell vertex will be safe. On the contrary, for criterion higher than 1.00, the shell vertex will be considered as not valid.

9.1.4.3 Reinforcement Design

The reinforcement designs produced by the various design methods designed in this chapter will be valid for a criterion value of 1.00 within a tolerance of 1%.

5.2. Wood-Armer Design Method

5.2.1. Hypothesis of the Calculation

The reinforcement design of shells under bending moments is accomplished by the method developed by R.H. Wood and G.S.T. Armer.

Once the reinforcement design moments have been calculated, a design for flexure is performed for each shell vertex.

5.2.2. Calculation Process of the Reinforcement Design Moments

Bending moments Mx and My and torsional moments Mxy are calculated from the shell calculation and obtained from the CivilFEM results file. Once these moments are obtained, the program searches for the pair of design moments Mx* and My*. This pair of moments is necessary for the reinforcement design and must include all the possible moments generated by Mx, My and Mxy in every direction.

CivilFEM provides the possibility of placing the reinforcement in two oblique directions: in the X direction of the element or in a direction at an angle a with the element Y direction.

armaplac

Design moments for the bottom reinforcement:

If either moment is negative, they will be defined as:

1. If Mx* < 0

2. If My* < 0

Design moments for the top reinforcement:

If either moment is positive, they will be defined as:

3. If Mx* > 0

4. If My* > 0

From these design moments, the required top and bottom reinforcement amounts will be calculated with the same procedure as for beams under bending moments.

5.2.3. Bending Design

5.2.3.2 Calculation Hypothesis

A rectangular diagram is adopted as the concrete stress-strain diagram. The diagram is formed by a rectangle with a height y given by a function of the neutral axis depth x and a width equal to 0.85 f_cd:

y = 0.8 x for x ≤ 1.25 h

y = h for x > 1.25 h

Where h is the depth of the cross-section.

The steel reinforcement stress-strain diagram is taken as bilinear with the horizontal plastic branch:

The center of gravity of the reinforcement will be placed at a point determined by the mechanical cover defined in each shell vertex.

In the absence of compression reinforcement, the engineering criteria will be taken as the maximum strength of the tensile reinforcement:

5.2.3.2 Calculation Process

Reinforcement design for flexure follows these steps:

1. Obtaining material strength properties. These properties are obtained from the material properties associated with each shell vertex, which should be previously defined in CivilFEM database.

2. Obtaining shell thickness geometrical data. Shell geometrical data must be defined within the CivilFEM shell structural element.

3. Obtaining reinforcement data. The only data concerning flexure design will be the values for the mechanical cover; these must be defined within the CivilFEM shell structural element.

4. Obtaining internal forces and moments.

5. Calculating the limit bending moment. Depending on the active code, the limit bending moment is calculated as follows:

Where:

Width (one unit length).

Effective depth: d = h – r_c

Shell thickness depth.

r_t

Mechanical cover for the tension reinforcement.

r_c

Mechanical cover for the compression reinforcement.

X_Lim

Neutral axis depth for the limit bending moment:

e_cu

Maximum strain of the extreme compression fiber of the concrete. Depends on the selected code (material EPSmin property).

e_sy

Elongation for the elastic limit:

Compression depth in the concrete rectangular diagram:

Eurocode 2	β = 0.8
EHE	β = 0.8
EB-FIP	β = 0.8
ACI 318 and ACI ACI 349	β = 0.8 if f_cd > 4000 psi
BS8110	β = 0.8 (values of the bellow figure do not apply for code BS8110)
AS 3600	β = 0.8 if f_cd ≤ 4000 psi
GB50010	β = 0.8
NBR6118	β = 0.8
AASHTO	β = 0.8 if f_cd  4000 psi
IS456	β = 0.8
S 52-101	β = 0.8

6. Calculating the required reinforcement. If the design bending moment (Md) is greater than the limit bending moment, both the tension and compression reinforcements will be designed. Otherwise, only the tension reinforcement will be designed.

Md ≤ M_lim

From X_n (neutral axis depth), the reinforcements are obtained by:

Tensile reinforcement:

Compression reinforcement: Asc=0

Md >M_lim

Stress in compression reinforcement is given by:

Therefore, the resultant reinforcement is:

Tensile reinforcement:

Compression reinforcement:

7. Obtaining design results. Design results are stored in the CivilFEM results file:

ASTX Reinforcement amount at X top.

ASBX Reinforcement amount at X bottom.

ASTY Reinforcement amount at Y top.

ASBY Reinforcement amount at Y bottom.

5.3. CEB-FIP Method

5.3.1. Calculation Hypothesis

Design under Bending Moment and In-Plane Loading:

1. The reinforcement design of shells under bending moment and in plane loading is accomplished by Model Code CEB-FIP 1990.

2. Reinforcements are defined as an orthogonal net (directions of this net are taken as element X and Y axes).

5.3.2. Equivalent Forces and Moments for Reinforcement Calculation

The shell is considered to be divided in three, ideal layers. The outer layers provide resistance to the in-plane effects of both bending and in-plane loading; the inner layer provides for a shear transfer between the outer layers.

From the forces and moments per unit length (m_Sdx, m_Sdy, m_Sdxy, n_Sdx, n_Sdy and v_Sd) that are calculated from the design and obtained from the CivilFEM results file, the following equivalent forces per unit length are obtained:

Where:

z_x, z_y, z_v	Lever arms between the axial forces in the X and Y directions respectively and the shear forces.
y	Lever arm between the shear forces (Distance from the mean plane of the slab to the selected force).

Following the Model Code, CivilFEM adopts the values:

Where h is the overall thickness of the plate.

So, the former equations change now to:

5.3.3. States and Resistance

These parameters are obtained by:

They are also represented in the following figure:

Depending on position of the point (a_x, a_y), the applicable procedure is as follows (If |v_Sd| » 0, the program utilizes the sign of n_Sdx and n_Sdy, to place the point in the correct zone). The internal system providing resistance to in-plane loading may be one of four cases:

CASE I - Tension in reinforcement in two directions and oblique compression in concrete.

CASE II - Tension in reinforcement in Y direction and oblique compression in concrete.

CASE III - Tension in reinforcement in X direction and oblique compression in concrete.

CASE IV - Biaxial compression in the concrete.

According to the case, resistances for the ultimate limit states are the following:

Case	Reinforcements	Concrete
I	f_ytd	f_cd2
II	f_ytd	f_cd2
III	f_ytd	f_cd2
IV	f_ytd	f_cd1

Where:

f_ytd= f_ytk/ g_sDesign tension strength of steel

f_cd2= 0.60 [1 - f_ck/250] f_cd (MPa)

f_cd1= 0.85 [1 - f_ck/250] f_cd (MPa)

5.3.4. Checking Outline

5.3.4.1. Cases

It is assumed that the shell is reinforced with an orthogonal mesh with dimensions of a_x and a_y.

The angle q is defined between the X-axis and the direction of compression. It can be defined by the user adhering to the condition of 1/3 ³ tan q ³ 3 (By default, q = 45º).

Forces and moments that support a cell of a_x x a_y dimensions are:

n_px = a_y ^. n_pSdx

n_py = a_x ^. n_pSdy

v_px = a_x ^. v_pSd

v_py = a_y ^. v_pSd

In general, v_px ¹v_py

1. CASE 1

The method of struts and ties will be applied to the following truss:

Applying the forces equilibrium in node A:

From the equilibrium of node B, the result is:

To check if these forces and moments are feasible, the strength of the concrete is checked.

Concrete area:

Stress on concrete struts:

This stress is compared to f_cd2 to obtain the concrete maximum compression criterion:

2. CASE II

By equilibrium in node A:

Nh1 cosq + Nh2 cosq = n_px

Nh1 sinq - Nh2 sinq = -V_py

By equilibrium in node B:

Na2 = sinq (Nh1+Nh2) + n_py

Maximum compression stress on concrete struts:

This stress is compared to f_cd2 to obtain the concrete maximum compression criterion:

3. CASE III

By equilibrium in node B:

Nh1 cosq - Nh2 cosq = v_px

Nh1 sinq + Nh2 sinq = n_py

By equilibrium in node A:

Na1 = (Nh1 + Nh2) cos q + n_px

The maximum compression stress on concrete struts:

This stress is compared to f_cd2 to obtain the maximum compression of the concrete criterion:

4. CASE IV – Assuming reinforcing bars are braced

In this situation, the struts and tie model will be the following:

Hyperstatic structure to be separated into two load states.

Both states have simple solutions due to symmetry.

- Solution of Structure 1:

· Node A:

2Nh ^. cos q + Na1 = n_px

· Node B:

2Nh ^. sin q + Na2 = n_py

· Movements compatibility

Where:

Ah = Concrete strut area

Aa1 = Horizontal steel amount

Aa2 = Vertical steel amount

Eh = Concrete modulus of elasticity

Ea = Steel modulus of elasticity

a = Cell width (ax)

b = Cell depth (ay), (b/a = tan q)

The length of the concrete struts before deformation:

Differentiating this expression:

However, Da and Db must coincide with the strain of steel bars:

DL must coincide with the strain of the concrete struts:

From the obtained equations, the following linear system is created:

Which when solved gives:

- Solution of Structure 2:

Due to non-symmetrical loads, the central bars (steel) are not applicable; therefore, equation 2 is determinant, and the following expression is obtained:

Nh2 sinq + Nh1 sinq = v_py

Nh2 cosq - Nh1 cosq = 0

Therefore:

Total Actions in Case IV

Adding the actions of 1 and 2:

Where:

With the assumption of braced bars, Na1 and Na2 signs correspond to compression for a + sign and tension for a - sign.

5. CASE IV – Assuming reinforcing bars are not braced

For steel bars without braces, there are two possible determinant truss configurations.

· Case 1

By equilibrium in A node:

Nh1 cosq + Nh2 cosq = n_px

Nh1 sinq - Nh2 sinq = v_py

By equilibrium in B node:

Na2 = sinq (Nh1+Nh2) - n_py > 0

· Case 2

By equilibrium in B node:

Nh1 cosq - Nh2 cosq = v_px

Nh1 sinq + Nh2 sinq = n_py

By equilibrium in A node:

Na1 = sinq (Nh1 + Nh2) - n_px > 0

· Discussion:

With this situation, CivilFEM will select whichever of the two cases satisfies:

Nh1, Nh2 ³ 0 and Na1, Na2 ³ 0

If neither case results in appropriate signs, it will be impossible to equilibrate the force and moment states without bracing the steel bars.

The maximum compression stress on the concrete struts is:

This stress is compared with f_cd1 to obtain the concrete maximum compression criterion:

5.3.4.2. Steel amount

For all the cases, steel reinforcement amounts per unit length of the shell are:

5.3.5. Reinforcement Checking in Intermediate Layer

The checking process described in 6.4.2.5 article of Model Code CEB-FIP1990 will be executed.

The principal shear force is:

Acting on a surface at an angle f, relative to the Y-axis

The following check is to performed: V1 £ V_Rdl

Where d is the total depth without the mechanical cover (in mm), and rx, ry are the ratios for the reinforcement closest to the face in tension, in the direction perpendicular to the surface that V1 acts on.

5.3.6. Required Parameters

5.3.6.1. General Requirements

Material properties described in section 9.3.3.

zx, zy, zv and y parameters which are defined for each element as a fraction of the depth at each point. As previously stated, CivilFEM uses the specifications from section 6.5.4 of the CEB Model Code.

The parameter that indicates whether the bars of the element are braced.

Angle q between the reinforcement X axis (element X axis) and the direction of compression. By default, q = 45º (although any angle is valid if 1/3 ³ tan q ³ 3).

5.3.6.2. Checking Requirements

Va1 and Va2 reinforcement amounts per unit length of the shell.

5.4. Design according to the Orthogonal Directions Method

5.4.1. Calculation Hypothesis

1. The design of reinforcement for bending moments and axial forces is performed independently for each direction.

2. Reinforcements are defined as an orthogonal mesh (directions of this mesh are taken as element X and Y axes).

MUD y OD 1

5.4.2. Design Forces and Moments

The axial forces (T^*_x, T^*_y) and bending moments (M^*_x, M^*_y) used for the design are those obtained for the reinforcement directions as follows:

If torsional moment and membrane shear force are neglected:

T^*_x= T_x

T^*_y= T_y

M^*_x= M_x

M^*_y= M_y

If torsional moment (M_xy) and membrane shear force (T_xy) are taken into account, then two processes are performed depending on considering membrane (in-plane) shear as tension and as compression.

1) Torsional moment and membrane shear force in tension:

2) Torsional moment and membrane shear force in compression:

If only torsional moment (M_xy) is considered:

T^*_x=T_x

T^*_y=T_y

Where X and Y represent the orthogonal directions of bending reinforcement of the shell.

5.4.3. Maximum Allowable Stress/Strain in Reinforcement

Reinforcement is designed using one of the following conditions:

The maximum strain allowed in tension is defined for the material (EPSMAX). It will be used as pivot A in the interaction diagram. This condition is typically used for Ultimate Limit States.
The maximum stress allowed is specified. This condition is typically used for Serviceability Limit States in order to control cracking.

5.4.4. Check and Design

Reinforcements design for the Orthogonal Directions method follows these steps:

1) Obtaining material strength properties. These properties are obtained from the material properties associated with each shell structural element, which should be previously defined in CivilFEM model.

2) Obtaining shell vertex geometrical data. Vertex geometrical data must be defined within the CivilFEM model.

3) Obtaining reinforcement data. The only data associated with the bending moment design are the mechanical cover values for the reinforcement; these must be defined within the CivilFEM shell structural elements.

4) Obtaining internal forces and moments. The acting bending moments and axial forces are those obtained for the X and Y directions of each element (T^*_x, T^*_y, M^*_x, M^*_y).

5) Check and design. Depending on the active code, the checking or design is performed using the pivot diagram described for the checking and design of concrete cross sections.

For checking, the criteria for axial force and bending moment are obtained as for the pivot diagram for beams for each direction.

All reinforcements are considered as scalable for design. The obtained reinforcement factor is therefore the value that must be used to multiply the upper and lower reinforcement amount to fulfill the code requirements.

6) Checking results. Checking results are stored in the CivilFEM results file:

Criterion for X direction.

Criterion for Y direction.

7) Design results. Design results are stored in the CivilFEM results file:

Reinforcement amount for X direction, top surface.

Reinforcement amount for X direction, bottom surface.

Reinforcement amount for Y direction, top surface.

Reinforcement amount for Y direction, bottom surface.

Design criterion for X direction.

Design criterion for Y direction.

5.5. Out-of-Plane Shear Load according to EC2 and ITER

Check and Design for Out-of-Plane Shear Loadings according to Eurocode 2 (EN 1992-1-1:2004/AC:2008) and ITER Design Code

5.5.1. Required Input Data

Shear check or design according to Eurocode 2 (EN 1992-1-1:2004/AC:2008) and ITER Design Code requires a series of parameters described below:

1) Materials strength properties. These properties are obtained from the material properties associated with each one of the shell vertices and for the active time. Those material properties should be previously defined. The required data are the following:

f_ckcharacteristic compressive strength of concrete.

f_cddesign strength of concrete.

f_yk characteristic yield strength of reinforcement.

f_ywd design strength of reinforcement.

γ_c partial safety factor for concrete.

γ_s partial safety factor for reinforcement.

2) Shell vertex geometrical data:

th thickness of the shell vertex (shell structural element).

3) Geometrical parameters. Required data are the following:

cbending reinforcement mechanical cover (shell structural element).

ρ_1i ratio of the longitudinal tensile reinforcement per unit length of the shell:

where:

A_ss area of the tensile reinforcement (shell structural element).

q angle of the compressive struts of concrete with the longitudinal axis of the member, (parameter THETA of shell structural element):

Eurocode 2 (EN 1992-1-1:2004/AC:2008)

ITER Design Code

Mean compressive stress

Mean tensile stress

4) Shell vertex reinforcement data. Required data are the following:

A_ss area of reinforcement per unit area, (parameter ASS of shell structural element).

The reinforcement ratio may also be obtained with the following data:

sx, sy spacing of the stirrups in each direction of the shell, (parameters SX and SY of shell structural element).

φ diameter of bars (parameter PHI of shell structural element).

n_x, n_y number of stirrups per unit length in each direction of the shell (parameters NX and NY of shell structural element).

5) Shell vertex internal forces. The shear force (V_Ed) acting on the vertex as well as the concomitant axial force (N_Ed) are obtained from the CivilFEM results file (.RCF).

which forms an angle with the axis Y

The value taken for the design compression force () is the maximum considering all directions:

Design compression force takes into account axial force in x, y directions and in-plane shear using Mohr’s circle stress transformation equations.

The total shear reinforcement is computed from those in each direction, according to equation LL.123 (Annex LL from EN 1992-2:2005):

5.5.2. Out-of-Plane Shear Checking

5.5.2.1. Checking whether shear reinforcement is required

Design shear force V_Ed is compared with the design shear resistance (V_Rd,c):

With the constraints:

Where:







		Eurocode 2 (EN 1992-1-1:2004/AC:2008)
		ITER Design Code

If shear reinforcement is defined in the section, V_Ed must be less than the minimum between the shear reinforcement force:

and the maximum design shear force resisted without crushing of concrete compressive struts:

Eurocode 2 (EN 1992-1-1:2004/AC:2008):

ITER Design Code:

where:

The shear reinforcement must be less than or equal to (Eurocode 2 only):

Results are written for each end in the CivilFEM results file:

If there is no shear reinforcement defined, the following results can be obtained:

Tensile strength for the longitudinal reinforcement

Shear reinforcement not defined

Shear reinforcement defined

Shear reinforcement not defined

, Shear reinforcement defined

5.5.2.2. Shear Criterion

The shear criterion indicates whether the shell vertex is valid for the design forces (if it is less than 1, the vertex satisfies the code provisions; whereas if it exceeds 1, the vertex will not be valid). Furthermore, it includes information about how close the design force is to the ultimate strength. The shear criterion is defined as follows:

If shear reinforcement is not defined.

If shear reinforcement is defined.

A value of 2¹⁰⁰for this criterion indicates that V_Rd,c, V_Rd,sor V_Rd,max are null.

5.5.3. Out-of-Plane Shear Design

5.5.3.1. Checking whether shear reinforcement is required

First, a check is made to determine if the design shear force V_Ed is less than or equal to the shear design resistance (V_Rd,c):

with constraints:

where:

	=
		in MPa
k	=	(d in mm)
	=	0.15
	=	MPa
		in mm²
		Eurocode 2 (EN 1992-1-1:2004/AC:2008)
𝝂	=

in N

Results are written for each end in the CivilFEM results file as the following parameters:

5.5.3.2. Maximum Design Shear Force Resisted Without Crushing of the Concrete Compressive Struts

A check is made to ensure that V_Ed does not exceed the maximum design shear force resisted without crushing of the concrete compressive struts.

Eurocode 2 (EN 1992-1-1:2004/AC:2008):

ITER Design Code:

where:

The following results will be saved:

If the design shear force is greater than the shear force required to crush the concrete compressive struts, the reinforcement design will not be feasible; as a result, the reinforcement parameter will be defined as 2¹⁰⁰.

In this case, the element will be marked as not designed.

5.5.3.3. Ratio of Reinforcement Required

The required strength of the reinforcement is given by:

The amount of reinforcement per length unit is given by:

The following is also verified (Eurocode 2 only):

If design shear force is greater than the shear force due to crushing of concrete compressive struts, the reinforcement design will not be feasible; therefore, the parameter containing this datum will be marked with 2¹⁰⁰. In this case, the element will be marked as not designed.

ASST and ASSB parameters store the amount of top and bottom reinforcement required due to the additional tensile force DFtd , in the longitudinal reinforcement due to shear VEd.

DFtd= 0,5 VEd ( )

ASST= DAsl for negative Bending Moments

ASSB= DAsl for positive Bending Moments

Results are written for each element end in the CivilFEM results file as the parameters:



design criterion

5.6. Out-of-Plane Shear Load according to Structural code (Spanish code)

Check and Design for Out-of-Plane Shear Loadings according to Structural Code (Annex 19)

5.6.1. Required Input Data

Shear check or design according to Structural Code (Annex 19) requires a series of parameters described below:

4) Materials strength properties. These properties are obtained from the material properties associated with each one of the shell vertices and for the active time. Those material properties should be previously defined. The required data are the following:

f_ckcharacteristic compressive strength of concrete.

f_cddesign strength of concrete.

f_yk characteristic yield strength of reinforcement.

f_ywd design strength of reinforcement.

γ_c partial safety factor for concrete.

γ_s partial safety factor for reinforcement.

5) Shell vertex geometrical data:

th thickness of the shell vertex (shell structural element).

6) Geometrical parameters. Required data are the following:

cbending reinforcement mechanical cover (shell structural element).

ρ_1i ratio of the longitudinal tensile reinforcement per unit length of the shell:

where:

A_ss area of the tensile reinforcement (shell structural element).

q angle of the compressive struts of concrete with the longitudinal axis of the member, (parameter THETA of shell structural element):

4) Shell vertex reinforcement data. Required data are the following:

A_ss area of reinforcement per unit area, (parameter ASS of shell structural element).

The reinforcement ratio may also be obtained with the following data:

sx, sy spacing of the stirrups in each direction of the shell, (parameters SX and SY of shell structural element).

φ diameter of bars (parameter PHI of shell structural element).

n_x, n_y number of stirrups per unit length in each direction of the shell (parameters NX and NY of shell structural element).

5) Shell vertex internal forces. The shear force (V_Ed) acting on the vertex as well as the concomitant axial force (N_Ed) are obtained from the CivilFEM results file (.RCF).

which forms an angle with the axis Y

The value taken for the design compression force () is the maximum considering all directions:

Design compression force takes into account axial force in x, y directions and in-plane shear using Mohr’s circle stress transformation equations.

The total shear reinforcement is computed from those in each direction, according:

5.6.2. Out-of-Plane Shear Checking

5.5.2.3. Checking whether shear reinforcement is required

Design shear force V_Ed is compared with the design shear resistance (V_Rd,c):

With the constraints:

Where:

If shear reinforcement is defined in the section, V_Ed must be less than the minimum between the shear reinforcement force:

and the maximum design shear force resisted without crushing of concrete compressive struts:

where:

The shear reinforcement must be less than or equal to :

Results are written for each end in the CivilFEM results file:

If there is no shear reinforcement defined, the following results can be obtained:

Tensile strength for the longitudinal reinforcement

Shear reinforcement not defined

Shear reinforcement defined

Shear reinforcement not defined

, Shear reinforcement defined

5.5.2.4. Shear Criterion

If shear reinforcement is not defined.

If shear reinforcement is defined.

A value of 2¹⁰⁰for this criterion indicates that V_Rd,c, V_Rd,sor V_Rd,max are null.

5.6.3. Out-of-Plane Shear Design

5.5.3.4. Checking whether shear reinforcement is required

First, a check is made to determine if the design shear force V_Ed is less than or equal to the shear design resistance (V_Rd,c):

with constraints:

where:

	=
		in MPa
k	=	(d in mm)
	=	0.15
	=	MPa
		in mm²
𝝂	=

in N

Results are written for each end in the CivilFEM results file as the following parameters:

5.5.3.5. Maximum Design Shear Force Resisted Without Crushing of the Concrete Compressive Struts

A check is made to ensure that V_Ed does not exceed the maximum design shear force resisted without crushing of the concrete compressive struts.

where:

The following results will be saved:

In this case, the element will be marked as not designed.

5.5.3.6. Ratio of Reinforcement Required

The required strength of the reinforcement is given by:

The amount of reinforcement per length unit is given by:

The following is also verified:

ASST and ASSB parameters store the amount of top and bottom reinforcement required due to the additional tensile force DFtd , in the longitudinal reinforcement due to shear VEd.

DFtd= 0,5 VEd ( )

ASST= DAsl for negative Bending Moments

ASSB= DAsl for positive Bending Moments

Results are written for each element end in the CivilFEM results file as the parameters:



design criterion

5.7. Out-of-Plane Shear Load according to ACI-318-05

5.7.1. Required Input Data

Shear checking or design according to ACI 318-05 requires the data described below:

1. Material strength properties. Material properties are assigned to each shell structural element. These material properties must be defined prior to the check and design process. The required properties are:

f’_c specified compressive strength of concrete.

f_y specified yield strength of reinforcement.

2. Shell vertex data:

th thickness of the shell vertex (shell structural element).

Required properties are:

3. Shell vertex reinforcement data.

cbending reinforcement mechanical cover (shell structural element).

A_ss the area of bending reinforcement per unit length. This parameter is used for checking (parameters of shell structural element).

4. Shell vertex shear reinforcement data.

A_ss area of shear reinforcement per unit of area. This parameter is used for checking (parameter of shell structural element).

The shear reinforcement ratio may also be obtained from:

A_ssX, A_ssYarea of shear reinforcement per unit of area in each direction of the shell. (parameters of shell structural element)

s_x, s_y spacing of the stirrups in each direction of the shell, (parameters of shell structural element).

diameter of bars in mm (shell structural element).

N_x, N_y number of stirrups per unit length in each direction of the shell (parameters of shell structural element).

5. Shell vertex internal forces. The shear force acting on the vertex as well as the concomitant membrane force are obtained from the CivilFEM results file (.RCF). For each direction of the shell vertex:

Force Description

V_u Design out-of-plane shear force

N_u Axial force (positive for compression).

5.7.2. Out-of-Plane Shear Checking

5.6.2.1. Shear Strength Provided by Concrete

The shear strength provided by concrete (V_c) is calculated with the following expression:

(ACI 318-05 Eqn:11-3)

where:

b_w = 1 (unit length)

square root of specified compressive strength of concrete, in psi (always taken as less than 100 psi).

For sections subject to a compressive axial force,

(ACI 318-05 Eqn:11-4)

where:

N_u/(th·b_w) expressed in psi.

If section is subjected to a tensile force so that the tensile stress is less than 500 psi:

(ACI 318-05 Eqn:11-8)

If the shell is subjected to a tensile force so that the tensile stress exceeds 500 psi, it is assumed V_c=0.

The calculation result for all elements is stored in the CivilFEM results file as the parameter VC (# is the direction of the shell, X or Y):

VC_# Shear strength provided by concrete.

5.6.2.2. Shear Strength Provided by Shear Reinforcement

The strength provided by the shear reinforcement (V_s) is calculated with the following expression:

(ACI 318-05 Eqn.11-15)

The calculation result for all elements is stored in the CivilFEM results file as the parameter VS (# is the direction of the shell, X or Y direction):

VS_# Shear strength provided by transverse reinforcement.

The following condition must be satisfied:

(ACI 318-01 Eqn.11.5.6.8)

This condition is reflected in the total criterion.

5.6.2.3. Nominal Shear Strength

The nominal shear strength (V_n) is the sum of the provided by concrete and by the shear reinforcement:

This nominal strength, is stored in the CivilFEM results file as the parameter VN (# is the direction of the shell, X or Y):

VN_# Nominal shear strength.

5.6.2.4. Minimum Reinforcement

If reinforcement is required, the minimum allowable value is:

(ACI 318-05 Eqn.11-13)

5.6.2.5. Shear Criterion

The shell vertex will be valid for shear if the following condition is satisfied and if the reinforcement is greater than the minimum required:

(ACI 318-05 Eqn.11-1 and 11-2)

Where f is strength reduction factor (φ = 0.75 according to chapter 9.3.2.3 of code requirements). Therefore, the shear criterion for the validity of the shell vertex is as follows:

For each element, this value is stored in the CivilFEM results file as the parameter CRT_#.

If the strength provided by concrete is null and the shear reinforcement is not defined in the shell vertex, and the criterion is equal to 2¹⁰⁰.

The φ∙V_n value is stored in CivilFEM results file as the parameter VFI_#.

The total checking criterion is defined as:

5.7.3. Out-of-Plane Shear Design

5.6.3.1. Shear Strength Provided by Concrete

The shear strength provided by the concrete (V_c) is calculated by:

(ACI 318-05 Eqn.11-8)

where:

b_w = 1 (unit length)

square root of specified compressive strength of concrete, in psi (always taken as less than 100 psi).

For sections subject to a compressive axial force,

(ACI 318-05 Eqn.11-4)

where:

N_u/(th·b_w) expressed in units of psi.

If the section is subjected to a tensile force such that the tensile stress is less than 500 psi,

(ACI 318-05 Eqn.11-8)

If the shell is subjected to a tensile force such that the tensile stress exceeds 500 psi, it is assumed that V_c=0.

The calculation result for all element ends is stored in the CivilFEM results file as the parameter VC (# is the direction of the shell, X or Y):

VC_# Shear strength provided by concrete.

5.6.3.2. Required Reinforcement Contribution

The shell must satisfy the following condition to resist the shear force:

(ACI 318-05 Eqn.11-1 and 11-2)

where: is the strength reduction factor (defined in Environment Configuration).

Therefore, the required shear strength of the reinforcement is:

Calculated results are stored in the CivilFEM results file for both element ends as the parameter VS (# is the direction of the shell, X or Y):

VS_# Shear resistance provided by the transverse reinforcement.

The following condition must be satisfied:

(ACI 318-01 Eqn.11.5.6.8)

If the required shear strength of the reinforcement does not satisfy the expression above, the shell vertex cannot be designed; therefore, the reinforcement parameter will be set as 2¹⁰⁰.

In this case, the element will be labeled as not designed.

5.6.3.3. Required Reinforcement

Once the required shear strength of the reinforcement has been determined, the reinforcement is calculated as the maximum of the following expressions (for both X and Y directions):

for both X and Y directions

(ACI 318-05 Eqn.11-15)

These reinforcement areas will be proportionally increased, if needed, to reach the minimum required ratio:

(ACI 318-05 Eqn.11-13)

The area of the designed reinforcement per unit length is stored in the CivilFEM results file as:

In this case, the element will be labeled as designed (providing the design process is correct for all element ends).

5.8. Out-of-Plane Shear Load according to ACI-318-14

5.8.1. Required Input Data

Shear checking or design according to ACI 318-14 requires the data described below:

f’_c specified compressive strength of concrete.

f_y specified yield strength of reinforcement.

modification factor for lightweight concrete ()

2. Shell vertex data:

th thickness of the shell vertex (shell structural element).

Required properties are:

3. Shell vertex reinforcement data.

cbending reinforcement mechanical cover (shell structural element).

A_ss the area of bending reinforcement per unit length. This parameter is used for checking (parameters of shell structural element).

4. Shell vertex shear reinforcement data.

A_ss area of shear reinforcement per unit of area. This parameter is used for checking (parameter of shell structural element).

The shear reinforcement ratio may also be obtained from:

A_ssX, A_ssYarea of shear reinforcement per unit of area in each direction of the shell. (parameters of shell structural element)

s_x, s_y spacing of the stirrups in each direction of the shell, (parameters of shell structural element).

diameter of bars in mm (shell structural element).

N_x, N_y number of stirrups per unit length in each direction of the shell (parameters of shell structural element).

Force Description

V_u Design out-of-plane shear force

N_u Axial force (positive for compression).

5.8.2. Out-of-Plane Shear Checking

5.7.2.1. Shear Strength Provided by Concrete

The shear strength provided by concrete (V_c) is calculated with the following expression:

(ACI 318-14 Eqn:11-3)

where:

b_w = 1 (unit length)

square root of specified compressive strength of concrete, in psi (always taken as less than 100 psi).

For sections subject to a compressive axial force,

(ACI 318-14 Eqn:11-4)

where:

N_u/(th·b_w) expressed in psi.

If section is subjected to a tensile force so that the tensile stress is less than 500 psi:

(ACI 318-14 Eqn:11-8)

If the shell is subjected to a tensile force so that the tensile stress exceeds 500 psi, it is assumed V_c=0.

The calculation result for all elements is stored in the CivilFEM results file as the parameter VC (# is the direction of the shell, X or Y):

VC_# Shear strength provided by concrete.

5.7.2.2. Shear Strength Provided by Shear Reinforcement

The strength provided by the shear reinforcement (V_s) is calculated with the following expression:

(ACI 318-14 Eqn.11-15)

The calculation result for all elements is stored in the CivilFEM results file as the parameter VS (# is the direction of the shell, X or Y direction):

VS_# Shear strength provided by transverse reinforcement.

The following condition must be satisfied:

(ACI 318-01 Eqn.11.5.6.8)

This condition is reflected in the total criterion.

5.7.2.3. Nominal Shear Strength

The nominal shear strength (V_n) is the sum of the provided by concrete and by the shear reinforcement:

This nominal strength, is stored in the CivilFEM results file as the parameter VN (# is the direction of the shell, X or Y):

VN_# Nominal shear strength.

5.7.2.4. Minimum Reinforcement

If reinforcement is required, the minimum allowable value is:

(ACI 318-14 Eqn.11-13)

5.7.2.5. Shear Criterion

The shell vertex will be valid for shear if the following condition is satisfied and if the reinforcement is greater than the minimum required:

(ACI 318-14 Eqn.11-1 and 11-2)

Where f is strength reduction factor (φ = 0.75 according to chapter 21.2 of code requirements). Therefore, the shear criterion for the validity of the shell vertex is as follows:

For each element, this value is stored in the CivilFEM results file as the parameter CRT_#.

If the strength provided by concrete is null and the shear reinforcement is not defined in the shell vertex, and the criterion is equal to 2¹⁰⁰.

The φ∙V_n value is stored in CivilFEM results file as the parameter VFI_#.

The total checking criterion is defined as:

5.8.3. Out-of-Plane Shear Design

5.7.3.1. Shear Strength Provided by Concrete

The shear strength provided by the concrete (V_c) is calculated by:

(ACI 318-14 Eqn.11-8)

where:

b_w = 1 (unit length)

square root of specified compressive strength of concrete, in psi (always taken as less than 100 psi).

For sections subject to a compressive axial force,

(ACI 318-14 Eqn.11-4)

where:

N_u/(th·b_w) expressed in units of psi.

If the section is subjected to a tensile force such that the tensile stress is less than 500 psi,

(ACI 318-14 Eqn.11-8)

If the shell is subjected to a tensile force such that the tensile stress exceeds 500 psi, it is assumed that V_c=0.

The calculation result for all element ends is stored in the CivilFEM results file as the parameter VC (# is the direction of the shell, X or Y):

VC_# Shear strength provided by concrete.

5.7.3.2. Required Reinforcement Contribution

The shell must satisfy the following condition to resist the shear force:

(ACI 318-14 Eqn.11-1 and 11-2)

where: is the strength reduction factor (defined in Environment Configuration).

Therefore, the required shear strength of the reinforcement is:

Calculated results are stored in the CivilFEM results file for both element ends as the parameter VS (# is the direction of the shell, X or Y):

VS_# Shear resistance provided by the transverse reinforcement.

The following condition must be satisfied:

(ACI 318-01 Eqn.11.5.6.8)

If the required shear strength of the reinforcement does not satisfy the expression above, the shell vertex cannot be designed; therefore, the reinforcement parameter will be set as 2¹⁰⁰.

In this case, the element will be labeled as not designed.

5.7.3.3. Required Reinforcement

Once the required shear strength of the reinforcement has been determined, the reinforcement is calculated as the maximum of the following expressions (for both X and Y directions):

for both X and Y directions

(ACI 318-14 Eqn.11-15)

These reinforcement areas will be proportionally increased, if needed, to reach the minimum required ratio:

(ACI 318-14 Eqn.11-13)

The area of the designed reinforcement per unit length is stored in the CivilFEM results file as:

In this case, the element will be labeled as designed (providing the design process is correct for all element ends).

5.9. Out-of-Plane Shear Load according to ACI-349-01

5.9.1. Required Input Data

Shear checking or design according to ACI 349-01 requires a series of parameters that are described below. The formulas listed in this section utilize U.S. (British) units: inch (in), pound (lb), and second (s).

1. Material strength properties. Material properties are assigned to each active shell vertex. These material properties must be defined prior to checking and design. The required properties are:

f’_c specified compressive strength of concrete.

f_y specified yield strength of reinforcement.

2. Shell vertex data:

th thickness of the shell vertex.

Required properties are:

3. Shell vertex reinforcement data.

cbending reinforcement mechanical cover.

A_ss the area of bending reinforcement per unit length. This parameter is used for checking (parameters of shell structural element).

4. Shell vertex shear reinforcement data.

A_ss area of shear reinforcement per unit of area. This parameter is used for checking (parameters of shell structural element).

The shear reinforcement ratio may also be obtained from:

A_ssX, A_ssYarea of shear reinforcement per unit of area in each direction of the shell. Parameters of shell structural element.

s_x, s_y spacing of the stirrups in each direction of the shell, parameters of shell structural element.

diameter of bars in mm.

N_x, N_y number of stirrups per unit length in each direction of the shell.

Force Description

V_u Design out-of-plane shear force

N_u Axial force (positive for compression).

5.9.2. Out-of-Plane Shear Checking

5.8.2.1. Shear Strength Provided by Concrete

The shear strength provided by concrete (V_c) is calculated by:

(ACI 349-01 Eqn:11-3)

where:

b_w= 1 (unit length)

square root of specified compressive strength of concrete, in psi (always taken as less than 100 psi).

For sections subject to an axial compressive force,

(ACI 349-01 Eqn:11-4)

where:

N_u/(th·b_w) expressed in units of psi.

If the section is subjected to a tensile force such that the tensile stress is less than 500 psi then,

(ACI 349-01 Eqn:11-8)

If the shell is subjected to a tensile force so that the tensile stress exceeds 500 psi, it is assumed V_c=0.

The calculation result for all elements is stored in the CivilFEM results file as the parameter VC (# is the direction of the shell, X or Y):

VC_# Shear strength provided by concrete.

5.8.2.2. Shear strength provided by shear reinforcement

The strength provided by shear reinforcement (V_s) is calculated with the following expression:

(ACI 349-01 Eqn.11-15)

The calculated result for all elements is stored in the CivilFEM results file as the parameter VS (# is the direction of the shell, X or Y):

VS_# Shear strength provided by transverse reinforcement.

The following condition must be satisfied:

(ACI 349-01 Eqn.11.5.6.8)

This condition is reflected in the total criterion.

5.8.2.3. Nominal shear strength

The nominal shear strength (V_n) is the sum of the concrete and shear reinforcement components calculated previously:

This nominal strength is stored in the CivilFEM results file as the parameter VN (# is the direction of the shell, X or Y):

VN_# Nominal shear strength.

5.8.2.4. Minimum reinforcement

If reinforcement is required, the minimum allowable value is:

(ACI 349-01 Eqn.11-13)

5.8.2.5. Shear criterion

The shell vertex will be valid for shear if the following condition is satisfied:

(ACI 349-01 Eqn.11-1 and 11-2)

where f is strength reduction factor (φ = 0.85 according to chapter 9.3.2.3 of code requirements ) and if the reinforcement is greater than the minimum required. Therefore, the validity shear criterion is defined as follows:

For each element, this value is stored in the CivilFEM results file as the parameter CRT_#.

If the strength provided by concrete is null and the shear reinforcement is not defined in the shell vertex, the criterion is set equal to 2¹⁰⁰.

The φ·V_n value is stored in the CivilFEM results file as the parameter VFI_#.

The total checking criterion is defined as:

5.9.3. Out-of-Plane Shear Design

5.8.3.1. Shear strength provided by concrete

The shear strength provided by concrete (V_c) is calculated with the following expression:

(ACI 349-01 Eqn.11-3)

where:

= 1 (unit length)

square root of specified compressive strength of concrete, in psi (it is always taken as less than 100 psi).

For sections subject to a compressive axial force,

(ACI 349-01 Eqn.11-4)

Where:

N_u/(th·b_w) is expressed in psi.

If the section is subjected to a tensile force such that the tensile stress is less than 500 psi:

(ACI 349-01 Eqn.11-8)

If the shell is subjected to a tensile force such that the tensile stress exceeds 500 psi, it is assumed that V_c=0.

The calculation result for all elements is stored in the CivilFEM results file as the parameter VC (# is the direction of the shell, X or Y):

VC_# Shear strength provided by concrete.

5.8.3.2. Required reinforcement contribution

The shell must satisfy the following condition to resist the shear force:

(ACI 349-01 Eqn.11-1 and 11-2)

Where f is the strength reduction factor (defined in Environment Configuration).

Therefore, the shear force the reinforcement must support is:

Calculation results are stored in the CivilFEM results file for all elements as the parameter VS (# is the direction of the shell, X or Y):

VS_# Shear resistance provided by the transverse reinforcement.

The following condition must be satisfied:

(ACI 349-01 Eqn.11.5.6.8)

If the shear force the reinforcement must support does not satisfy the expression above, the shell vertex cannot be designed, so the parameters where the reinforcement is stored are set to 2¹⁰⁰. Then:

In this case, the element will labeled as not designed.

5.8.3.3. Required reinforcement

Once the shear force that the shear reinforcement must support has been obtained, the reinforcement is calculated as follows:

(ACI 349-01 Eqn.11-15)

for each direction X and Y

These reinforcement areas will be increased proportionally, if needed, to reach the minimum required ratio:

(ACI 349-01 Eqn.11-13)

The area of the designed reinforcement per unit of area is stored in the CivilFEM results file as:

ASSH_X = Shear reinforcement in X direction.

ASSH_Y = Shear reinforcement in Y direction.

ASSH = ASSH_X + ASSH_Y

In this case, the element will be marked as designed (providing the design process is correct for all element directions).

5.10. Out-of-Plane Shear Load according to EHE-08

5.10.1. Required Input Data

Shear checking or design according to EHE-08 requires the following parameters:

1) Materials strength properties. These properties are obtained from the material properties associated with each one of shell structural element and for the active time. Those material properties should be previously defined. The required data are the following:

f_ck characteristic compressive strength of concrete.

f_yk characteristic yield strength of reinforcement.

f_ct,m mean tensile strength of concrete.

γ_c partial safety factor for concrete.

γ_s partial safety factor for reinforcement.

2) Shell vertex geometrical data:

th thickness of the shell structural element.

3) Geometrical parameters. Required data are the following:

cBending reinforcement mechanical cover.

ρ₁ ratio of the longitudinal tensile reinforcement per unit length of shell:

where:

A_ss the area of the tensile reinforcement.

q angle of the compressive struts of concrete with the longitudinal axis of member.

4) Shell vertex reinforcement data. Data concerning reinforcements of the shell vertex must be included within CivilFEM database. Required data are the following:

A_ss area of reinforcement per unit area.

The reinforcement ratio may also be obtained with:

sx, sy spacing of the stirrups in each direction of the shell.

φ diameter of bars.

n_x, n_y number of stirrups per unit length in each direction of the shell.

5) Shell vertex internal forces. The shear force acting on the vertex as well as the concomitant axial force are obtained from the CivilFEM results file (.RCF).

Design shear force (V_rd) is obtained from the shear forces in the X and Y directions:

Which forms an angle with the axis Y:

The value taken for the design compression force () is the maximum considering all directions:

Design compression force takes into account axial force in x, y directions and in-plane shear using Mohr’s circle stress transformation equations.

The total shear reinforcement is computed from those in each direction, according to equation LL.123 (Annex LL from EN 1992-2:2005):

5.10.2. Out-of-Plane Shear Checking

5.9.2.1. Checking Failure by Compression

The design shear force (V_rd) is compared to the oblique compression resistance of concrete (V_u1):

where:

f_1cd design compressive strength of concrete.

K reduction factor by axial forces effect

s’_cd effective axial stress in concrete (compression positive) accounting for the axial stress taken by reinforcement in compression.

For each element end, calculation results are written in the CivilFEM results file:

VU1 Ultimate shear strength due to oblique compression of the concrete.

CRTVU1 Ratio of the design shear (V_rd) to the resistance V_u1.

5.9.2.2. Checking Failure by Tension in the Web

The design shear force (V_rd) must be less than or equal to the shear force due to tension in the web (V_u2):

V_sucontribution of transverse shear reinforcement in the web to the shear strength.

V_cu contribution of concrete to the shear strength.

Members Without Shear Reinforcement

where:

(Compression positive)

< 2, d in mm

Member With Shear Reinforcement

Where A_s/s is the shear reinforcement area per unit length

In this case, the concrete contribution to shear strength is:

where:

q_e inclination angle of cracks, obtained from:

σ_xd, σ_yd design normal stresses, at the center of gravity, parallel to the longitudinal axis of member and to the shear force V_d respectively (tension positive)

Taking

In addition, the increment in tensile force due to shear force is calculated with the following equation:

For each end, calculation results are written in the CivilFEM results file:

VSU Contribution of the shear reinforcement to the shear strength.

VCU Contribution of concrete to the shear strength.

VU2 Ultimate shear strength by tension in the web.

CRTVU2 Ratio of the design shear force (V_rd) to the resistance V_u2 .

If V_u2 = 0, the CTRVU2 criterion is assigned the value of 2¹⁰⁰.

The increase in longitudinal reinforcement due to shear is stored in ASST and ASSB parameters (for top and bottom surfaces of the shell respectively).

5.9.2.3. Shear Criterion

For each end, this value is stored in the CivilFEM results file as the parameter CRT_TOT.

A value of 2¹⁰⁰ for this criterion indicates V_u2 is equal to zero.

5.10.3. Out-of-Plane Shear Design

5.9.3.1. Checking Compression Failure in the Web

The design shear force (V_rd) is compared to the oblique compression resistance of concrete (V_u1):

where:

f_1cd design compressive strength of concrete

K reduction coefficient by axial force effect

s’_cd effective axial stress in concrete (compression positive) accounting for the axial stress taken by the reinforcement in compression.

For each element end, calculation results are written in the CivilFEM results file:

VU1 Ultimate shear strength due to oblique compression of the concrete in web.

CRTVU1 Ratio of the design shear force (V_rd) to the resistance V_u1.

If design shear force is greater than shear force that causes the failure by oblique compression of concrete in the web, the reinforcement design is not feasible. Therefore, the reinforcement parameter will be defined as 2¹⁰⁰.

In this case, the element is labeled as not designed.

If there is no failure due to oblique compression, the calculation process continues.

5.9.3.2. Checking If the Shell Requires Shear Reinforcement

First, a check is made to ensure the design shear force V_d is less than the strength provided by concrete in members without shear reinforcement (V_cu):

Where:

(Compression positive)

< 2, d in mm

limited to 60 MPa

If the shell does not require shear reinforcement, the following parameters are defined:

VCU Contribution of concrete to the shear strength.

VU2 Ultimate shear strength by tension.

VSU Contribution of the shear reinforcement to the shear strength.

ASSH Required amount of shear reinforcement.

5.9.3.3. Contribution of the Required Transverse Reinforcement

If the shell requires shear reinforcement, sections under shear force will be valid if they satisfy the following condition:

V_sucontribution of shear transverse reinforcement in the web to shear strength.

V_cu contribution of concrete to shear strength.

where:

q_e inclination angle of cracks, obtained from:

σ_xd, σ_yd design normal stresses at the gravity center, parallel to the longitudinal axis of the member and to the shear force V_d, respectively (tension positive)

Taking

Therefore, the shear reinforcement contribution is given by the equation below:

For each element end, the value of V_cu and V_suis stored in the CivilFEM results file as the following parameters:

VCU Contribution of concrete to the shear strength.

VU2 Ultimate shear strength by tension.

VSU Contribution of the shear reinforcement to the shear strength.

5.9.3.4. Required Reinforcement Ratio

Once the required shear strength of the reinforcement has been obtained, the reinforcement can be calculated from the equation below:

The area of designed reinforcement per unit of shell area is stored in the CivilFEM results file as the parameter:

In this case, the element will be labeled as designed (provided the design process is correct for all element shell vertices).

If the design is not possible, the reinforcement will be marked as 2¹⁰⁰ and the element will not be designed.

ASST and ASSB parameters store the amount of top and bottom reinforcement required due to the additional tensile force DFtd , in the longitudinal reinforcement due to shear VEd.

ASST= DAsl for negative Bending Moments

ASSB= DAsl for positive Bending Moments

5.11. In-Plane Shear Load according to ACI 349-01

5.11.1. Required Input Data

Shear checking or design according to ACI 349 require the parameters described below. The formulas listed in this section utilize U.S. (British) units: inch (in), pound (lb), and second (s).

1. Material strength properties. This data is obtained from the material properties assigned to each active shell vertex. These material properties must be defined prior to check and design. The required properties are:

f’_c specified compressive strength of concrete.

f_y specified yield strength of reinforcement.

2. Shell vertex data:

th thickness of the shell vertex.

Required properties are:

3. Shell vertex reinforcement data.

cbending reinforcement mechanical cover.

A_ss the area of bending reinforcement per unit length.

4. Shell vertex shear reinforcement data.

A_ssipX, A_ssipX area of in plane shear reinforcement per unit of length in each direction of the shell.

5. Shell vertex internal forces. The shear force that acts on the vertex as well as the concomitant membrane force are obtained from the CivilFEM results file (.RCF). For each direction of the shell vertex:

Force Description

V_u Design in plane shear force

N_u Membrane force (positive for compression) perpendicular to V_u

6. Type of check/design. In-plane shear check/design according to ACI 349-01 is divided into the three following types:

· Walls with non-seismic loads. Covers chapter 14 of ACI 349-01 for walls.

· Walls with seismic loads. Covers chapters 14 and 21 of ACI 349-01 for walls.

· Slabs with seismic loads. Covers chapter 21 of ACI 349-01 for slabs.

5.11.2. In-Plane Shear Checking for Walls

5.10.2.1. Shear strength provided by concrete

For sections subjected to an axial compressive force, the shear strength provided by concrete (V_c) is calculated as:

(ACI 349-01 11.10.4 and 11.10.5)

Where:

square root of specified compressive strength of concrete, in psi (always taken less than 100 psi).

If the section is subjected to a tensile force such that the tensile stress is less than 500 psi then,

(ACI 349-01 11.10.5, 11.3.2.3)

If the shell is subjected to a tensile force such that the tensile stress exceeds 500 psi, it is assumed V_c=0.

The calculation result for all elements is stored in the CivilFEM results file as the parameter VC (# is the direction of the shell, X or Y):

VC_# Shear strength provided by concrete.

5.10.2.2. Shear strength provided by shear reinforcement

The strength provided by shear reinforcement (V_s) is calculated with the following expression:

(ACI 349-01 11.10.4 Eqn: 11-33)

The calculated result for all elements is stored in the CivilFEM results file as the parameter VS (# is the direction of the shell, X or Y):

VS_# Shear strength provided by reinforcement.

5.10.2.3. In-plane shear criterion – Non seismic loads

The nominal shear strength (V_n) is the sum of the concrete and shear reinforcement components calculated previously:

The shell vertex will be valid for shear if the following conditions are satisfied:

(ACI 349-01 Eqn: 11-1 and 11-2)

(ACI 349-01 11.10.3 and 11.10.4)

(ACI 349-01 11.10.9.2)

Where f is the strength reduction factor.

The shear criteria are calculated as:

(# is the direction of the shell, X or Y)

Therefore, the validity shear criterion is defined as follows:

These values are stored for all elements in the CivilFEM results file as the parameters and .

If the strength provided by concrete is null and the shear reinforcement is not defined in the shell vertex, then V_n=0, and the criterion CRT_1 will be set equal to 2¹⁰⁰.

If the shear reinforcement is not defined in the shell vertex, then the criterion CRT_3 is set equal to 2¹⁰⁰.

The φ·V_n value is stored in the CivilFEM results file as the parameter VPHI_# (# is the direction of the shell, X or Y).

5.10.2.4. In-plane shear criterion – Seismic loads

The nominal shear strength (V_n) is the sum of the concrete and shear reinforcement components:

But also limited by:

(ACI 349-01 21.6.5.2)

where A_cv is the area of concrete:

The shell vertex will be valid for shear if the following conditions are satisfied:

(ACI 349-01 21.6.5.2)

(ACI 349-01 21.6.5.6)

(ACI 349-01 21.6.2.1)

Where f is the strength reduction factor.

The shear criteria are calculated as:

(# is the direction of the shell, X or Y)

Therefore, the validity shear criterion is defined as follows:

These values are stored for all elements in the CivilFEM results file as the parameters and.

In case the strength provided by concrete is null and the shear reinforcement is not defined in the shell vertex, then V_n=0, and the criterion CRT_1 is set equal to 2¹⁰⁰.

If shear reinforcement is not defined in the shell vertex, then the criterion CRT_3 is set equal to 2¹⁰⁰.

The φ·V_n value is stored in the CivilFEM results file as the parameter VPHI_# (# is the direction of the shell, X or Y).

5.11.3. In-Plane Shear Design for Walls

5.10.3.1. Shear strength provided by concrete

For sections subject to an axial compressive force, the shear strength provided by concrete (V_c) is calculated by:

(ACI 349-01 11.10.4 and 11.10.5)

Where:

square root of specified compressive strength of concrete, in psi (always taken as less than 100 psi).

If the section is subjected to a tensile force such that the tensile stress is less than 500 psi:

(ACI 349-01 11.10.5, 11.3.2.3)

If the shell is subjected to a tensile force so that the tensile stress exceeds 500 psi, it is assumed V_c=0.

The calculated result for each element is stored in the CivilFEM results file as the parameter VC (# is the direction of the shell, X or Y):

VC_# Shear strength provided by concrete.

5.10.3.2. Required reinforcement contribution

The shell must satisfy the following condition to resist the shear force:

(ACI 349-01 11-1 and 11-2)

Where f is the strength reduction factor.

Required shear strength of the reinforcement:

The calculated result for each element is stored in the CivilFEM results file as the parameter VS (# is the direction of the shell, X or Y):

VS_# Shear strength provided by reinforcement.

5.10.3.3. Required reinforcement – Non seismic loads

The reinforcement amount is obtained by inserting the value of V_s, determined above, into the following equation:

(ACI 349-01 11.10.4 Eqn: 11-33)

The reinforcement amount has a minimum requirement of:

(ACI 349-01 11.10.9.2)

Therefore:

for each direction X and Y

The area of the designed reinforcement per unit length is stored in the CivilFEM results file as:

Also, the following condition must be satisfied:

(ACI 349-01 11.10.3 and 11.10.4)

This criterion is calculated as:

(# is the direction of the shell, X or Y)

If CRT_2_# is greater than 1.0, the condition will not be satisfied, and therefore, the element will not be designed. ASSIP_# will be set to 2¹⁰⁰ and the element will be labeled as not designed.

The criterion below compares the calculated reinforcement with the minimum reinforcement requirement:

(# is the direction of the shell, X or Y)

5.10.3.4. Required reinforcement – Seismic loads

The shell vertex will be valid for shear if the following conditions are satisfied:

(ACI 349-01 Eqn: 11-1 and 11-2)

With

(ACI 349-01 Eqn: 11-33)

and

(ACI 349-01 21.6.5.2)

where A_cv is the area of concrete:

Therefore the reinforcement amount is the minimum value that satisfies both expressions:

The reinforcement amount has a minimum requirement of:

(ACI 349-01 21.6.2.1)

Therefore:

for each direction X and Y

The area of the designed reinforcement per unit length is stored in the CivilFEM results file as:

Also, the following condition must be satisfied:

(ACI 349-01 21.6.5.6)

This criterion is calculated as:

(# is the direction of the shell, X or Y)

If CRT_2_# is greater than 1.0, the condition will not be satisfied, and therefore, the element will not be designed. ASSIP_# will then be set to 2¹⁰⁰ and the element will be labeled as not designed.

The criterion below compares the calculated reinforcement with the minimum required reinforcement:

(# is the direction of the shell, X or Y)

5.11.4. In-Plane Shear Checking for Slabs (Seismic Loads)

5.10.4.1. In plane shear criterion

The nominal shear strength (V_n) is limited by:

(ACI 349-01 21.6.5.2)

Where A_cv is the area of concrete:

The shell vertex will be valid for shear if the following conditions are satisfied:

(ACI 349-01 21.6.5.2)

(ACI 349-01 21.6.5.6)

(ACI 349-01 21.6.2.1, 7.12.2)

Note: A minimum reinforcement amount is not calculated for a thickness greater or equal than 48 in.

Where f is the strength reduction factor.

The shear criteria are calculated as:

(# is the direction of the shell, X or Y)

Therefore, the validity shear criterion is defined as follows:

These values are stored for each element in the CivilFEM results file as the parameters and .

If the strength provided by concrete is null and shear reinforcement is not defined in the shell vertex, then V_n=0, and the criterion CRT_1 is set equal to 2¹⁰⁰.

If shear reinforcement is not defined in the shell vertex, then the criterion CRT_3 is set equal to 2¹⁰⁰.

The φ·V_n value is stored in the CivilFEM results file as the parameter VPHI_# (# is the direction of the shell, X or Y).

5.11.5. In-Plane Shear Design for Slabs (Seismic Loads)

5.10.5.1. Required reinforcement

The shell vertex will be valid for shear if the following condition is satisfied:

(ACI 349-01 21.6.5.2)

where A_cv is the area of concrete:

The reinforcement amount has a minimum requirement of:

(ACI 349-01 21.6.2.1, 7.12.2)

Note: A minimum reinforcement amount is not calculated for a thickness greater or equal than 48 in.

Therefore the reinforcement amount is the minimum value that satisfies the following expressions for both X and Y directions:

The area of the designed reinforcement per unit length is stored in the CivilFEM results file as:

Also, the following condition must be satisfied:

(ACI 349-01 21.6.5.6)

This criterion is calculated as:

(# is the direction of the shell, X or Y)

If CRT_2_# is greater than 1.0, the condition above will not be satisfied and therefore the element cannot be designed. ASSIP_# will be set to 2¹⁰⁰ and the element will be labeled as not designed.

To determine if a minimum reinforcement amount has been defined, the CRT_3_# criterion is defined as:

5.12. Cracking Checking according to Eurocode 2 (EN 1992-1-1:2004/AC:2008)

5.12.1. Cracking Checking

The cracking check calculates the crack width and checks the following condition:

where:

Design crack width.

Maximum crack width (option in the Checking menu)

The design crack width is obtained from the following expression (Art. 7.3.4):

Maximum spacing between cracks.

Mean strain in the reinforcement.

Mean strain in the concrete between bars.

f Reinforcement bar size in mm (cross section code property).

Effective reinforcement ratio, where A_c,eff is the effective area of concrete in tension, A_s is the area of reinforcement contained within the effective concrete area and A_p’ is the area of pre- or post-tensioned tendons within A_c,eff CivilFEM calculates this value with and

Coefficient accounting for the influence of the bond properties of the bonded reinforcement (option in the Checking menu).

Coefficient accounting for the influence of the form of the strain distribution:

Where is the larger tensile strain and is the smaller tensile strain at the boundary of a section subjected to eccentric tension.

Constants defined in the National Annexes (option in the Checking menu).

c Cover to the longitudinal reinforcement. (Cross section code property).

Stress in the tensile reinforcement calculated for a cracked section.

Elastic modulus of the longitudinal reinforcement.

Coefficient accounting for the influence of the duration of the loading (option in the Checking menu).

Ratio between steel-concrete elastic modulus (E_s/E_cm).

5.12.2. Reinforcement Stress Calculation

During the calculation process, it is necessary to determine the reinforcement stress under service loads (σs) with the assumption the section is cracked.

The calculation of these stresses is an iterative process in which CivilFEM searches for the deformation plane that causes a stress state that is in equilibrium with the external loads. The reinforcement stress is obtained from this deformation plane and from the reinforcement position.

The design loads are taken as external loads for the case of serviceability stress calculation. For the stress calculation at the instant the crack appears, the external loads are taken as homothetic to the design loads that cause a stress equivalent to the concrete tensile strength in the fiber under the greatest amount of tension.

If the loads acting on the cross section cause collapse under axial plus bending checking, the cross section and the associated element are labeled as non-checked.

5.12.3. Checking results

Checking results are stored in the corresponding CivilFEM result file.

The following results are available:

CRT_TOT_X

Cracking criterion.

SIGMA_X

Maximum tensile stress.

WK_X

Design crack width

SRMAX_X

Maximum spacing between cracks.

EM_X

Difference between the mean strain in the reinforcement and the mean strain in concrete.

POS_X

Cracking position inside the section

1	Upper fiber.
-1	Lower fiber.
0	Upper and lower fibers.

CRT_TOT_Y

Cracking criterion.

SIGMA_Y

Maximum tensile stress.

WK_Y

Design crack width

SRMAX_Y

Maximum spacing between cracks.

EM_Y

Difference between the mean strain in the reinforcement and the mean strain in concrete.

POS_Y

Cracking position inside the section.

1	Upper fiber.
-1	Lower fiber.
0	Upper and lower fibers.

For the cracking check (w_max > 0) the total criterion is defined as:

For decompression checking (w_max = 0) the total criterion is defined as:

where

concrete design compressive strength

Maximum section stress (positive tension). It corresponds to the SIGMA result. (If CRT_TOT is negative, it’s taken as zero)

Therefore, values for the total criterion larger than one indicate that the section does not pass as valid for this code.

5.13. Cracking Checking according to Structural Code (Spanish code)

5.13.1. Cracking Checking

The cracking check calculates the crack width and checks the following condition:

where:

Design crack width.

Maximum crack width (option in the Checking menu)

The design crack width is obtained from the following expression (Art. 7.3.4):

Maximum spacing between cracks.

Mean strain in the reinforcement.

Mean strain in the concrete between bars.

f Reinforcement bar size in mm (cross section code property).

Coefficient accounting for the influence of the bond properties of the bonded reinforcement (option in the Checking menu).

Coefficient accounting for the influence of the form of the strain distribution:

Where is the larger tensile strain and is the smaller tensile strain at the boundary of a section subjected to eccentric tension.

Constants defined in the National Annexes (option in the Checking menu).

c Cover to the longitudinal reinforcement. (Cross section code property).

Stress in the tensile reinforcement calculated for a cracked section.

Elastic modulus of the longitudinal reinforcement.

Coefficient accounting for the influence of the duration of the loading (option in the Checking menu).

Ratio between steel-concrete elastic modulus (E_s/E_cm).

5.13.2. Reinforcement Stress Calculation

During the calculation process, it is necessary to determine the reinforcement stress under service loads (σs) with the assumption the section is cracked.

If the loads acting on the cross section cause collapse under axial plus bending checking, the cross section and the associated element are labeled as non-checked.

5.13.3. Checking results

Checking results are stored in the corresponding CivilFEM result file.

The following results are available:

CRT_TOT_X

Cracking criterion.

SIGMA_X

Maximum tensile stress.

WK_X

Design crack width

SRMAX_X

Maximum spacing between cracks.

EM_X

Difference between the mean strain in the reinforcement and the mean strain in concrete.

POS_X

Cracking position inside the section

1	Upper fiber.
-1	Lower fiber.
0	Upper and lower fibers.

CRT_TOT_Y

Cracking criterion.

SIGMA_Y

Maximum tensile stress.

WK_Y

Design crack width

SRMAX_Y

Maximum spacing between cracks.

EM_Y

Difference between the mean strain in the reinforcement and the mean strain in concrete.

POS_Y

Cracking position inside the section.

1	Upper fiber.
-1	Lower fiber.
0	Upper and lower fibers.

For the cracking check (w_max > 0) the total criterion is defined as:

For decompression checking (w_max = 0) the total criterion is defined as:

where

concrete design compressive strength

Maximum section stress (positive tension). It corresponds to the SIGMA result. (If CRT_TOT is negative, it’s taken as zero)

Therefore, values for the total criterion larger than one indicate that the section does not pass as valid for this code.

5.14. Cracking Checking according to ACI 318-05 and ACI 318-14

5.14.1. Cracking Checking

Checking of the Cracking Limit State according to ACI 318-05 and ACI 318-14 consists of the following condition:

Where:

Reinforcement spacing closest to the fiber in tension (option in the Checking menu)

S Design reinforcement spacing

CivilFEM checks this condition by applying the general calculation method for the reinforcement spacing (Art. 10.6.4):

where:

Calculated stress in reinforcement at service loads (in ksi).

Geometrical cover (cross section code property) (in inches).

5.14.2. Reinforcement Stress Calculation

During the calculation process, it’s necessary to determine the reinforcement stress under service loads (fs).

The calculation of the stresses is an iterative process in which the program searches for the deformation plane that causes a stress state that is in equilibrium with the external loads. The reinforcement stress is obtained from this deformation plane and from the reinforcement position.

The design loads are taken as external loads.

If the loads acting on the cross section cause collapse under axial plus bending checking, the cross section and the element to which it belongs are marked as non checked.

5.14.3. Checking results

Checking results are stored in the corresponding CivilFEM results file.

The following results are available:

CRT_TOT_X

Cracking criterion in X direction.

S_X

Design reinforcement spacing in X direction.

FS_X

Reinforcement stress in X direction.

SIGMA_X

Maximum tensile stress in X direction.

POS_X

Cracking position inside the section in X direction.

1	Upper fiber.
-1	Lower fiber.
0	Upper and lower fibers.

CRT_TOT_Y

Cracking criterion in Y direction.

S_Y

Design reinforcement spacing in Y direction.

FS_Y

Reinforcement stress in Y direction.

SIGMA_Y

Maximum tensile stress in Y direction.

POS_Y

Cracking position inside the section in Y direction.

1	Upper fiber.
-1	Lower fiber.
0	Upper and lower fibers.

For the cracking check (s_d > 0) the total criterion is defined as:

For decompression checking (s_d = 0) the total criterion is defined as:

where

concrete design compressive strength.

Maximum section stress (positive tension), corresponding to the SIGMA result. (If CRT_TOT is negative, it is taken as zero)

Therefore, the values for the total criterion larger than one indicate that the section is not considered valid for this code.

6.1. Introduction

Checking and reinforcement designing of reinforced concrete beams in CivilFEM is available for structures formed by 2D and 3D beam elements under axial loading plus biaxial bending, axial loading plus bending (particular case), shear, torsion and combined shear and torsion.

The check and design process of reinforced concrete beams under axial loading plus biaxial bending is based on the 3D interaction diagram of the analysed transverse section. This 3D interaction diagram contains forces and moments (FX, MY, MZ) corresponding to the sections ultimate strength states. Using this diagram, the program is able to check and design the section accounting for forces and moments previously obtained that act on the section. This process considers both generic sections and sections formed by different concretes and reinforcement steels.

The codes CivilFEM considers for the checking and design of reinforced beams subjected to axial force and biaxial bending are: ACI 318, EHE, Eurocode 2, ITER Design code, British Standard 8110, Australian Standard 3600, CEB-FIP 1990 model code, the Chinese code GB50010, NBR6118, AASHTO Standard Specifications for Highway Bridges, Russian Code СП 52-101-03, Indian Standard IS 456 and ACI 349.

6.2. 2D Interaction Diagram

6.2.1. Pivots Diagram

The interaction diagram is a graphical summary that contains the forces and moments (FX, MY) or (FX, MZ) corresponding to the section ultimate strength states. In CivilFEM the ultimate strength states are determined through the pivots diagram.

The “Pivot” concept is related to the limit behavior of the cross section with respect to steel and concrete material characteristics.

A pivot is a strain limit associated with a material and its position in the section. If the strain in a section’s pivot exceeds the limit for that pivot, the section will be considered as cracked. Thus, pivots establish the positions of the strain plane. In an ultimate strength state, the strain plane supports at least one pivot of the section.

In CivilFEM, pivots are defined as material properties and these properties (pivots) are extrapolated to all the section’s points, taken into account the material of each point. Therefore, for the section’s strain plane determination, the following pivots and their corresponding material properties will be considered:

A Pivot	EPSmax. Maximum allowable strain in tension at any point of the section (largest value of the maximum strains allowable for each point of the section if there are different materials in the section).
B Pivot	EPSmin. Maximum allowable strain in compression at any point of the section (largest value of the maximum strains allowable for each point of the section).
C Pivot	EPSint. Maximum allowable strain in compression at the interior points of the section.

Navier’s hypothesis is assumed for the determination of the strains plane. The strain’s plane is determined according to the following equation:

where:

e (y,z)	Strain of a section point as a function of the Y, Z axes of the section.
	Strain in the origin of the section (center of gravity).
	Curvature in Z axis.
	Curvature in Y axis.

In CivilFEM, the three elements e_g, Kz, Ky are substituted by the elements , , K to determine the strain plane. The relationship between (Kz, Ky) and (q, K) is the following:

= K·cos(q)

= K·sin(q)

q = Angle of the neutral axis with respect to the section’s Y axis

6.2.2. Diagram Construction Process

As stated in the previous section, CivilFEM uses the elements to determine the strains plane (ultimate strength plane) of the section.
and q are used as independent variables. The process is composed of the following steps:

1. Values of and q are chosen arbitrarily inside the extreme values allowed for these variables, which are:

EPSmin (B pivot ) EPSmax (A pivot)

-180º < q< +180º

If there is no A pivot, (if there is no reinforcement steel or if ACI, AS3600 or BS8110 codes are used) the tension limit does not exist and is considered infinite.

2. From the angle q, the program can identify which points are inside and outside the nucleus of the section.

3. Once the interior and exterior points are known, the two extreme admissible strains, EPSmin and EPSmax, are defined in each of the points (for each point based on its material).

4. For each point of the section, the minimum ultimate strength curvature (K) is calculated.

5. The K curvature will be adopted as the minimum of all the curvatures of all the section points, according to the condition K ³ 0.

6. From the obtained K curvature and e_g (strain imposed in the section’s center of gravity), the deformation corresponding to each of the section points e (x, y), is determined using the equations shown previously.

7. From the e (x, y) strain, the stress corresponding to each point of the section (sp) is calculated and entered into the stress-strain diagram for that point. Through this method, the stress distribution inside the section is determined.

8. Thus, as the elements are determined, the ultimate forces and moments (FX, MY, MZ) corresponding to the e_g strain and the q angle defined in step 1 are obtained by the summation of stresses at each of the section’s points multiplied by its corresponding weight.

Where: NP = number of points of the section

, , = weights at each point of the section.

Note: For the design process, two components of forces and moments will be calculated: the component relating to the fixed points (corresponding to the reinforcement defined as fixed and to the concrete) and the component relating to the scalable points (corresponding to the part of the section reinforcement defined as scalable, see Chapter 4.6.). The final forces and moments will be equal to the sum of the forces and moments of both components. The forces and moments due to the component for scalable points will be multiplied by the reinforcement factor (w).

(FX, MY, MZ)_real = (FX, MY, MZ)_fixed + w.(FX, MY, MZ)_scalable

9. Steps 1 to 8 are repeated, adjusting the eg and q values and calculating the corresponding ultimate force and moments (FX, MY, MZ). Each defined couple (e_g and q) represents a point in the 3D interaction diagram of the section. The greater the number of e_g and q values used (inside the interval specified in step 1), the larger of the number of points in the diagram, and therefore the accuracy of the diagram will increase.

With all of the 2D points previously obtained, the program constructs the interaction diagram by calculating the convex hull of these points. Once the convex hull is calculated, the “convexity criterion” of the diagram is determined; this criterion is the minimum of the criteria calculated for all the points of the diagram. The ideal value of the convexity criterion of the diagram is 1. In CivilFEM, it is not recommended to perform the check and design described above with interaction diagrams whose convexity criterion is less than 0.95.

It has been proven that the interaction diagram of sections composed by materials whose stress-strain law (for sections analysis) presents a descending branch has a very low convexity criterion. The check and design process with the diagram of these sections may lead to unsafe solutions. Therefore, it is NOT RECOMMENDED to use materials with this characteristic.

6.2.3. Determination of the Diagram Center

Normal interaction diagrams contain the coordinates’ origin in their interior, but in some cases the origin may be a point belonging to the surface or even a point outside the diagram (such as for prestressed concrete sections). In this situation, the section is cracked for null forces and moments.

To avoid these situations, CivilFEM changes the axes, placing the origin of the coordinate system inside the geometric center of the diagram. In this case, the calculation of the safety criterion is executed according to the new coordinate’s origin instead of the real origin.

If these changes are not made, safety forces and moments (in the diagram interior) could have a safety factor less than 1.00 and vice versa. If the coordinate’s origin is close to the diagram’s surface (although still inside), it will also be necessary to change the origin coordinates. In these cases, although the safety factors maintain values greater than 1.0 for safe sections and less than 1.0 for unsafe ones, they may adopt arbitrary values not very related to the section’s real safety factor.

Therefore, CivilFEM establishes a criterion to determine whether to use the real coordinate system origin or a modified one as a reference. Thus, if the following condition is fulfilled, the origin of the coordinates will be modified, moving the diagram’s real center to its geometric center.

Where:

Distance	Minimum distance from any point of the diagram to the real coordinate system origin.
Delta	Variable parameter which may be defined inside the [0,1] range. By default Delta=0.05.
Diameter	Diagonal of the rectangle which involves the diagram surface points.

6.2.4. Considerations

- The selection of the strains values at the origin of the section (eg) inside the interval (EPSmin, EPSmax) for each adopted angle of the neutral axis (q) is made uniformly spaced for sections with reinforcements below the center of gravity (bottom reinforcement). Half of it is distributed in the tension zone and the other half in the compression zone, avoiding a concentration of points in the ultimate tension zone and obtaining an even distribution of points.

- If the section does not have bottom reinforcement for each q or the reinforcement does not have pivot (EPSmax) (as in the case of the ACI or BS8110 codes), the distribution of the tension zone is hyperbolic. The compression zone will continue to have uniform distribution. By default the number of the values adopted by e_g is 30. The number of values must be a multiple of 2.

- At the same time, the selection of the q values is also uniform, inside the interval (-180º, +180º). The number of values must be a multiple of 4 in order to embrace the 4 quadrants of the section. By default, the number of values adopted by the program is 28.

- Although the number of the values of e_g and q used for the construction of the diagram can be defined by the user, it is recommended to choose numbers close to the default values. These values have been chosen in consideration of the calculation time and precision. If a number of values for either variable is a great deal higher than the default value, the processing time increases significantly.

On the other hand, if the number of values of e_g and q is reduced significantly, the precision in the calculation of the diagram may be affected.

6.3. Axial Load and Biaxial Bending Checking

6.3.1. Calculation Hypothesis

This checking procedure only verifies the section’s strength requirements; thus, requirements relating to serviceability conditions, minimum reinforcement amounts or reinforcement distribution for each code and structural typology will be not be considered.

Navier’s hypothesis is always assumed as valid; therefore, the deformed section will remain plane. The longitudinal strain of concrete and steel will be proportional to the distance from the neutral axis.

6.3.2. Calculation Process

Checking elements for axial force and biaxial bending adheres to the following steps:

1. Obtaining the acting forces and moments of the section (FXd, MYd, MZd). The acting forces and moments are obtained, following a calculation, directly from the CivilFEM results file (file .RCF).

2. Constructing the interaction diagram of the section. The ultimate strain state is determined such that the ultimate forces and moments are homothetic to the acting forces and moments with respect to the diagram center.

Obtaining the strength criterion of the section. This criterion is defined as the ratio between two distances. As shown above, the distance to the “center” of the diagram (point A of the figure) from the point representing the acting forces and moments (point P of the figure) is labeled as d₁ and the distance to the center from the point representing the homothetic ultimate forces and moments (point B) is d₂.

If this criterion is less than 1.00, the forces and moments acting on the section will be inferior to its ultimate strength, and the section will be safe. On the contrary, for criterion larger than 1.00, the section will not be considered as valid.

6.3.3. Check Results

Total Criterion, if this criterion is less than 1.0, in such a way that the forces and moments acting on the section are inferior to its ultimate strength, the section is safe (element is OK). On the contrary, for criterion higher than 1.0, the section will be considered as not valid (element is NOT OK).

Interaction Diagram, it includes all the necessary information for checking as well as design. Effects of actions, ultimate strength, safety information, as well as strength with and without reinforcement can be seen. The criterion provided is the ratio between the distances of the center of the diagram to the design loads point and the center of the diagram to the ultimate strength.

6.4. Axial Load and Biaxial Bending Design

6.4.1. Calculation Hypothesis

For the design of sections under axial loading and biaxial bending, the same hypothesis for the axial load and biaxial bending check is adopted.

6.4.2. Calculation Process

For the design, an optimization process is carried out through successive iterations; within this process, the safety factor of the section (or its criterion) must be strict (»1.00). These values are determined by the following steps:

1. Obtaining the minimum and maximum reinforcement factors. The maximum and minimum reinforcement factors (w_{max ,}w_min) are introduced by the user. The designed reinforcement of the section will always be more than w_min times and less than w_max times the initial distribution.

2. Obtaining the reinforcement data of the section. The reinforcements of the section to be designed must be defined by the class (only reinforcements defined as scalable are modified), type, position and initial amount (see Chapter 4.4). The designed reinforcement will be homothetic to the one defined in the section, in such a way that it complies with the strength requirements of the section. If the reinforcement amount is null, the program will not perform the design.

3. Obtaining the forces and moments acting on the section. Forces and moments () acting on the section are obtained directly from the CivilFEM results file (file .RCF).

4. Constructing the 2D interaction diagram. The diagram of the section is constructed for reinforcement corresponding to w_mintimes the initial distribution to determine the ultimate forces and moments of the section with this configuration.

5. From the interaction diagram of the previous step the ultimate strain state homothetic to the acting forces and moments can be determined with respect to the diagram center.

6. Obtaining the strength criterion of the section. This criterion is determined following the same process as described in the checking section.

7. If the value of the criterion is less than 1.00 (the forces and moments acting on the section are inferior to its ultimate strength), the section will be assigned reinforcement equal to times the initial distribution and the calculation will be terminated.

8. Repetition of steps 4, 5 and 6 for a reinforcement corresponding to times the initial reinforcement distribution.

9. If the value of the strength criterion of the section is more than 1.00 (acting forces are larger than the ultimate strength of the section), the program will indicate it is not possible to design the section and will not assign reinforcement nor will it continue calculating.

10. Optimization of the section reinforcement through successive iterations. From the forces and moments previously determined (FX, MY, MZ)_fixed and (FX, MY, MZ)_scalable, a search is done to obtain a reinforcement factor w that will produce a value of the section criterion between 0.99 and 1.01. The program will then assign reinforcement equal to w times the initial distribution of the section.

6.4.3. Design results

CivilFEM can obtain the needed reinforcement (design) in order to fulfill the code requirements. CivilFEM uses the interaction diagram of each section, taking into account the design stress-strain curve for each of the materials of the section. Moments in two directions are applied to the section. Scalable reinforcement will be increased/decreased until the section reaches a safety factor of 1.0 according to the code.

Design Total Criterion, elements with values equal to unity means that those elements were designed and a reinforcement factor was found within the provided range of ω_min and ω_max.

Designed elements

If the result is out of range then 2¹⁰⁰ values will appear.

Not

Designed elements

Reinforcement factor, depending on the range of ω_min and ω_max provided, different results appear:
1) Obtained reinforcement factor is inside (ω_min ,ω_max), then REINFACT value times the defined reinforcement amount gives the needed reinforcement.
2) ω_max is smaller than the reinforcement factor obtained, then REINFACT = 2¹⁰⁰for those elements.
3) ω_min is greater than the reinforcement factor obtained, then REINFACT = ω_min for those elements.

If CivilFEM is not able to design reinforcement with considered section, materials and initial reinforcement amount, then 2¹⁰⁰ values will appear.

Total scalable reinforcement (SCALAREA): This option gives the the product of the REINFACT previously obtained and the total scalable area of all reinforcement groups defined as scalable:

The user should note that reinforcement defined as Fixed will not be included in the calculation. If REINFACT is 2¹⁰⁰ , SCALAREA will also be assigned the value 2¹⁰⁰ .

6.5. Axial Force and Biaxial Bending Calculation Codes

For the check and design of reinforced concrete beams with different codes, the only variation will be the consideration of the pivots relative to the concrete (corresponding to EPSmin) and to the steel (corresponding to EPSmax). Therefore the pivots diagram for each code will differ in the construction of the section interaction diagram.

Codes provided by CivilFEM for the check and design of reinforced concrete beams under axial load and biaxial bending include: Eurocode 2, ITER Design code, Spanish code EHE, American codes ACI 318 and ACI 349, British Standard 8110, Australian Standard 3600, CEB-FIP model code, Chinese code GB50010, Brazilian code NBR6118, AASHTO Standard Specifications for Highway Bridges and ITER Structural Design Code for Buildings.

The strain limits defined hereafter are default values, but can be changed for each of the materials defined in the model.

6.5.1. Eurocode 2, ITER Design Code and Structural Code (Spanish code)

If the active code is Eurocode 2 ,ITER Structural Design Code for Buildings or Structural Code (Spanish code), the strain states relative to concrete and reinforcement steel are those defined in the following figure:

Eurocode 2.png

If concrete has , the concrete strain limits are the following:

EPSmin (‰) =

EPSint (‰) =

6.5.2. EHE Spanish Code

If the active code is EHE, the strain states relative to concrete and reinforcement steel are those defined in the following figure:

If concrete has f_ck > 50 MPa, the concrete strain limits are the following:

EPSmin (‰) =

EPSint (‰) = .

6.5.3. ACI 318-05

If the active code is ACI 318-05, the strain states relative to concrete and reinforcement steel are those defined in the following figure. It can be noted that there is no pivot relative to steel (EPSmax), considering the section does not fail due to reinforcement steel deformation.

ACI 318.png

The theoretical values of the interaction diagram are affected by the strength reduction factor f according to Chapter 9.3 of Building Code Requirements for Structural Concrete Structures (ACI 318-05) document:

Where e_t is the maximum strain obtained at the reinforcement and is the strength reduction factor for compression controlled sections:

For ACI 318-05 (according to chapter 9.3.2 from code requirements)

Member with spiral reinforcement =0.70

Other reinforcement members =0.65 (default value)

Furthermore, according to Chapter 10.3.6 of Building Code Requirements for Structural Concrete Structures (ACI 318-05) document, design axial strength φP_n of compression members must not be greater than:

1. For member with spiral reinforcement:

2. For other reinforcement:

Where A_g is the gross area of concrete section and A_st is the total area of longitudinal reinforcement.

6.5.4. ACI 318-14

If the active code is ACI 318-14, the strain states relative to concrete and reinforcement steel are those defined in the following figure. It can be noted that there is no pivot relative to steel (EPSmax), considering the section does not fail due to reinforcement steel deformation.

ACI 318.png

The theoretical values of the interaction diagram are affected by the strength reduction factor f according to Chapter 21.2.2 of Building Code Requirements for Structural Concrete Structures (ACI 318-14) document

Where e_t is the maximum strain obtained at the reinforcement and is the strength reduction factor for compression controlled sections:

For ACI 318-14 (according to chapter 21.2.2 from code requirements)

Member with spiral reinforcement =0.75

Other reinforcement members =0.65 (default value)

Furthermore, according to Chapter 22.4.2 of Building Code Requirements for Structural Concrete Structures (ACI 318-14) document, design axial strength φP_n of compression members must not be greater than:

1. For member with spiral reinforcement:

2. For other reinforcement:

Where A_g is the gross area of concrete section and A_st is the total area of longitudinal reinforcement.

6.5.5. ACI 349-01

If the active code is ACI 349-01, the strain states relative to concrete and reinforcement steel are the ones defined in the following figure. It can be noted that there is no pivot relative to steel (EPSmax), considering the section does not fail due to reinforcement steel deformation.

ACI 349.png

The theoretical values of the interaction diagram are affected by the strength reduction factor f according to Chapter 9.3 of Code Requirements for Nuclear Safety Related Concrete Structures (ACI 349-01) document:

Where is the axial load (tension positive), is the concrete gross area and is the strength reduction factor for compression controlled sections:

For ACI 349-01 (according to chapter 9.3.2 from code requirements)

Axial tension, and axial tension with flexure

      Axial compression and axial compression with flexure:
a) Member with spiral reinforcement         =0.75
b) Other reinforcement members    =0.70 (default value)

Furthermore, according to Chapter 10.3.5 of Code Requirements for Nuclear Safety Related Concrete Structures (ACI 349-01) document, design axial strength φP_n of compression members must not be greater than:

1. For member with spiral reinforcement:

2. For other reinforcement:

Where A_g is the gross area of concrete section and A_st is the total area of longitudinal reinforcement.

6.5.6. ACI 349-06

If the active code is ACI 349-06, the strain states relative to concrete and reinforcement steel are the ones defined in the following figure. It can be noted that there is no pivot relative to steel (EPSmax), considering the section does not fail due to reinforcement steel deformation.

ACI 349.png

The theoretical values of the interaction diagram are affected by the strength reduction factor f according to Chapter 9.3 of Code Requirements for Nuclear Safety-Related Concrete Structures (ACI 349-06) document:

Where e_t is the maximum strain obtained at the reinforcement and is the strength reduction factor for compression controlled sections:

For ACI 349-06 (according to chapter 9.3.2 from code requirements)

Axial tension, and axial tension with flexure

      Axial compression and axial compression with flexure:
a) Member with spiral reinforcement         =0.70
b) Other reinforcement members    =0.65 (default value)

Furthermore, according to Chapter 10.3.6 of Code Requirements for Nuclear Safety Related Concrete Structures (ACI 349-06) document, design axial strength φP_n of compression members must not be greater than:

1. For member with spiral reinforcement:

2. For other reinforcement:

Where A_g is the gross area of concrete section and A_st is the total area of longitudinal reinforcement.

6.5.7. ACI 349-13

If the active code is ACI 349-13, the strain states relative to concrete and reinforcement steel are the ones defined in the following figure. It can be noted that there is no pivot relative to steel (EPSmax), considering the section does not fail due to reinforcement steel deformation.

ACI 349.png

The theoretical values of the interaction diagram are affected by the strength reduction factor f according to Chapter 9.3.2 of Code Requirements for Nuclear Safety-Related Concrete Structures (ACI 349-13) document:

Where e_t is the maximum strain obtained at the reinforcement and is the strength reduction factor for compression controlled sections:

For ACI 349-13 (according to chapter 9.3.2 from code requirements)

Axial tension, and axial tension with flexure

      Axial compression and axial compression with flexure:
a) Member with spiral reinforcement         =0.75
b) Other reinforcement members    =0.65 (default value)

Furthermore, according to Chapter 10.3.6 of Code Requirements for Nuclear Safety Related Concrete Structures (ACI 349-13) document, design axial strength φP_n of compression members must not be greater than:

3. For member with spiral reinforcement:

4. For other reinforcement:

Where A_g is the gross area of concrete section and A_st is the total area of longitudinal reinforcement.

6.5.8. CEB-FIP

If the active code is CEB-FIP, the strain states relative to concrete and reinforcement steel are those defined in the following figure:

6.5.9. British Standard 8110

If the active code is BS8110, the strain states relative to concrete and reinforcement steel are those defined in the following figure. It can be noted that there is no pivot relative to steel (EPSmax), considering the section does not fail due to reinforcement steel deformation:

6.5.10. Australian Standard 3600

If the active code is AS3600, CivilFEM uses the same parameters as the ACI 318 code for material properties.

The theoretical values of the interaction diagram are affected by the strength reduction factor f. This value is taken from the member properties.

6.5.11. Chinese Code GB50010

If the active code is GB50010, the strain states relative to concrete and reinforcement steel are the ones defined in the following figure:

Where EPScu = 0.0033-(f_cuk-50)*10⁵ [MPa]

6.5.12. Brazilian Code NBR6118

If the active code is NBR6118, the strain states relative to concrete and reinforcement steel are those defined in the following figure:

6.5.13. AASHTO Standard Specifications for Highway Bridges

If the active code is AASHTO Standard Specifications for Highway Bridges CivilFEM uses the same parameters as the ACI 318 code for material properties.

The theoretical values of the interaction diagram are affected by the strength reduction factor f.

Where e_t is the maximum strain obtained at the reinforcement.

For AASHTO (according to chapter 5.5.4.2 from AASHTO LRFD Bridge Design Specifications):

Axial tension, and axial tension with flexure

Axial compression and axial compression with flexure

Furthermore, according to Chapter 5.7.4.4, design axial strength φP_n of compression members must not be greater than:

1. For member with spiral reinforcement:

2. For other reinforcement:

Where A_g is the gross area of concrete section and A_st is the total area of longitudinal reinforcement.

6.5.14. Indian Standard 456

If the active code is the Indian Standard 456, the strain states relative to concrete are the ones defined in the following figure:

It can be noted that there is no pivot relative to steel (EPSmax), considering the section does not fail due to reinforcement steel deformation.

6.5.15. Russian Code SP 52-101

If the active code is SP 52-101, the strain states relative to concrete and reinforcement steel are the ones defined in the following figure:

SP 52-101.png

6.6. Shear and Torsion

6.6.1. Previous considerations

Valid reinforced concrete sections for shear and torsion check and design are the following:

Table 1‑1 Valid Sections for Shear and Torsion Checking

SECTION	Y SHEAR	Z SHEAR	TORSION
Rectangular	Yes	Yes	Yes
Box	Yes	Yes	Yes
Circular	Yes	Yes	Yes
Annular	Yes	Yes	Yes
Double T/I-shape	Yes	No	No
T	Yes	No	No

For each one of these sections and directions, a set of geometrical parameters in accordance with the code is automatically defined. These parameters are required for the calculating process. Later on, there is a detailed explanation on how to obtain these parameters for each valid section.

6.6.2. Shear and torsion code properties

Parameters required for the check and design processes for shear and torsion are the following:

EUROCODE 2 AND ITER

REC:

Reinforcement cover.

BW_VY:

Minimum width of the section over the effective depth for shear in Y.

BW_VZ:

Minimum width of the section over the effective depth for shear in Z.

DY:

Effective depth of the section in the Y direction.

DZ:

Effective depth of the section in the Z direction.

RHO1:

Reinforcement ratio:

Where:

	Area of the tension reinforcement extending not less than beyond the section considered.
	Minimum width of the section over the effective depth.
d	Effective depth.

Equivalent thickness of the wall:

Where:

A	Total area of the cross-section within the outer circumference, including inner hollow areas.
u	Outer circumference.

This equivalent thickness cannot be greater than the real thickness of the wall nor less than twice the cover.

AK:

Area enclosed within the centre-line of the thin-walled cross-section.

UK:

Circumference of the AK area.

KEYAST:

Indicator of the position of the torsion reinforcement in the section:

= 0 if closed stirrups are placed on both faces of each wall of the equivalent hollow section or on each wall of a box section (value by default for hollow sections).

= 1 if there are only closed stirrups distributed around the periphery of the member (value by default for solid sections).

THETA:

Angle of the concrete compressive struts with the longitudinal axis of member.

*ACI 318-05 and ACI 349-01*
REC:	Reinforcement cover.
BW_VY:	Web width or diameter of circular section for shear in Y (Art. 11.1).
BW_VZ:	Web width, or diameter of circular section for shear in Z (Art. 11.1).
DY:	Distance from extreme compression fiber to centroid of longitudinal tension reinforcement in Y, (for circular sections, this distance should not be less than the distance from extreme compression fiber to centroid of tension reinforcement in the opposite half of the member) (Art. 11.1).
DZ:	Distance from extreme compression fiber to centroid of longitudinal tension reinforcement in Z, (for circular sections, this distance should not be less than the distance from extreme compression fiber to centroid of tension reinforcement in the opposite half of the member) (Art. 11.1).
ACP:	Area enclosed by outside perimeter of concrete cross section (Art. 11.6.1).
PCP:	Outside perimeter of the concrete cross section (Art. 11.6.1).
AOH:	Area enclosed by center-line of the outermost closed transverse torsional reinforcement (Art. 11.6.3).
PH:	Perimeter of centerline of outermost closed transverse torsional reinforcement (Art. 11.6.3).
AO:	Gross area enclosed by shear flow path (Art. 11.6.3).

*BS 8110*
REC:	Reinforcement cover.
BW_VY:	Minimum web width, for shear in Y (Art.3.4.5.1 Part 1).
BW_VZ:	Minimum web width, for shear in Z (Art.3.4.5.1 Part 1).
DY:	Effective depth of section in the Y direction (Art.3.4.5.1 Part 1).
DZ:	Effective depth of section in the Z direction (Art.3.4.5.1 Part 1).
AS:	Longitudinal tension reinforcement (Art.3.4.5.4 Part 1).
X_W:	Torsional modulus for checking and dimensioning purposes.
X1:	Minimum dimension of the rectangular torsion stirrups (Art.2.4.2 Part 2).
Y1:	Maximum dimension of the rectangular torsion stirrups (Art.2.4.2 Part 2).

*GB 50010*
REC:	Reinforcement cover.
BW_VY:	Minimum width of the section over the effective depth for shear in Y (Art. 7.5.1).
BW_VZ:	Minimum width of the section over the effective depth for shear in Z (Art. 7.5.1).
DY:	Effective depth of the section in Y (Art. 7.5.1).
DZ:	Effective depth of the section in Z (Art. 7.5.1).
HW_VY:	Effective depth of the web in Y (Art. 7.5.1).
HW_VZ:	Effective depth of the web in Z (Art. 7.5.1).
:	Area enclosed within the hoop reinforcements for torsion A_st1 (Art. 7.6.4).
:	Area enclosed within the hoop reinforcements for torsion A_st1 (Art. 7.6.4) of branch 1(e. x. Flange).
:	Area enclosed within the hoop reinforcements for torsion A_st1 (Art. 7.6.4) of branch 2(e. x. Flange).
:	Perimeter of the area (Art. 7.6.4).
:	Perimeter of the area of branch 1 (Art. 7.6.4).
:	Perimeter of the area of branch 2 (Art. 7.6.4).
:	Plastic resistance of torsion moment (Art. 7.6.4).
:	Plastic resistance of torsion moment of branch 1 (Art. 7.6.4).
:	Plastic resistance of torsion moment of branch 2 (Art. 7.6.4).
ALF:	Ratio of the web depth to the web width (Art. 7.6.1).
:	Affected factor of the thickness of web for torsion (Art. 7.6.6).
Tky	For rectangular sections: Section width in Y.
Tkz	For rectangular sections: Section width in Z.

AASHTO Standard Specifications for Highway Bridges
REC:	Reinforcement cover.
BW_VY:	Web width or diameter of circular section for shear in Y (Art. 8.15.5).
BW_VZ:	Web width or diameter of circular section for shear in Z (Art. 8.15.5).
DY:	Distance from extreme compression fiber to centroid of longitudinal tensile reinforcement in Y (for circular sections, this distance should not to be less than the distance from extreme compression fiber to centroid of tensile reinforcement in the opposite half of the member) (Art. 8.15.5).
DZ:	Distance from extreme compression fiber to centroid of longitudinal tensile reinforcement in Z, (for circular sections, this distance should not to be less than the distance from extreme compression fiber to centroid of tensile reinforcement in the opposite half of the member) (Art. 8.15.5).
ACP:	Area enclosed by outside perimeter of concrete cross section (taken from ACI 318 Art. 11.6.1).
PCP:	Outside perimeter of the concrete cross section (taken from ACI 318 Art. 11.6.1).
AOH:	Area enclosed by center-line of the outermost closed transverse torsion reinforcement (taken from ACI 318 Art. 11.6.3).
PH:	Perimeter of centerline of outermost closed transverse torsion reinforcement (taken from ACI 318 Art. 11.6.3).
AO:	Gross area enclosed by shear flow path (taken from ACI 318 Art. 11.6.3).

EHE

REC:

Reinforcement cover.

BW_VY:

Width of element in VY direction equal to the total width in solid sections or in case of box sections, the width equals the sum of the width of both webs.

BW_VZ:

Width of element in VZ direction equal to the total width in solid sections or in case of box sections, the width equals the sum of the width of both webs.

DY:

Effective depth of the section in Y (Art. 44.2.3).

DZ:

Effective depth of the section in Z (Art. 44.2.3).

RHO1:

Geometric ratio of the longitudinal tensile reinforcement anchored at a distance greater than or equal to d (Art. 44.2.3.2).

Where:

	Area of the longitudinal tensile reinforcement anchored at a distance greater than or equal to d beyond the section considered.
	Width of the web.
d	Effective depth.

HE:

Equivalent thickness of the wall (Art. 45.2.1):

Where:

A	Total area of the cross-section within the outer circumference, including inner hollow areas.
u	Outer circumference.

This equivalent thickness cannot be greater than the real thickness of the wall nor less than twice the cover.

AE:

Area inside the center-line of the design effective hollow section (Art. 45.2.2).

UE:

Perimeter of the center-line of the design effective hollow section (Art. 45.2.2).

KEYAST:

Indicator of the position of the torsion reinforcement in the section (Art. 45.2.2.1):

=0 if closed stirrups are placed on both faces of each wall of the equivalent hollow section or of the real hollow section (value by default for hollow sections).

= 1 if there are only closed stirrups distributed around the periphery of the member (value by default for solid sections).

THETA:

Angle of the concrete compressive struts with the longitudinal axis of member (Art. 44.2.3).

6.6.3. Code Dependent Parameters for Each Section

The following section describes how to compute the required parameters for shear and torsion according to each code. Shear and torsion calculations are performed taking for each end its section for shear considerations without accounting for reductions or enlargements due to depth variations. The mechanical cover for bending longitudinal reinforcement is required for the calculations of some parameters. The default mechanical cover for every case is equal to 5 cm.

6.6.3.1 Rectangular Section Parameters

Where Tky Section width in Y.

Tkz Section width in Z.

Eurocode 2 and ITER






.

ACI 318 and ACI 349

BS 8110




	MIN

EHE






.

GB50010

AASHTO Standard Specifications for Highway Bridges

6.6.3.2 Box Section Parameters

Where: Tky Section width in Y.

Tkz Section width in Z.

Twy Thickness of walls in Y.

Twz Thickness of walls in Z.

Eurocode 2 and ITER

ACI 318 and ACI 349

BS8110




Ac = gross concrete area	Xw is considered solid rectangular if Twy > 0.25Tky and Twz > 0.25Tkz. Otherwise: Xw = 2^.MIN(Twy,Twz)^.(Tkay,Twy)^.(Tkz,Twz)
X1 = MIN(Tky,Tkz) – 2^.REC	Y1 = MAX(Tky,Tkz) – 2^.REC

EHE

GB50010

REC = 0.05 m (by default)
BW_VY = 2 Twz	BW_VZ = 2 Twy
DY= Tky – REC	DZ = Tkz – REC
HW_VY = Tky– 2´TWY	HW_VZ = Tkz –2·TWZ
A_cor= (Tkz –2·REC) ·(Tky– 2·REC)	A_cor1= 0.0
A_cor2= 0.0	U_cor= 2·(Tkz +Tky– 4·REC)
U_cor1= 0.0	U_cor2= 0.0

AASHTO Standard Specifications for Highway Bridges

REC = 0.05 m (by default)
BW_VY = 2 Twz	BW_VZ = 2 Twy
DY= Tky – REC	DZ = Tkz – REC


AO = 0.85 AOH

6.6.3.3 Circular Section Parameters

Where: OD Diameter of the section.

Eurocode 2 and ITER

REC = 0.05 m (by default)
(The width of the square within the circumference is used)	(The width of the square within the circumference is used)
DY = OD - REC	DZ = OD - REC
RHO1 = 0.0015

KEYAST = 1 (outer reinforcement)	THETA = 45°

ACI 318 and ACI 349

REC = 0. 05 m (by default)
BW_VY = OD	BW_VZ = OD

(In both directions, the distance from extreme compression fiber to centroid of reinforcement in the opposite half of the section is used, assuming that this reinforcement is uniformly distributed and considering the cover of REC.)


AO = 0.85 AOH

BS8110

REC = 0.05 m (by default)
BW_VY = Tkz	BW_VZ = Tky
DY = Tky - REC	DZ = Tkz - REC
AS = 0.002^.Ac
X1 = OD – 2^.REC	Y1 = OD – 2^.REC

EHE

REC = 0.04 m (by default)

DY = OD - REC	DZ = OD - REC
RHO1 = 0.0028

KEYAST = 1 (outer reinforcement)	THETA = 45º

GB50010

REC = 0.05 m (by default)
BW_VZ = 0.88·OD	BW_VY = 0.88·OD
DY = 0.8·OD	DZ = 0.8·OD
HW_VY = 0.8·OD	HW_VZ = 0.8·OD




	ALF = 0.91

AASHTO Standard Specifications for Highway Bridges

REC = 0. 05 m (by default)
BW_VY = OD	BW_VZ = OD

(In both directions the distance from extreme compression fiber to centroid of reinforcement in the opposite half of the section is used, assuming that this reinforcement is uniformly distributed and considering the cover of REC.)


AO = 0.85 AOH

6.6.3.4 Circular Hollow Section Parameters

Where: OD Diameter of the section.

TKWALL Thickness of the wall.

Eurocode 2 and ITER

REC = 0.05 m (by default)
BW_VY =2 · TKWALL	BW_VZ =2 · TKWALL
DY= OD - REC	DZ = OD - REC
RHO1 = 0.0015

KEYAST = 0 (inner and outer reinforcement).	THETA = 45°

ACI 318 and ACI 349

REC = 0. 05 m (by default)
BW_VY = 2 · TKWALL	BW_VZ = 2 · TKWALL

(In both directions the distance from extreme compression fibre to centroid of reinforcement in the opposite half of the section is used, assuming that this reinforcement is uniformly distributed and considering the cover of REC.)


AO = 0.85 AOH

BS 8110

REC = 0.04 m (by default)
BW_VY = 2 · TKWALL	BW_VZ = 2 · TKWALL
DY = OD - REC	DZ = OD - REC
AS = 0.002 ^.Ac	XW is considered a solid circular section if (Tkwall > 0.25^.OD) Otherwise:
X1 = OD - 2^.REC	Y1 = OD – 2^.REC

EHE

REC = 0.04 m (by default)


DY = OD - REC	DZ = OD - REC
RHO1 = 0.0028

KEYAST = 0 (outer and inner reinforcement).	THETA = 45º

GB50010

REC = 0. 05 m (by default)
BW_VY = 2 ·TKWALL	BW_VZ = 2 ·TKWALL
DY = 0.8·OD	DZ = 0.8·OD
HW_VY = not defined	HW_VZ = not defined




	ALF = 0.91

AASHTO Standard Specifications for Highway Bridges

REC = 0. 05 m (by default)
BW_VY = 2 · TKWALL	BW_VZ = 2 · TKWALL

(In both directions the distance from extreme compression fibre to centroid of reinforcement in the opposite half of the section is used, assuming that this reinforcement is uniformly distributed and considering the cover of REC.)


AO = 0.85 AOH

6.6.3.5 Double T / I-Section Parameters

Where: DEPTH Depth of the section (in Y).

TW Web thickness.

Eurocode 2 and ITER

REC = 0.05 m (by default)
BW_VY = TW	BW_VZ = undefined
DY = DEPTH - REC	DZ = undefined
RHO1 = 0.0015	T = undefined
AK = undefined	UK = undefined
KEYAST = undefined	THETA = 45°

ACI 318 and ACI 349

REC = 0.04 m (by default)
BW_VY = TW	BW_VZ = undefined
DY = DEPTH - REC	DZ = undefined
ACP = undefined	PCP = undefined
AOH = undefined	PH = undefined
AO = undefined

BS 8110

REC = 0.04 m (by default)
BW_VY = Tkz	BW_VZ = undefined
DY = Tky - REC	DZ = Tkz - REC
AS = 0.002^.Ac Ac = concrete gross section	XW = undefined
X1 = undefined	Y1 = undefined

EHE

REC = 0.04 m (by default)
BW_VY = TW	BW_VZ = undefined
DY = DEPTH - REC	DZ = undefined
RHO1 = 0.0028	HE = undefined
AE = undefined	U= undefined
KEYAST = undefined	THETA = 45º

GB50010

REC = 0.04 m (by default)
BW_VY = TW	BW_VZ = undefined
DY = DEPTH – REC	DZ = undefined
HW_VY = DEPTH – TFTOP – TFBOT	HW_VZ = undefined

AASHTO Standard Specifications for Highway Bridges

REC = 0.04 m (by default)
BW_VY = TW	BW_VZ = undefined
DY = DEPTH - REC	DZ = undefined
ACP = undefined	PCP = undefined
AOH = undefined	PH = undefined
AO = undefined

6.6.3.6 T-Section Parameters

Where: DEPTH Depth of the section (in Y).

TW Web thickness.

Eurocode 2 and ITER

REC = 0.05 m (by default)
BW_VY = TW	BW_VZ = undefined
DY = DEPTH - REC	DZ = undefined
RHO1 = 0.0015	T = undefined
AK = undefined	UK = undefined
KEYAST = undefined	THETA = 45º

ACI 318 and ACI 349

REC = 0.05 m (by default)
BW_VY = TW	BW_VZ = undefined
DY = DEPTH - REC	DZ = undefined
ACP = undefined	PCP = undefined
AOH = undefined	PH = undefined
AO = undefined

EHE

REC = 0.04 m (by default)
BW_VY = TW	BW_VZ = undefined
DY = DEPTH - REC	DZ = undefined
RHO1 = 0.0028	HE = undefined
AE = undefined	U = undefined
KEYAST = undefined	THETA = 45º

BS 8110

REC = 0.05 m (by default)
BW_VY = Tkz	BW_VZ = undefined
DY = Tky - REC	DZ = Tkz - REC
AS = 0.002^.Ac Ac = concrete gross section	XW = undefined
X1 = undefined	Y1 = undefined

GB50010

REC = 0.05 m (by default)
BW_VY = TW	BW_VZ = TF
DY = DEPTH – REC	DZ = BF– REC
HW_VY = DEPTH – TF – REC	HW_VZ = undefined

AASHTO Standard Specifications for Highway Bridges

REC = 0.05 m (by default)
BW_VY = TW	BW_VZ = undefined
DY = DEPTH - REC	DZ = undefined
ACP = undefined	PCP = undefined
AOH = undefined	PH = undefined
AO = undefined

6.6.4. Shear and Torsion according to Eurocode 2 (EN 1992-1-1:2004/AC:2008) and ITER Design Code

6.6.4.1. Shear Check

Checking elements for shear according to Eurocode 2 (EN 1992-1-1:2004/AC:2008) and ITER Design Code follows the steps below:

1) Obtaining strength properties of the materials. The required material properties associated with each transverse cross section at the active time are:

characteristic compressive strength of concrete.

design strength of concrete.

characteristic yield strength of reinforcement.

design strength of shear reinforcement.

2) Obtaining geometrical data of the section. Required data for shear checking are the following ones:

total cross-sectional area of the concrete section.

3) Obtaining geometrical parameters depending on code. Required data are as follows:

minimum width of the section over the effective depth.

deffective depth of the section.

ratio of the tension longitudinal reinforcement

where:

the area of the tension reinforcement extending not less than beyond the section considered.

q angle of the compressive struts of concrete with the member’s longitudinal axis, (parameter THETA):

Eurocode 2 (EN 1992-1-1:2004/AC:2008)

ITER Design Code

Compressive mean stress

Tensile mean stress

Section 6.6.1. provides detailed information on how to calculate the required data for each code and valid section.

4) Obtaining reinforcement data of the section. Required data are as follows:

a angle between shear reinforcement and the longitudinal axis of the member section, (parameter ALPHA).

area of reinforcement per unit length, (parameters ASSY or ASSZ).

The reinforcement ratio may also be obtained with the following data:

total area of the reinforcement legs, (parameters ASY or ASZ, both Y and Z directions are available).

s spacing of the stirrups.

or with the following ones:

s spacing of the stirrups.

φ diameter of bars, (parameter PHI).

N number of reinforcement legs, (parameters NY or NZ for Y and Z directions).

5) Obtaining the section’s internal forces and moments. The shear force that acts on the section, as well as the concomitant axial force and bending moment, are obtained from the CivilFEM results file (.RCF).

Force Description

Design shear force (³ 0)

Design axial force (positive for compression)

Design bending moment (³ 0)

6) Checking whether the section requires shear reinforcement. First, the design shear () is compared to the design shear resistance ():

with the constraints:

where:

	=
	=	in MPa
k	=	(d en mm)
k₁	=	0.15
	=
		in mm²
	=	Eurocode 2 (EN 1992-1-1:2004/AC:2008)
	=	ITER Design Code
	=
		in N

If shear reinforcement has not been defined for the section, a check is made to ensure is less than the lowest value between the shear reinforcement resistance,

and the maximum design shear reinforcement resistance:

Eurocode 2 (EN 1992-1-1:2004/AC:2008):

ITER Design Code:

Where :

The shear reinforcement must be equal to or less than (Eurocode 2 only)

Results are written for each end in the CivilFEM results file as the following parameters:

VRDC

VRDS

VRDMAX

TENS

Tension resistance of the longitudinal reinforcement

CRT_1

CRT_2

0,		If there is no shear reinforcement.
,		If there is shear reinforcement.

CRT_3

0,		If there is no shear reinforcement.
,		If there is shear reinforcement.

7) Obtaining shear criterion. The shear criterion indicates whether the section is valid for the design forces (if it is less than 1, the section satisfies the code provisions; whereas if it exceeds 1, the section will not be valid). Furthermore, it includes information pertaining to how close the design force is to the ultimate section strength. The shear criterion is defined as follows:

CRT_TOT

If there is no shear reinforcement

If there is shear reinforcement

A value of 2¹⁰⁰ for this criterion indicates that or are equal to zero.

6.6.4.2. Torsion Check

The torsion checking according to Eurocode 2 (EN 1992-1-1:2004/AC:2008) and ITER Design Code follows the steps below:

1) Obtaining strength properties of the materials. These properties are obtained from the material properties associated to the transverse cross section and for the active time.

The Required data are as follows:

characteristic strength of concrete.

calculation strength of concrete.

characteristic yield strength of reinforcement.

calculation torsion resistance of reinforcement. The same material is considered for transverse and longitudinal reinforcement

2) Obtaining geometrical parameters depending on specified code. The required data are as follows:

t equivalent thickness of wall.

area enclosed within the centre-line of the thin-walled cross-section.

circumference of area A_k.

q Angle of the compressive struts of concrete with the member’s longitudinal axis:

1.0 £ cotan q £ 2.5 Eurocode 2 (EN 1992-1-1:2004/AC:2008)

1.0 £ cotan q £ cotan q₀ ITER Design Code

Compressive mean stress

Tensile mean stress

Section 6.6.1. provides detailed information on how to calculate the required data for each code and valid section.

3) Obtaining reinforcement data of the section. Required data are as follows:

Transverse reinforcement

area of transverse reinforcement per unit length.

The reinforcement ratio can alternatively be defined using the following data:

closed stirrups area for torsion.

s spacing of closed stirrups.

Or with the following data:

s spacing of closed stirrups.

diameter of the closed stirrups.

Longitudinal Reinforcement

total area of the longitudinal reinforcement.

The reinforcement ratio can alternatively be defined using the following data:

diameter of longitudinal bars.

N number of longitudinal bars.

4) Obtaining section internal forces and moments. The torsional moment that acts on the section is obtained from the CivilFEM results file (.RCF).

Moment Description

Design torsional moment

5) Calculating the maximum torsional moment that can be resisted by the concrete compressive struts. The design torsional moment () must be less than or equal to the maximum torsional moment that can be resisted by the concrete compressive struts (); therefore, the following condition must be fulfilled:

Where the values de of and are the same as those used in shear checking,

Results are written in the CivilFEM results file for both element ends as the parameters:

TRDMAX	=
CRT_1	=

6) Calculating the maximum torsional moment that can be resisted by the reinforcement. The design torsional moment () must be less than or equal to the maximum design torsional moment that can be resisted by the reinforcement (); consequently, the following condition must be fulfilled:

Calculation results are written in the CivilFEM results file for both element ends as the parameters:

TRD	=
CRT_2	=

If transverse reinforcement is not defined, and the criterion will take the value of 2¹⁰⁰.

7) Calculating the required longitudinal reinforcement. The required longitudinal reinforcement is calculated from as follows:

If longitudinal reinforcement is not defined, and the criterion will be 2¹⁰⁰.

ALT	=
CRTALT	=

8) Obtaining torsion criterion. The torsion criterion is defined as the ratio of the design moment to the section ultimate resistance: if it is less than 1, the section is valid; whereas if it exceeds 1, the section is not valid. The criterion pertaining to the validity for torsion is defined as follows:

This value is stored in the CivilFEM results file for each end.

A value 2¹⁰⁰for this criterion indicates that any one of the torsion reinforcement groups are undefined.

6.6.4.3. Combined Shear and Torsion Check

For checking sections subjected to shear force and concomitant torsional moment, we follow the steps below:

1) Torsion checking considering a null shear force. This check follows the same procedure as for the check of elements subjected to pure torsion according to Eurocode 2 (EN 1992-1-1:2004/AC:2008) and ITER Design Code.

2) Shear checking assuming a null torsional moment. . This check follows the same steps as for the check of elements subjected to pure shear according to Eurocode 2 (EN 1992-1-1:2004/AC:2008) and ITER Design Code.

3) Checking the concrete ultimate strength condition. The design torsional moment () and the design shear force () must satisfy the following condition:

4) Obtaining the combined shear and torsion criterion. This criterion comprehends pure shear, pure torsion and ultimate strength condition criteria of concrete. The criterion determines whether the section is valid and is defined as follows:

A value 2¹⁰⁰for this criterion indicates that or are equal to zero or that one of the torsion reinforcement groups has not been defined.

6.6.4.4. Shear Design

Shear reinforcement design according to Eurocode 2 (EN 1992-1-1:2004/AC:2008) and ITER Design Code follows the steps below:

1) Obtaining strength properties of the materials. The required material properties associated with each transverse cross section at the active time are:

characteristic strength of concrete.

characteristic design strength of concrete.

characteristic yield strength of reinforcement.

design strength of shear reinforcement.

2) Obtaining geometrical data of the section. Required data for shear design are the following:

total cross-sectional area of the concrete section.

3) Obtaining geometrical parameters depending on specified code. Required data are as follows:

minimum width of the section over the effective depth.

deffective depth of the section.

ratio of the longitudinal tensile :

where:

the area of the tensile reinforcement extending not less than beyond the section considered.

q angle of the compressive struts of concrete with the member’s longitudinal axis:

1.0 £ cotan q£ 2.5 Eurocode 2 (EN 1992-1-1:2004/AC:2008)

1.0 £ cotan q £ cotan q₀ ITER Design Code

Compressive mean stress

Tensile mean stress

Section 6.6.1. provides detailed information on how to calculate the required data for each code and valid section.

4) Obtaining reinforcement data of the section. For shear reinforcement design, it is possible to define the angle between the reinforcement and the longitudinal axis of member can be indicated. This angle should be included in the reinforcement definition of each element. If this angle is null or is not defined, =90° is used. Other reinforcement data will be ignored.

5) Obtaining forces and moments acting on the section. The shear force that acts on the section as well as the concomitant axial force and bending moment, are obtained from the CivilFEM results file (.RCF).

Force Description

Design shear force

Design axial force (positive for compression)

Design bending moment (³ 0)

6) Checking whether the section requires shear reinforcement. First, the design shear () is compared to the design shear resistance ():

with the constraints:

where:

	=
		in MPa
k	=	(d in mm)
	=
	=	0.15
	=	MPa
		in mm²
=		Eurocode 2 (EN 1992-1-1:2004/AC:2008)
=		ITER Design Code
	=
		in N

Results are written for each element end in the CivilFEM results file as the parameters:

7) Calculating the maximum shear force that can be resisted by the concrete compressive struts.

A check is made to ensure that is less than:

Eurocode 2 (EN 1992-1-1:2004/AC:2008):

ITER Design Code:

where:

a = 90º if shear reinforcement was determined as not necessary in the previous step. If reinforcement is necessary, the angle a will be read from in the reinforcement definition data.

Results are written for each element end in the CivilFEM results file as the parameters:

If design shear force is greater than the force required to crush the concrete compressive struts, the reinforcement design will not be feasible, so the parameter containing this datum will be marked with 2¹⁰⁰.

If the struts are not crushed by oblique compression, the calculating process continues.

8) Calculating required amount of transverse reinforcement. The section validity condition pertaining to shear force is:

Therefore, the reinforcement amount per length unit should be:

While also satisfying the following condition (Eurocode 2 only):

If the design is not possible, the reinforcement will be defined as 2¹⁰⁰ and labeled as not designed.

The design criterion will be 1 (Ok) if the element was designed or 0 (Not Ok) if not.

For each element end, the results are included in the CivilFEM results file as the following parameters:



DSG_CRT	=	Design criterion

6.6.4.5. Torsion Design

Torsion reinforcement design according to Eurocode 2 (EN 1992-1-1:2004/AC:2008) and ITER Design Code follows the steps below:

1) Obtaining strength properties of the materials. These properties are obtained from the material properties associated to each transverse cross section and for the active time. Those material properties should be previously defined. The Required data are as follows:

characteristic strength of concrete.

characteristic design strength of concrete.

characteristic yield strength of reinforcement.

design strength of shear reinforcement. The same material will be considered for transverse and longitudinal reinforcement.

2) Obtaining geometrical parameters depending on specified code. The required data are as follows:

t equivalent thickness of wall.

area enclosed within the centre-line of the thin-walled cross-section.

circumference of area .

q angle between the concrete compressive struts and the longitudinal axis of the member:

1.0 £ cotan q £ 2.5 Eurocode 2 (EN 1992-1-1:2004/AC:2008)

1.0 £ cotan q £ cotan q₀ ITER Design Code

Compressive mean stress

Tensile mean stress

Section 6.6.1. provides detailed information on how to calculate the required data for each code and valid section.

3) Obtaining forces and moments acting on the section. The torsional moment that acts on the section is obtained from the CivilFEM results file.

Moment Description

Design torsional moment in I-section.

4) Checking crushing of concrete compressive struts. First, it is necessary to check that the design torsional moment () is less than or equal to the maximum torsional moment that can be resisted by the concrete compressive struts ():

Where the values and are the same as the used previously.

Calculation results are written in the CivilFEM results file for both element ends as the parameters:

If the design torsional moment is greater than the moment required to crush the concrete compressive struts, the reinforcement design will not be feasible. As a result, the parameter for the reinforcement will contain a value of 2¹⁰⁰.

for transverse reinforcement

for longitudinal reinforcement

In this case, the element will be labeled as not designed.

If there is no crushing due to compression, the calculation process continues.

5) Determining the required transverse reinforcement ratio. The required transverse reinforcement is defined by this expression:

The area of the designed transverse reinforcement per unit length is stored in the CivilFEM results file as the parameter:

6) Determining the required longitudinal reinforcement ratio. The longitudinal reinforcement is calculated as:

The area of the designed longitudinal reinforcement is stored in the CivilFEM results file as the parameter:

If both transverse and longitudinal reinforcements are designed for both element sections, this element will be labeled as designed.

Design criterion (DSG_CRT) is 1 (Ok) if the element was designed, 0 (Not OK) if not.

6.6.4.6. Combined Shear and Torsion Design

The design of sections subjected to shear force and concomitant torsional moment, follows the steps below:

1) Torsion design considering a null shear force. This design follows the same steps as for the design of elements subjected to pure torsion according to Eurocode 2 (EN 1992-1-1:2004/AC:2008) and ITER Design Code.

2) Shear design considering a null torsion force. This design is accomplished with the same steps as for the design of elements subjected to pure shear according to Eurocode 2 (EN 1992-1-1:2004/AC:2008) and ITER Design Code.

3) Checking concrete ultimate strength condition. The design torsional moment () and the design shear force () must satisfy the following condition:

4) Obtaining required shear and torsion reinforcement ratios. If the concrete ultimate strength condition is fulfilled (i.e. the concrete can resist the combined shear and torsion action) the reinforcements calculated in steps 1 and 2 are taken as the designed reinforcements. The element is then labeled as designed.

If the concrete ultimate strength condition is not fulfilled, the parameters corresponding to each type of reinforcement will take the value of 2¹⁰⁰.

The design criterion is 1 (Ok) if the element has been designed, and 0 if not.

6.6.5. Shear and Torsion according Structural Code (Spanish Code)

6.6.4.7. Shear Check

Checking elements for shear according to Structuaral Code (Annex 19) follows the steps below:

1) Obtaining strength properties of the materials. The required material properties associated with each transverse cross section at the active time are:

characteristic compressive strength of concrete.

design strength of concrete.

characteristic yield strength of reinforcement.

design strength of shear reinforcement.

2) Obtaining geometrical data of the section. Required data for shear checking are the following ones:

total cross-sectional area of the concrete section.

3) Obtaining geometrical parameters depending on code. Required data are as follows:

minimum width of the section over the effective depth.

deffective depth of the section.

ratio of the tension longitudinal reinforcement

where:

the area of the tension reinforcement extending not less than beyond the section considered.

q angle of the compressive struts of concrete with the member’s longitudinal axis, (parameter THETA):

Section 6.6.1. provides detailed information on how to calculate the required data for each code and valid section.

4) Obtaining reinforcement data of the section. Required data are as follows:

a angle between shear reinforcement and the longitudinal axis of the member section, (parameter ALPHA).

area of reinforcement per unit length, (parameters ASSY or ASSZ).

The reinforcement ratio may also be obtained with the following data:

total area of the reinforcement legs, (parameters ASY or ASZ, both Y and Z directions are available).

s spacing of the stirrups.

or with the following ones:

s spacing of the stirrups.

φ diameter of bars, (parameter PHI).

N number of reinforcement legs, (parameters NY or NZ for Y and Z directions).

Force Description

Design shear force (³ 0)

Design axial force (positive for compression)

Design bending moment (³ 0)

6) Checking whether the section requires shear reinforcement. First, the design shear () is compared to the design shear resistance ():

with the constraints:

where:

	=
	=	in MPa
k	=	(d en mm)
k₁	=	0.15
	=
		in mm²
	=
	=
	=
		in N

If shear reinforcement has not been defined for the section, a check is made to ensure is less than the lowest value between the shear reinforcement resistance,

and the maximum design shear reinforcement resistance:

Where :

The shear reinforcement must be equal to or less than

Results are written for each end in the CivilFEM results file as the following parameters:

VRDC

VRDS

VRDMAX

TENS

Tension resistance of the longitudinal reinforcement

CRT_1

CRT_2

0,		If there is no shear reinforcement.
,		If there is shear reinforcement.

CRT_3

0,		If there is no shear reinforcement.
,		If there is shear reinforcement.

8) Obtaining shear criterion. The shear criterion indicates whether the section is valid for the design forces (if it is less than 1, the section satisfies the code provisions; whereas if it exceeds 1, the section will not be valid). Furthermore, it includes information pertaining to how close the design force is to the ultimate section strength. The shear criterion is defined as follows:

CRT_TOT

If there is no shear reinforcement

If there is shear reinforcement

A value of 2¹⁰⁰ for this criterion indicates that or are equal to zero.

6.6.4.8. Torsion Check

The torsion checking according to Structuaral Code (Annex 19) follows the steps below:

1) Obtaining strength properties of the materials. These properties are obtained from the material properties associated to the transverse cross section and for the active time.

The Required data are as follows:

characteristic strength of concrete.

calculation strength of concrete.

characteristic yield strength of reinforcement.

calculation torsion resistance of reinforcement. The same material is considered for transverse and longitudinal reinforcement

2) Obtaining geometrical parameters depending on specified code. The required data are as follows:

t equivalent thickness of wall.

area enclosed within the centre-line of the thin-walled cross-section.

circumference of area A_k.

q Angle of the compressive struts of concrete with the member’s longitudinal axis:

0.5 £ cotan q £ 2

Section 6.6.1. provides detailed information on how to calculate the required data for each code and valid section.

3) Obtaining reinforcement data of the section. Required data are as follows:

Transverse reinforcement

area of transverse reinforcement per unit length.

The reinforcement ratio can alternatively be defined using the following data:

closed stirrups area for torsion.

s spacing of closed stirrups.

Or with the following data:

s spacing of closed stirrups.

diameter of the closed stirrups.

Longitudinal Reinforcement

total area of the longitudinal reinforcement.

The reinforcement ratio can alternatively be defined using the following data:

diameter of longitudinal bars.

N number of longitudinal bars.

4) Obtaining section internal forces and moments. The torsional moment that acts on the section is obtained from the CivilFEM results file (.RCF).

Moment Description

Design torsional moment

Where the values de of and are the same as those used in shear checking,

Results are written in the CivilFEM results file for both element ends as the parameters:

TRDMAX	=
CRT_1	=

Calculation results are written in the CivilFEM results file for both element ends as the parameters:

TRD	=
CRT_2	=

If transverse reinforcement is not defined, and the criterion will take the value of 2¹⁰⁰.

7) Calculating the required longitudinal reinforcement. The required longitudinal reinforcement is calculated from as follows:

If longitudinal reinforcement is not defined, and the criterion will be 2¹⁰⁰.

ALT	=
CRTALT	=

This value is stored in the CivilFEM results file for each end.

A value 2¹⁰⁰for this criterion indicates that any one of the torsion reinforcement groups are undefined.

6.6.4.9. Combined Shear and Torsion Check

For checking sections subjected to shear force and concomitant torsional moment, we follow the steps below:

5) Torsion checking considering a null shear force. This check follows the same procedure as for the check of elements subjected to pure torsion according to Structuaral Code (Annex 19).

6) Shear checking assuming a null torsional moment. . This check follows the same steps as for the check of elements subjected to pure shear according to Structuaral Code (Annex 19).

7) Checking the concrete ultimate strength condition. The design torsional moment () and the design shear force () must satisfy the following condition:

8) Obtaining the combined shear and torsion criterion. This criterion comprehends pure shear, pure torsion and ultimate strength condition criteria of concrete. The criterion determines whether the section is valid and is defined as follows:

A value 2¹⁰⁰for this criterion indicates that or are equal to zero or that one of the torsion reinforcement groups has not been defined.

6.6.4.10. Shear Design

Shear reinforcement design according to Structuaral Code (Annex 19) follows the steps below:

1) Obtaining strength properties of the materials. The required material properties associated with each transverse cross section at the active time are:

characteristic strength of concrete.

characteristic design strength of concrete.

characteristic yield strength of reinforcement.

design strength of shear reinforcement.

2) Obtaining geometrical data of the section. Required data for shear design are the following:

total cross-sectional area of the concrete section.

3) Obtaining geometrical parameters depending on specified code. Required data are as follows:

minimum width of the section over the effective depth.

deffective depth of the section.

ratio of the longitudinal tensile :

where:

the area of the tensile reinforcement extending not less than beyond the section considered.

q angle of the compressive struts of concrete with the member’s longitudinal axis:

0.5 £ cotan q£ 2

Section 6.6.1. provides detailed information on how to calculate the required data for each code and valid section.

Force Description

Design shear force

Design axial force (positive for compression)

Design bending moment (³ 0)

6) Checking whether the section requires shear reinforcement. First, the design shear () is compared to the design shear resistance ():

with the constraints:

where:

	=
		in MPa
k	=	(d in mm)
	=
	=	0.15
	=	MPa
		in mm²
=
=
	=
		in N

Results are written for each element end in the CivilFEM results file as the parameters:

7) Calculating the maximum shear force that can be resisted by the concrete compressive struts.

A check is made to ensure that is less than:

where:

a = 90º if shear reinforcement was determined as not necessary in the previous step. If reinforcement is necessary, the angle a will be read from in the reinforcement definition data.

Results are written for each element end in the CivilFEM results file as the parameters:

If the struts are not crushed by oblique compression, the calculating process continues.

8) Calculating required amount of transverse reinforcement. The section validity condition pertaining to shear force is:

Therefore, the reinforcement amount per length unit should be:

While also satisfying the following condition (Eurocode 2 only):

If the design is not possible, the reinforcement will be defined as 2¹⁰⁰ and labeled as not designed.

The design criterion will be 1 (Ok) if the element was designed or 0 (Not Ok) if not.

For each element end, the results are included in the CivilFEM results file as the following parameters:



DSG_CRT	=	Design criterion

6.6.4.11. Torsion Design

Torsion reinforcement design according to Structuaral Code (Annex 19) follows the steps below:

characteristic strength of concrete.

characteristic design strength of concrete.

characteristic yield strength of reinforcement.

design strength of shear reinforcement. The same material will be considered for transverse and longitudinal reinforcement.

2) Obtaining geometrical parameters depending on specified code. The required data are as follows:

t equivalent thickness of wall.

area enclosed within the centre-line of the thin-walled cross-section.

circumference of area .

q angle between the concrete compressive struts and the longitudinal axis of the member:

0.5 £ cotan q £ 2.0

Section 6.6.1. provides detailed information on how to calculate the required data for each code and valid section.

3) Obtaining forces and moments acting on the section. The torsional moment that acts on the section is obtained from the CivilFEM results file.

Moment Description

Design torsional moment in I-section.

Where the values and are the same as the used previously.

Calculation results are written in the CivilFEM results file for both element ends as the parameters:

for transverse reinforcement

for longitudinal reinforcement

In this case, the element will be labeled as not designed.

If there is no crushing due to compression, the calculation process continues.

5) Determining the required transverse reinforcement ratio. The required transverse reinforcement is defined by this expression:

The area of the designed transverse reinforcement per unit length is stored in the CivilFEM results file as the parameter:

6) Determining the required longitudinal reinforcement ratio. The longitudinal reinforcement is calculated as:

The area of the designed longitudinal reinforcement is stored in the CivilFEM results file as the parameter:

If both transverse and longitudinal reinforcements are designed for both element sections, this element will be labeled as designed.

Design criterion (DSG_CRT) is 1 (Ok) if the element was designed, 0 (Not OK) if not.

6.6.4.12. Combined Shear and Torsion Design

The design of sections subjected to shear force and concomitant torsional moment, follows the steps below:

1) Torsion design considering a null shear force. This design follows the same steps as for the design of elements subjected to pure torsion according to Structuaral Code (Annex 19).

2) Shear design considering a null torsion force. This design is accomplished with the same steps as for the design of elements subjected to pure shear according to Structuaral Code (Annex 19).

3) Checking concrete ultimate strength condition. The design torsional moment () and the design shear force () must satisfy the following condition:

If the concrete ultimate strength condition is not fulfilled, the parameters corresponding to each type of reinforcement will take the value of 2¹⁰⁰.

The design criterion is 1 (Ok) if the element has been designed, and 0 if not.

6.6.6. Shear and Torsion according to ACI 318-05

Strength reduction factor φ is taken as φ = 0.75 for shear and torsion according to Chapter 9.3.2 of Building Code Requirements for Structural Concrete Structures (ACI 318-05) document.

6.6.5.1. Shear Check

Shear checking according to ACI 318-05 is described in this section. These equations refer to US (British) units which include force, length, and time units of lb, in, and sec.

1) Obtaining strength properties of the materials. The required material properties associated with each transverse cross section at the active time are:

specified compressive strength of concrete.

specified yield strength of reinforcement.

2) Obtaining geometrical data of the section. Required data for shear checking:

area of concrete section.

3) Obtaining geometrical parameters depending on specified code. Required data:

web width or diameter of circular section.

ddistance from the extreme compressed fiber to the centroid of the longitudinal tensile reinforcement in the Y direction, (for circular sections this should not be less than the distance from the extreme compressed fiber to the centroid of the tensile reinforcement in the opposite half of the member).

Section 6.6.1. provides detailed information on how to calculate the required data for each code and valid section.

4) Obtaining reinforcement data of the section. Required data are as follows:

a angle between shear reinforcement and the longitudinal axis of the member section.

area of the reinforcement per unit length (reinforcement ratio) in both the Y and Z directions.

The reinforcement ratio may also be obtained with the following data:

total area of the reinforcement legs.

s spacing of the stirrups.

or with the following input:

s spacing of the stirrups.

φ diameter of bars.

N number of reinforcement legs.

5) Obtaining forces and moments acting on the section. The forces that act on the section are obtained from the CivilFEM results file (.RCF).

Force Description

Factored design shear force

Factored axial force occurring simultaneously to the shear force (positive for compression).

6) Calculating the shear strength provided by concrete for nonprestressed members. First, the shear strength provided by concrete (V_c) is calculated with the following expression:

where:

square root of specified compressive strength of concrete, in psi (always taken as less than 100 psi).

For sections subject to a compressive axial force,

If section is subjected to a tensile force so that the tensile stress is less than 500 psi,

If the section is subjected to a tensile force so that the tensile stress exceeds 500 psi, it is assumed .

The calculation result for both element ends is stored in the CivilFEM results file as the parameter VC:

VC Shear strength provided by concrete.

7) Calculating the shear strength provided by shear reinforcement. The strength provided by shear reinforcement () is calculated with the following expression:

where:

yield strength of the shear reinforcement (not greater than 60000 psi).

The calculation result for both element ends is stored in the CivilFEM results file as the parameter VS:

V_S Shear strength provided by transverse reinforcement.

8) Calculating the nominal shear strength of section. The nominal shear strength () is the summation of the provided by concrete and by the shear reinforcement:

This nominal strength as well as its ratio to the design shear are stored in the CivilFEM results file as the parameters:

VN Nominal shear strength.

CRTVN Ratio of the design shear force (V_u) to the resistance _.

If the strength provided by concrete is null, and the shear reinforcement is not defined in the section, then , and the criterion is equal to –1.

9) Obtaining shear criterion. The section will be valid for shear if the following condition is fulfilled:

φ strength reduction factor of the section. φ = 0.75 for shear and torsion according to Chapter 9.3 of Building Code Requirements for Structural Concrete Structures (ACI 318-05) document.

Therefore, the validity shear criterion is defined as follows:

For each element, this value is stored in the CivilFEM results file as the parameter CRT_TOT.

If the strength provided by concrete is null and the shear reinforcement is not defined in the section, then , and the criterion is equal to 2¹⁰⁰.

The value is stored in CivilFEM results file as the parameter VFI.

6.6.5.2. Torsion Check

The torsion checking according to ACI 318-05 is described in this section. These equations refer to US (British) units which include force, length, and time units of lb, in, and sec.

1) Obtaining strength properties of the materials. These properties are obtained from the material properties associated with each transverse cross section at the active time:

specified compressive strength of concrete.

specified yield strength of reinforcement.

2) Obtaining geometrical parameters depending on specified code. The required data are as follows:

web width or diameter of circular section.

ddistance from the extreme compression fiber to the centroid of the longitudinal tensile reinforcement in Y, (for circular sections this should not be less than the distance from the extreme compression fiber to the centroid of the tensile reinforcement in the opposite half of the member).

area enclosed by outside perimeter of concrete cross section.

outside perimeter of the concrete cross section.

area enclosed by centerline of the outermost closed transverse torsional reinforcement.

perimeter of centerline of outermost closed transverse torsional reinforcement.

gross area enclosed by shear flow path.

Section 6.6.1. provides detailed information on how to calculate the required data for each code and valid section.

3) Obtaining reinforcement data of the section. Required data are as follows:

Transverse Reinforcement

area of transverse reinforcement per unit of length.

The reinforcement ratio can alternatively be defined using the following data:

closed stirrups area for torsion.

s spacing of closed stirrups.

Or with the following data:

s spacing of closed stirrups.

diameter of the closed stirrups.

Longitudinal Reinforcement

total area of the longitudinal reinforcement.

The reinforcement ratio can alternatively be defined using the following data:

diameter of longitudinal bars.

N number of longitudinal bars.

4) Obtaining section’s internal forces and moments. The torsional moment that acts on the section is obtained from the CivilFEM results file (.RCF).

Moment Description

Factored design torsional moment.

5) Checking if torsion effects will be considered. Torsion effects are only considered if the design torsional moment () satisfies the condition below:

If the design torsional moment is less than this value, its effects can be neglected and it will be considered as null for checking.
Checking section dimensions. Section dimensions must satisfy the following requirements:

In hollow sections, if the section wall’s thickness is less than, this value will be replaced by the minimum thickness of the section in the previous formula.

The ratio of the two coefficients is stored in the CivilFEM results file for both element ends as the parameter:

6) Calculating the nominal torsional moment strength of the section. The nominal torsional moment strength () is evaluated with the following expression:

where:

specified yield strength of torsional reinforcement (not greater than 60,000 psi).

This nominal torsional moment strength and its ratio to the design shear force are stored in the CivilFEM results file for both element ends as the parameters:

TN Nominal torsional moment strength.

CRTTN Ratio of the design torsional moment () to the torsional moment strength .

The required longitudinal reinforcement area is given by:

Calculation results are stored in the CivilFEM results file for both element ends as the parameters:

ALT Area of longitudinal torsion reinforcement required in accordance with the transverse torsion reinforcement defined.

CRTALT Ratio of the area of longitudinal torsion reinforcement required to the area of longitudinal torsion reinforcement defined.

If longitudinal reinforcement is not defined, then and the criterion is equal to 2¹⁰⁰.

7) Obtaining torsion criterion. The section will be valid for torsion if the following condition is fulfilled:

φ strength reduction factor of the section, (0.75 for shear and torsion).

Therefore, the validity torsion criterion is defined as follows:

For each element end, this value is stored in the CivilFEM results file as CRT_TOT.

If the strength provided by concrete is null and the torsion reinforcement is not defined in the section, the criterion will be 2¹⁰⁰.

The value is stored in the CivilFEM results file for both element ends as the parameter TFI.

6.6.5.3. Combined Shear and Torsion Check

For checking sections subjected to shear force and concomitant torsional moment, the following steps are taken:

1) Checking if torsion effects will be considered. Torsion effects are only considered if the design torsional moment () satisfies the condition below:

If the design torsional moment is less than this value, its effects can be neglected and it is considered as null for checking.

2) Checking section dimensions. For shear force and the associated torsional moment, section dimensions must satisfy the following requirements:

a) Solid sections:

b) Hollow sections:

In hollow sections, if the section wall’s thickness is less than , this value is replaced in the expression above by the section’s minimum thickness.

The ratio between these two factors is stored in the CivilFEM results file for both element ends.

a) Solid sections:

b) Hollow sections:

3) Checking for shear force with concomitant torsional moment. This check is accomplished with the same steps as the check of elements subjected to pure shear force according to ACI 318-05. The same results as for shear checking will be calculated.

Except for this check, the CRT_TOT criterion is stored in the CivilFEM results file as CRTSHR for each element end.

4) Checking for torsion with shear force. This check follows the same steps considered for the check of elements subjected to pure torsion according to ACI 318-05. The same results as in torsion checking will be calculated.

Except for this check, the CRT_TOT criterion is stored in the CivilFEM results file as CRTTRS for each element end.

5) Obtaining the combined shear and torsion criterion. This criterion determines whether the section is valid or not. It is defined as follows:

For each end, this value is stored in the CivilFEM results file.

A value equal to 2¹⁰⁰ for this criterion indicates:

h the shear strength provided by concrete is equal to zero and the shear reinforcement has not been defined.

h the shear strength provided by concrete is equal to zero and the transverse torsion reinforcement has not been defined.

h the longitudinal torsion reinforcement has not been defined.

6.6.5.4. Shear Design

The shear designing according to ACI 318-05 is described in this section. These equations refer to US (British) units which include force, length, and time units of lb, in, and sec.

1) Obtaining strength properties of the materials. The required material properties associated with each transverse cross section at the active time are:

specified compressive strength of concrete.

specified yield strength of reinforcement.

2) Obtaining geometrical data of the section. Required data for shear designing are the following ones:

area of concrete section.

3) Obtaining geometrical parameters depending on specified code. The Required data are as follows:

web width or diameter of the circular section.

ddistance from the extreme compressed fiber to the centroid of the longitudinal tension reinforcement in Y, (for circular sections this should not be less than the distance from the extreme compressed fiber to the centroid of the tension reinforcement in the opposite half of the member).

Section 6.6.1. provides detailed information on how to calculate the required data for each code and valid section.

4) Obtaining reinforcement data of the section. For shear reinforcement design, it is possible to define the angle a between the reinforcement and the longitudinal axis of the member. This angle must be stored in the shear reinforcement data of each element. If this angle is equal to zero or it is not defined, = 90º. Other data pertaining to reinforcements will be ignored.

5) Obtaining forces and moments acting on the section. The shear force that acts on the section as well as the concomitant axial force are obtained from the CivilFEM results file (.RCF).

Force Description

Design shear force

Nu Axial force (positive for compression)

6) Calculating the shear strength provided by concrete. The shear strength provided by concrete () is calculated with the following expression:

where:

square root of specified compressive strength of concrete, in psi (always taken as less than 100 psi).

For sections subject to a compressive axial force,

If the section is subjected to a tensile force so that the tensile stress is less than 500 psi,

If the section is subjected to a tensile force so that the tensile stress exceeds 500 psi, it is assumed.

The calculation result is stored in the CivilFEM results file for both element ends as the parameter:

VC Shear strength provided by concrete:

7) Calculating the required reinforcement contribution to the shear strength. The section must satisfy the following condition to resist the shear force:

Therefore, the reinforcement shear resistance must satisfy:

If the shear resistance of the reinforcement does not satisfy the expression above, the section cannot be designed. As a result, the parameters for the reinforcement ratio will be equal to 2¹⁰⁰.

For this case, the element will be labeled as not designed.

Calculation results are stored in the CivilFEM results file for both element ends as the parameter:

VS Shear resistance provided by the transverse reinforcement.

8) Calculating the required reinforcement ratio. Once the shear resistance of the reinforcement has been obtained, the reinforcement can be calculated with the following expression:

Where:

area of the cross-section of the shear reinforcement.

s spacing of the stirrups measured along the longitudinal axis.

yield strength of the shear reinforcement (not greater than 60000 psi).

The area of the designed reinforcement per unit length is stored in the CivilFEM results file for both element ends:

In this case, the element will be labeled as designed (providing the design process is correct for both element sections).

6.6.5.5. Torsion Design

The torsion designing according to ACI 318-05 is described in this section. These equations refer to US (British) units which include force, length, and time units of lb, in, and sec.

1) Obtaining strength properties of the materials. These properties are obtained from the material properties associated with each transverse cross section at the active time.

specified compressive strength of concrete.

specified yield strength of reinforcement.

2) Obtaining geometrical parameters depending on specified code. The required data are as follows:

web width or diameter of the circular section.

ddistance from the extreme compressed fiber to the centroid of the longitudinal tensile reinforcement in Y, (for circular sections this should not be less than the distance from the extreme compressed fiber to the centroid of the tensile reinforcement in the opposite half of the member).

Area enclosed by outside perimeter of concrete cross section.

Outside perimeter of the concrete cross section.

Area enclosed by centerline of the outermost closed transverse torsional reinforcement.

Perimeter of centerline of outermost closed transverse torsional reinforcement.

Gross area enclosed by shear flow path.

Section 6.6.1. provides detailed information on how to calculate the required data for each code and valid section.

3) Obtaining forces and moments acting on the section. The torsional moment that acts on the section is obtained from the CivilFEM results file (.RCF).

Moment Description

Design torsional moment in l section.

4) Checking if torsion effects will be considered. Torsion effects are only considered if the design torsional moment () satisfies the condition below:

If the design torsional moment is less than this value, its effects can be neglected and it is consider as null for the design.

5) Checking section dimensions. Section dimensions must satisfy the following requirements:

For hollow sections, if the thickness of the section walls is less than , this value will be replaced by the minimum thickness of the section in the equation above.

The torsion reinforcement will not be designed if the previous expression is not fulfilled; consequently, the parameters for the reinforcement will be equal to 2¹⁰⁰.

for transverse reinforcement

for longitudinal reinforcement

In this case the element will be marked as not designed and it will be stored in the TRS_NOT OK component.

The ratio of the two coefficients is stored in the CivilFEM results file for both element ends:

6) Calculating the required transverse reinforcement. In order to resist the torsional moment, the section must satisfy the condition below:

cross-sectional area of one leg of a closed stirrup resisting torsion.

s spacing of the stirrups.

Therefore, the required transverse torsion reinforcement is:

The area of designed transverse reinforcement per unit length is stored in the CivilFEM results file for both element ends:

7) Calculating the required longitudinal reinforcement. The longitudinal reinforcement area is given by the following expression:

The area of the designed longitudinal reinforcement is stored in the CivilFEM results file for both element ends:

If transverse and longitudinal reinforcements are designed for both element ends, this element will be labeled as designed.

6.6.5.6. Combined Shear and Torsion Design

The designing of sections subjected to shear force and concomitant torsional moment, follows the steps below:

1) Checking if torsion effects will be considered. Torsion effects are only considered if the design torsional moment () satisfies the condition below:

If the design torsional moment is less than this value, its effects can be neglected and it is considered as null for the design.

2) Checking section dimensions. For shear force and concomitant torsional moment, section dimensions must satisfy the following requirements:

a) Solid sections:

b) Hollow sections:

For hollow sections, if the section wall’s thickness is less than , this value will be
replaced by the minimum thickness of the section in the expression above.

The torsion reinforcement will not be designed if the expression above is not fulfilled; consequently, the parameters for the reinforcement will be equal to 2¹⁰⁰.

for transverse reinforcement

for longitudinal reinforcement

In this case, the element will be marked as not designed.

The ratio of the two coefficients is stored in the CivilFEM results file for both element ends.

a) Solid sections:

b) Hollow sections:

3) Shear design assuming a null torsional moment. This design follows the same procedure as for the design of elements subjected to pure shear force according to ACI 318-05.

4) Torsion design considering a null shear force. This design is accomplished with the same steps as for the design of elements subjected to pure torsion according to ACI 318-05.

6.6.7. Shear and Torsion according to ACI 318-14

Strength reduction factor φ is taken as φ = 0.75 for shear and torsion according to Chapter 21.2.1 of Building Code Requirements for Structural Concrete Structures (ACI 318-14) document.

6.6.6.1. Shear Check

Shear checking according to ACI 318-14 is described in this section. These equations refer to US (British) units which include force, length, and time units of lb, in, and sec.

1) Obtaining strength properties of the materials. The required material properties associated with each transverse cross section at the active time are:

specified compressive strength of concrete.

specified yield strength of reinforcement.

modification factor for lightweight concrete ().

2) Obtaining geometrical data of the section. Required data for shear checking:

area of concrete section.

3) Obtaining geometrical parameters depending on specified code. Required data:

web width or diameter of circular section.

Section 6.6.1. provides detailed information on how to calculate the required data for each code and valid section.

4) Obtaining reinforcement data of the section. Required data are as follows:

a angle between shear reinforcement and the longitudinal axis of the member section.

area of the reinforcement per unit length (reinforcement ratio) in both the Y and Z directions.

The reinforcement ratio may also be obtained with the following data:

total area of the reinforcement legs.

s spacing of the stirrups.

or with the following input:

s spacing of the stirrups.

φ diameter of bars.

N number of reinforcement legs.

5) Obtaining forces and moments acting on the section. The forces that act on the section are obtained from the CivilFEM results file (.RCF).

Force Description

Factored design shear force

Factored axial force occurring simultaneously to the shear force (positive for compression).

6) Calculating the shear strength provided by concrete for nonprestressed members. First, the shear strength provided by concrete (V_c) is calculated with the following expression for sections without axial force:

where:

square root of specified compressive strength of concrete, in psi (always taken as less than 100 psi).

For sections subject to a compressive axial force,

If section is subjected to significant tensile force,

The calculation result for both element ends is stored in the CivilFEM results file as the parameter VC:

VC Shear strength provided by concrete.

7) Calculating the shear strength provided by shear reinforcement. The strength provided by shear reinforcement () is calculated with the following expression:

where:

yield strength of the shear reinforcement (not greater than 60000 psi).

The calculation result for both element ends is stored in the CivilFEM results file as the parameter VS:

V_S Shear strength provided by transverse reinforcement.

8) Calculating the nominal shear strength of section. The nominal shear strength () is the summation of the provided by concrete and by the shear reinforcement:

This nominal strength as well as its ratio to the design shear are stored in the CivilFEM results file as the parameters:

VN Nominal shear strength.

CRTVN Ratio of the design shear force (V_u) to the resistance _.

If the strength provided by concrete is null, and the shear reinforcement is not defined in the section, then , and the criterion is equal to –1.

9) Obtaining shear criterion. The section will be valid for shear if the following condition is fulfilled:

φ strength reduction factor of the section (0.75 for shear and torsion).

Therefore, the validity shear criterion is defined as follows:

For each element, this value is stored in the CivilFEM results file as the parameter CRT_TOT.

If the strength provided by concrete is null and the shear reinforcement is not defined in the section, then , and the criterion is equal to 2¹⁰⁰.

The value is stored in CivilFEM results file as the parameter VFI.

6.6.6.2. Torsion Check

The torsion checking according to ACI 318-14 is described in this section. These equations refer to US (British) units which include force, length, and time units of lb, in, and sec.

1) Obtaining strength properties of the materials. These properties are obtained from the material properties associated with each transverse cross section at the active time:

specified compressive strength of concrete.

specified yield strength of reinforcement.

modification factor for lightweight concrete.

2) Obtaining geometrical parameters depending on specified code. The required data are as follows:

web width or diameter of circular section.

area enclosed by outside perimeter of concrete cross section.

outside perimeter of the concrete cross section.

area enclosed by centerline of the outermost closed transverse torsional reinforcement.

perimeter of centerline of outermost closed transverse torsional reinforcement.

gross area enclosed by shear flow path.

Section 6.6.1.. provides detailed information on how to calculate the required data for each code and valid section.

3) Obtaining reinforcement data of the section. Required data are as follows:

Transverse Reinforcement

area of transverse reinforcement per unit of length.

The reinforcement ratio can alternatively be defined using the following data:

closed stirrups area for torsion.

s spacing of closed stirrups.

Or with the following data:

s spacing of closed stirrups.

diameter of the closed stirrups.

Longitudinal Reinforcement

total area of the longitudinal reinforcement.

The reinforcement ratio can alternatively be defined using the following data:

diameter of longitudinal bars.

N number of longitudinal bars.

4) Obtaining section’s internal forces and moments. The torsional moment that acts on the section is obtained from the CivilFEM results file (.RCF).

Moment Description

Factored design torsional moment.

5) Checking if torsion effects will be considered. Torsion effects are only considered if the design torsional moment () satisfies the condition below:

Hollow sections:

The ratio of the two coefficients is stored in the CivilFEM results file for both element ends as the parameter (solid sections):

Hollow sections:

6) Calculating the nominal torsional moment strength of the section. The nominal torsional moment strength () is evaluated with the following expression:

where:

specified yield strength of torsional reinforcement (not greater than 60,000 psi).

This nominal torsional moment strength and its ratio to the design shear force are stored in the CivilFEM results file for both element ends as the parameters:

TN Nominal torsional moment strength.

CRTTN Ratio of the design torsional moment () to the torsional moment strength .

The required longitudinal reinforcement area is given by:

Calculation results are stored in the CivilFEM results file for both element ends as the parameters:

ALT Area of longitudinal torsion reinforcement required in accordance with the transverse torsion reinforcement defined.

CRTALT Ratio of the area of longitudinal torsion reinforcement required to the area of longitudinal torsion reinforcement defined.

If longitudinal reinforcement is not defined, then and the criterion is equal to 2¹⁰⁰.

7) Obtaining torsion criterion. The section will be valid for torsion if the following condition is fulfilled:

φ strength reduction factor of the section, (0.75 for shear and torsion).

Therefore, the validity torsion criterion is defined as follows:

For each element end, this value is stored in the CivilFEM results file as CRT_TOT.

If the strength provided by concrete is null and the torsion reinforcement is not defined in the section, the criterion will be 2¹⁰⁰.

The value is stored in the CivilFEM results file for both element ends as the parameter TFI.

6.6.6.3. Combined Shear and Torsion Check

For checking sections subjected to shear force and concomitant torsional moment, the following steps are taken:

6) Checking if torsion effects will be considered. Torsion effects are only considered if the design torsional moment () satisfies the condition below:

If the design torsional moment is less than this value, its effects can be neglected and it is considered as null for checking.

7) Checking section dimensions. For shear force and the associated torsional moment, section dimensions must satisfy the following requirements:

a) Solid sections:

b) Hollow sections:

In hollow sections, if the section wall’s thickness is less than , this value is replaced in the expression above by the section’s minimum thickness.

The ratio between these two factors is stored in the CivilFEM results file for both element ends.

a) Solid sections:

b) Hollow sections:

8) Checking for shear force with concomitant torsional moment. This check is accomplished with the same steps as the check of elements subjected to pure shear force according to ACI 318-14. The same results as for shear checking will be calculated.

Except for this check, the CRT_TOT criterion is stored in the CivilFEM results file as CRTSHR for each element end.

9) Checking for torsion with shear force. This check follows the same steps considered for the check of elements subjected to pure torsion according to ACI 318-05. The same results as in torsion checking will be calculated.

Except for this check, the CRT_TOT criterion is stored in the CivilFEM results file as CRTTRS for each element end.

10) Obtaining the combined shear and torsion criterion. This criterion determines whether the section is valid or not. It is defined as follows:

For each end, this value is stored in the CivilFEM results file.

A value equal to 2¹⁰⁰ for this criterion indicates:

h the shear strength provided by concrete is equal to zero and the shear reinforcement has not been defined.

h the shear strength provided by concrete is equal to zero and the transverse torsion reinforcement has not been defined.

h the longitudinal torsion reinforcement has not been defined.

6.6.6.4. Shear Design

The shear designing according to ACI 318-14 is described in this section. These equations refer to US (British) units which include force, length, and time units of lb, in, and sec.

1) Obtaining strength properties of the materials. The required material properties associated with each transverse cross section at the active time are:

specified compressive strength of concrete.

specified yield strength of reinforcement.

modification factor for lightweight concrete.

2) Obtaining geometrical data of the section. Required data for shear designing are the following ones:

area of concrete section.

3) Obtaining geometrical parameters depending on specified code. The Required data are as follows:

web width or diameter of the circular section.

Section 6.6.1.. provides detailed information on how to calculate the required data for each code and valid section.

4) Obtaining reinforcement data of the section. For shear reinforcement design, it is possible to define the angle a between the reinforcement and the longitudinal axis of the member. This angle must be stored in the shear reinforcement data of each element. If this angle is equal to zero or it is not defined, alpha= 90º. Other data pertaining to reinforcements will be ignored.

5) Obtaining forces and moments acting on the section. The shear force that acts on the section as well as the concomitant axial force are obtained from the CivilFEM results file (.RCF).

Force Description

Design shear force

Nu Axial force (positive for compression)

6) Calculating the shear strength provided by concrete. The shear strength provided by concrete () is calculated with the following expression:

where:

square root of specified compressive strength of concrete, in psi (always taken as less than 100 psi).

For sections subject to a compressive axial force,

If the section is subjected to a significant tensile force,

The calculation result is stored in the CivilFEM results file for both element ends as the parameter:

VC Shear strength provided by concrete:

7) Calculating the required reinforcement contribution to the shear strength. The section must satisfy the following condition to resist the shear force:

Therefore, the reinforcement shear resistance must satisfy:

If the shear resistance of the reinforcement does not satisfy the expression above, the section cannot be designed. As a result, the parameters for the reinforcement ratio will be equal to 2¹⁰⁰.

For this case, the element will be labeled as not designed.

Calculation results are stored in the CivilFEM results file for both element ends as the parameter:

VS Shear resistance provided by the transverse reinforcement.

8) Calculating the required reinforcement ratio. Once the shear resistance of the reinforcement has been obtained, the reinforcement can be calculated with the following expression:

Where:

area of the cross-section of the shear reinforcement.

s spacing of the stirrups measured along the longitudinal axis.

yield strength of the shear reinforcement (not greater than 60000 psi).

The area of the designed reinforcement per unit length is stored in the CivilFEM results file for both element ends:

In this case, the element will be labeled as designed (providing the design process is correct for both element sections).

6.6.6.5. Torsion Design

The torsion designing according to ACI 318-14 is described in this section. These equations refer to US (British) units which include force, length, and time units of lb, in, and sec.

1) Obtaining strength properties of the materials. These properties are obtained from the material properties associated with each transverse cross section at the active time.

specified compressive strength of concrete.

specified yield strength of reinforcement.

modification factor for lightweight concrete.

2) Obtaining geometrical parameters depending on specified code. The required data are as follows:

web width or diameter of the circular section.

Area enclosed by outside perimeter of concrete cross section.

Outside perimeter of the concrete cross section.

Area enclosed by centerline of the outermost closed transverse torsional reinforcement.

Perimeter of centerline of outermost closed transverse torsional reinforcement.

Gross area enclosed by shear flow path.

Section 6.6.1.. provides detailed information on how to calculate the required data for each code and valid section.

3) Obtaining forces and moments acting on the section. The torsional moment that acts on the section is obtained from the CivilFEM results file (.RCF).

Moment Description

Design torsional moment in l section.

4) Checking if torsion effects will be considered. Torsion effects are only considered if the design torsional moment () satisfies the condition below:

If the design torsional moment is less than this value, its effects can be neglected and it is consider as null for the design.

Checking section dimensions. Section dimensions must satisfy the following requirements for solid sections:

Hollow sections:

For hollow sections, if the thickness of the section walls is less than , this value will be replaced by the minimum thickness of the section in the equation above.

The torsion reinforcement will not be designed if the previous expression is not fulfilled; consequently, the parameters for the reinforcement will be equal to 2¹⁰⁰.

for transverse reinforcement

for longitudinal reinforcement

In this case the element will be marked as not designed and it will be stored in the TRS_NOT OK component.

The ratio of the two coefficients is stored in the CivilFEM results file for both element ends:

a) Solid sections:

b) Hollow sections:

5) Calculating the required transverse reinforcement. In order to resist the torsional moment, the section must satisfy the condition below:

cross-sectional area of one leg of a closed stirrup resisting torsion.

s spacing of the stirrups.

Therefore, the required transverse torsion reinforcement is:

The area of designed transverse reinforcement per unit length is stored in the CivilFEM results file for both element ends:

6) Calculating the required longitudinal reinforcement. The longitudinal reinforcement area is given by the following expression:

The area of the designed longitudinal reinforcement is stored in the CivilFEM results file for both element ends:

If transverse and longitudinal reinforcements are designed for both element ends, this element will be labeled as designed.

6.6.6.6. Combined Shear and Torsion Design

The designing of sections subjected to shear force and concomitant torsional moment, follows the steps below:

5) Checking if torsion effects will be considered. Torsion effects are only considered if the design torsional moment () satisfies the condition below:

If the design torsional moment is less than this value, its effects can be neglected and it is considered as null for the design.

6) Checking section dimensions. For shear force and concomitant torsional moment, section dimensions must satisfy the following requirements:

a) Solid sections:

b) Hollow sections:

For hollow sections, if the section wall’s thickness is less than , this value will be
replaced by the minimum thickness of the section in the expression above.

The torsion reinforcement will not be designed if the expression above is not fulfilled; consequently, the parameters for the reinforcement will be equal to 2¹⁰⁰.

for transverse reinforcement

for longitudinal reinforcement

In this case, the element will be marked as not designed.

The ratio of the two coefficients is stored in the CivilFEM results file for both element ends.

a) Solid sections:

b) Hollow sections:

7) Shear design assuming a null torsional moment. This design follows the same procedure as for the design of elements subjected to pure shear force according to ACI 318-14.

8) Torsion design considering a null shear force. This design is accomplished with the same steps as for the design of elements subjected to pure torsion according to ACI 318-14.

6.6.8. Shear and Torsion according to ACI 349-01 and ACI349-06

6.6.7.1. Shear Check

Shear checking according to ACI 349-01 and 349-06 is described in this section. Units in these equations refer to the US (British) force, length, time units measured in pounds, inches, and seconds.

1) Obtaining material strength properties. The required material properties associated with each transverse cross section at the active time are:

specified compressive strength of concrete.

specified yield strength of reinforcement.

2) Obtaining geometrical data of the section. Required data for shear checking:

area of concrete section.

3) Obtaining geometrical parameters depending on specified code. Geometrical parameters used for shear calculations must be defined. The required data:

web width or diameter of circular section.

ddistance from the extreme compressed fiber to the centroid of the longitudinal tensile reinforcement in the Y direction, (for circular sections, this must not be less than the distance from the extreme compressed fiber to the centroid of the tensile reinforcement in the opposite half of the member).

Section 6.6.1. “Previous Considerations to Shear and Torsion Calculation” provides detailed information on how to calculate the required data for each code and valid section.

4) Obtaining section reinforcement data. Required data includes:

a angle between shear reinforcement and the longitudinal axis of the member section.

area of reinforcement per unit length (reinforcement ratio) in both the Y and Z directions.

The reinforcement ratio may also be obtained with the following data:

total area of the reinforcement legs.

s spacing of the stirrups.

or with the data below:

s spacing of the stirrups.

diameter of bars.

N number of reinforcement legs.

5) Obtaining forces acting on the section. The forces that act on the section are obtained from the CivilFEM results file (.RCF).

Force Description

Factored design shear force in the section

Factored axial force occurring simultaneously to the shear force (positive for compression).

6) Calculating the shear strength provided by concrete for nonprestressed members. First, the shear strength provided by concrete (V_c) is calculated with the following expression:

where:

square root of specified compressive strength of concrete, in psi (always taken as less than 100 psi).

For sections subject to a compressive axial force:

If the section is subjected to a tensile force such that the tensile stress is less than 500 psi:

If the section is subjected to a tensile force such that the tensile stress exceeds 500 psi, it is assumed that .

The calculated result at both element ends is stored in the CivilFEM results file as the parameter VC:

VC Shear strength provided by concrete.

7) Calculating the shear strength provided by the shear reinforcement. The strength provided by the shear reinforcement (V_s) is calculated with the following expression:

where:

yield strength of the shear reinforcement (not greater than 60,000 psi).

The calculated result at both element ends is stored in the CivilFEM results file as the parameter VS:

VS Shear strength provided by transverse reinforcement.

8) Calculating the nominal shear strength of section. The nominal shear strength (V_n) is the sum of the shear strength provided by the concrete and the shear reinforcement as described in the previous sections:

This nominal shear strength as well as its ratio to the design shear are stored in the CivilFEM results file as the parameters:

VN Nominal shear strength.

CRTVN Ratio of the design shear force (V_u) to the resistance V_n.

If the shear strength provided by the concrete is null and shear reinforcement is not defined in the section, then , and the criterion is set equal to –1.

9) Obtaining shear criterion. The section will be valid for shear if the following condition is satisfied

φ strength reduction factor of the section, (0.85 for shear and torsion).

Therefore, the validity of the shear criterion is defined as follows:

For each element, this shear utilization value is stored in the CivilFEM results file as the parameter CRT_TOT.

In cases where the strength provided by the concrete is null and the shear reinforcement is not defined in the section, the shear strength , and the criterion is set equal to 2¹⁰⁰.

The value is stored in the CivilFEM results file as the parameter VFI.

6.6.7.2. Torsion Check

Torsion checking according to ACI 349-01 and 349-06 is described in this section. Units in these equations refer to the US (British) force, length, time units measured in pounds, inches, and seconds.

1) Obtaining material strength properties. These properties are obtained from the material properties associated with each transverse cross section at the active time are:

specified compressive strength of concrete.

specified yield strength of reinforcement.

2) Obtaining geometrical parameters depending on specified code. Geometrical parameters used for torsion calculations must be defined. The required data are as follows:

web width or diameter of circular section.

ddistance from the extreme compression fiber to the centroid of the longitudinal tensile reinforcement in Y, (for circular sections, this must not be less than the distance from the extreme compression fiber to the centroid of the tensile reinforcement in the opposite half of the member).

Area enclosed by outside perimeter of the concrete cross section.

Outside perimeter of the concrete cross section.

Area enclosed by the centerline of the outermost closed transverse torsional reinforcement.

Perimeter of the centerline of the outermost closed transverse torsional reinforcement.

Gross area enclosed by the shear flow path.

Section 6.6.1. “Previous Considerations to Shear and Torsion Calculation” provides detailed information on how to calculate the required data for each valid section.

3) Obtaining reinforcement data of the section. Required data are as follows:

Transverse Reinforcement

area of transverse reinforcement per unit length.

The reinforcement ratio can alternatively be defined using the following data:

closed stirrups area for torsion.

s spacing of closed stirrups.

Or with the data below:

s spacing of closed stirrups.

diameter of the closed stirrups.

Longitudinal Reinforcement

total area of the longitudinal reinforcement.

The reinforcement ratio can also be defined using the following data:

diameter of longitudinal bars.

N number of longitudinal bars.

4) Obtaining section internal forces and moments. The torsional moment that acts on the section is obtained from the CivilFEM results file (.RCF).

Moment Description

Factored design torsional moment.

5) Checking whether torsion effects will be considered. Torsion effects are only considered if the design torsional moment (T_u) satisfies the following equation:

If the design torsional moment is less than this value, its effects can be neglected and it is considered as null for checking.

6) Checking section dimensions. Section dimensions must satisfy the following requirements:

In hollow sections, if the section wall thickness is less than A_oh/P_h, this value must be substituted with the minimum thickness of the section in the expression above.

The ratio of the two coefficients is stored in the CivilFEM results file at both element ends as the parameter:

7) Calculating the nominal torsional moment strength of the section. The nominal torsional moment strength (T_n) is evaluated with the following expression:

where:

specified yield strength of torsional reinforcement (not greater than 60000 psi).

This nominal torsional moment strength and its ratio to the design shear force are stored in the CivilFEM results file at both element ends as the parameters:

TN Nominal torsional moment strength.

CRTTN Ratio of the design torsional moment (T_u) to the torsional moment strength T_n .

The needed longitudinal reinforcement area is given by:

The calculated results are stored in the CivilFEM results file at both element ends as the parameters:

ALT Area of torsion longitudinal reinforcement required in accordance to the torsion transverse reinforcement defined.

CRTALT Ratio of the area of torsion longitudinal reinforcement required to the area of torsion longitudinal reinforcement defined.

If longitudinal reinforcement is not defined, then , and the criterion is set equal to 2¹⁰⁰.

8) Obtaining torsion criterion. The section will be valid for torsion if the following condition is satisfied:

φ strength reduction factor of the section, (=0.85 for shear and torsion).

Therefore, the torsion design utilization is defined as follows:

For each element end, this value is stored in the CivilFEM results file.

In cases where the strength provided by concrete is null and the torsion reinforcement is not defined in the section, the criterion will be set to 2¹⁰⁰.

The value is stored in the CivilFEM results file at both element ends as the parameter TFI.

6.6.7.3. Combined Shear and Torsion Checking

For checking sections subjected to combined shear force and torsional moment, the following steps are taken:

1) Checking if torsion effects must be considered. Torsion effects are only considered if the design torsional moment (T_u) satisfies the condition below:

If the design torsional moment is less than this value its effects can be neglected and it is considered as null for checking.

2) Checking section dimensions. For shear force and associated torsional moment, section dimensions must satisfy the following requirements:

a) Solid sections:

b) Hollow sections:

In hollow sections if the section wall thickness is lower than , this value is changed in the previous expression by the section minimum thickness.

The ratio between these two factors is stored in the CivilFEM results file at both element ends.

a) Solid sections:

b) Hollow sections:

3) Checking for shear force with associated torsional moment. This checking is accomplished following the same steps considered for the checking of elements subjected only to shear force according to ACI 349. The same results as defined in the shear check are calculated.

4) Checking for torsion with shear force. This checking is accomplished following the same steps considered for the checking of elements subjected only to torsion according to ACI 349. The same results as defined in the torsion check are calculated.

5) Obtaining the combined shear and torsion criterion. This criterion determines whether the section is valid or not. The utilization is defined as follows:

For each end, this value is stored in the CivilFEM results file.

A value equals to 2¹⁰⁰ for this criterion would indicate one of the following:

h the shear strength provided by concrete is equal to zero and shear reinforcement has not been defined

h the shear strength provided by concrete is equal to zero and transverse torsion reinforcement has not been defined

h the longitudinal torsion reinforcement has not been defined

6.6.7.4. Shear Design

Shear design according to ACI 349-01 and 349-06 is described in this section. Units in these equations refer to the US (British) force, length, time units measured in pounds, inches, and seconds.

1) Obtaining material strength properties. The required material properties associated with each transverse cross section at the active time are:

specified compressive strength of concrete.

specified yield strength of reinforcement.

2) Obtaining section geometrical data. Required data for shear design:

area of concrete section.

3) Obtaining geometrical parameters depending on specified code. Geometrical parameters used for shear designing must be defined. The required data:

web width or diameter of the circular section

ddistance from the extreme compressed fiber to the centroid of the longitudinal tensile reinforcement in Y, (for circular sections, this must not be less than the distance from the extreme compressed fiber to the centroid of the tensile reinforcement in the opposite half of the member).

Section “6.6.1. Previous Considerations to Shear and Torsion Calculation” provides detailed information on how to calculate the required data for each code and valid section.

4) Obtaining reinforcement data of the section. In shear reinforcement designing, it is possible to define the angle a between the reinforcement and the longitudinal axis of the member. This angle must be stored in the shear reinforcement data of each element. If this angle is equal to zero or is not defined, a=90º. Other data concerning to reinforcements are ignored.

5) Obtaining forces and moments acting on the section. The shear force that acts on the section as well as the associated axial force are obtained from the CivilFEM results file (.RCF).

Force Description

Factored design shear force.

Factored axial force occurring simultaneously with the shear force (positive for compression).

6) Calculating the shear strength provided by concrete for nonprestressed members. First, the shear strength provided by the concrete (V_c) is calculated with the following expression:

where:

square root of specified compressive strength of concrete, in psi (always taken as less than 100 psi).

For sections subject to a compressive axial force:

If section is subjected to a tensile force so that the tensile stress is less than 500 psi:

If the section is subjected to a tensile force such that the tensile stress exceeds 500 psi, it is assumed that V_c=0.

The calculated result is stored in the CivilFEM results file at both element ends as the parameter:

VC Shear strength provided by concrete.

7) Calculating the required reinforcement contribution to the shear strength. The section must satisfy the following condition to resist the shear force:

Therefore, the required shear strength of the reinforcement must be:

If the required shear strength of the reinforcement does not satisfy the expression above, the section cannot be designed; consequently, the reinforcement parameter will be defined as 2¹⁰⁰. Then:

In this case, the element will be labeled as not designed, the program then advances to the following element.

The calculated result at both element ends is stored in the CivilFEM results file as the parameter VS:

VS Shear resistance provided by the transverse reinforcement.

8) Calculating the required reinforcement ratio. Once the shear force that the shear reinforcement must support has been obtained, the reinforcement is obtained from the following expression:

Where:

area of the cross-section of the shear reinforcement.

s spacing of the stirrups measured along the longitudinal axis.

yield strength of the shear reinforcement (not greater than 60000 psi).

The area of the designed reinforcement per unit length is stored in the CivilFEM results file at both element ends:

In this case, the element will be labeled as designed (providing the design process is correct at both element ends).

6.6.7.5. Torsion Design

The design of torsion reinforcements according to ACI 349-01 and 349-06 follows these steps:

1) Obtaining material resistant properties. These properties are obtained from the material properties associated with each transverse cross section and for the active time:

specified compressive strength of concrete.

specified yield strength of reinforcement.

2) Obtaining geometrical parameters depending on specified code. The required data is as follows:

web width or diameter of the circular section

ddistance from the extreme compressed fiber to the centroid of the longitudinal tensile reinforcement in Y, (for circular sections, this should not be less than the distance from the extreme compressed fiber to the centroid of the tensile reinforcement in the opposite half of the member).

Area enclosed by outside perimeter of the concrete cross section.

Outside perimeter of the concrete cross section.

Area enclosed by the centerline of the outermost closed transverse torsional reinforcement.

Perimeter of the centerline of the outermost closed transverse torsional reinforcement.

Gross area enclosed by the shear flow path.

Section 11-A.7 “Previous Considerations to Shear and Torsion Calculation” provides detailed information on how to calculate the required data for each valid section.

3) Obtaining forces and moments acting on the section. The torsional moment that acts on the section is obtained from the CivilFEM results file (.RCF).

Moment Description

Factored design torsional moment.

4) Checking whether torsion effects will be considered. Torsion effects are only considered if the design torsional moment (T_u) satisfies the condition below:

If the design torsional moment is less than this value, its effects can be neglected and it is consider as null for the design.

5) Checking section dimensions. Section dimensions must satisfy the following requirements:

In hollow sections, if the section’s wall thickness is less than A_oh/P_h, this value will be equal to the minimum thickness of the section in the formula above.

The torsion reinforcement will not be designed if the previous expression is not satisfied, so the parameters where the reinforcement is stored would be marked with 2¹⁰⁰. Then:

for transverse reinforcement

for longitudinal reinforcement

In this case, the element will be marked as not designed.

The ratio of the two coefficients is stored in the CivilFEM results file at both element ends:

6) Calculating the required transverse reinforcement. In order to resist the torsional moment, the section must satisfy the following condition:

cross-sectional area of one leg of a closed stirrup of the transverse reinforcement.

s spacing of the stirrups.

Therefore, the required transverse torsion reinforcement is:

The area of the designed transverse reinforcement per unit length is stored in the CivilFEM results file at both element ends:

7) Determining the longitudinal reinforcement requirement. The longitudinal reinforcement area is given by the following expression:

The area of the designed longitudinal reinforcement is stored in the CivilFEM results file at both element ends:

If both transverse and longitudinal reinforcements are designed at both element ends, this element will be labeled as designed.

6.6.7.6. Combined Shear and Torsion Design

The design of sections subjected to combined shear force and torsional moment, follows the steps below:

1) Checking whether torsion effects will be considered. Torsion effects are only considered if the design torsional moment (T_u) satisfies the condition below:

If the design torsional moment is less than this value, its effects can be neglected and it will be considered as null for designing.

2) Checking section dimensions. For shear force and associated torsional moment, section dimensions must satisfy the following requirements:

a) Solid sections:

b) Hollow sections:

In hollow sections, if the section wall thickness is less than A_oh/P_h, this last value will be equal to the minimum thickness of the section in the equation above.

If the expression above is not satisfied, the torsion reinforcement will not be designed; as a result, the reinforcement parameters will be defined as:

for transverse reinforcement

for longitudinal reinforcement

In this case, the element will be labeled as not designed, and the program will then advance to the next element.

The ratio of the two coefficients is stored in the CivilFEM results file at both element ends.

a) Solid sections:

b) Hollow sections:

3) Shear design assuming a null torsional moment. This design is accomplished with the same procedure as for the design of elements subjected to pure shear force according to ACI 349-01 and 349-06.

4) Torsion design considering a null shear force. This design is follows the same procedure as for the design of elements subjected to pure torsion according to ACI 349-01 and 349-06.

6.6.9. Shear and Torsion according to BS8110

6.6.8.1. Shear Check

1) Obtaining material strength properties. These properties are obtained from the material properties associated to each transverse cross section and for the active time.

The required data are the following:

characteristic compressive strength of concrete.

characteristic yield strength of reinforcement.

concrete partial safety factor.

2) Obtaining geometrical data of the section. Required data for shear checking are the following:

total area of the concrete transverse section.

h total depth in the shear direction considered.

3) Obtaining geometrical parameters depending on specified code. Required data are the following ones:

minimum width of the section.

deffective depth of the section.

Area of the longitudinal tension reinforcement that extends at least a distance d beyond the considered section.

Section 6.6.1.. provides detailed information on how to calculate the required data for each code and valid section.

4) Obtaining reinforcement data of the section. Required data are the following:

a angle between shear reinforcement and the longitudinal axis of the member. For this code,a = 90º.

area of reinforcement per unit length.

The reinforcement ratio may also be obtained with the following data:

total area of the reinforcement legs.

s spacing of the stirrups.

Or with the data below:

s spacing of the stirrups.

f diameter of bars.

N number of reinforcement legs.

5) Obtaining forces and moments acting on the section. The shear force that acts on the section as well as the concomitant axial force and bending moment are obtained from the CivilFEM results file (.RCF).

Force Description

Design shear force

Concomitant axial force

M Concomitant bending moment

6) Checking compression failure in the web. First, a check is made to ensure the design shear force () is less than or equal to the oblique compression resistance of concrete section ():

For each element end, calculated results are written in the CivilFEM results file in the following parameters:

VU1 Ultimate shear strength due to oblique compression of the concrete in web.

CRTVU1 Ratio of the design shear () to the resistance .

7) Calculating the shear resistance of concrete. Shear resistance of concrete () is checked using the following expression:

Where:

Area of the longitudinal tension reinforcement that extends at least a distance d beyond the considered section.

Considering the following restrictions:

If , the results are multiplied by

If the section is subjected to an axial force, then the following expression will be used:

Where:

h total depth in the shear direction considered.

concrete shear resistance without axial forces.

Taking into account that h / M always has to be = 1

For each element end, calculated results are written in the CivilFEM results file as the following parameters:

VC concrete shear resistance:

8) Calculaing the steel reinforcement shear resistance. Shear resistance provided by the steel reinforcement () is checked using the following expression:

Where:

area per unit length of shear reinforcement.

characteristic yield strength of shear reinforcement.

, always less than 460 N/mm²

For each element end, calculated results are written in the CivilFEM results file in the following parameters:

VS shear resistance provided by the transverse reinforcement

9) Calculating the total shear resistance of section. The total shear resistance (V_U2) is the sum of the shear resistance provided by the concrete and the shear resistance provided by the reinforcement:

For each element end, calculated results are written in the CivilFEM results file in the following parameters:

VU2 Total shear resistance of section.

CRTVU2 ratio of shear design force (V) and the resistance force

If = 0, a value of 2¹⁰⁰ is assigned to criterion CRTVU2.

10) Calculating the shear criterion. The shear criterion indicates the validity of the section (if less than 1, the section conforms to code specifications, and if greater than 1, the section is not valid). Moreover, it provides information with regards to how much more additional load the section can resist. The shear criterion is defined as follows:

For each element end, calculated results are written in the CivilFEM results file in the parameter CRT_TOT.

A value of 2¹⁰⁰ for this criterion indicates that the shear resistance () has a value of zero, as indicated in the previous step.

6.6.8.2. Torsion Check

The torsion checking according to BS8110 follows the steps below:

1) Obtaining material strength properties. These properties are obtained from the material properties associated to each transverse cross section and for the active time.

The required data are the following ones:

characteristic compressive strength of concrete.

characteristic yield strength of reinforcement.

2) Obtaining geometrical parameters depending on specified code. Geometrical parameters used for torsion calculations must be defined within CivilFEM database. The required data are the following ones:

torsion modulus for torsion checking and design.

minimum distance of the rectangular stirrups.

maximum distance of the rectangular stirrups.

Section 6.6.1.. provides detailed information on how to calculate the required data for each code and valid section.

3) Obtaining section reinforcement data. Required data are the following:

Transverse Reinforcement

area of transverse reinforcement per unit length.

The reinforcement ratio can also be obtained with the following data:

closed stirrups area for torsion.

s spacing of closed stirrups.

Or with the data below:

s spacing of closed stirrups.

diameter of the closed stirrups bars.

Longitudinal Reinforcement

total area of the longitudinal reinforcement.

The reinforcement ratio can also be obtained with the following data:

f diameter of longitudinal bars.

N number of longitudinal bars.

4) Obtaining section internal forces and moments. The torsional moment that acts on the section is obtained from the CivilFEM results file (.RCF).

Moment Description

Design torsional moment

5) Checking if torsion effects will be considered. Torsion effects are only considered if design torsional moment (T_d) satisfies the condition below:

with

Where is the minimum torsional stress.

If the design torsional moment is less than this value, its effects can be neglected and its default value taken as 0 for checking purposes.

6) Checking concrete failure. The design torsional moment must be less than or equal to the maximum torsional moment resisted by the concrete ():

If y1< 550 mm

where:

N/mm²is the maximum allowable stress.

torsion modulus for torsion check and design.

For each element end, calculated results are written in the CivilFEM results file in the following parameters:

TU1 Maximum torsional moment resisted by the section.

CRTTU1 Ratio of the design torsional moment (T_d) to the resistance T_u1.

If the torsion transverse reinforcement is not defined, the criterion is taken as 2¹⁰⁰.

7) Checking the maximum torsional moment resisted by the reinforcement. The design torsional moment must be less than or equal to the maximum torsional moment that the reinforcement can resist (), therefore:

where:

area of transverse reinforcement per unit length

For each element end, calculated results are written in the CivilFEM results file in the following parameters:

TU2 Maximum torsional moment that can be resisted by the reinforcement.

CRTTU2 Ratio of the design torsional moment () to the resistance .

In case the longitudinal reinforcement is not defined, the criterion is taken as 2¹⁰⁰.

8) Obtaining the necessary torsion reinforcement. The necessary longitudinal reinforcement is calculated as a function of the transverse reinforcement, using the following expression:

Where:

defined longitudinal reinforcement

necessary longitudinal reinforcement

area of transverse reinforcement

For each element end, calculated results are written in the CivilFEM results file in the following parameters:

ALT Area of necessary longitudinal torsion reinforcement in compliance with the defined transverse reinforcement.

CRTALT Ratio between the area of the required longitudinal torsion reinforcement and the area of the defined longitudinal torsion reinforcement.

9) Obtaining torsion criterion. The torsion criterion identifies the ratio of the design moment to the section’s ultimate strength (if it is less than 1, the section is valid; whereas if it exceeds 1, the section is not valid). The criterion concerning the validity for torsion is defined as follows:

For each element end, this value is stored in the CivilFEM results file as CRT_TOT.

A value 2¹⁰⁰ for this criterion indicates that any one of the torsion reinforcements are not defined.

6.6.8.3. Combined Shear and Torsion Check

Checking sections subjected to shear force and concomitant torsional moment follows the steps below:

1) Shear checking disregarding the torsional moment. This check follows the same procedure as the check of elements subjected to shear.

In this case, the total shear criterion CRT_TOT is named as CRTSHR.

2) Torsion checking disregarding the shear force. This check will be accomplished with the same procedure as the check of elements subjected to torsion, considering the torsional force due to shear in the calculation of concrete failure.

In this case, the total torsion criterion CRT_TOT is named as CRTTRS.

3) Obtaining the criterion of combined shear and torsion. This criterion contains both shear and torsion criteria:

For each element end, calculated results are written in the CivilFEM results file in the parameter CRT_TOT.

6.6.8.4. Shear Design

The shear design according to BS8110 follows these steps:

1) Obtaining material strength properties. These properties are obtained from the material properties associated to each transverse cross section and for the active time.

The required data are the following:

characteristic compressive strength of concrete.

characteristic yield strength of reinforcement.

concrete partial safety factor.

2) Obtaining geometrical data of the section. Required data for shear checking are the following:

total area of the concrete transverse section.

h total depth in the shear direction considered.

3) Obtaining geometrical parameters depending on specified code. Required data are the following:

minimum width of the section.

deffective depth of the section,.

Area of the longitudinal tension reinforcement that extends at least a distance d beyond the considered section.

Chapter 6.6.1. “Previous Considerations to Shear and Torsion Calculation” provides detailed information on how to calculate the required data for each code and valid section.

4) Obtaining reinforcement data of the section. Required data are the following ones:

a angle between shear reinforcement and the longitudinal axis of the member. For this code, a = 90º.

Force Description

Design shear force

Concomitant axial force

M Concomitant bending moment

6) Checking the crushing of the web in compression. First, a check is made to ensure the design shear force () is less than or equal to the oblique compression resistance of concrete section ():

For each element end, calculated results are written in the CivilFEM results file in the following parameters:

VU1 Ultimate shear strength due to oblique compression of the concrete in web.

CRTVU1 Ratio of the design shear () to the resistance .

If the design shear force is greater than the shear force that causes failure in the web, the section will not be designed. Therefore, the parameter for the reinforcement data will be defined as 2¹⁰⁰.

For this case, the element will be labeled as not designed.

7) Calculating the concrete shear resistance. The shear resistance of concrete (Vc) is checked using the following expression:

Where:

Area of the longitudinal tension reinforcement that extends at least a distance d beyond the considered section.

Taking into account the following restrictions:

If the results are multiplied by

If the section is subjected to an axial force, then the following expression will be used:

Where:

h total depth in the shear direction considered.

concrete shear resistance without axial forces.

Taking into account that

For each element end, calculated results are written in the CivilFEM results file in the following parameters:

VC concrete shear resistance:

8) Determining the contribution of the required transverse reinforcement to the shear force. If the section requires shear reinforcement, the condition for the validity of sections subjected to shear force is the following:

is the reinforcement contribution.

is the concrete contribution.

For each element end, calculated results are written in the CivilFEM results file in the following parameter:

VS Transverse reinforcement shear resistance.

9) Calculating the required reinforcement ratio. Once the shear force that must be carried by the shear reinforcement has been obtained, this can be calculated from the equation below:

where:

area per unit length of shear reinforcement.

characteristic yield strength of shear reinforcement.

The area of designed reinforcement per unit length is stored in the CivilFEM results file for both ends:

In this case the element is marked as designed (provided that the design process is correct for both element sections).

6.6.8.5. Torsion Design

Torsion reinforcement design according to BS8110 follows the following steps:

1) Obtaining material strength properties. These properties are obtained from the material properties associated to each transverse cross section and for the active time.

The required data are the following ones:

characteristic compressive strength of concrete.

characteristic yield strength of reinforcement.

torsion modulus for torsion checking and dimensioning.

minimum distance of the rectangular stirrups.

maximum distance of the rectangular stirrups.

Section 6.6.1.. provides detailed information on how to calculate the required data for each code and valid section.

3) Obtaining section internal forces and moments. The torsional moment that acts on the section is obtained from the CivilFEM results file (.RCF).

Moment Description

Design torsional moment

4) Checking if torsion effects must be considered. Torsion effects are only considered if design torsional moment () satisfies the condition below:

with

Where:

minimum torsional stress

If the design torsional moment is less than this value, its effects can be neglected and its default value will be defined as 0 for checking purposes.

5) Checking concrete failure. The design torsional moment T_d must be less than or equal to the maximum torsional moment that concrete can resist (); therefore:

If y1< 550mm

Where:

N/mm²is the maximum allowable stress.

torsion modulus for torsion check and design.

For each element end, calculated results are written in the CivilFEM results file in the following parameters:

TU1 Maximum torsional moment that can be resisted by the section.

CRTTU1 Ratio of the design torsional moment (T_d) to the resistance T_u1.

In case the torsion transverse reinforcement is not defined, the criterion is taken as 2¹⁰⁰.

If the design torsional moment is greater than the torsional moment that causes the compression failure of concrete, the reinforcement design will not be feasible. Therefore, the parameters for reinforcement data will be assigned a value of 2¹⁰⁰.

for transverse reinforcement

for longitudinal reinforcement

In this case, the element is marked as not designed, and the program then advances to the next element.

If there is no failure due to oblique compression, the calculation process continues.

6) Calculating the transverse reinforcement required. The design torsional reinforcement must be less than or equal to the resistance torsional reinforcement:

Where:

area of transverse reinforcement per unit length

characteristic yield strength of reinforcement

Therefore, the required transverse reinforcement is:

The area per unit length of the designed transverse reinforcement is stored in the CivilFEM results file for both element ends as:

7) Calculating the longitudinal reinforcement required. The longitudinal reinforcement is calculated as a function of the transverse reinforcement using the expression:

Where:

required longitudinal reinforcement.

area per unit length of transverse reinforcement.

For each element end, calculated results are written in the CivilFEM results file in the following parameter:

ASLT Area of longitudinal torsion reinforcement.

6.6.8.6. Shear and Torsion Design

The design of sections subjected to shear force and concomitant torsional moment follows the steps below:

1) Shear design assuming a null torsional moment. This design follows the same steps as for the design of elements subjected to pure shear according to BS8110.

2) Torsion design assuming a null shear force. This design is accomplished with the same procedure as for the designing of elements subjected to torsion force according to BS8110. However, this design considers the stress due to shear in the calculation of concrete failure.

Where:

maximum combined shear stress (shear plus torsion).

torsion modulus for torsion check and design.

6.6.10. Shear and Torsion according to GB50010

6.6.9.1. Shear Check

Shear checking for elements according to GB50010-2010 follows the steps below:

1) Obtaining materials strength properties. The required data are the following:

design compressive strength of concrete.

design tensile strength of concrete.

steel design tensile strength for of shear reinforcement.

2) Obtaining geometrical data of the section. Required data for shear checking are the following:

total cross-sectional area of the concrete section.

3) Obtaining geometrical parameters depending on specified code. Required data are the following:

bminimum width of the section over the effective depth.

effective height of the section.

the web height.

4) Obtaining the reinforcement data of the section. The necessary data are:

a angle between shear reinforcement and the longitudinal axis of the member.

Reinforcement area per length unit.

Alternatively, the amount of reinforcement can be determined from:

total area in the reinforcement legs.

s spacing among stirrups.

Or from the data below:

s spacing among stirrups.

φ diameter among bars.

N reinforcement leg number.

5) Obtaining the section internal forces and moments. The shear force that acts on the section as well as the concomitant axial force and bending moment are obtained from the CivilFEM results file (.RCF).

Force Description

V Design shear force

N Axial force

6.6.9.2. Shear Check without Seismic Action

1) Checking whether the section dimensions meet the requirement. First, a check is made to ensure the design shear (V) is less than or equal to maximum shear resistance of the section ():

where β_cis a coefficient depending on the concrete strength:

· For concrete C50 (fc= 23.1 N/mm²) or under, ;

· For concrete C80 (fc= 35.9 N/mm²),

· For concrete C55-75, a linear interpolation is made for according to the values of fc.

Results are written for each end in the CivilFEM results file as the following parameters:

VRD1 Maximum shear resistance.

CRVRD1 Ratio of the design shear force V to the resistance .

2) Checking if shear reinforcement will be required.

If shear reinforcement has not been defined for the section, a check is made to ensure the design shear force V is less than the maximum design shear force that can be resisted by the concrete without reinforcements ():

Where

is the section height factor,

If reinforcement has been defined, axial forces are not present (N=0), and the shear force from the concentrated load for an independent beam is less than 75%:

If N is compressive (N < 0)

If N is tensile (N > 0)

The following are given in CivilFEM results:

VRD2 Maximum design shear force resisted by the section without the crushing of the concrete compressive struts.

CRVRD2 Ratio of the design shear force V to the resistance .

For sections subjected to an applied tensile axial force so that , CRVRD2 is taken as 2¹⁰⁰.

3) Checking of elements requiring shear reinforcement. The shear resistance calculation of a section with reinforcement (V_Rd3) will differ according to whether the concentrated load exists.

Conditions below must be verified:

where

design shear load capacity of reinforcement.

cross-sectional area of the shear reinforcement.

s spacing of the stirrups measured along the longitudinal axis.

design tensile strength of shear reinforcement.

Results obtained are written for each end in the CivilFEM results file as the following parameters:

Shear strength of the reinforcement.

VRD3 Design shear resistance.

CRVRD3 Ratio of the design shear force V to the shear resistance .

If , CRVRD3 is taken as 2¹⁰⁰.

4) Obtaining the shear criterion. The shear criterion indicates the validity of the section (if less than 1, the section will be valid; if greater than 1 the section, is not good). Moreover, it provides information with regards to how much more load the section can resist. The shear criterion is defined as follows:

For each element end, calculated results are written in the CivilFEM results file in the parameter CRT_TOT.

A value of 2¹⁰⁰ in this criterion will indicate that shear resistance () is not been considered, as indicated in the previous step.

6.6.9.3. Shear Check with Seismic Action

Shear checking of elements according to GB50010-2010 and GB50011-2010 follows the steps below:

1) Determining the factor for seismic fortification, used to adjust the shear capacity and performing the check for shear. Firstly, this checking method differs from the other typical checking methods:

V Design shear force

V_R/ γ_RE Design shear resistance

γ_RE factor for seismic fortification, used to adjust the shear capacity. If the combination of the cases does not include the horizontal seismic action, γ_RE=1.

Otherwise, it is selected as illustrated in the following table.

Table 10‑2 FACTORS FOR SEISMIC FORTIFICATION

Member	Status	γ_RE
Beam	Bending	0.75
Column	Eccentric compression and	0.75
	Eccentric compression and	0.8
Shear wall	Eccentric compression	0.85
Other	Shear Eccentric tension	0.85

2) Checking whether section dimensions meet requirements under the actions of seismic loads. First, a check is made to ensure the design shear (V) is less than or equal to sectional maximum possible resistance () under the seismic loads:

For beam:

Where:

effective height of the section

Length between restraints

For column:

VRD1 Maximum possible shear resistance.

CRVRD1 Ratio of the design shear force V to the resistance .

3) Checking whether shear reinforcement will be required for the section under actions of seismic loads.

If the member is a beam, axial forces are not present (N=0), and the shear force from the concentrated load is less than 75%:

If the member is an independent beam and the shear force from concentrated load is more than 75%:

If the member is a column and N is compressive (N < 0)

If N is tensile (N > 0)

The following are given in CivilFEM results:

VRD2 Maximum design shear force resisted by the section without crushing of the concrete compressive struts.

CRVRD2 Ratio of the design shear force V to the resistance V_Rd2.

For sections subjected to an applied tensile axial force so that , CRVRD2 is taken as 2¹⁰⁰.

4) Checking of elements that will require shear reinforcement under the actions of seismic loads. The calculated of the shear resistance of a section with reinforcement () differs according to whether the concentrated load exists.

The following condition is checked:

where

is the design shear load capacity of reinforcement.

is the cross-sectional area of the shear reinforcement.

s is the spacing of the stirrups measured along the longitudinal axis.

is the design tensile strength of shear reinforcement.

Results obtained are written for each end in the CivilFEM results file as the following parameters:

Shear strength of the reinforcement.

VRD3 Design shear resistance.

CRVRD3 Ratio of the design shear force V to the shear resistance .

If , CRVRD3 is taken as 2¹⁰⁰.

5) Obtaining the shear criterion. The shear criterion indicates the validity of the section (if less than 1, the section conforms to code specifications; if greater than 1, the section is not valid). Moreover, it provides information with regards to how much more load section can resist. The shear criterion is defined as follows:

For each element end, calculated results are written in the CivilFEM results file in the parameter CRT_TOT.

A value of 2¹⁰⁰ for this criterion indicates that shear resistance () is not considered, as indicated in the previous step.

6.6.9.4. Torsion Check

The torsion checking according to GB50010-2010 follows the steps below:

1) Obtaining material strength properties. These properties are obtained from the material properties associated to the transverse cross section and for the active time.

The required data are the following:

design compressive strength of concrete.

design tensile strength of concrete.

design tensile strength for torsion reinforcement.

2) Obtaining section geometrical data. Required data for shear checking are the following ones:

total cross-sectional area of the concrete section.

thickness of a box section (TWY)

3) Obtaining geometrical parameters depending on specified code. The required data are the following:

bminimum width of the section over the effective depth or section inner diameter for circular section.

height of the section or section outer diameter for circular section.

the web height.

Plastic resistance of torsion moment.

Core area.

Core perimeter.

Plastic resistance of torsion moment for branch 1 for T and double T section/I-section.

Core area for branch 1 for T and double T section/I-section.

Core perimeter for branch 1 for T and double T section/I-section.

Plastic resistance of torsion moment for branch 2 for T and double T section/I-section.

Core area for branch 2 for T and double T section/I-section.

Core perimeter for branch 2 for T and double T section/I-section.

Section 11-A.7 “Previous Considerations to Shear and Torsion Calculation” provides detailed information on how to calculate the required data for each code and valid section.

4) Obtaining the reinforcement data section. The required data are:

Transverse Reinforcement

transverse reinforcement area per length unit.

Alternatively, the amount of the reinforcement can be calculated from:

critical tensile zone.

s spacing between stirrups.

Or from the data below:

s spacing between stirrups.

diameter of the bar of the stirrup.

Longitudinal Reinforcement

Total area of the longitudinal reinforcement.

Alternatively, the amount of the reinforcement can determined from:

Longitudinal bar diameter.

N Longitudinal bar number.

5) Obtaining section internal forces and moments. The torsional moment that acts on the section is obtained from the CivilFEM results file (.RCF).

Moment Description

T Design torsion moment

N Axial force

6) Checking if the section dimensions meet the requirement.

if then

Results are written in the CivilFEM results file for both element ends as the parameters:

TRD1 Maximum possible resistance of torsional moment

CRTRD1 Ratio of the design torsional moment T to the resistance .

7) Calculating the maximum torsional moment resisted without reinforcements.

Where

For rectangular and circular sections:

N (< 0) is the compressive axial force, if, assume.

For box sections (axial forces cannot be resisted):

is the influence coefficient of the wall thickness of the box section.

, if , assume,

For T and double T sections/I-sections, these are divided into rectangle sections and therefore, follow the procedure according to rectangular sections.

Results are written in the CivilFEM results file for both element ends as the parameters:

TRD2 Maximum design torsional moment resisted by the section without crushing the concrete compressive struts.

CRTRD2 Ratio of the design torsional moment T to the resistance TRd2.

8) Calculating the maximum torsional moment resisted by the reinforcement. The design torsional moment T must be less than or equal to the maximum design torsional moment resisted by concrete and the reinforcement (); as a result, the following condition must be satisfied:

where

the ratio between longitudinal reinforcement and hoop

reinforcement strength

if, assume

Calculated results are written in the CivilFEM results file for both element ends as the parameters:

Torsion strength of the reinforcement.

TRD3 Maximum design torsional moment resisted by concrete and the torsion reinforcement.

CRTRD3 Ratio of the design torsional moment T to the resistance .

If transverse reinforcement is not defined, .

9) Obtaining criterion of torsion checking.

CRT_TOT = MAX (CRTRD1, CRTRD3)

6.6.9.5. Combined Shear and Torsion Check

1) Checking for whether section dimensions meet the requirements.

Where

If or then

If or = 6 then

Linear interpolation for or

Results are written in the CivilFEM results file for both element ends as the parameters:

VRD1 Maximum shear resistance.

TRD1 Maximum possible resistance of torsional moment

CRVRD1 Ratio of the design shear and torsion resistance V to the shear resistance .

CRTRD1 Ratio of the design shear torsion resistance T to the torsion resistance .

2) Checking whether the section will require reinforcement.

If where or

No shear reinforcement is necessary.

If where or,

No torsion reinforcement is necessary.

Results are written in the CivilFEM results file for both element ends as the parameters:

VRD2 Design shear resistance without considering the reinforcement.

CRVRD2 Ratio of the design shear force V to the resistance V_Rd1.

For sections subjected to an axial tensile force so that V_Rd2=0, CRVRD1 is taken as 2¹⁰⁰.

TRD2 Maximum design torsional moment resisted by the section without crushing the concrete compressive struts.

CRTRD2 Ratio of the design torsional moment T to the resistance T_Rd1.

If reinforcement has been defined:

The wall thickness influence coefficient for box sections, , if . or for sections other than box, assume .

Torsion reduction coefficient for elements under shear

and torsion.

For compressed rectangle section frame columns:

Results obtained are written for each end in the CivilFEM results file as the following parameters:

VRD2Shear strength of concrete.

Torsion strength of concrete.

3) Calculating the maximum load that can be resisted by the reinforcement.

where

For compressed rectangle section frame columns:

Results obtained are written for each end in the CivilFEM results file as the following parameters:

VRD3 Design shear resistance.

CRVRD3 Ratio of the design shear force (V) to the shear resistance V_Rd3.

If , CRVRD3 is taken as 2¹⁰⁰.

TRD3 Maximum design torsional moment resisted by the torsion reinforcement.

CRTRD3 Ratio of the design torsional moment T to the resistance T_Rd3.

If transverse reinforcement is not defined, T_Rd3=0, and the criterion would be assigned a value of 2¹⁰⁰.

4) Obtaining the criterion of shear & torsion checking.

This criterion considers pure shear, pure torsion, shear-torsion and ultimate strength condition of concrete criteria. The criterion determines whether the section is valid and is defined as follows

CRT_TOT= MAX(CRVRD1, CRVRD3, CRTRD1, CRTRD3)

For each end, the value of this criterion is stored in the CivilFEM results file as the parameter CRT_TOT.

6.6.9.6. Shear Design

Elements shear design according to GB50010-2010 follows the steps below:

1) Obtaining materials strength properties. The required data are the following:

design compressive strength of concrete.

design tensile strength of concrete.

design tensile strength for of shear reinforcement.

2) Obtaining geometrical data of the section. Required data for shear checking are the following:

total cross-sectional area of the concrete section.

3) Obtaining geometrical parameters depending on specified code. Required data are the following:

bminimum width of the section over the effective depth.

effective height of the section.

the web height.

4) Obtaining reinforcement data of the section. Required data are the following:

area of reinforcement per unit of length.

a angle between shear reinforcement and the longitudinal axis of the member.

Force Description

V Design shear force

N Axial force

6.6.9.7. Shear Design without Seismic Action

1) Checking whether the section dimensions meet the requirement. Firstly, a check is made to ensure the design shear (V) is less than or equal to the maximum resistance of the section (V_Rd1):

If ,

where is a coefficient depending on the concrete strength:

· For concrete C50 (fc= 23.1 N/mm²) or under, =1. 0;

· For concrete C80 (fc= 35.9 N/mm²), β_c =0.8,

· For concrete C55-75, a linear interpolation is made for β_caccording to the values of fc.

Results are written for each end in the CivilFEM results file as the following parameters:

VRD1 Maximum possible shear resistance.

CRVRD1 Ratio of the design shear force V to the resistance V_Rd1.

2) Maximum shear force resisted without shear reinforcements.

If shear reinforcement has not been defined for the section, the design shear force V must be less than the maximum design shear force that can be carried by the concrete without reinforcements (V_Rd2):

Where:

is the section height factor,

If , assume ;

if , assume .

If reinforcement has been defined, axial forces are not present (N=0), and the shear force from the concentrated load for an independent beam is less than 75%,

If N is compressive (N < 0):

-0.07N

If N is tensile (N > 0):

The following are given in CivilFEM results:

VRD2 Maximum design shear force resisted by the section without crushing the concrete compressive struts.

CRVRD2 Ratio of the design shear force V to the resistance V_Rd2.

For sections subjected to an axial tensile force so that V_Rd2=0, CRVRD2 is taken as 2¹⁰⁰.

If design shear force is greater than the shear force required to crush the concrete compressive struts, the reinforcement design will not be feasible; as a result, the parameter pertaining to the reinforcement data will be defined as 2¹⁰⁰:

In this case, the element will be labeled as not designed, and the program will advance to the next element.

If there is no crushing by oblique compression, the calculation process continues.

3) Determining the shear strength contribution of the required transverse reinforcement. The condition for the validity of the section subjected to shear force is:

shear reinforcement contribution.

Therefore, the reinforcement contribution should be:

For each element end, the V_svalue is included in the CivilFEM results file as the parameter:

4) Calculating the required transverse reinforcement ratio. Once the required shear strength of the reinforcement has been obtained, the reinforcement can be calculated from the equation below:

where:

cross-sectional area of the shear reinforcement.

s spacing of the stirrups measured along the longitudinal axis.

The area of designed reinforcement per unit length is stored in the CivilFEM results file as the parameter:

In this case, the element will be labeled as designed (provided that design process is correct for both element sections).

If the section is labeled as not designed, the reinforcement will be defined as 2¹⁰⁰.

6.6.9.8. Shear Design with Seismic Action

Shear checking of elements according to GB50010-2010 and GB50011-2010 follows the steps below:

V Design shear force

V_R/ γ_RE Design shear resistance

γ_RE factor for seismic fortification, used to adjust the shear capacity. If the combination of the cases does not include the horizontal seismic action, γ_RE=1.

Otherwise, it is selected as illustrated in the following table.

Table 10‑3 FACTORS FOR SEISMIC FORTIFICATION

Member	Status	γ_RE
Beam	Bending	0.75
Column	Eccentric compression and	0.75
	Eccentric compression and	0.8
Shear wall	Eccentric compression	0.85
Other	Shear Eccentric tension	0.85

2) Checking whether section dimensions meet requirements under the actions of seismic loads. First, a check is made to ensure the design shear (V) is less than or equal to the maximum resistance of the section () under the seismic loads:

For beams:

For columns:

VRD1 Maximum shear resistance.

CRVRD1 Ratio of the design shear force V to the resistance V_Rd1.

The design process stops if CRVRD1>1.0

3) Maximum shear force resisted without shear reinforcements under the actions of seismic loads.

If the member is a beam, axial forces are not present (N=0), and the shear force from the concentrated load is less than 75%:

If the member is an independent beam and the shear force from the concentrated load is more than 75%,

If the member is a column and N is compressive (N < 0)

If N is tensile (N > 0)

The following are given in CivilFEM results:

VRD2 Maximum design shear force resisted by the section without crushing of the concrete compressive struts.

CRVRD2 Ratio of the design shear force V to the resistance V_Rd2.

For sections subjected to an axial tensile force so that V_Rd2=0, CRVRD2 is taken as 2¹⁰⁰.

The design process stops if CRVRD2=1.0 because the reinforcement will not be required for the strength (minimum reinforcements are still necessary).

4) Determining the shear strength contribution of the required transverse reinforcement. The condition for the validity of the section concerning shear force is:

V_s shear reinforcement contribution.

Therefore, the reinforcement contribution should be:

For each element end, the V_svalue is included in the CivilFEM results file as the parameter:

5) Calculating the required transverse reinforcement ratio. Once the required shear strength of the reinforcement has been obtained, the reinforcement area per unit length can be calculated:

where:

cross-sectional area of the shear reinforcement.

s spacing of the stirrups measured along the longitudinal axis.

The area of the designed reinforcement per unit length is stored in the CivilFEM results file as the parameter:

In this case, the element will be labeled as designed (provided that design process is correct for both element sections).

If the design is not possible, the reinforcement will be assigned the value 2¹⁰⁰.

6.6.9.9. Torsion Design

Torsion checking according to GB50010-2010 follows the steps below:

1) Obtaining materials strength properties. These properties are obtained from the material properties associated to the transverse cross section and for the active time.

The required data are the following:

design compressive strength of concrete.

design tensile strength of concrete.

design tensile strength for torsion reinforcement.

2) Obtaining geometrical data of the section. Required data for shear checking are the following:

total cross-sectional area of the concrete section.

thickness of a box section (TWY)

3) Obtaining geometrical parameters depending on specified code. The required data are the following:

bminimum width of the section over the effective depth or section inner diameter for circular section.

height of the section or outer diameter for circular section.

the web height.

Plastic resistance of torsion moment

Core area

Core perimeter

Plastic resistance of torsion moment for branch 1 for T and double T section/I-section.

Core perimeter for branch 1 for T and double T section/I-section.

Plastic resistance of torsion moment for branch 2 for T and double T section/I-section.

Core perimeter for branch 2 for T and double T section/I-section.

Section 6.6.1.. provides detailed information on how to calculate the required data for each code and valid section.

4) Obtaining reinforcement data of the section. Required data are the following ones:

Transverse Reinforcement

Area of transverse reinforcement per unit length.

Longitudinal Reinforcement

total area of the longitudinal reinforcement.

5) Obtaining section internal forces and moments. The torsional moment that acts on the section is obtained from the CivilFEM results file (.RCF).

Moment Description

T Design torsion moment

N Axial force

6) Checking if the section dimensions meet the requirement.

Results are written in the CivilFEM results file for both element ends as the parameters:

TRD1 Maximum resistance of torsional moment

CRTRD1 Ratio of the design torsional moment T to the resistance T_Rd1.

7) Calculating the maximum torsional moment resisted without reinforcement.

where

For rectangular and circular sections

N (< 0) compressive axial force, if, assume.

For box section (no axial force resistance),

The influence coefficient of the wall thickness of the box section.

, if

For T and double T sections, these are divided into rectangle sections, following the proceedure according to rectangular sections.

Results are written in the CivilFEM results file for both element ends as the parameters:

TRD2 Maximum design torsional moment resisted by the section without crushing of the concrete compressive struts.

CRTRD2 Ratio of the design torsional moment T to the resistance T_Rd1.

8) Calculating the required transverse reinforcement ratio. The design torsional moment T must be less than or equal to the maximum design torsional moment resisted by concrete and the reinforcement (T_Rd2); consequently, the following condition must be satisfied:

Where:

is the ratio between longitudinal reinforcement and hoop reinforcement strength ; if, assume

The required transverse reinforcement is given by this expression:

The area of the designed transverse reinforcement per unit length is stored in the CivilFEM results file as the parameter:

9) Calculating the required longitudinal reinforcement ratio. The longitudinal reinforcement is calculated from:

where:

area of the designed longitudinal reinforcement.

hoop reinforcements

The area of the designed longitudinal reinforcement is stored in the CivilFEM results file as the parameter:

If both transverse and longitudinal reinforcements are designed for both element sections, this element will be labeled as designed.

6.6.9.10. Combined Shear and Torsion Design

The check of sections subjected to shear force and concomitant torsional moment we follow the steps below:

1) Obtaining material strength properties. The required data are the following:

design compressive strength of concrete.

design tensile strength of concrete.

design tensile strength for torsion reinforcements

design tensile strength for shear hoop reinforcements

2) Obtaining geometrical data of the section.

total cross-sectional area of the concrete section.

3) Obtaining geometrical parameters depending on code. Required data are the following:

bminimum width of the section over the effective depth or section inner diameter for circular section.

effective height of the section or outer diameter for circular section.

the web height.

Plastic resistance of torsion moment for branch 1 for T and double T section/I-section.

Core perimeter for branch 1 for T and double T section/I-section.

Plastic resistance of torsion moment for branch 2 for T and double T section/I-section.

Core perimeter for branch 2 for T and double T section/I-section.

4) Obtaining reinforcement data of the section. Required data are the following:

Shear Reinforcement

area of reinforcement per unit length.

Transverse Torsion Reinforcement

area of reinforcement per unit length.

Torsion Longitudinal Reinforcement

total area of the longitudinal reinforcement.

5) Obtaining the section internal forces and moments. The shear force that acts on the section, as well as the concomitant axial force and bending moment, are obtained from the CivilFEM results file (.RCF).

Force Description

V Design shear force

N Axial force

T Design torsion moment

1) Checking for whether section dimensions meet the requirements.

Where

If or then

If or = 6 then

Linear interpolation for or

Results are written in the CivilFEM results file for both element ends as the parameters:

VRD1 Maximum shear resistance.

TRD1 Maximum possible resistance of torsional moment

CRVRD1 Ratio of the design shear and torsion resistance V to the shear resistance .

CRTRD1 Ratio of the design shear torsion resistance T to the torsion resistance .

2) Checking whether the section will require reinforcement.

If where or

Then no shear reinforcement is necessary.

If where or,

Then no torsion reinforcement is necessary.

Results are written in the CivilFEM results file for both element ends as the parameters:

VRD2 Design shear resistance without considering the reinforcement.

CRVRD2 Ratio of the design shear force V to the resistance V_Rd1.

For sections subjected to an axial tensile force so that V_Rd2=0, CRVRD1 is taken as 2¹⁰⁰.

TRD2 Maximum design torsional moment resisted by the section without crushing the concrete compressive struts.

CRTRD2 Ratio of the design torsional moment T to the resistance T_Rd1.

If reinforcement has been defined:

The wall thickness influence coefficient for box sections, , if . or for sections other than box, assume .

Torsion reduction coefficient for elements under shear

and torsion.

For compressed rectangle section frame columns:

Results obtained are written for each end in the CivilFEM results file as the following parameters:

VRD2Shear strength of concrete.

Torsion strength of concrete.

3) Calculating the maximum load that can be resisted by the reinforcement.

where

For compressed rectangle section frame columns:

Results obtained are written for each end in the CivilFEM results file as the following parameters:

VRD3 Design shear resistance.

CRVRD3 Ratio of the design shear force (V) to the shear resistance V_Rd3.

If , CRVRD3 is taken as 2¹⁰⁰.

TRD3 Maximum design torsional moment resisted by the torsion reinforcement.

CRTRD3 Ratio of the design torsional moment T to the resistance T_Rd3.

If transverse reinforcement is not defined, T_Rd3=0, and the criterion would be assigned a value of 2¹⁰⁰.

6) Obtaining required shear and torsion reinforcement ratios.

Shear:

Torsion:

where

cross-sectional area of the shear reinforcement.

cross-sectional area of the bars used as closed-stirrups.

s spacing of the closed stirrups of the transverse reinforcement.

design yield strength of torsion reinforcement.

the ratio between longitudinal and hoop reinforcement

reinforcement strength ; if , assume

The area of the designed reinforcement per unit length is stored in the CivilFEM results file as the parameter:

7) Calculating the required longitudinal requirement ratio.

The area of the designed longitudinal reinforcement is stored in the CivilFEM results file as the parameter:

If both transverse and longitudinal reinforcements are designed for both element sections, this element will be labeled as designed.

6.6.11. Shear and Torsion according to AASHTO Standard Specifications for Highway Bridges

6.6.10.1. Shear Check

Shear checking according to AASHTO Standard Specifications for Highway Bridges follows these steps:

1) Obtaining material strength properties. These properties are obtained from the material properties associated with each transverse cross section and for the active time.

The required data are the following ones:

specified compressive strength of concrete.

specified yield strength of reinforcement.

2) Obtaining geometrical data of the section. Required data for shear checking are the following:

area of concrete section.

3) Obtaining geometrical parameters depending on specified code. The required data are the following:

web width or diameter of circular section.

ddistance from the extreme compressed fiber to the centroid of the longitudinal tensile reinforcement in the Y direction, (for circular sections, this should be greater than the distance from the extreme compressed fiber to the centroid of the tensile reinforcement in the opposite half of the member).

Section 6.6.1. provides detailed information on how to calculate the required data for each code and valid section.

4) Obtaining section reinforcement data. Required data are the following:

a angle between shear reinforcement and the longitudinal axis of the member section.

area of reinforcement per unit length.

The reinforcement ratio may also be obtained with the following data:

total area of the reinforcement legs.

s spacing of the stirrups.

or with the following ones:

s spacing of the stirrups.

φ diameter of bars.

N number of reinforcement legs.

5) Obtaining forces and moments acting on the section. The shear force that acts on the section as well as the concomitant axial force are obtained from the CivilFEM results file (.RCF).

Force Description

Design shear force in Y direction for I-section

6) Calculating the shear strength provided by concrete. First, the shear strength provided by concrete (V_c) is calculated by the following expression:

where:

square root of specified compressive strength of concrete, in psi (always taken as less than 100 psi).

For sections subject to a compressive axial force:

Where N_u/A_g is expressed in psi.

If section is subjected to a tensile force so that the tensile stress is less than 500 psi:

If section is subjected to a tensile force so that the tensile stress exceeds 500 psi, it is assumed .

The calculated result for both element ends is stored in the CivilFEM results file as the parameter VC:

VC Shear strength provided by concrete.

7) Calculating the shear strength provided by shear reinforcement. The strength provided by shear reinforcement (V_s) is calculated with the following expression:

where:

area of the cross-section of shear reinforcement.

s spacing of the stirrups measured along the longitudinal axis.

The calculated result for both element ends is stored in the CivilFEM results file as the parameter VS:

VS Shear strength provided by transverse reinforcement.

8) Calculating the nominal shear strength of the section. The nominal shear strength (V_n) is the sum of the provided by concrete and by the shear reinforcement:

This nominal strength as well as its ratio with the design shear are stored in the CivilFEM results file as the parameters:

VN Nominal shear strength.

CRTVN Ratio of the design shear force (V_u) to the resistance V_n.

If the strength provided by concrete is null and the shear reinforcement is not defined in the section, then V_n=0 and the criterion will be equal to –1.

9) Obtaining shear criterion. The section will be valid for shear if the following condition is satisfied:

φ strength reduction factor of the section, (0.85 for shear and torsion).

Therefore, the shear criterion for the validity of the section is defined as follows:

For each element, this value is stored in the CivilFEM results file as the parameter CRT_TOT.

If the strength provided by concrete is null and the shear reinforcement is not defined in the section, then , and the criterion will be equal to 2¹⁰⁰.

The value is stored in CivilFEM results file as the parameter VFI.

6.6.10.2. Torsion Check

Torsion checking of elements is done according to ACI-318, with φ=0.85.

6.6.10.3. Combined Shear and Torsion Check

For checking sections subjected to shear force and concomitant torsional moment, the same procedure as for the ACI-318 code is followed, with φ=0.85.

6.6.10.4. Shear Design

The shear design according to AASHTO Specific Standards for Highway Bridges follows these steps:

1) Obtaining material strength properties. These properties are obtained from the material properties associated with each transverse cross section and for the active time.

The required data are the following:

specified compressive strength of concrete.

specified yield strength of reinforcement.

2) Obtaining geometrical data of the section. Required data for shear designing are the following:

area of concrete section.

3) Obtaining geometrical parameters depending on specified code. The required data are the following:

web width or diameter of the circular section.

Section 6.6.1. provides detailed information on how to calculate the required data for each code and valid section.

4) Obtaining reinforcement data of the section. In shear reinforcement designing, it is possible to define the angle α between the reinforcement and the longitudinal axis of the member. This angle must be stored in the shear reinforcement data of each element. If this angle is equal to zero or is not defined, α=90º. Other data concerning the reinforcements are ignored.

5) Obtaining forces and moments acting on the section. The shear force that acts on the section, as well as the concomitant axial force, is obtained from the CivilFEM results file (.RCF).

Force Description

Design shear force in Y

6) Calculating the shear strength provided by concrete. First, we calculate the shear strength provided by concrete (V_c) with the following expression:

where:

square root of specified compressive strength of concrete, in psi (always taken as less than 100 psi).

For sections subject to a compressive axial force:

Where is expressed in psi.

If section is subjected to a tensile force so that the tensile stress is less than 500 psi:

If section is subjected to a tensile force so that the tensile stress exceeds 500 psi, it is assumed .

The calculated result is stored in the CivilFEM results file for both element ends as the parameter:

VC Shear strength provided by concrete.

7) Determining the required reinforcement contribution to the shear strength. The section must satisfy the following condition to resist the shear force:

Therefore, the required shear force of the reinforcement must be:

If the required shear strength of the reinforcement does not satisfy the expression above, the section will not be designed. Consequently, the parameters for the reinforcement data will be defined as 2¹⁰⁰. Therefore:

In this case, the element will be labeled as not designed, and the program will then advance to the following element.

Calculated results are stored in the CivilFEM results file for both element ends as the parameter:

VS Shear resistance provided by the transverse reinforcement.

8) Calculating the required reinforcement ratio. Once the required shear strength of the reinforcement has been obtained, the reinforcement can be calculated with the following expression:

Where:

area of the cross-section of the shear reinforcement.

s spacing of the stirrups measured along the longitudinal axis.

The area of the designed reinforcement per unit length is stored in the CivilFEM results file for both element ends:

In this case, the element will be labeled as designed (providing the design procedure is correct for both element sections).

6.6.10.5. Torsion Design

Torsion reinforcements are designed according to ACI-318.

6.6.10.6. Combined Shear and Torsion Design

The design of sections subjected to shear force and concomitant torsional moment follows the method used for the ACI-318 code.

6.6.12. Shear and Torsion according to NBR6118

6.6.11.1. Shear Check

The checking for shear according to NBR6118 follows these steps:

1) Obtaining material strength properties. These properties are obtained from the material properties associated with each transverse cross section and for the active time.

The required data are the following:

characteristic compressive strength of concrete.

characteristic yield strength of reinforcement.

concrete partial safety factor.

steel partial safety factor.

2) Obtaining geometrical data of the section. Required data for shear checking are the following ones:

total area of the concrete section.

3) Obtaining geometrical parameters depending on specified code. Geometrical parameters used for shear calculations must be defined:

minimum width of the section at a height equal to ¾ the effective depth.

deffective depth of the section.

q Angle of the concrete compressive struts with the longitudinal axis of member

30º < q < 45º

Section 6.6.1. provides detailed information on how to calculate the required data for each code and valid section.

4) Obtaining reinforcement data of the section. Required data are the following:

a angle between shear reinforcement and the longitudinal axis of the member.

area of reinforcement per unit of length.

The reinforcement ratio may also be obtained with the following data:

total area of the reinforcement legs.

s spacing of the stirrups.

Or from the data below:

s spacing of the stirrups.

f diameter of bars.

N number of reinforcement legs.

5) Obtaining forces and moments acting on the section. The shear force that acts on the section is obtained from the CivilFEM results file (.RCF).

Force Description

Design shear force

6) Checking failure by compression in the web. First, a check is made to ensure the design shear force (V_Sd) is less than or equal to the oblique compression resistance of the concrete in the web (V_Rd2). V_Rd2 is calculated with Model I if q = 45º and with Model II if q ≠ 45º:

Model I

Where

( in MPa).

Model II

Where

( in MPa).

For each element end, calculated results are written in the CivilFEM results file:

VRD2 Ultimate shear strength due to oblique compression of the concrete in web.

CRTVRD2 Ratio of the design shear (V_sd) to the resistance V_Rd2.

7) Checking failure by tension in the web. The design shear force (V_sd) must be less than or equal to the shear force due to tension in the web (V_Rd3). V_Rd3 is calculated with Model I if q = 45º and with Model II if q ≠ 45º:

contribution of web shear transverse reinforcement to the shear strength.

contribution of concrete to the shear strength.

Model I

Where

shear reinforcement area per unit length.

design strength of reinforcement limited to 435 MPa.

Model II

Where

shear reinforcement area per unit of length.

design strength of reinforcement limited to 435 MPa.

Interpolating linearly in between these values.

Where

For each end, calculated results are written in the CivilFEM results file:

VSW Contribution of the shear reinforcement to the shear strength.

VC Contribution of concrete to the shear strength.

VRD3 Ultimate shear strength by tension in the web.

CRTVRD3 Ratio of the design shear force (V_sd) to the resistance V_Rd3.

If , the CTRVRD3 criterion is taken as 2¹⁰⁰.

8) Obtaining shear criterion. The shear criterion indicates whether the section is valid for the design forces (if it is less than 1, the section satisfies the code prescriptions; whereas if it exceeds 1, the section will not be valid). Furthermore, it includes information about how close the design force is to the ultimate section strength. The shear criterion is defined as follows:

For each element end, this value is stored in the CivilFEM results file as CRT_TOT.

A value 2¹⁰⁰for this criterion indicates that the shear strength due to tension in the web (V_Rd3) is equal to zero, as was indicated in the previous step.

6.6.11.2. Torsion Checking

Checking for torsion according to NBR6118 follows the steps below:

1) Obtaining material strength properties. These properties are obtained from the material properties associated with each transverse cross section and for the active time.

The required data are the following:

characteristic strength of concrete

characteristic yield strength of reinforcement

concrete partial safety factor

reinforcement steel partial safety factor

2) Obtaining geometrical parameters depending on specified code. Geometrical parameters used for torsion calculations must be defined within CivilFEM database. The required data are the following:

effective thickness.

area involved by the center-line of the effective hollow section.

perimeter of the center-line of the effective hollow section.

q Angle of the compressive struts of concrete with the longitudinal axis of member:

30º < q < 45º

Section 6.6.1.. provides detailed information on how to calculate the required data for each code and valid section.

3) Obtaining reinforcement data of the section. Required data are the following:

Transverse Reinforcement

area of transverse reinforcement per unit of length.

The reinforcement ratio can also be obtained with the following data:

closed stirrups area for torsion.

s spacing of closed stirrups.

Or from the data below:

s spacing of closed stirrups.

diameter of the closed stirrups bars.

Longitudinal Reinforcement

total area of the longitudinal reinforcement.

The reinforcement ratio can also be obtained from the following data:

 diameter of longitudinal bars.

N number of longitudinal bars.

4) Obtaining section internal forces and moments. The torsional moment that acts on the section is obtained from the CivilFEM results file (.RCF).

Moment Description

Design torsional moment in the section

5) Checking compression failure of concrete. Firstly, a check is made to ensure the design torsional moment (T_Sd) is less than or equal to the ultimate torsional moment cause by the compression of the concrete (T_Rd2); therefore, the following condition must be satisfied:

Where:

( in MPa).

Calculated results are stored in the CivilFEM results file as:

TRD2 Maximum torsional moment resisted by the section without crushing the concrete compressive struts due to compression.

CRTTRD2 Ratio of the design torsional moment (T_Sd) to the resistance T_Rd2.

6) Checking transverse reinforcement failure. The condition for tensile failure of the transverse reinforcement when a torsional moment T_Sd is applied is as follows:

where:

cross-sectional area of one of the bars used as transverse torsional reinforcement.

s spacing of closed stirrups of transverse torsional reinforcement.

design strength of reinforcement, limited to 435 MPa.

Calculated results are stored in the CivilFEM results file as:

TRD3 Maximum torsional moment resisted by the section without tensile failure of the transverse reinforcement.

CRTTRD3 Ratio of the design torsional moment (T_Sd) to the resistance T_Rd3.

If the transverse torsion reinforcement is not defined, the criterion is taken as 2¹⁰⁰.

7) Checking longitudinal reinforcement failure. The condition of tensile failure for the longitudinal reinforcement when a torsional moment T_Sd is applied is as follows:

where:

area of the longitudinal torsion reinforcement.

design strength of reinforcement limited to 435 MPa.

Calculated results are stored in the CivilFEM results file as:

TRD4 Maximum torsional moment resisted by the section without tensile failure of transverse reinforcement.

CRTTRD4 Ratio of the design torsional moment (T_Sd) to the resistance T_Rd3.

In case the longitudinal reinforcement is not defined, the criterion is taken as 2¹⁰⁰.

8) Obtaining torsion criterion. The torsion criterion indicates the ratio of the design moment to the section ultimate strength (if it is less than 1, the section is valid; whereas if it exceeds 1, the section is not valid). The criterion for the validity of the section for torsion is defined as follows:

For each element end, this value is stored in the CivilFEM results file as CRT_TOT.

A value 2¹⁰⁰ for this criterion would indicate the non-definition of one of the torsion reinforcements.

6.6.11.3. Combined Shear and Torsion Checking

For checking sections subjected to shear force and concomitant torsional moment, we follow the steps below:

1) Torsion checking considering a null shear force. This check is accomplished with the same steps as for the check of elements subjected to pure torsion according to NBR6118.

Except for this check, the CRT_TOT criterion is stored in the CivilFEM results file as CRTTRS for each element end.

1) Shear checking assuming a null torsional moment. This check follows the same procedure as for the checking of elements only subjected to shear according to NBR6118.

Except for this check, the CRT_TOT criterion is stored in the CivilFEM results file as CRTSHR for each element end.

3) Checking the concrete ultimate strength condition by compression. The design torsional moment (T_Sd) and the design shear force (V_Sd) must satisfy the following condition:

where:

ultimate shear force by compression of concrete.

ultimate torsional moment due to compression of concrete.

For each element, this criterion value is stored in the CivilFEM results file as CRTCST.

4) Obtaining the combined shear and torsion criterion. This criterion considers pure shear, pure torsion and concrete ultimate strength condition criteria. The criterion determines whether the section is valid and is defined as follows:

For each element, this criterion value is stored in the CivilFEM results file as CRT_TOT.

A value 2¹⁰⁰ for this criterion indicates that one of the denominators is null, and therefore, one of the reinforcements is not defined.

6.6.11.4. Shear Design

The shear designing according to NBR6118 follows these steps:

1) Obtaining material strength properties. These properties are obtained from the material properties associated with each transverse cross section and for the active time.

The required data are the following:

characteristic strength of concrete.

characteristic yield strength of reinforcement.

concrete safety factor.

steel safety factor.

2) Obtaining section geometrical data. Required data for shear designing are the following:

total area of the concrete section.

3) Obtaining geometrical parameters depending on specified code. Required data are the following:

minimum width of the section in a height equal to ¾ the effective depth.

deffective depth of the section.

q angle of the concrete compressive struts with the longitudinal axis of member.

30º < q < 45º

Section 6.6.1.. provides detailed information on how to calculate the required data for each code and valid section.

4) Obtaining reinforcement data of the section. With the shear reinforcement design, it is possible to indicate the angle a btetweeen the reinforcement and the longitudinal axis of the member. If this angle is null or it is not defined, a = 90º. Other reinforcement data are ignored.

5) Obtaining forces and moments acting on the section. The shear force that acts on the section is obtained from the CivilFEM results file (.RCF).

Force Description

Design shear force

6) Checking compression failure in the web. Firstly, a check is made to ensure the design shear force (V_Sd) is less than or equal to the oblique compression resistance of concrete in the web (V_Rd2). V_Rd2 is calculated with Model I if  = 45º and with Model II if 45º:

Model I

Where

( in MPa).

Model II

Where

( in MPa).

For each element end, calculated results are written in the CivilFEM results file as:

VRD2 Ultimate shear strength due to oblique compression of the concrete in web.

CRTVRD2 Ratio of the design shear (V_sd) to the resistance V_Rd2.

If design shear force is greater than shear force that causes the failure by oblique compression of concrete in the web, the reinforcement design is not feasible. Therefore, the parameter for the reinforcement data is defined as 2¹⁰⁰.

In this case, the element is labeled as not designed and the program then advances then to next element.

In the case there is no failure due to oblique compression, the calculation process continues.

7) Checking if shear reinforcement will be required. First, a check is made to ensure the design shear force (V_sd) is less than or equal to the strength provided by the concrete in members without shear reinforcement (V_c). V_Rd3 is calculated with Model I if  = 45º and with Model II if 45º:

Model I

Model II

Interpolating linearly in between these values.

Where

If the section does not require shear reinforcement, the following parameters are defined (for both element ends):

If the section requires shear reinforcement the calculation process continues.

8) Determining the shear strength contribution of the required transverse reinforcement. If the section requires shear reinforcement, the condition pertaining to the validity of sections under shear force is as follows:

contribution of web shear transverse reinforcement to the shear strength.

contribution of concrete to the shear strength.

is calculated with Model I if  = 45º and with Model II if 45º:

Model I

Where

shear reinforcement area per unit length.

design strength of reinforcement limited to 435 MPa.

Model II

Where

shear reinforcement area per unit length.

design strength of reinforcement, limited to 435 MPa.

Therefore, the shear reinforcement contribution is given by the equation below:

For each element end, the value of V_c and V_swis stored in the CivilFEM results file:

10) Caculating the required reinforcement ratio. Once the required shear strength of the reinforcement has been obtained, the reinforcement ratio can be calculated:

Where:

cross-sectional area of the designed shear reinforcement per unit length.

design strength of reinforcement, limited to 435 MPa.

The area of designed reinforcement per unit length is stored in the CivilFEM results file for both ends:

In this case the element is labeled as designed (provided that the design process is correct for both element sections).

6.6.11.5. Torsion Design

Torsion reinforcement design according to NBR6118 follows the following steps:

1) Obtaining material strength properties. These properties are obtained from the material properties associated with each transverse cross section and for the active time.

The required data are the following:

characteristic strength of concrete

characteristic yield strength of reinforcement

concrete partial safety factor

reinforcement partial safety factor

2) Obtaining geometrical parameters depending on specified code. Geometrical parameters used for torsion designing must be defined for each code in data at member level according to chapter 5 of this manual. The required data are the following:

area enclosed by the center-line of the effective hollow section.

perimeter of the center-line of the effective hollow section.

 angle of the concrete compressive struts with the longitudinal axis of member: 30º    45º

Section 6.6.1.. provides detailed information on how to calculate the required data for each code and valid section.

3) Obtaining forces and moments acting on the section. The torsional moment that acts on the section is obtained from the CivilFEM results file (.RCF).

Moment Description

Design torsional moment

4) Checking compression failure of concrete. First, the design torsional moment (T_Sd) must be less than or equal to the ultimate torsional moment due to compression in the concrete (T_Rd2); therefore, the following condition must be satisfied:

Where:

( in MPa).

Calculated results are stored in the CivilFEM results file:

TRD2 Maximum torsional moment resisted by the section without crushing the concrete compressive struts due to compression.

CRTTRD2 Ratio of the design torsional moment (T_Sd) to the resistance T_Rd2.

If design torsional moment is greater than the torsional moment that causes the compression failure of concrete, the reinforcement design is not feasible. Therefore, the parameters for reinforcement data are assigned a value of 2¹⁰⁰.

for transverse reinforcement

for longitudinal reinforcement

In this case, the element is labeled as not designed, and the program then advances to the next element.

In the case there is no failure due to oblique compression, the calculation process continues.

5) Calculating the transverse reinforcement required. The ultimate strength condition of the transverse reinforcement is:

where:

cross-sectional area of one of the bars used as transverse torsional reinforcement.

s spacing of closed stirrups of transverse torsional reinforcement.

design strength of reinforcement, limited to 435 MPa.

Therefore, the required transverse reinforcement is:

The area per unit length of the designed transverse reinforcement is stored in the CivilFEM results file for both element ends as:

6) Calculating the longitudinal reinforcement required. The ultimate strength condition of the longitudinal reinforcement is:

where:

area of the longitudinal torsion reinforcement.

design strength of reinforcement limited to 435 MPa.

Consequently, the longitudinal reinforcement required is:

The area of the designed longitudinal reinforcement is stored in the CivilFEM results file for both element ends as:

If the design for both element sections is completed for both transverse and longitudinal reinforcements, the element will be labeled as designed.

6.6.11.6. Combined Shear and Torsion Design

The design of sections subjected to shear force and concomitant torsional moment follows the steps below:

1) Torsion design considering a null shear force. This design is accomplished with the same steps as for the designing of elements subjected to pure torsion according to NBR6118.

2) Shear design assuming a null torsional moment. This design follows the same procedure as for the design of elements only subjected to shear force according to NBR6118.

3) Checking the failure condition by compression in the concrete. The design torsional moment (T_Sd) and the design shear force (V_Sd) must satisfy the following condition:

where:

ultimate shear force by compression of concrete.

ultimate torsional moment due to compression of concrete.

For each element end, this criterion value is stored in the CivilFEM results file as CRTCST.

4) Obtaining required shear and torsion reinforcement ratios. If the concrete ultimate strength condition is satisfied (i.e. the concrete can resist the combined shear and torsion action), the reinforcements calculated are taken as the designed reinforcements. The element will be labeld as designed.

If the concrete ultimate strength condition is not satisfied, the parameters corresponding to each reinforcement group take the value of 2¹⁰⁰.

6.6.13. Shear and Torsion according to EHE-08

6.6.12.1. Shear Check

The checking for shear according to EHE-08 follows the steps below:

1) Obtaining material strength properties. These properties are obtained from the material properties associated to each transverse cross section and for the active time.

The required data are the following:

characteristic compressive strength of concrete.

characteristic yield strength of reinforcement.

mean tensile strength of concrete.

characteristic tensile strength of concrete (fctk_005).

concrete partial safety factor.

steel partial safety factor.

2) Obtaining section geometrical data. Section geometrical requirements must be defined within CivilFEM. Required data for shear checking are the following:

total area of the concrete section.

3) Obtaining geometrical parameters depending on specified code. Geometrical parameters used for shear calculations must be defined. Required data are the following ones:

Width of element equal to the total width in solid sections or in case of box sections, the width equals the sum of the width of both webs.

deffective depth of the section.

geometric ratio of the tensile longitudinal reinforcement anchored at a distance greater than or equal to d from the considered section:

q angle of the concrete compressive struts with the longitudinal axis of member:

Section “Previous Considerations to Shear and Torsion Calculation” provides detailed information on how to calculate the required data for each code and valid section.

4) Obtaining reinforcement data of the section. Data concerning reinforcements of the section must be included within CivilFEM. Required data are the following ones:

a angle between shear reinforcement and the longitudinal axis of the member.

area of reinforcement per unit length.

The reinforcement ratio may also be obtained with the following data:

total area of the reinforcement legs.

s spacing of the stirrups.

Or with the data below:

s spacing of the stirrups.

φ diameter of bars.

N number of reinforcement legs.

5) Obtaining forces and moments acting on the section. The shear force that acts on the section, as well as the concomitant axial force and bending moment, are obtained from the CivilFEM results file.

Force Description

Design shear force in Y

Axial force

6) Checking failure by compression in the web. First, a check is made to ensure the design shear force () is less than or equal to the oblique compression resistance of concrete in the web ():

where:

design compressive strength of concrete.

K reduction factor by axial forces effect

effective axial stress in concrete (compression positive) considering the axial stress taken by compressed reinforcement.

For each element end, calculated results are written in the CivilFEM results file:

VU1 Ultimate shear strength due to oblique compression of the concrete in web.

CRTVU1 Ratio of the design shear (V_rd) to the resistance .

7) Checking failure by tension in the web. A check is made to ensure the design shear force (V_rd) is less than or equal to the shear force due to tension in the web ():

contribution of web shear transverse reinforcement to the shear strength.

contribution of concrete to the shear strength.

Members without shear reinforcement

If shear reinforcement has not been defined:

where:

< 2, d in mm

limited to 60 MPa

Members with shear reinforcement

If shear reinforcement has been defined:

where:

shear reinforcement area per unit of length

design strength of reinforcement

In this case, the concrete contribution to shear strength is:

where:

reference angle of cracks inclination, obtained from:

, design normal stresses, at the section’s center of gravity, parallel to the longitudinal axis of member and the shear force respectively (tension positive)

Taking à

In addition, the increment in tensile force due to shear force is calculated with the following equation:

For each end, calculated results are written in the CivilFEM results file as:

VSU Contribution of the shear reinforcement to the shear strength.

VCU Contribution of concrete to the shear strength.

VU2 Ultimate shear strength by tension in the web.

CRTVU2 Ratio of the design shear force to the resistance .

If , the CTRVU2 criterion is taken as 2¹⁰⁰.

The tension increment due to shear force is stored in the CivilFEM results file as INCTENS.

8) Obtaining shear criterion. The shear criterion indicates whether the section is valid or not for the design forces (if it is less than 1, the section satisfies the code provisions; whereas if it exceeds 1, the section will not be valid). Furthermore, it includes information about how close the design force is to the ultimate section strength. The shear criterion is defined as follows:

For each element end, this value is stored in the CivilFEM results file as CRT_TOT.

A value 2¹⁰⁰for this criterion indicates that the shear strength for tension in the web () is equal to zero, as was described in the previous step.

6.6.12.2. Torsion Checking

The torsion checking according to EHE-08 follows the steps below:

1) Obtaining material strength properties. These properties are obtained from the material properties associated to each transverse cross section and for the active time.

The required data are the following:

characteristic strength of concrete

characteristic yield strength of reinforcement

concrete partial safety factor

reinforcement steel partial safety factor

2) Obtaining geometrical parameters depending on specified code. Geometrical parameters used for torsion calculations must be defined within CivilFEM. The required data are the following:

effective thickness.

area enclosed by the center-line of the effective hollow section.

perimeter of the center-line of the effective hollow section.

KEYAST indicator of the position of torsional reinforcement in the section:

= 0 if closed stirrups are placed in both faces of the equivalent hollow section wall or of the real hollow section (value by default for hollow sections).

= 1 if there are closed stirrups only along the periphery of the member (value by default for solid sections).

q Angle of the compressive struts of concrete with the longitudinal axis of member:

“Previous Considerations to Shear and Torsion Calculation” provides detailed information on how to calculate the required data for each code and valid section.

3) Obtaining section reinforcement data. Data concerning reinforcements of the section must be included within CivilFEM database. Required data are the following:

Transverse Reinforcement

area of transverse reinforcement per unit of length.

The reinforcement ratio can also be obtained with the following data:

closed stirrups area for torsion.

s spacing of closed stirrups.

Or with the data below:

s spacing of closed stirrups.

diameter of the closed stirrups bars.

Longitudinal Reinforcement

total area of the longitudinal reinforcement.

The reinforcement ratio can also be obtained with the following data:

diameter of longitudinal bars.

N number of longitudinal bars.

4) Obtaining the section’s internal forces and moments. The torsional moment that acts on the section is obtained from the CivilFEM results file (.RCV).

Moment Description

Design torsional moment in the section

5) Checking compression failure of concrete. First, a check is made to ensure the design torsional moment () is less than or equal to the ultimate torsional moment due to compression in the concrete (); as a result, the following condition must be satisfied:

Where:

design compressive strength of concrete

K reduction factor by axial forces effect

a 0.60 if only there are stirrups along the periphery of the member;

0.75 if closed stirrups are placed at both faces of the wall of the effective hollow section or real hollow section.

Calculated results are stored in the CivilFEM results file as:

TU1 Maximum torsional moment that can be resisted by the section without crushing due to compression of concrete compressive struts.

CRTTU1 Ratio of the design torsional moment () to the resistance .

6) Checking transverse reinforcement failure. The tensile failure condition of the transverse reinforcement in a section subjected to a torsional moment is:

where:

cross-sectional area of one of the bars used as transverse torsional reinforcement.

s spacing of closed stirrups of transverse torsional reinforcement.

design yield strength of torsion reinforcement (  400 N/mm²). The same steel type will be used for both transverse and longitudinal torsion reinforcement.

Calculated results are stored in the CivilFEM results file as:

TU2 Maximum torsional moment resisted by the section so without causing failure in the transverse reinforcement due to tension.

CRTTU2 Ratio of the design torsional moment () to the resistance .

If the torsion transverse reinforcement is not defined, the criterion is taken as 2¹⁰⁰.

7) Checking longitudinal reinforcement failure. The tensile failure condition of the longitudinal reinforcement in a section subjected to a torsional moment is:

Where is the area of the longitudinal torsion reinforcement.

Calculated results are stored in the CivilFEM results file as:

TU3 Maximum torsional moment resisted by the section without causing tensile failure in the longitudinal reinforcement.

CRTTU3 Ratio of the design torsional moment (T_d) to the resistance T_u3.

In the case the longitudinal reinforcement is not defined, the criterion is taken as 2¹⁰⁰.

8) Obtaining torsion criterion. The torsion criterion identifies the ratio of the design moment to the section’s ultimate strength (if it is less than 1, the section is valid; whereas if it exceeds 1, the section is not valid). The criterion concerning the validity for torsion is defined as follows:

For each element end, this value is stored in the CivilFEM results file as CRT_TOT.

A value 2¹⁰⁰ for this criterion indicates that any one of the torsion reinforcements are not defined.

6.6.12.3. Combined Shear and Torsion Checking

Checking sections subjected to shear force and concomitant torsional moment follows the steps below:

1) Torsion checking considering a null shear force. This check is accomplished with the same steps as for the check of elements subjected to pure torsion according to EHE-08.

For each element end, this value is stored in the CivilFEM results file as CRTTRS.

2) Shear checking assuming a null torsional moment. Follows the same procedure as for the check of elements only subjected to shear according to EHE-08.

For each element end, this value is stored in the CivilFEM results file as CRTSHR.

3) Checking the ultimate compressive strength condition of concrete. The design torsional moment () and the design shear force () must satisfy the following condition:

Where:

ultimate torsional moment due to compression of concrete, calculated in step No. 1.

ultimate shear force by compression of concrete, calculated in step No. 2.

For each element, this criterion value is stored in the CivilFEM results file as CRTCST.

4) Obtaining the combined shear and torsion criterion. This criterion comprehends pure shear, pure torsion and concrete ultimate strength condition criteria. The criterion determines whether the section is valid or not, and it is defined as follows:

For each element, this criterion value is stored in the CivilFEM results file as CRT_TOT.

A value 2¹⁰⁰ for this criterion indicates that one of the denominators is null, because one of the reinforcements is not defined.

6.6.12.4. Shear Design

The shear designing according to EHE-08 follows these steps:

1) Obtaining material strength properties. These properties are obtained from the material properties associated to each transverse cross section and for the active time.

The required data are the following ones:

characteristic strength of concrete.

characteristic yield strength of reinforcement.

mean tensile strength of concrete.

concrete safety factor.

steel safety factor.

2) Obtaining geometrical data of the section. Section geometrical requirements must be defined within CivilFEM database:

total area of the concrete section.

3) Obtaining geometrical parameters depending on specified code. Geometrical parameters used for shear design must be defined within the CivilFEM. Required data are the following ones:

Width of element equal to the total width in solid sections or in case of box sections, the width equals the sum of the width of both webs.

deffective depth of the section.

geometric ratio of the tension longitudinal reinforcement anchored at a distance greater than or equal to d from the considered section.

angle of the concrete compressive struts with the longitudinal axis of member:

Section “Previous Considerations to Shear and Torsion Calculation” provides detailed information on how to calculate the required data for each code and valid section.

4) Obtaining reinforcement data of the section. In the shear reinforcement design, it is possible to define the angle between the reinforcement and the longitudinal axis of the member. If this angle is null or it is not defined, it’s defined as 90º. Other reinforcement data are ignored.

5) Obtaining forces and moments acting on the section. The shear force that acts on the section as well as the concomitant axial force are obtained from the CivilFEM results file.

Force Description

Design shear force in Y

Design axial force

6) Checking compression failure in the web. First, a check is made to ensure the design shear force () is less than or equal to the oblique compression resistance of concrete in the web ():

where:

design compressive strength of concrete

K reduction factor by axial forces effect

effective axial stress in concrete (compression positive) considering the axial stress taken by reinforcement in compression.

For each element end, calculated results are written in the CivilFEM results file as:

VU1 Ultimate shear strength due to oblique compression of the concrete in web.

CRTVU1 Ratio of the design shear force () to the resistance .

If the design shear force is greater than the shear force that causes failure due to oblique compression in the concrete of the web, the reinforcement design will not be feasible. The parameter where the reinforcement data is stored will be defined as 2¹⁰⁰.

In this case, the element is labeled as not designed, and the program then advances to next element.

In the case there is no failure due to oblique compression, the calculation process continues.

7) Checking if section requires shear reinforcement. First, a check is made to ensure the design shear force is less than the strength provided by the concrete in members without shear reinforcement ():

where:

(Compression positive)

< 2, d in mm

limited to 60 MPa

If the section does not require shear reinforcement, the following parameters are defined (for both element ends):

If section requires shear reinforcement, the calculation process continues.

8) Determining the contribution of the required transverse reinforcement to the shear strength. If the section requires shear reinforcement, the condition for the validity of the sections under shear force is the following:

contribution of transverse shear reinforcement in the web to the shear strength.

contribution of concrete to the shear strength.

where:

reference angle of cracks inclination, obtained from the following expression:

, design normal stresses, at the center of gravity of the section, parallel to the longitudinal axis of the member or to the shear force , respectively (tension positive)

Taking

Therefore, the shear reinforcement contribution is given by:

For each element end, the value of V_cu and V_suis stored in the CivilFEM results file:

9) Required reinforcement ratio. Once the required shear strength of the shear reinforcement has been obtained, the reinforcement ratio can be calculated from the equation below:

Where:

cross-sectional area of the designed shear reinforcement per unit length.

The area of the designed reinforcement per unit length is stored in the CivilFEM results file for both ends:

In this case, the element is labeled as designed (provided that the design process is correct for both element sections).

6.6.12.5. Torsion Design

Torsion reinforcement design according to EHE-08 follows the following steps:

1) Obtaining material strength properties. These properties are obtained from the material properties associated to each transverse cross section and for the active time.

The required data are the following ones:

characteristic strength of concrete

characteristic yield strength of reinforcement

concrete partial safety factor

reinforcement partial safety factor

2) Obtaining geometrical parameters depending on specified code. Geometrical parameters utilized used for torsion design must be defined for each code at member level according to chapter 5 of this manual. The required data are the following ones:

area enclosed by the center-line of the effective hollow section.

perimeter of the center-line of the effective hollow section.

KEYAST indicator of the position of the torsion reinforcement in the section.

= 0 if closed stirrups are placed in both faces of the equivalent hollow section wall or of the real hollow section (value by default for hollow sections).

= 1 if closed stirrups are only placed along the periphery of the member (value by default for solid sections).

q angle of the concrete compressive struts with the longitudinal axis of member:

Section “Previous Considerations to Shear and Torsion Calculation” provides detailed information on how to calculate the required data for each code and valid section.

3) Obtaining forces and moments acting on the section. The torsional moment that acts on the section is obtained from the CivilFEM results file.

Moment Description

Design torsional moment

4) Checking compression failure of concrete. First, a check is made to ensure the design torsional moment () is less than or equal to the ultimate torsional moment for compression in concrete (); therefore, the following condition must be satisfied:

where:

concrete compressive strength

K reduction factor by axial forces effect

a 1.20 if stirrups are only placed along the periphery of the member.

1.50 if closed stirrups are placed at both faces of the wall of the effective hollow section or of the real hollow section.

Calculated results are stored in the CivilFEM results file:

TU1 Maximum torsional moment resisted by the section without causing crushing due to compression of concrete compressive struts.

CRTTU1 Ratio of the design torsional moment () to the resistance .

If design torsional moment is greater than the torsional moment that causes the compression failure of concrete, the reinforcement design will not be feasible. Therefore, the parameters for the reinforcement data will be defined as 2¹⁰⁰.

for transverse reinforcement

for longitudinal reinforcement

In this case, the element is labeled as not designed, and the program then advances to the next element.

In the case there is no failure due to oblique compression, the calculation process continues.

5) Calculating the transverse reinforcement required. The ultimate strength condition of the transverse reinforcement is:

where:

area of the section of one of the bars used as transverse reinforcement for torsion.

s spacing of the closed stirrups of the transverse reinforcement for torsion.

Therefore, the required transverse reinforcement is:

The area per unit length of the designed transverse reinforcement is stored in the CivilFEM results file for both element ends as:

6) Calculating the longitudinal reinforcement required. The ultimate strength condition of the longitudinal reinforcement is:

Where is the area of the torsional longitudinal reinforcement.

Consequently, the longitudinal reinforcement required is:

The area of the designed longitudinal reinforcement is stored in the CivilFEM results file for both element ends as:

If design for both element sections is done for both transverse and longitudinal reinforcements, and the element will be labeled as designed.

6.6.12.6. Combined Shear and Torsion Design

The design of sections subjected to shear force and concomitant torsional moment follows the steps below:

1) Torsion design considering a null shear force. This design is accomplished with the same steps as for the design of elements subjected to pure torsion according to EHE-08.

2) Shear design assuming a null torsional moment. This design follows the same procedure as for the design of elements only subjected to shear force according to EHE-08.

3) Checking the failure condition by compression in the concrete. The design torsional moment (T_d) and the design shear force (V_rd) must to satisfy the following condition:

where:

ultimate torsional moment due to compression of concrete, calculated in step 1.

ultimate shear strength due to compression of concrete, calculated in step 2.

For each element end, this criterion value is stored in the CivilFEM results file as CRTCST.

4) Obtaining required shear and torsion reinforcement ratios. If the concrete ultimate strength condition is satisfied (i.e. the concrete can resist the combined shear and torsion action), the reinforcements calculated in steps 1 and 2 are taken as the designed reinforcements. The element will be labeled as designed.

If the concrete ultimate strength condition is not satisfied, the parameters corresponding to each reinforcement group will take the value 2¹⁰⁰.

6.6.14. Shear and Torsion according to IS 456

6.6.13.1 Shear Checking

Shear checking of elements according to IS 456 follow the steps below:

1) Obtaining material strength properties. These properties are obtained from the material properties associated with each transverse cross section and for the active time. Those material properties should be previously defined. The required data are the following:

characteristic compressive strength of concrete.

characteristic yield strength of reinforcement.

partial safety factor for concrete.

partial safety factor for reinforcement.

2) Obtaining geometrical data of the section. Section geometrical requirements must be defined within the CivilFEM. Required data for shear checking are the following:

total cross-sectional area of the concrete section.

3) Obtaining geometrical parameters depending on code. Geometrical parameters used for shear calculations must be defined within CivilFEM. Required data are the following:

effective width of the section.

deffective depth of the section.

ratio of the longitudinal tensile reinforcement extending beyond the effective depth of the considered section, except in supports where the total area of the tensile reinforcement is used.:

Section “Previous Considerations to Shear and Torsion Calculation” provides detailed information on how to calculate the required data for each code and valid section.

4) Obtaining reinforcement data of the section. Data concerning reinforcements of the element section must be included within the CivilFEM database. Required data are the following:

a angle between shear reinforcement and the longitudinal axis of the member section.

area of reinforcement per unit length.

The reinforcement ratio may also be obtained with the following data:

total area of the reinforcement legs.

s spacing of the stirrups.

or with the data below:

s spacing of the stirrups.

φ diameter of bars.

N number of reinforcement legs.

5) Obtaining the section internal forces and moments. The shear force that acts on the section as well as the concomitant axial force are obtained from the CivilFEM results file.

Force Description

Design shear force

Concomitant axial force

6) Calculating the nominal shear stress. The nominal shear stress is calculated by the following expression:

This stress is written for each end of the element in the CivilFEM results file as:

TAOV Shear strength

7) Checking of the maximum shear stress. The nominal shear stress must be less than or equal to the maximum shear stress:

where is given in Table 20 according to the concrete type:

Results are stored for each end in the CivilFEM results file as the following parameters:

TCMAX Maximum shear stress.

CRTCMAX Ratio of the nominal shear stress to the shear maximum stress.

8) Calculating the shear resistance of the section. The shear resistance is calculated as the sum of the resistance provided by the concrete and the shear reinforcement:

where:

shear resistance of the section

concrete contribution to the shear resistance

shear reinforcement contribution to the shear resistance

The concrete contribution to the resistance is:

where _cis given in Table 19 according to the concrete type and the amount of the longitudinal tension reinforcement:

For members subjected to axial compression P_u, the design shear strength of concrete, given in Table 19, shall be multiplied by the following factor:

The reinforcement contribution to the shear resistance shall be calculated as:

total cross sectional area of the shear reinforcement

s spacing of the stirrups along the axis of the member

Results are stored for each end in the CivilFEM results file as the following parameters:

TC Design shear stress.

VUC Contribution of concrete to the shear resistance.

VUS Contribution of shear reinforcement to the shear resistance.

VUT Design shear resistance of the section.

CRVUT Ratio of the design shear force (V_u) to the shear resistance V_ut.

If , CRVUT is taken as 2¹⁰⁰.

9) Obtaining shear criterion. The shear criterion indicates whether the section is valid or not for the design forces (if it is less than 1, the section satisfies the code prescriptions, whereas if it exceeds 1, the section will not be valid). Furthermore, it includes information about how close is the design force from the ultimate section strength. The shear criterion is defined as follows:

For each end, this value is stored in the CivilFEM results file as the parameter CRT_TOT.

A value of 2¹⁰⁰ for this criterion would mean that V_ut are equal to zero.

6.6.13.2 Axial and Bending with combined Shear and Torsion Checking

The axial and bending with combined shear and torsion checking according to IS 456 follows the steps below:

1) Obtaining material strength properties. These properties are obtained from the material properties associated with the transverse cross section and for the active time.

2) Obtaining of the geometrical parameters of the section. Geometrical parameters of the section must be defined within the CivilFEM database.

3) Obtaining geometrical parameters depending on specified code. The required data are the following:

effective width of the section.

deffective depth of the section.

ratio of the longitudinal tensile reinforcement extending beyond the effective depth of the considered section, except in supports where the total area of the tensile reinforcement is used:

, center to center distances between corner bars situated between transversal stirrups, measured along the width and the flange of the section respectively.

Section “Previous Considerations to Shear and Torsion Calculation” provides detailed information on how to calculate the required data for each code and valid section.

4) Obtaining reinforcement data of the section. Data concerning reinforcements of the section must be included within CivilFEM. Required data are the following:

Longitudinal Bending Reinforcement

It is obtained from the bending reinforcement distribution of the section

Transverse Shear Reinforcement

a angle between the shear reinforcement and the longitudinal axis of the member section.

area of transverse reinforcement per unit length.

The reinforcement ratio may also be obtained with the following data:

total area of the reinforcement legs.

s spacing of the stirrups.

or with the data below:

s spacing of the stirrups.

q diameter of bars.

N number of reinforcement legs.

TransverseTorsional Reinforcement

area of transverse reinforcement per unit length.

The reinforcement ratio can also be obtained with the following data:

closed stirrups area for torsion.

s spacing of closed stirrups.

Or with the data below:

s spacing of closed stirrups.

diameter of the closed stirrups.

Longitudinal Shear Reinforcement

This reinforcement will be ignored.

5) Obtaining section internal forces and moments. The forces and moments that acts on the section are obtained from the CivilFEM results file.

Force/Moment Description

Design shear force

Design torsional moment

Concomitant axial force

Concomitant bending moment

6) Calculating the equivalent shear. Equivalent shear shall be calculated from the following formula:

Where V_e is the equivalent shear force.

7) Calculating the equivalent nominal shear stress. The equivalent nominal shear stress shall be calculated from the following formula:

Results are written in the CivilFEM results file for both element ends as the parameters:

TAOVE Nominal shear stress

8) Checking with the maximum shear stress. The equivalent nominal shear stress must be less than or equal to the maximum shear stress:

where _c
max is given in Table 20 according to the type of concrete:

Results are stored for each end in the CivilFEM results file as the following parameters:

TCMAX Maximum shear stress.

CRTCMAX Ratio of the nominal shear stress to the maximum shear stress.

9) Checking whether the section will require transverse reinforcement. Transverse reinforcement will not be required if the equivalent nominal shear stress is less than or equal to the maximum shear stress:

where _cis given in Table 19 according to the concrete type and the amount of the longitudinal tension reinforcement:

Results are stored for each end in the CivilFEM results file as the following parameters:

ATT Area of the necessary transverse reinforcement.

CRTATT Ratio of the area of the necessary transverse reinforcement to the area of the defined transverse reinforcement (sum of shear and torsional transverse reinforcement).

10) Calculating the transverse reinforcement required. If the equivalent nominal stress exceeds the maximum shear stress, the necessary transverse reinforcement will be calculated with the following expression:

ATT Area of the necessary transverse reinforcement

CRTATT Ratio of the area of the necessary transverse reinforcement to the area of the defined transverse reinforcement (sum of shear and torsional transverse reinforcement).

If the shear and torsional transverse reinforcement is zero, A_ss/s+A_st/s=0, the criterion is taken as 2¹⁰⁰.

11) Checking of the longitudinal reinforcement. We check if the defined longitudinal bending reinforcement resists an equivalent bending moment given by the formula:

where

equivalent bending moment

increment due to torsional moment:

D overall depth

This equivalent moment is used in the axial bending checking (in the direction defined in the command argument). For further information about this calculation procedure, see chapters about axial load and biaxial bending of the Theory Manual.

The calculation results are stored in the CivilFEM results file for both element ends as the parameters:

MT increment of the bending moment due to torsional moment

MEL equivalent bending moment

CRTASL Ratio of the forces and moments that acts on the section to the ultimate forces and moments.

12) Obtaining total criterion. The criterion of the combined axial, bending, shear and torsional checking is obtained from the enveloping of the partial criterions. If it is less than 1, the section is valid; if it exceeds 1, the section is not valid:

CRT_TOT = Max (CRTCMAX; CRTATT; CRTASL)

This value is stored in the CivilFEM results file for both element ends as the parameter CRT_TOT.

A value of 2¹⁰⁰for this criterion indicates that the shear and torsion transverse reinforcements have not been defined.

6.6.13.3 Shear Design

Shear reinforcement design according to IS 456 follows the steps below:

1) Obtaining material strength properties. These properties are obtained from the material properties associated with the transverse cross section and for the active time. The required data are the following:

characteristic compressive strength of concrete.

characteristic yield strength of reinforcement.

partial safety factor for concrete.

partial safety factor for reinforcement.

2) Obtaining section geometrical data. Section geometrical requirements must be defined within CivilFEM database. Required data for shear designing are the following:

total cross-sectional area of the concrete section.

3) Obtaining geometrical parameters depending on specified code. Geometrical parameters used for shear designing must be defined within the CivilFEM. Required data are the following ones:

effective width of the section.

deffective depth of the section.

ratio of the tensile reinforcement extending beyond the effective depth of the considered section, except in supports where the total area of the tensile reinforcement is used.:

Section “Previous Considerations to Shear and Torsion Calculation” provides detailed information on how to calculate the required data for each code and valid section.

4) Obtaining reinforcement data of the section. In shear reinforcement design, it is possible to define the angle between the reinforcement and the longitudinal axis of the member. This angle should be included in the reinforcement definition of each element. If this angle is null or it is not defined, =90º. Other reinforcement data are ignored.

5) Obtaining forces and moments acting on the section. The shear force that acts on the section as well as the concomitant axial force and bending moment are obtained from the CivilFEM results file.

Force Description

Design shear force

Concomitant axial force

6) Calculating the nominal shear stress. The nominal shear stress is calculated from the following expression:

This stress is written for each end in the CivilFEM results file as:

TAOV Shear strength

7) Checking of the maximum shear stress. The nominal shear stress must be less than or equal to the maximum shear stress:

where _{c max} is given in Table 20 according to the concrete type:

Results are stored for each end in the CivilFEM results file as the following parameters:

TCMAX Maximum shear stress.

CRTCMAX Ratio of the nominal shear stress to the shear maximum stress.

If the nominal shear stress is greater than the maximum shear stress, the reinforcement design will not be possible; therefore, the parameter where the reinforcement amount is stored will be defined as 2¹⁰⁰.

In this case, the element will be labeled as not designed, advancing then to the following element end.

8) Determining the required transverse reinforcement contribution to the shear strength. The shear resistance is calculated as the sum of the resistance provided by the concrete and the resistance provided by the shear reinforcement:

where:

design shear force

shear resistance of the section

concrete contribution to the shear strength

shear reinforcement contribution to the shear strength

Therefore, the shear reinforcement contribution shall be:

The concrete contribution to the strength is:

where _cis given in Table 19 according to the concrete type and the amount of the longitudinal tension reinforcement:

For members subjected to axial compression P_u, the design shear strength of concrete, given in Table 19, shall be multiplied by the following factor:

For each element end, the V_us value is included in the CivilFEM results file as the parameter:

VUS reinforcement design shear force

9) Calculating the required reinforcement ratio. The resistance contribution of the shear reinforcement is calculated with the following expression:

area of the cross-section of the shear reinforcement

s spacing of the stirrups measured along the longitudinal axis

Therefore:

The area of the designed reinforcement per unit length is stored in the CivilFEM results file for both element ends:

In this case, the element will be labeled as designed (providing the design procedure is correct for both element sections).

If the reinforcement design is not possible, the reinforcement value is taken as 2¹⁰⁰ and the element will be considered not designed.

DSG_CRT Design criterion (Ok the element is designed and NotOk the element is not designed).

10.6.11.4 Axial and Bending with Combined Shear and Torsion Design

Axial and bending with shear and torsion longitudinal and transverse reinforcement design according to IS 456 follows the following steps:

1) Obtaining material strength properties. These properties are obtained from the material properties associated to each transverse cross section and for the active time,.

The required data are the following:

characteristic compressive strength of concrete.

characteristic yield strength of reinforcement.

partial safety factor for concrete.

partial safety factor for reinforcement.

2) Obtaining geometrical parameters. Geometrical parameters must be defined within CivilFEM database.

gross area of the concrete section.

3) Obtaining geometrical parameters depending on specified code. Geometrical parameters used for torsion designing must be defined within the CivilFEM. The required data are the following:

effective width of the section.

d effective depth.

ratio of the tensile reinforcement extending beyond the effective depth of the considered section, except in supports where the total area of the tensile reinforcement is used.:

Section “Previous Considerations to Shear and Torsion Calculation” provides detailed information on how to calculate the required data for each code and valid section.

4) Obtaining reinforcement data of the section. In longitudinal reinforcement design, it is necessary to define the distribution of bending reinforcement. In transversal reinforcement design, it is possible to define the angle α between the reinforcement and the longitudinal axis of member can be indicated. This angle should be stored in the section data of each element. If this angle is null or it is not defined, α=90º. Other reinforcement data will be ignored.

5) Obtaining forces and moments acting on the section. The forces and moments that act on the section are obtained from the CivilFEM results file:

Force/Moment Description

Design shear force

Design torsional moment

Concomitant axial force

Concomitant bending moment

6) Calculating the equivalent shear. Equivalent shear shall be calculated from the following formula:

Where V_e is the equivalent shear force.

7) Calculating the equivalent nominal shear stress. The equivalent nominal shear stress shall be calculated from the following formula:

Results are written in the CivilFEM results file for both element ends as the parameters:

TAOVE Nominal shear stress

8) Checking with the maximum shear stress. The equivalent nominal shear stress must be less than or equal to the maximum shear stress:

where _c
max is given in Table 20 according to the type of concrete:

Results are stored for each end in the CivilFEM results file as the following parameters:

TCMAX Maximum shear stress.

CRTCMAX Ratio of the nominal shear stress to the shear maximum stress.

If the nominal shear stress is greater than the maximum shear stress, the reinforcement design will not be possible; therefore the parameter for the area per unit length of the reinforcement will be taken as 2¹⁰⁰.

9) Checking whether the section will require transverse reinforcement. This reinforcement is not required if the equivalent nominal shear stress is less than or equal to the maximum shear stress:

where _cis given in Table 19 according to the concrete type and the amount of the longitudinal tension reinforcement:

Results are stored for each end in the CivilFEM results file as the following parameters:

ATT Area of the required transverse reinforcement.

10) Calculating the required transverse reinforcement. If the equivalent nominal stress exceeds the maximum shear stress, the required transverse reinforcement will be calculated by:

ATT Area of the necessary transverse reinforcement

11) Calculating the longitudinal reinforcement amount. A check is made to ensure the defined longitudinal bending reinforcement resists an equivalent bending moment given by the formula:

where

equivalent bending moment

increment due to torsional moment:

D overall depth

This equivalent moment is used in the axial bending design (in the direction defined in the command argument). For further information on the calculation procedure, see chapters 11-A.3 and 11-A.4 of the Theory Manual.

The calculated results are stored in the CivilFEM results file for both element ends as the parameters:

MT increment of the bending moment due to torsional moment

MEL equivalent bending moment

REINFACT Factor to multiply the scalable longitudinal bending reinforcement to satisfy the code provisions.

If the reinforcement factor is greater than the upper reinforcement limit established by the command, the design will not be possible; therefore, the reinforcement factor is defined as 2¹⁰⁰.

If the reinforcement design is not possible at both ends, the reinforcement value is taken as 2¹⁰⁰ and the element will be considered not designed.

DSG_CRT Design criterion (Ok the element is designed and NotOk the element is not designed).

6.7. Cracking Checking

6.7.1 Cracking according to Eurocode 2 (EN 1992-1-1:2004/AC:2008)

10.7.2.10 Cracking Checking

The cracking check calculates the crack width and checks the following condition:

where:

Design crack width.

Maximum crack width

The design crack width is obtained from the following expression (Art. 7.3.4):

Maximum spacing between cracks.

Mean strain in the reinforcement.

Mean strain in the concrete between bars.

f Reinforcement bar size in mm.

Coefficient accounting for the influence of the bond properties of the bonded reinforcement.

Coefficient accounting for the influence of the form of the strain distribution:

Where is the larger tensile strain and is the smaller tensile strain at the boundary of a section subjected to eccentric tension.

Constants defined in the National Annexes.

c Cover to the longitudinal reinforcement.

Stress in the tensile reinforcement calculated for a cracked section.

Elastic modulus of the longitudinal reinforcement.

Coefficient accounting for the influence of the duration of the loading.

Ratio between steel-concrete elastic modulus (E_s/E_cm).

10.7.1.2 Reinforcement Stress Calculation

During the calculation process, it is necessary to determine the reinforcement stress under service loads (s_s) with the assumption the section is cracked.

If the loads acting on the cross section cause collapse under axial plus bending checking, the cross section and the associated element are labeled as non-checked.

10.7.2.41 Reinforcement Stress Calculation

Checking results are stored in the corresponding alternative in the CivilFEM results file.

The following results are available:

CRT_TOT

Cracking criterion.

SIGMA

Maximum tensile stress.

Design crack width. (Not valid for decompression checking).

SRMAX

Maximum spacing between cracks. (Not valid for decompression checking).

Difference between the mean strain in the reinforcement and the mean strain in concrete. (Not valid for decompression checking).

POS

Cracking position inside the section. (Not valid for decompression checking).

1	Upper fiber.
-1	Lower fiber.
0	Upper and lower fibers.

For the cracking check (w_max > 0) the total criterion is defined as:

Therefore, values for the total criterion larger than one indicate that the section does not pass as valid for this code.

6.8. Cracking Checking

6.7.2 Cracking according to Structural Code (Spanish code)

10.7.2.10 Cracking Checking

The cracking check calculates the crack width and checks the following condition:

where:

Design crack width.

Maximum crack width

The design crack width is obtained from the following expression (Art. 7.3.4):

Maximum spacing between cracks.

Mean strain in the reinforcement.

Mean strain in the concrete between bars.

f Reinforcement bar size in mm.

Coefficient accounting for the influence of the bond properties of the bonded reinforcement.

Coefficient accounting for the influence of the form of the strain distribution:

Where is the larger tensile strain and is the smaller tensile strain at the boundary of a section subjected to eccentric tension.

Constants defined in the National Annexes.

c Cover to the longitudinal reinforcement.

Stress in the tensile reinforcement calculated for a cracked section.

Elastic modulus of the longitudinal reinforcement.

Coefficient accounting for the influence of the duration of the loading.

Ratio between steel-concrete elastic modulus (E_s/E_cm).

10.7.1.2 Reinforcement Stress Calculation

During the calculation process, it is necessary to determine the reinforcement stress under service loads (s_s) with the assumption the section is cracked.

If the loads acting on the cross section cause collapse under axial plus bending checking, the cross section and the associated element are labeled as non-checked.

10.7.2.41 Reinforcement Stress Calculation

Checking results are stored in the corresponding alternative in the CivilFEM results file.

The following results are available:

CRT_TOT

Cracking criterion.

SIGMA

Maximum tensile stress.

Design crack width. (Not valid for decompression checking).

SRMAX

Maximum spacing between cracks. (Not valid for decompression checking).

Difference between the mean strain in the reinforcement and the mean strain in concrete. (Not valid for decompression checking).

POS

Cracking position inside the section. (Not valid for decompression checking).

1	Upper fiber.
-1	Lower fiber.
0	Upper and lower fibers.

For the cracking check (w_max > 0) the total criterion is defined as:

Therefore, values for the total criterion larger than one indicate that the section does not pass as valid for this code.

6.7.3 Cracking according to ACI 318-05

10.7.2.1 Cracking Checking

Checking of the Cracking Limit State according to ACI 318-05 consists of the following condition:

Where:

Reinforcement spacing closest to the fiber in tension

s Design reinforcement spacing

CivilFEM checks this condition by applying the general calculation method for the reinforcement spacing (Art. 10.6.4):

where:

Calculated stress in reinforcement at service loads.

Geometrical cover

10.7.2.2 Reinforcement Stress Calculation

During the calculation process, it’s necessary to determine the reinforcement stress under service loads (f_s).

The design loads are taken as external loads.

If the loads acting on the cross section cause collapse under axial plus bending checking, the cross section and the element to which it belongs are marked as non checked.

10.7.2.3 Checking Results

The following results are available:

CRT_TOT

Cracking criterion.

Design reinforcement spacing. (Not valid for decompression checking).

Reinforcement stress. (Not valid for decompression checking).

SIGMA

Maximum tensile stress.

POS

Cracking position inside the section. (Not valid for decompression checking).

1	Upper fiber.
-1	Lower fiber.
0	Upper and lower fibers.

ELM_OK

Plots Ok and not Ok elements.

For the cracking check (s_d > 0) the total criterion is defined as:

For decompression checking (s_d = 0) the total criterion is defined as:

where

concrete design compressive strength.

Maximum section stress (positive tension), corresponding to the SIGMA result. (If CRT_TOT is negative, it is taken as zero)

Therefore, the values for the total criterion larger than one indicate that the section is not considered valid for this code.

7.1. Steel Structures According to Eurocode 3

For checking steel structures according to Eurocode 3 in CivilFEM, it is possible to check structures composed by welded or rolled shapes under axial forces, shear forces and bending moments in 3D. The calculations made by CivilFEM correspond to the recommendations of Eurocode 3: Design of steel structures Part 1-1: General rules and rules for buildings (EN 1993-1-1:2005).

With CivilFEM it is possible to accomplish the following check and analysis types:

Check steel sections subjected to
- Tension	Art. 6.2.3
- Compression	Art. 6.2.4
- Bending	Art. 6.2.5
- Shear force	Art. 6.2.6
- Bending and Shear	Art. 6.2.8
- Bending and axial force	Art. 6.2.9
- Bending, shear and axial force	Art. 6.2.10
Check for buckling
- Compression members with constant cross-section	Art. 6.3.1
- Lateral-torsional buckling of beams	Art. 6.3.2
- Members subjected to bending and axial tension	N/A
- Members subjected to bending and axial compression	Art. 6.3.3

Valid cross-sections supported by CivilFEM for checks according to Eurocode 3 are the following:

All rolled shapes included in the program libraries (see the hot rolled shapes library).

The following welded beams: double T shapes, U or channel shapes, T shapes, box, equal and unequal legs angles and pipes.

Structural steel sections defined by plates.

CivilFEM considers the above sections as sections composed of plates; for example, an I-section is composed by five plates: four flanges and one web. These cross sections are therefore adapted to the method of analysis of Eurocode 3. Obviously circular sections cannot be decomposed into plates, so these sections are analyzed separately.

7.1.1. Reference axis

With checks according to Eurocode 3, CivilFEM includes three different coordinate reference systems. All of these systems are right-handed:

1. CivilFEM Reference Axis. (X_CF, Y_CF, Z_CF).

2. Cross-Section Reference Axis. (X_S, Y_S, Z_S).

3. Eurocode 3 Reference Axis. (Code axis). (X_EC3, Y_EC3, Z_EC3).

For the Eurocode 3 axes system:

The origin matches to the CivilFEM axes origin.

X_EC3 axis coincides with CivilFEM X-axis.

Y_EC3 axis is the relevant axis for bending and its orientation is defined by the user (in steel check process).

Z_EC3 axis is perpendicular to the plane defined by X and Y axis, to ensure a right-handed system.

To define this reference system, the user must indicate which direction of the CivilFEM axis (-Z, -Y, +Z or +Y) coincides with the relevant axis for positive bending. The user may define this reference system when checking according to this code. In conclusion, the code reference system coincides with that of CivilFEM, but it is rotated a multiple of 90 degrees, as shown in table below.

Relevant Axis for Bending in CivilFEM Reference System	Angle of Rotation (clockwise) of Eurocode 3 Reference System respect to the CivilFEM Reference System
- Z_CF	90 º (Default value)
- Y_CF	180 º
+ Z_CF	270 º
+ Y_CF	0 º

7.1.2. Material properties

For Eurocode 3 checking, the following material properties are used:

Description	Property
Steel yield strength	Fy(th)
Ultimate strength	Fu(th)
Partial safety factors	g_M0 g_M1 g_M2
Elasticity modulus	E
Poisson coefficient	n
Shear modulus	G

*th =thickness of the plate

7.1.3. Section data

Eurocode 3 considers the following data set for the section:

Gross section data

Net section data

Effective section data

Data belonging to the section and plates class.

Gross section data correspond to the nominal properties of the cross-section. For the net section, only the area is considered. This area is calculated by subtracting the holes for screws, rivets and other holes from the gross section area. The area of holes is introduced within the structural steel code properties.

Effective section data and section and plates class data are obtained in the checking process according to the effective width method. For class 4 cross-sections, this method subtracts the non-resistance zones for local buckling. However, for cross-sections of a lower class, the sections are not reduced for local buckling.

In the following tables, the section data used in Eurocode 3 are shown:

Description

Data

Input data:

1.- Height

2.- Web thickness

3.- Flanges thickness

4.- Flanges width

5.- Distance between flanges

6.- Radius of fillet (Rolled shapes)

7.- Toe radius (Rolled shapes)

8.- Weld throat thickness (Welded shapes)

9.- Web free depth

r₁

r₂

Output data

(None)

Description

Data

Reference axis

Input data:

1.- Depth in Y

2.- Depth in Z

3.- Cross-section area

4.- Moments of inertia for torsion

5.- Moments of inertia for bending

6.- Product of inertia

7.- Elastic resistant modulus

8.- Plastic resistant modulus

9.- Radius of gyration

10.- Gravity center coordinates

11.- Extreme coordinates of the perimeter

12.- Distance between GC and SC in Y and in Z

13.- Warping constant

14.- Shear resistant areas

15.- Torsional resistant modulus

16.- Moments of inertia for bending about U, V

17.- Angle Y->U or Z->V

Tky

tkz

Iyy, Izz

Izy

Wely, Welz

Wply, Wplz

iy, iz

Ycdg, Zcdg

Ymin, Ymax,

Zmin, Zmax

Yms, Zms

Yws, Zws

Xwt

Iuu, Ivv

CivilFEM

Section

CivilFEM

Principal

CivilFEM

Output data:

(None)

The effective section depends on the section geometry and on the forces and moments that are applied to it. Consequently, for each element end, the effective section is calculated.

Description

Data

Reference axis

Imput data:

(None)

Output data:

1.- Cross-section area

2.- Moments of inertia for bending

3.- Product of inertia

4.- Elastic resistant modulus

5.- Gravity center coordinates

6.- Distance between GC and SC in Y and in Z

7.- Warping constant

8.- Shear resistant areas

Aeff

Iyyeff, Izzeff

Izyeff

Wyeff, Wzeff

Ygeff, Zgeff

Ymseff, Zmseff

Yws, Zws

CivilFEM

Section

CivilFEM

7.1.4. Structural steel code properties

For Eurocode 3 checking, besides the section properties, more data are needed for buckling checks. These data are shown in the following table.

Description	EN 1993-1-1:2005
Input data:
1.- Unbraced length of member (global buckling). Length between lateral restraints (lateral-torsional buckling).	L
2.- Buckling effective length factors in XY, XZ planes YZ (Effective buckling length for plane XY =LK XY ) (Effective buckling length for plane XZ =LK XZ ).	K XY, K XZ
3.- Lateral buckling factors, depending on the load and restraint conditions.	C1, C2, C3
4.- Equivalent uniform moment factors for flexural buckling.	CMy, CMz
5.- Equivalent uniform moment factors for lateral-torsional buckling.	CMLt
6.- Effective length factor regarding the boundar conditions.	K
7.- Warping effective factor.	KW

7.1.5. Check Process

The checking process includes the evaluation of the following expression:

Evaluation steps:

1. Read the loading check requested by the user.

2. Read the CivilFEM axis to be considered as the relevant axis for bending so that it coincides with the Y axis of Eurocode 3. In CivilFEM, by default, the principle bending axis that coincides with the +Y axis of Eurocode 3 is the –Z.

3. The following operations are necessary for each selected element:

a. Obtain material properties of the element stored in CivilFEM database and calculate the rest of the properties needed for checking:
Properties obtained from CivilFEM database:

Calculated properties:

Epsilon, material coefficient:

b. Obtain the cross-section data corresponding to the element.

c. Initialize values of the effective cross-section.

d. Initialize reduction factors of section plates and the rest of plate parameters necessary for obtaining the plate class.

e. If necessary for the type of check (check for buckling), calculate the critical forces and moments of the section for buckling: elastic critical forces for the XY and XZ planes and elastic critical moment for lateral-torsional buckling. (See section: Calculation of critical forces and moments).

f. Obtain internal forces and moments: , , , _, , within the section.

g. Specific section checking according to the type of external load. The specific check includes:

1. If necessary, selecting the forces and moments considered for the determination of the section class and used for the checking process.

2. Obtaining the cross-section class and calculating the effective section properties.

3. Checking the cross-section according to the external load and its class by calculating the check criterion.

h. Store the results.

7.1.6. Section Class and Reduction Factors Calculation

Sections, according to Eurocode 3, are made up by plates. These plates can be classified according to:

1. Plate function: webs and flanges in Y and Z axis, according to the considered relevant axis of bending.

2. Plate union condition: internal plates or outstand plates.

For sections included in the program libraries, the information above is defined for each plate. CivilFEM classifies plates as flanges or webs according to their axis and provides the plate union condition for each end. Ends can be classified as fixed or free (a fixed end is connected to another plate and free end is not).

For checking the structure for safety, Eurocode 3 classifies sections as one of four possible classes:

Class 1	Cross-sections which can form a plastic hinge with the rotation capacity required for plastic analysis.
Class 2	Cross-sections which can reach their plastic moment resistance, but have limited rotation capacity.
Class 3	Cross-sections for which the stress in the extreme compression fiber of the steel member can reach the yield strength, but local buckling is liable to prevent the development of the plastic moment resistance.
Class 4	Cross-sections for which it is necessary to make explicit allowances for the effects of local buckling when determining their moment resistance or compression resistance.

The cross-section class is the highest (least favorable) class of all of its elements: flanges and webs (plates). First, the class of each plate is determined according to the limits of Eurocode 3. The plate class depends on the following:

1. The geometric width to thickness ratio with the plate width properly corrected according to the plate and shape type.

GeomRat = Corrected_Width / thickness

The width correction consists of subtracting the zone that does not contribute to buckling resistance in the fixed ends. This zone depends on the shape type of the section. Usually, the radii of the fillet in hot rolled shapes or the weld throats in welded shapes determine the deduction zone. The values of the corrected width that CivilFEM uses for each shape type include:

· Welded Shapes:

Double T section:

Internal webs or flanges:

Corrected width = d

d Web free depth

Outstand flanges:

Corrected width

Where:

B	Flanges width
T_w	Web thickness
	Radius of fillet

T section:

Internal webs or flanges:

Corrected width = d

Outstand flanges:

Corrected width = B/d

C section:

Internal webs or flanges:

Corrected width = d

Outstand flanges:

Corrected width

B – –

L section:

Corrected width =

Angle flange width

Box section:

Internal webs:

Corrected width = H

H Height

Internal flanges:

Corrected width

Web thickness

Circular hollow section

Corrected width = H

· Rolled Shapes:

Double T section:

Internal webs or flanges:

Corrected width = d

d Web free depth

Outstand flanges:

Corrected width = B/2

B Flanges width

T Section:

Internal webs or flanges:

Corrected width = d

Outstand flanges:

Corrected width = B/2

C Section:

Internal webs or flanges:

Corrected width = d

Outstand flanges:

Corrected width = B

L Section:

Corrected width =

Angle flange width

Box section:

Internal webs:

Corrected width = d

Internal flanges:

Corrected width

Flanges thickness

Pipe section:

Corrected width = H

2. The limit listed below for width to thickness ratio. This limit depends on the material parameter e and the normal stress distribution in the plate section. The latter value is given by the following parameters: a, and k₀, and the plate type, internal or outstand; the outstand case depends on if the free end is under tension or compression.

Limit (class)

where:

a	Compressed length / total length
y
	Buckling factor
	The higher stress in the plate ends.
	The lower stress in the plate ends.

A linear stress distribution on the plate is assumed.

The procedure to determine the section class is as follows:

1. Obtain stresses at first plate ends from the stresses applied on the section, properly filtered according to the check type requested by the user.

2. Calculate the parameters: a, and k₀

For internal plates:

	ENV 1993-1-1:1992	EN 1993-1-1:2005



	= infinite

For outstand plates with an absolute value of the stress at the free end greater than the corresponding value at the fixed end:

For

= infinite

For outstand plates with an absolute value of the stress at the free end lower than the corresponding value at the fixed end:

For

= infinite

Cases in which infinite are not included in Eurocode 3. With these cases, the plate is considered to be practically in tension and it will not be necessary to determine the class. These cases have been included in the program to avoid errors, and the value has been adopted because the resultant plate class is 1 and the plate reduction factor is r = 1 (the same values as if the whole plate was in tension). The reduction factor is used later in the effective section calculation.

3. Obtain the limiting proportions as functions of: a, and k₀and the plate characteristics (internal, outstand: free end in compression or tension).

EN 1993-1-1:2005:

Internal plates:

	for
	for
	for
	for
	for
	for

Outstand plates, free end in compression:

Outstand plates, free end in tension:

Above is the general equation used by the program to obtain the limiting proportions for determining plate classes. In addition, plates of Eurocode 3 may be checked according to special cases.

For example:

In sections totally compressed:

a= 1; = 1 for all plates

In sections under pure bending:

a = 0.5; = -1 for the web

a = 1; = 1 for compressed flanges

4. Obtain the plate class:

If		GeomRat	< Limit(1)	Plate Class = 1
If	Limit(1) ≤	GeomRat	< Limit(2)	Plate Class = 2
If	Limit(2) ≤	GeomRat	< Limit(3)	Plate Class = 3
If	Limit(3) ≤	GeomRat		Plate Class = 4

Repeat these steps (1,2,3,4) for each section plate.

5. Assign of the highest class of the plates to the entire section.
In tubular sections, the section class is directly determined as if it were a unique plate, with GeomRat and the Limits calculated as follows:

6. GeomRat = outer diameter/ thickness.

For class 4 sections, the section resistance is reduced, using the effective width method.

For each section plate, the effective lengths at both ends of the plate and the reduction factors and are calculated. These factors relate the length of the effective zone at each plate end to its width.

Effective_length_end 1 =

Effective_length_end 2 =

The following formula from Eurocode 3 has been implemented for this process:

1. Internal plates:

For (Both ends compressed)

ec3_1

corrected plate width

plate_width = real plate width

For (end 1 in compression and end 2 in tension)

ec3_2

2. Outstand plates:

For (Both ends in compression: end 1 fixed, end 2 free)

ec3_3

For (end 1 fixed and in tension, end 2 free and in compression)

ec3_4

For (end 1 fixed and in compression, end 2 free and in tension)

ec3_5

If end 2 is the fixed end, the values and are switched.

The global reduction factor r is obtained by as follows:

EN 1993-1-1:2005:

For internal compression elements

For

For outstands compression elements:

For

Both Eurocode define as the plate slendernesss given by:

where:

= corrected plate width

t = relevant thickness

e = material parameter

= buckling factor

To determine effective section properties, three steps are followed:

1. Effective widths of flanges are calculated from factors α and these factors are determined from the gross section properties. As a result, an intermediate section is obtained with reductions taken in the flanges only.

2. The resultant section properties are obtained and factors α and are calculated again.

3. Effective widths of webs are calculated so that the finalized effective section is determined. Finally, the section properties are recalculated once more.

The recalculated section properties are included in the effective section data table. Checking can be accomplished with the gross, net or effective section properties, according to the section class and checking type.

Each checking type follows a specific procedure that will be explained in the following sections.

7.1.7. Checking of Members in Axial Tension

Corresponds to chapter 6.2.3 in EN 1993-1-1:2005.

1. Forces and moments selection.
The forces and moments considered for this checking type are:

= FX Design value of the axial force (positive if tensile, element not processed if compressive).

2. Class definition and effective section properties calculation.
For this checking type, the section class is always 1 and the considered section is either the gross or net section.

3. Criteria calculation.
For members under axial tension, the general criterion Crt_TOT is checked at each section. This criterion coincides with the axial criterion Crt_N.

where is the design tension resistance of the cross-section, taken as the smaller value of:

plastic design strength

of the gross cross-section

ultimate design strength

of the net cross-section

4. Output results are written in the CivilFEM results file (.CRCF). Checking results: criteria and variables are described in the following table:

Result	Concepts	Description
NED		Design value of the tensile force (EN 1993-1-1:2005).
NTRD		Design tensile strength of the cross-section.
CRT_N		Axial criterion.
CRT_TOT		Eurocode 3 global criterion.
NPLRD		Design plastic strength of the gross cross-section.
NURD		Ultimate design strength

7.1.8. Checking of Members in Axial Compression

Corresponds to chapter 6.2.4 in EN 1993-1-1:2005.

1. Forces and moments selection.
The forces and moments considered for this checking type are:

= FX Design value of the axial force (positive if compressive, element not processed if tensile).

2. Class definition and effective section properties calculation.
The section class is determined by the general processing of the section with the previously selected forces and moments if the selected option is partial or with all the forces and moments if the selected option is full. The entire calculation process is accomplished with the gross section properties..

3. Criteria calculation.
For members in axial compression, the general criterion Crt_TOT is checked at each section. This criterion coincides with the axial criterion Crt_N:

where is the design compression resistance of the cross-section

Class 1,2 or 3 cross-sections:

design plastic resistance of the gross section

Class 4 cross sections:

EN 1993-1-1:2005:

4. Output results written in the CivilFEM results file (.CRCF) . Checking results: criteria and variables are described at the following table.

Result	Concepts	Description
NED		Design axial force (EN 1993-1-1:2005).
NCRD		Design compression strength of the cross-section.
CRT_N		Axial criterion.
CRT_TOT		Eurocode 3 global criterion.
CLASS		Section Class.
AREA		Area of the section (Gross or Effective).

7.1.9. Checking of Members under Bending Moment

Corresponds to chapter 6.2.5 in EN 1993-1-1:2005.

1. Forces and moments selection.
The forces and moments considered for this checking type are:

Design value of the bending moment along the relevant axis for bending.

3. Criteria calculation.
For members subjected to a bending moment in the absence of shear force, the following condition is checked at each section:

where:

design value of the bending moment

design moment resistance of the cross-section

Class 1 or 2 cross-sections:

Class 3 cross sections:

Class 4 cross sections:

EN 1993-1-1:2005:

4. Output results are written in the CivilFEM results file (.CRCF). Checking results: criteria and variables are described in the following table.

Result	Concepts	Description
MED		Design value of the bending moment (EN 1993-1-1:2005).
MCRD		Design moment resistance of the cross-section.
CRT_M		Bending criterion.
CRT_TOT		Eurocode 3 global criterion.
CLASS		Section Class.
W		Used section modulus (Elastic, Plastic or Effective).

7.1.10. Checking of Members under Shear Force

Corresponds to chapter 6.2.6 in EN 1993-1-1:2005.

1. Forces and moments selection.
The forces and moments considered for this checking type are:

Design value of the shear force perpendicular to the relevant axis of bending.

2. Class definition and effective section properties calculation.
For this checking type, the section class is always 1 and the effective section is the gross section.

3. Criteria calculation.
With members under shear force, the following condition is checked at each section:

where:

	design value of the shear force
	design plastic shear resistance:
	shear area, obtained subtracting from the gross area the summation of the flanges areas:

Modifications to the previous computation of are as follows:

· Rolled I and H sections, load parallel to web:

· Rolled channel sections, load parallel to web:

EN 1993-1-1:2005 specifies additional cases for the calculation of :

· Rolled I and H sections with load parallel to web:

but not less than η

· Rolled T shaped sections with load parallel to web:

Where:

η = 1.2 for steels with fy = 460 MPa

η= 1.0 for steels with fy > 460 MPa

Web depth

Web thickness

4. Output results are written in the CivilFEM results file (.CRCF). Checking results: criteria and variables are described in the following table.

Result	Concepts	Description
VED		Design value of the shear force (EN 1993-1-1:2005).
VPLRD		Design plastic shear resistance.
CRT_S		Shear criterion.
CRT_TOT		Eurocode 3 global criterion.
CLASS		Section Class.
S_AREA	Av	Shear area.

7.1.11. Checking of Members under Bending Moment and Shear Force

Corresponds to chapter 6.2.8 in EN 1993-1-1:2005.

1. Forces and moments selection.
The forces and moments considered for this checking type are:

Design value of the shear force perpendicular to the relevant axis of bending.

Design value of the bending moment along the relevant axis of bending.

2. Class definition and effective section properties calculation.
The section class is determined by the general processing of the sections with the previously selected forces and moments if the selected option is partial or with all the forces and moments if the selected option is full. The entire calculation is accomplished with gross section properties.

3. Criteria calculation.
For members subjected to bending moment and shear force, the following condition is checked at each section:

Where:

design resistance moment of the cross-section, reduced by the presence of shear.

The reduction for shear is applied if the design value of the shear force exceeds 50% of the design plastic shear resistance of the cross-section; written explicitly as:

The design resistance moment is obtained as follows:

EN 1993-1-1:2005:

a. For double T cross-sections with equal flanges, bending about the major axis:

b. For other cases the yield strength is reduced as follows:

Note: This reduction of the yield strength fy is applied to the entire section. Eurocode 3 only requires the reduction to be applied to the shear area, and therefore, it is a conservative simplification.

For both cases, is the smaller value of either or .

is the design moment resistance of the cross-section, calculated according to the class.

4. Output results are written in the CivilFEM results file (.CRCF). Checking results: criteria and variables are described in the following table.

Result	Concepts	Description
MED		Design value of the bending moment (EN 1993-1-1:2005).
VED		Design value of the shear force (EN 1993-1-1:2005).
MVRD		Reduced design resistance moment of the cross-section.
CRT_BS		Bending and Shear criterion.
CRT_TOT		Eurocode 3 global criterion.
CLASS		Section Class.
S_AREA		Shear area.
W		Used section modulus (Elastic, Plastic or Effective).
VPLRD		Design plastic shear resistance.
RHO		Reduction factor.

7.1.12. Checking of Members under Bending Moment and Axial Force

Corresponds to chapter 6.2.9 in EN 1993-1-1:2005.

1. Forces and moments selection.
The forces and moments considered for this checking type are:

	Design value of the axial force.
	Design value of the bending moment along the relevant axis of bending.
	Design value of the bending moment about the secondary axis of bending.

2. Class definition and effective section properties calculation.
The section class is determined by the general processing of the sections with the previously selected forces and moments if the selected option is partial, or with all the forces and moments if the selected option is full. These calculations are accomplished with the gross section properties.

3. Criteria calculation.
For members subjected to bi-axial bending and in absence of shear force, the following conditions at each section are checked:

Class 1 and 2 sections:

This condition is equivalent to:

Where and are the design moment resistance of the cross-section, reduced by the presence of the axial force:

Where a and b are constants, which may take the following values:

For I and H sections:

a = 2 and b =5n

For circular tubes:

a = 2 and b =2

For rectangular hollow sections:

but

For solid rectangles and plates (the rest of sections):

Furthermore, the code specifies that in the case of rolled shapes for I or H sections or other sections with flanges, it is not necessary to reduce the design plastic strength for bending around the y-y axis due to the axial force if the following two conditions are fulfilled:

(if it does not reach half the tension strength of the web)

The same is applicable for bending around the z-z axis due to the axial force. There is no reduction when the following condition is fulfiled:

In absence of , the previous check can be reduced to:

Condition equivalent to:

Class 3 sections (without holes for fasteners):

Condition equivalent to:

Crt_TOT = Crt_N + Crt_My + Crt_Mz £ 1

Where is the elastic resistant modulus about the y axis and is the elastic resistant modulus about the z axis.

In absence of , the above criterion becomes:

Which is equivalent to:

Crt_TOT = Crt_N + Crt_My £ 1

Class 4 sections:

Condition equivalent to:

Crt_TOT = Crt_N + Crt_My + Crt_Mz £ 1

Where:

	effective area of the cross-section
	effective section modulus of the cross-section when subjected to a moment about the y axis
	effective section modulus of the cross-section when subjected to a moment about the z axis
	shift of the center of gravity along the y axis
	shift of the center of gravity along the z axis

Without , the above criterion becomes:

which is equivalent to:

Crt_TOT = Crt_N + Crt_My + Crt_Mz £ 1

4. Output results are written in the CivilFEM results file (.CRCF). Checking results: criteria and variables are described in the following table.

Result	Concepts	Description
NED		Design value of the axial force (EN 1993-1-1:2005).
MYED		Design value of the bending moment about Y axis (EN 1993-1-1:2005).
MZED		Design value of the bending moment about Z axis (EN 1993-1-1:2005).
NCRD		Design compression resistance of the cross-section
MNYRD		Reduced design moment resistance of the cross-section about Y axis
MNZRD		Reduced design moment resistance of the cross-section about Z axis
CRT_N		Axial criterion
CRT_MY		Bending criterion along Y
CRT_MZ		Bending criterion along Z
ALPHA	α	Alpha constant
BETA	β	Beta constant
CRT_TOT	Crt_tot £ 1	Eurocode 3 global criterion
CLASS		Section Class
AREA		Area of the section utilized (Gross or Effective)
WY		Used section Y modulus (Elastic, Plastic or Effective)
WZ		Used section Z modulus (Elastic, Plastic or Effective)
SIGXED		Maximum longitudinal stress
ENY		Shift of the Z axis in Y direction
ENZ		Shift of the Y axis in Z direction
USE_MY		Modified design value of the bending moment about Y axis
USE_MZ		Modified design value of the bending moment about Z axis
PARM_N	n	Parameter n

7.1.13. Checking of Members under Bending, Shear and Axial Force

Corresponds to chapter 6.2.10 in EN 1993-1-1:2005.

1. Forces and moments selection. The forces and moments considered for this checking type are:

	Design value of the axial force.
	Design value of the shear force perpendicular to the secondary axis of bending.
	Design value of the shear force perpendicular to the relevant axis of bending.
	Design value of the bending moment about the relevant axis of bending.
	Design value of the bending moment about the secondary axis of bending.

2. Class definition and effective section properties calculation.
The section class is determined by the general processing of the sections with the previously selected forces and moments if the selected option is partial, or with all the forces and moments if the selected option is full. The entire calculation is accomplished with the gross section properties.

3. Criteria calculation.
For members subjected to bending, axial and shear force, the same conditions of the bending +axial force and bi-axial bending are checked at each section, reducing the design plastic resistance moment for the presence of shear force.
The shear force effect is taken into account when it exceeds 50% of the design plastic resistance of the cross-section. In this case, both the axial and the shear force are taken into account.

The axial force effects are included as stated in the previous section, and the shear force effects are taken into account considering a yield strength for the cross-section, reduced by the factor (1-r), as follows:

where:

for

	for

This yield strength reduction is selectively applied to the resistance of the cross-section along each axis, according to the previous conditions.

Note: The yield strength reduction is applied to the entire cross-section; however, Eurocode only requires the reduction to be applied to the shear area. Thus, it is a conservative simplification.

4. Output results are written in the CivilFEM results file (.CRCF). Checking results: criteria and variables are described in the following table.

Result	Concepts	Description
NED		Design value of the axial force (EN 1993-1-1:2005).
VZED		Design value of the shear force (EN 1993-1-1:2005).
VYED		Design value of the shear force (EN 1993-1-1:2005).
MYED		Design value of the bending moment about Y axis (EN 1993-1-1:2005).
MZED		Design value of the bending moment about Z axis (EN 1993-1-1:2005).
NCRD		Design compression resistance of the cross-section.
MNYRD		Reduced design moment Y resistance of the cross-section.
MNZRD		Reduced design moment Z resistance of the cross-section.
CRT_N		Axial criterion.
CRT_MY		Bending Y criterion.
CRT_MZ		Bending Z criterion.
ALPHA	α	Alpha constant.
BETA	β	Beta constant.
RHO_Y	ρ	Reduction factor for MNYRD.
RHO_Z	ρ	Reduction factor for MNZRD.
CRT_TOT	Crt_tot £ 1	Eurocode 3 global criterion.
AREA		Used area of the section (Gross or Effective).
WY		Used section Y modulus (Elastic, Plastic or Effective).
WZ		Used section Z modulus (Elastic, Plastic or Effective).
SIGXED		Maximum longitudinal stress.
ENY		Shift of the Z axis in Y direction.
ENZ		Shift of the Y axis in Z direction.
USE_MY		Modified design value of the bending moment about Y axis.
USE_MZ		Modified design value of the bending moment about Z axis.
SHY_AR		Shear Y area.
SHZ_AR		Shear Z area.
PARM_N	n	Parameter n.

7.1.14. Checking for Buckling of Members in Compression

Corresponds to chapter 6.3.1 in EN 1993-1-1:2005.

1. Forces and moments selection.
The forces and moments considered in this checking type are:

Design value of the axial force (positive if compressive, otherwise element is not processed).

2. Class definition and effective section properties calculation.
The section class is determined by the sections general processing with the previously selected forces and moments if the selected option is partial, or with all the forces and moments if the selected option is full. The entire calculation is accomplished with the gross section properties.

3. Criteria calculation.
When checking the buckling of compression members, the criterion is given by:

where:

Design buckling resistance.

b = 1 for class 1, 2 or 3 sections.

b = for class 4 sections.

Reduction factor for the relevant buckling mode, the program does not consider the torsional or the lateral-torsional buckling.

The c calculation in members of constant cross-section may be determined from:

where a is an imperfection factor that depends on the buckling curve. This curve depends on the cross-section type, producing the following values for a:

Section type	Limits	Buckling axis	Steel f_y	Buckling curve		a
Rolled I	h/b>1.2 and t40mm	y – y	< 460 MPa	a		0.21
			≥ 460 MPa	a0		0.13
Rolled I	h/b>1.2 and t40mm	z – z	< 460 MPa	b		0.34
			≥ 460 MPa	a0		0.13
Rolled I	h/b>1.2 and 40mm<t100mm	y – y	< 460 MPa	b		0.34
			≥ 460 MPa	a		0.21
Rolled I	h/b>1.2 and 40mm<t100mm	z – z	< 460 MPa	c		0.49
			≥ 460 MPa	a		0.21
Welded I	h/b1.2 and t100mm	y – y	< 460 MPa	b		0.34
			≥ 460 MPa	a		0.21
Welded I	h/b1.2 and t100mm	z – z	< 460 MPa	c		0.49
			≥ 460 MPa	a		0.21
Rolled I	t>100mm	y – y	< 460 MPa	d		0.76
			≥ 460 MPa	c		0.49
Rolled I	t>100mm	z – z	< 460 MPa	d		0.76
			≥ 460 MPa	c		0.49

Welded I	t40mm	y – y	all	b	0.34
Welded I	t40mm	z – z	all	c	0.49
Welded I	t >40mm	y – y	all	c	0.49
Welded I	t >40mm	z – z	all	d	0.76

Pipes	Hot finished	all	< 460 MPa	a	0.21
			≥ 460 MPa	a0	0.13
	Cold formed	all	all	c	0.49
Reinforced box sections	Thick weld: a/t>0.5 b/t<30 h/tw<30	all	all	c	0.49
	In other case	all	all	b	0.34

U, T, plate	-	all	all	c	0.49

L	-	all	all	b	0.34

Where is the elastic critical force for the relevant buckling mode. (See section for Critical Forces and Moments Calculation).

In the case of angular sections, the buckling length will be taken as the highest among the buckling lengths on the Y and Z axis.

4. The elastic critical axial forces are calculated in the planes XY (Ncr_xy) and XZ (Ncr_xz) and the corresponding values of c_xy and c_{xz ,}and the correspondent to the principal axis Ncr_u and Ncr_v and the values for c_u and c_v taking the smaller one as the final value for c.

5. Output results are written in the CivilFEM results file (.CRCF). Checking results: criteria and variables are described in the following table.

Result	Concepts	Description
NED		Design value of the compressive force (EN 1993-1-1:2005).
NBRD		Design buckling resistance of a compressed member.
CRT_CB		Compression buckling criterion.
CRT_TOT		Eurocode 3 global criterion.
CHI		Reduction factor for the relevant buckling mode.
BETA_A		Ratio of the used area to gross area.
AREA	A	Area of the gross section.
CHI_Y		Reduction factor for the relevant My buckling mode.
CHI_Z		Reduction factor for the relevant Mz buckling mode.
CHI_V		Reduction factor for the principal axis V.
CHI_U		Reduction factor for the principal axis U.
CLASS		Section Class.
PHI_Y		Parameter Phi for bending My.
PHI_Z		Parameter Phi for bending Mz.
PHI_V		Parameter Phi for the principal axis V.
PHI_U		Parameter Phi for the principal axis U.
LAM_Y		Non-dimensional reduced slenderness for bending My.
LAM_Z		Non-dimensional reduced slenderness for bending Mz.
LAM_V		Non-dimensional reduced slenderness for the principal axis V.
LAM_U		Non-dimensional reduced slenderness for the principal axis U.
NCR_Y		Elastic critical force for the relevant My buckling mode.
NCR_Z		Elastic critical force for the relevant Mz buckling mode.
NCR_V		Elastic critical force for the principal axis V.
NCR_U		Elastic critical force for the principal axis U.
ALP_Y		Imperfection factor for bending My.
ALP_Z	αz	Imperfection factor for bending Mz.

7.1.15. Checking for Lateral-Torsional Buckling of Beams Subjected to Bending

Corresponds to chapter 6.3.2 in EN 1993-1-1:2005.

1. Forces and moments selection.
The forces and moments considered for this checking type are:

Design value of the bending moment about the relevant axis of bending.

2. Class definition and effective section properties calculation.
The section class is determined by the general processing of sections with the previously selected forces and moments if the selected option is partial, or with all the forces and moments if the selected option is full. The entire calculation is accomplished with the gross section properties.

3. Criteria calculation.
When checking for lateral-torsional buckling of beams, the criterion shall be taken as:

where:

Design buckling resistance moment of a laterally unrestrained beam.

b_w = 1 for class 1and 2 sections.

b_w = for class 3 sections.

b_w = for class 4 sections.

c_LT

Reduction factor for lateral-torsional buckling.

The value of c_LT is calculated as:

Where:

is the imperfection factor for lateral-torsional buckling:

Section type	Limits	Buckling curve	α
Rolled I	h/b≤2 h/b>2	a b	0.21 0.34
Welded I	h/b≤2 h/b>2	c d	0.49 0.76
Others			0.76

is the elastic critical moment for lateral-torsional buckling.

4. Output results are written in the CivilFEM results file (.CRCF). Checking results: criteria and variables are described in the following table.

Result	Concepts	Description
MED		Design value of the bending moment (EN 1993-1-1:2005).
MBRD		Buckling resistance moment of a laterally unrestrained beam.
CRT_LT		Lateral-torsional buckling criterion.
CRT_TOT		Eurocode 3 global criterion.
CLASS		Section Class.
CHI_LT		Reduction factor for lateral-torsional buckling.
BETA_W		Ratio of the used modulus to plastic modulus.
WPL		Plastic modulus.
PHI_LT		Parameter Phi for lateral-torsional buckling.
LAM_LT		Non-dimensional reduced slenderness.
MCR	Mcr	Elastic critical moment for lateral-torsional buckling.
ALP_LT		Imperfection factor for lateral-torsional buckling.

7.1.16. Checking for Lateral-Torsional Buckling of Members Subjected to Bending and Axial Compression

Corresponds to chapter 6.3.3 in EN 1993-1-1:2005.

1. Forces and moments selection.
The forces and moments considered in this checking type are:

= FX	Design value of the axial compression (positive if compressive, otherwise element not processed if tensile).
= MY or MZ	Design value of the bending moment about the relevant axis of bending.
= MZ or MY	Design value of the bending moment about the secondary axis of bending.

3. Criteria calculation.

EN 1993-1-1:2005 and Annex B (method 2)

The following criterion will always be calculated:

Crt_1 = Crt_N1 + Crt_My1 + Crt_Mz1 £ 1

Elements without torsional buckling:

Elements which may have torsional buckling:

à Crt_2 = Crt_N2 + Crt_My2 + Crt_Mz2 £ 1

à Crt_TOT = Max (Crt_1, Crt_2)

Where:

	Axial force criterion 1.
	Bending moment criterion for principal axis 1.
	Bending moment criterion for secondary axis 1
Crt_TOT1	General criterion 1.
	Axial force criterion 2.
	Bending moment criterion 2 for principal axis without torsional buckling
	Bending moment criterion 2 for principal axis when torsional buckling is considered.
	Bending moment criterion 2 for secondary axis.
Crt_TOT2	Criterion 2
Crt_TOT=max (Crt_TOT1, Crt_TOT2 )	Global criterion.

Where:

( when torsional buckling is not considered).

and are the reduction factors defined for the section corresponding to the check for Buckling of Compression Members.

lateral buckling factor according to 6.3.2.2. Assumes the value of 1 for members not susceptible to torsional deformations.

and shifts of the centroid of the effective area relative to the centre of gravity of the gross section in class 4 members for y, z axes.

, and are equivalent uniform moment factors for flexural bending. These factors are entered as member properties at member level. (See and ). These factors may be taken from Table B.3 from Annex B of code EN 1993-1-1:2005.

Checking Parameters:

Class	A
1	A	0.6	0.6	0	0
2	A	0.6	0.6	0	0
3	A	0.8	1	0	0
4		0.8	1	Depending on members and stresses	Depending on members and stresses

Interaction Factors:

Class	Section type
1 y 2	I, H
1 y 2	RHS
3 y 4	All sections

where:

Limited slenderness values for y-y and z-z axes, less than 1.

4. Output results are written in the CivilFEM results file (.CRCF). Checking results: criteria and variables are described in the following table.

Result	Concepts	Description
NED		Design value of the axial compression force.
MYED		Design value of the bending moment about Y axis.
MZED		Design value of the bending moment about Z axis.
NBRD1		Design compression resistance of the cross-section.
MYRD1		Reduced design moment resistance of the cross-section about Y axis.
MZRD1		Reduced design moment resistance of the cross-section about Z axis.
NBRD2		Design compression resistance of the cross-section.
MYRD2		Reduced design moment resistance of the cross-section about Y axis.
MZRD2		Reduced design moment resistance of the cross-section about Z axis.
K_Y		Parameter _.
K_Z		Parameter _.
K_LT		Parameter _.
CRT_N1		Axial criterion.
CRT_MY1		Bending Y criterion.
CRT_MZ1		Bending Z criterion.
CRT_1	CRT_N1+CRT_MY1+CRT_MZ1	Criterion 1
CRT_N2	/	Axial criterion.
CRT_MY2		Bending Y criterion. K= if torsion exists and if not present K=
CRT_MZ2		Bending Z criterion.
CRT_2	CRT_N2+CRT_MY2+CRT_MZ2	Criterion 2
CRT_TOT	Crt_tot £ 1	Eurocode 3 global criterion.
CLASS		Section Class.
CHIMIN		Reduction factor for the relevant buckling mode.
CHI_Y		Reduction factor for the relevant My buckling mode.
CHI_Z		Reduction factor for the relevant Mz buckling mode.
CHI_LT		Reduction factor for lateral-torsional buckling.
AREA		Used area of the section (Gross or Effective).
WY		Used section Y modulus (Elastic, Plastic or Effective).
WZ		Used section Z modulus (Elastic, Plastic or Effective).
ENY		Shift of the Z axis in Y direction.
ENZ		Shift of the Y axis in Z direction.
NCR_Y		Elastic critical force for the relevant My buckling mode.
NCR_Z		Elastic critical force for the relevant Mz buckling mode.
MCR		Elastic critical moment for lateral-torsional buckling.
LAM_Y		Non-dimensional reduced slenderness for bending My.
LAM_Z		Non-dimensional reduced slenderness for bending Mz.
LAM_LT		Non-dimensional reduced slenderness for lateral-torsional buckling.

7.1.17. Critical Forces and Moments Calculation

The critical forces and moments, and M_cr, are needed for the different types of buckling checks. They are calculated based on the following formulation:

where:

	Elastic critical axial force in plane XY.
	Elastic critical axial force in plane XZ.
A	Gross area.
E	Elasticity modulus.
	Member slenderness in plane XY.
	Member slenderness in plane XZ.
	Radius of gyration of the member in plane XY.
	Radius of gyration of the member in plane XZ.
	Buckling length of member in plane XY.
	Buckling length of member in plane XZ.

The buckling length in both planes is the length between the ends restrained against lateral movement and it is obtained from the member properties, according to the following expressions:

where:

Cfbuckxy	Buckling factor in plane XY.
Cfbuckxz	Buckling factor in plane XZ.

For the calculation of the elastic critical moment for lateral-torsional buckling, Mcr, the following equation shall be used. This equation is only valid for uniform symmetrical cross-sections about the minor axis (Annex F, ENV 1993-1-1:1992). Eurocode 3 does not provide a method for calculating this moment in nonsymmetrical cross-sections or sections with other symmetry plane (angles, channel section, etc.).

where:

	Elastic critical moment for lateral-torsional buckling.
	Factors depending on the loading and end restraint conditions.
	Effective length factors.
E	Elasticity modulus.
	Moment of inertia about the principal axis.
	Moment of inertia about the minor axis.
L	Length of the member between end restraints.
G	Shear modulus.

	Coordinate of the point of load application. By default the load is applied at the center of gravity, therefore:.
	Coordinate of the shear center.
A	Cross-section area.

Factors C and k are read from the properties at structural element level.

The integration of the previous equation is calculated as a summation extending to each plate. This calculation is accomplished for each plate according to its ends coordinates: and and its thicknesses.

where:

= thickness of plate i

dA = * dl

= plate width

7.2. Steel Structures According to AISC ASD/LRFD 13^thEd.

7.2.1. Material properties

For AISC 13^th Edition checking, the following material properties are used:

Description	Property
Steel yield strength	Fy(th)
Ultimate strength	Fu(th)
Elasticity modulus	E
Poisson coefficient	n
Shear modulus	G

*th =thickness of the plate

7.2.2. Section data

AISC 13^th Edition considers the following data set for the section:

- Gross section data

- Net section data

- Effective section data.

- Data belonging to the section and plates class.

Gross section data correspond to the nominal properties of the cross-section. For the net section, only the area is considered. This area is calculated by subtracting the holes for screws, rivets and other holes from the gross section area. (The area of holes is introduced within the structural steel code properties).

The effective section data and the section and plates class data are obtained in the checking process according to chapter B, section B4 of the code. This chapter classifies steel sections into three groups (compact, noncompact and slender), depending upon the width-thickness ratio and other mandatory limits.

The AISC 13^TH Edition module utilizes the gross section data in user units and the CivilFEM axis or section axis as initial data. The program calculates the effective section data and the class data, and stores them in CivilFEM’s results file, in user units and in CivilFEM or section axis.

The section data used in AISC 13^TH Edition are shown in the following tables:

Description

Data

Input data:

1.- Height

2.- Web thickness

3.- Flanges thickness

4.- Flanges width

5.- Distance between flanges

6.- Radius of fillet (Rolled shapes)

7.- Toe radius (Rolled shapes)

8.- Weld throat thickness (Welded shapes)

9.- Web free depth

r₁

r₂

Output data

(None)

Description

Data

Reference axes

Input data:

1.- Depth in Y

2.- Depth in Z

3.- Cross-section area

4.- Moments of inertia for torsion

5.- Moments of inertia for bending

6.- Product of inertia

7.- Elastic resistant modulus

8.- Plastic resistant modulus

9.- Radius of gyration

10.- Gravity center coordinates

11.- Extreme coordinates of the perimeter

12.- Distance between GC and SC in Y and in Z

13.- Warping constant

14.- Shear resistant areas

15.- Torsional resistant modulus

16.- Moments of inertia for bending about U, V

17.- Angle Y->U or Z->V

Tky

tkz

Iyy, Izz

Izy

Wely, Welz

Wply, Wplz

iy, iz

Ycdg, Zcdg

Ymin, Ymax,

Zmin, Zmax

Yms, Zms

Yws, Zws

Xwt

Iuu, Ivv

CivilFEM

Section

CivilFEM

Principal

CivilFEM

Output data:

(None)

Description

Data

Input data:

1.- Gross section area

2.- Area of holes

Agross

Aholes

Output data:

1.- Cross-section area

Anet

The effective section depends upon the geometry of the section; thus, the effective section is calculated for each element and each of the ends of the element.

Description

Data

Input data:

(None)

Output data:

1.- Reduction factor

2.- Reduction factor

3.- Reduction factor

7.2.3. Structural steel code properties

For AISC 13^th Edition checking, besides the section properties, more data are needed for bucling checks. These data are shown in the following table.

Description

Data

Input data:

1.- Unbraced length of member (global buckling)

2.- Effective length factors Y direction

3.- Effective length factors Z direction

4.- Effective length factors for torsional buckling

5.- Flexural factor relative to bending moment

6.- Length between lateral restraints

KTOR

Output data:

1.- Compression class

2.- Bending class

CLS_COMP

CLS_FLEX

7.2.4. Check Process

Necessary steps to conduct the different checks in CivilFEM are as follows:

a) Obtain material properties corresponding to the element stored in CivilFEM database and calculate the rest of the properties needed for checking:
Properties obtained from CivilFEM database (materials):

Elasticity modulus	E
Poisson’s ratio	
Yield strength	Fy (th)
Ultimate strength	Fu (th)
Shear modulus	G
Thickness of corresponding plate	th

b) Obtain the cross-sectional data corresponding to the element.

c) Initiate the values of the plate’s reduction factors and the other plate’s parameters to determine its class.

d) Perform a check of the section according to the type of external load.

e) Results. In CivilFEM, checking results for each element end are stored in the results file .CRCF

7.2.5. Design requirements

7.2.5.1. Design for Strength Using Load and Resistance Factor Design (LRFD)

Design shall be performed in accordance with:

Where:

	Required strength (LRFD).
	Nominal strength.
	Resistance factor.
	Design strength

7.2.5.2. Design for Strength Using Allowable Strength Design (ASD)

Design shall be performed in accordance with:

Where:

	Required strength (ASD)
	Nominal strength.
	Safety factor
	Allowable strength

Section Class and Reduction Factors Calculation.

Steel sections are classified as compact, noncompact or slender-element sections. For a section to qualify as compact its flanges must be continuously connected to the web or webs and the width-thickness ratios of its compression elements must not exceed the limiting width-thickness ratios (see table B4.1 of AISC 13^th Edition). If the width-thickness ratio of one or more compression elements exceeds but does not exceed, the section is noncompact. If the width-thickness ratio of any element exceeds, (see table B4.1 of AISC 13^th Edition), the section is referred to as a slender-element compression section.

Therefore, the code suggests different lambda values depending on if the element is subjected to compression, flexure or compression plus flexure.

The section classification is the worst-case scenario of all of its plates. Therefore, the class is calculated for each plate with the exception of pipe sections, which have their own formulation because it cannot be decomposed into plates. This classification will consider the following parameters:

a) Length of elements:

The program will define the element length (b or h) as the length of the plate (distance between the extreme points), except when otherwise specified.

b) Flange or web distinction:

To distinguish between flanges or webs, the program follows the criteria below:

If (increments of end coordinates) and flexure is in the Y axis, it will be considered a web; if not, it will be a flange. The reverse will hold true for flexure in the Z-axis.

· Hot rolled Steel Shapes:

Section I and C:

The length of the plate h will be taken as the value d for the section dimensions.

Section Box:

The length of the plate will be taken as the width length minus three times the thickness.

7.2.5.3. Members subjected to compression

In order to check for compression it is necessary to determine if the element is stiffened or unstiffened.

- For stiffened elements:

Pipe sections

Box sections

- Unstiffened elements:

Angular sections

Stem of T sections

7.2.5.4. Members subjected to bending

The bending check is only applicable to very specific sections. Therefore, the slenderness factor is listed for each section:

· Section I and C:

=	69 MPa for hot rolled shapes (10 ksi)
	114 MPa for welded sections (16.5 ksi)

= minimum of () and () where and are the of flange and web respectively.

Flanges of rolled sections:

Flanges of welded sections:

Flange:

Always:

is the compression axial force (taken as positive). If in tension, it will be taken as zero.

· Pipe section:

Box section:

Flanges of box section:

Flanges: the program distinguishes between the flange and web upon the principal axis chosen by the user.

Always:

· T section:

Stem:

Flanges:

7.2.6. Checking of Members for Tension (Chapter D)

The axial tension force must be taken as positive (if the tension force has a negative value, the element will not be checked)

Design tensile strength and the allowable tensile strength , of tension members, shall be the lower value of :

a) yielding in the gross section:

b) rupture in the net section:

= 2.00 (ASD)

Being:

	Effective net area.
	Gross area.
	Minimum yield stress.
	Minimum tensile strength.

The effective net area will be taken as – A_HOLES. The user will need to enter the correct value for A_HOLES (the code indicates that the diameter is 1/16^th in. (2 mm) greater than the real diameter).

7.2.7. Checking of Members in Axial Compression (Chapter E)

The design compressive strength, ,and the allowable compressive strength, , are determined as follows:

The nominal compressive strength, , shall be the lowest value obtained according to the limit states of flexural buckling, torsional buckling and flexural-torsional buckling.

7.2.8. Compressive Strength for Flexural Buckling

This type of check can be carried out for compact sections as well as for noncompact or slender sections. These three cases adhere to the following steps:

Nominal compressive strength, :

(E3-1)

a) For :

b) for

Where:

	Gross area of member.
r	Governing radius of gyration about the buckling axis.
K	Effective length factor.
l	Unbraced length.
	Elastic critical buckling stress

Factor Q for compact and noncompact sections is always 1. Nevertheless, for slender sections, the value of Q has a particular procedure. Such procedure is described below:

Factor Q for slender sections:

For unstiffened plates, Qs must be calculated and for stiffened plates, Qa must be determined. If these cases do not apply (box sections or angular sections, for example), a value of 1 for these factors will be taken.

For circular sections, there is a particular procedure of calculating Q. Such procedure is described below:

· For circular sections, Q is:

Factor Qs:

If there are several plates free, the value of Qs is taken as the biggest value of all of them. The program will check the slenderness of the section in the following order:

· Angular

If
If

· Stem of T

If
If

· Rolled shapes

If
If

· Other sections

If
If

Where l is the element slenderness and

	for I sections
	for other sections

Factor Qa:

The calculation of factor Qa is an iterative process. Its procedure is the following:

1) An initial value of Q equal to Qs is taken.

2) With this value is calculated.

3) This value is taken to calculate

4) For elements with stiffened plates, the effective width b_e is calculated.

5) With b_e the effective area is calculated.

6) With the value of the effective area, Qa is calculated, and the process starts again.

· For a box section

· For other sections

If it is not within those limits, = b

With the values for each plate, the part that does not contribute [t·(b‑)] is subtracted from the area (where t is the plate thickness). Using this procedure, the effective area is calculated.

Finally, with Qs and Qa, Q is calculated, and is obtained.

Output results are written in the CivilFEM results file (.CRCF).

7.2.9. Compressive Strength for Flexural-Torsional Buckling

This type of check can be carried out for compact sections as well as for noncompact or slender sections. The steps for these three cases are as follows:

Nominal compressive strength,:

c) for

(b) for

Where:

Factor Q for compact and noncompact sections is 1. Nevertheless, for slender sections, the Q factor has a particular procedure of calculation. Such procedure is equal to the one previously described.

The elastic stress for critical torsional buckling or flexural-torsional buckling is calculated as the lowest root of the following third degree equation, in which the axis have been changed to adapt to the CivilFEM normal axis:

Where:

	Effective length factor for torsional buckling.
G	Shear modulus (MPa).
	Warping constant (mm⁶).
J	Torsional constant (mm⁴).
	Moments of inertia about the principal axis (mm⁴).
	Coordinates of shear center with respect to the center of gravity (mm).

where:

A	Cross-sectional area of member.
l	Unbraced length.
	Effective length factor, in the z and y directions.
	Radii of gyration about the principal axes.
	Polar radius of gyration about the shear center.

In this formula, CivilFEM principal axes are used. If the CivilFEM axes are the principal axes ±5º sexagesimal degrees, and are calculated with respect to the Y and Z-axes of CivilFEM. If this is not the case (angular shapes, for example) axes U and V will be used as principal axes, with U as the axis with higher inertia.

The torsional inertia (Ixx in CivilFEM, J in AISC 13^TH Edition) is calculated for CivilFEM sections, but not for captured sections. Therefore the user will have to introduce this parameter in the mechanical properties of CivilFEM.

Output results are written in the CivilFEM results file (.CRCF).

7.2.10. Compressive Strength for Flexure

Chapter F is only applicable to members subject to simple bending about one principal axis.

The design flexural strength,, and the allowable flexural strength, , shall be determined as follows:

For all provisions: = 0.90 (LRFD) = 1.67 (ASD)

Where is the lowest value of four checks according to sections F2 through F12:

a) Yielding

b) Lateral-torsional buckling

c) Flange local buckling

d) Web local buckling

The value of the nominal flexural strength with the following considerations:

For compact sections, if Lb < Lp only yielding of steel will be checked.
For T sections, and other compact sections, only yielding and torsional buckling will be checked.
The case of lateral-torsional buckling does not apply to sections loaded on the minor axis of inertia nor box or square sections.
The case of lateral-torsional buckling only applies for sections with double symmetry, channel and T sections. Therefore the rest of sections will be checked for torsion plus combined loads and will not be checked under flexure.
For slender sections, the code contemplates the following cases:

Shape	Limit State	Mr	Fcr	l	lp	lr
I, C loaded in the axis of higher inertia.	LTB
	FLB		rolled welded		Class B4.1	Class B4.1
	WLB		N.A.		Class B4.1	Class B4.1

Shape	Limit State	Mr	Fcr	l	lp	lr
I, C loaded in the axis of lower inertia.	LTB	N.A.	N.A.	N.A.	N.A.	N.A.
	FLB				Class B4.1	Class B4.1
	WLB	N.A.	N.A.	N.A.	N.A.	N.A.

Shape	Limit State	Mr	Fcr	l	lp	lr
Box	LTB
	FLB				Class B4.1	Class B4.1
	WLB		N.A.		Class B4.1	Class B4.1

Shape	Limit State	Mr	Fcr	l	lp	lr	Notes
Pipe	LTB	NA	NA	NA	NA	NA	Limited by Class B4.1
	FLB	Slender: Non-compact:			Class B4.1	Class B4.1
	WLB	NA	NA	NA	NA	NA

Shape	Limit State	Mr	Fcr	l	lp	lr
T, loaded in web plane	LTB		N.A.	N.A.	N.A.	N.A.
	FLB	N.A.	N.A.	N.A.	N.A.	N.A.
	WLB	N.A.	N.A.	N.A.	N.A.	N.A.

Where:

(positive sign if the stem is under tension, negative if it is under compression)

In T sections: stem in tension; stem in compression.

For slender webs the nominal flexural strength is the minimum of the following checks:

tension-flange yield
compression flange buckling

The first check uses the following formula:

where:

	Section modulus referred to tension flange.
	Yield strength of tension flange.

The second check uses the following formula:

where:

The critical stress depends upon different slenderness parameters such as l, , and in the following way:

For
For
For

The slenderness values have to be calculated for the following limit states:

Lateral torsional buckling

(International System units)

is the radius of gyration of compression flange plus one third of the compression portion of the web (mm).

By default, the program takes a conservative value of .

Flange local buckling

(IS units)

where:

and

Between these two slenderness, the program will choose values the value that produces a lower critical stress.

Output results are written in the CivilFEM results file (.CRCF).

7.2.11. Checking of Members for Shear (Chapter G)

The design shear strength, , and the allowable shear strength, , shall be determined as follows:

For all provisions: = 0.90 (LRFD) = 1.67 (ASD)

According to the limit states of shear yielding and shear buckling, the nominal shear strength, , of unstiffened webs is:

For webs of rolled I-shaped members with :

= 1.00 (LRFD) = 1.50 (ASD)

= 1.0 (web shear coefficient)

For webs of all other doubly symmetric shapes and singly symmetric shapes and channels is determined as follows:

= 1.0

Where is the overall depth times the web thickness.

It is assumed that there are no stiffeners; therefore, the web plate buckling coefficient will be calculated as a constant equal to 5.0.

Output results are written in the CivilFEM results file (.CRCF).

7.2.12. Checking of Members for Combined Flexure and Axial Tension / Compression (Chapter H)

For this check, it is first necessary to determine the value of Mn. This value comes into play in the checking of formulas. The value of M_n, will be calculated in the same way as members subjected to flexure; thus, the nominal flexure strength () is the minimum of four checks:

1. Yielding

2. Lateral-torsional buckling

3. Flange local buckling

4. Web local buckling

In the case of having bending plus tension or bending plus compression, the interaction between flexure and axial force is limited by the following equations:

(a) For

(H1-1a)

(b) For

(H1-1b)

If the axial force is tension:

	Required tensile strength (N).
	Available tensile strength (N): (LRFD) or (ASD)
	Required flexural strength (N·mm).
	Available flexural strength (N·mm): Design: (LRFD) or Allowable: (ASD)
y	Strong axis bending.
z	Weak axis bending.
	Resistance factor for tension (Sect.D2)
	Resistance factor for flexure = 0.90
	Safety factor for tension (Sect D2)
	Safety factor for flexure = 1.67

If the axial force is compression:

	Required compressive strength (N).
	Available compressive strength (N): Design: (LRFD) or Allowable: (ASD)
	Required flexural strength (N·mm).
	Available flexural strength (N·mm): Design: (LRFD) or Allowable: (ASD)
Y	Strong axis of bending.
Z	Weak axis of bending.
	Resistance factor for compression =0.90
	Resistance factor for flexure = 0.90
	Safety factor for compression =1.67
	Safety factor for flexure = 1.67

The following checks are carried out by CivilFEM:

Axial force and flexural buckling
Bending moment Z direction
Bending moment Y direction

If one of these checks do not meet the code requirements, it will not be possible to check the member under flexure plus tension / compression.

Output results are written in the CivilFEM results file (.CRCF).

7.2.13. Checking of Members for Combined Torsion, Flexure, Shear and/or Axial Force (Chapter H)

The design torsional strength, f_TT_n , and the allowable torsional strength, T_n/Ω_T, shall be the lowest value obtained according to the limit states of yielding under normal stress, shear yielding under shear stress or buckling, determined as follows:

= 0.90 (LRFD) = 1.67 (ASD)

· For the limit state of yielding, under normal stress:

· For the limit state of yielding, under shear stress:

· For the limit state of buckling:

- Where is calculated

Output results are written in the CivilFEM results file (.CRCF).

7.3. Steel Structures According to British Standard 5950

The British Standard BS 5950:2000 supersedes BS 5950:1985, which has been withdrawn. BS 5950:2000 is the British Standard for the structural use of steelwork in building, widely in use in regions which experience or have experienced British influence. The purpose of this manual is to define the reach and method of implementing this method within CivilFEM.

The types of analyses considered in this standard have been developed according to the ultimate limit state in agreement with the simple and continuous design methods. Semi-continuous design and experimental verification fall beyond the scope of this specification.

The applicable cross sections for checking procedures include rolled or welded sections subjected to axial forces, shear, and bending in 2D and 3D as well as solid sections subjected to the aforementioned forces.

The calculations made by CivilFEM correspond to the design guidelines of British Standard 5950:2000 Structural use of steelwork in building: Part 1. Code of practice for design – Rolled and welded sections.

7.3.1 Checking Types

With CivilFEM it is possible to accomplish the following checking and analysis types:

Checking of sections subjected to:

- Bending	British Standard 5950 (2000) apt. 4.2
- Bending and Shear	British Standard 5950 (2000) apt. 4.2
- Lateral Torsional Buckling	British Standard 5950 (2000) apt. 4.3
- Axial Tension	British Standard 5950 (2000) apt. 4.6
- Axial Compression	British Standard 5950 (2000) apt. 4.7
- Axial Tension with Moments	British Standard 5950 (2000) apt. 4.8.2
- Axial Compression with Moments	British Standard 5950 (2000) apt. 4.8.3

7.3.2 Reference Axis

With performing checks according to BS 5950:2000, CivilFEM includes three different coordinate reference systems. All of these systems are right-handed:

1. CivilFEM Reference Axes ().

2. Cross-Section Reference Axes (, , ).

3. BS 5950:2000 Reference Axes (Code Axes), ().

For the BS 5950:2000 axes axes system:

The origin matches to the CivilFEM axes origin.

X_EC3 axis coincides with CivilFEM X-axis.

Y_EC3 axis is the relevant axis for bending and its orientation is defined by the user (in steel check process).

Z_EC3 axis is perpendicular to the plane defined by X and Y axis, to ensure a right-handed system.

7.3.3 Material Properties

BS 5950:2000 uses the following material properties in its checks:

Description	Properties, symbol
Yield strength
Tensile strength
Design strength	p_y(table 9 of BS 5950-1:2000 and table 3 of EN10113-2:1993)
Material strength factor	= 1
Modulus of elasticity	E = 205 kN/mm²
Shear Modulus
Poisson’s ratio	= 0.3
Coefficient of linear thermal expansion
Effective net area coefficient	(BS 5950-1:2000 – Section 3.4.3)
Constant є

The code uses other safety factors () which depend on the type of loads and which must be used when performing load combinations.

7.3.4 Section Data

BS 5950:2000 considers the following data set for the cross section:

Gross section data

Net section data

Effective section data

Data concerning the section and element class.

Gross section data correspond to the nominal properties of the cross-section.

From the net section, the net area and the effective net area are considered. The net area is calculated by subtracting the area of holes for screws, rivets and other holes from the gross section area, taking into account the deduction for fastener holes according to section 3.4.4 of the code (see figures 3 and 4 of the code). The area of holes is introduced within the structural steel code properties.

The effective net area is obtained from the net area, multiplying it by a coefficient which depends on type of steel used. This coefficient is calculated by the program and stored together with the material properties.

Effective section data are obtained in the checking process according to the effective width method (Sect. 3.6 of BS 5950:2000). This method discounts the non-resistance zones for local buckling in class 4 cross-sections. For cross-sections of a lower class, this method does not reduce the section because of local buckling.

As an alternative method for slender cross sections calculation, a reduced design strength () may be calculated at which the cross section would be class 3 (section 3.6.5 of the code).

Section and element class data are obtained using tables 11 and 12 of BS 5950:2000 (section 3.5.2). The classification of each element is based on its width to thickness ratio and according to section type (hot-rolled or welded), element type (web or flange) and position (internal or external element). CivilFEM assumes the section class as the largest from all the elements (least favorable).

The initial required data for the BS 5950:2000 module includes the gross section data in user units and the CivilFEM axis or section axis (see the section corresponding to Reference axis in beam sections in Chapter 5 of this Manual). The data are then properly converted from the section’s axis into the BS 5950:2000 axis and the results are given in the code axis. The program calculates the effective and net section data and the class data and stores them into CivilFEM’s results file in user units and in the CivilFEM coordinate system.

The section data used in BS 5950:2000 is shown in the following tables:

I.- Section Dimensions

Description

Data

Input data:

1.- Height

2.- Web thickness

3.- Flanges thickness

4.- Flanges width

5.- Distance between flanges

6.- Radius of fillet (Rolled shapes)

7.- Toe radius (Rolled shapes)

8.- Weld throat thickness (Welded shapes)

9.- Web free depth

r₁

r₂

Output data

(Nothing)

I.- Gross Section Resistant Properties

Description	Data
Input: 1.- Area 2.- Moments of inertia for torsion 3.- Moments of inertia for bending 4.- Product of inertia 5.- Elastic resistant modulus 6.- Plastic resistant modulus 7.- Radius of gyration 8.- Coordinates of the center of gravity 9.- Distance between GC and SC in X and in Y 10.- Distance CG to shear center along Y axis 11.- Distance CG to shear center along X axis 12.- Warping Constant 13.- Shear resistant areas 14.- Torsional resistant modulus	A It Ixx, Iyy Ixy Wx, Wy Wpx, Wpy ix, iy Ymn, Ymx, Xmn, Xmx Xm, Ym Ys Xs Iw Yws, Xws Zwt
Output Data: 1.- Shear area for major axis (X) 2.- Sv parameter for major axis (X) 3.- Shear area for minor axis (Y) 4.- Sv parameter for minor axis (X) 5.- Critical shear strength of web panel for major axis 6.- Critical shear strength of web panel for minor axis 7.- Y coordinate of plastic center 8.- X coordinate of plastic center	Avx Svx Avy Svy Vcrx Vcry Yp Xp
* The section properties listed here in are related to the BS coordinate system (X_BS, Y_BS, Z_BS)

III.- Net section data

Description	Data
Input data: AHOLES*
Output data: 1.- Net area 2.- Effective net area	Ant Aneff
= A - AHOLES = with £ A (Gross area)

* Deduction for holes are introduced as a code property

IV.- Effective section data

Description

Data

Input data:

None

Output data:

1.- Effective Area

2.- Moments of inertia for torsion

3.- Moments of inertia for Y bending

4.- Moments of inertia for X bending

5.- Elastic resistant Y modulus

6.- Elastic resistant X modulus

7.- Plastic resistant Y modulus

8.- Plastic resistant X modulus

Aeff

Iyyeff

Ixxeff

Wyeff

Wxeff

Wpyeff

Wpxeff

9.- Section class

10.- Web class for shear buckling

Cls

ClsAlm

V.- Section element data

Description

Data

Input data:

1.- Number of elements

2.- Element type: flange or web (for the relevant axis of bending)

3.- Union condition at the ends: free or fixed

4.- Element thickness

5.- Coordinates of the extreme points of the element (using Section axes)

Pltype

Cp1, Cp2

Yp1, Yp2,

Zp1, Zp2

Output data:

6.- Element class

7.- Reduction factor (for class 4 section- alternative method)

8.- Web Class

f_r

Webclass

7.3.5 Structural steel code properties

For BS 5950:2000 check, besides the section properties, more data are needed for buckling checks. These data are shown in the following table.

Description

Data

Article

Input data:

1.- Unbraced length of member

2.- Compression buckling factor for X axis

3.- Compression buckling factor for Y axis

4.- Lateral torsional buckling factor for X axis

5.- Lateral torsional buckling factor for Y axis

6.- Factors by which multiply “L” to found the length between restrictions in planes xz and yz, respectively

7.- Robertson Constant

8.- Equivalent uniform moment factor for major axis flexural bending

9.- Equivalent uniform moment factor for minor axis flexural bending

10.- Equivalent uniform moment factor for lateral torsional buckling

11.- Depth of the compression flanges lip

12.- Intermediate stiffeners depth

11.- CivilFEM Axis which is the X axis in BS 5950:2000

0: Not defined

1: -Z CivilFEM

2: +Y CivilFEM

3: +Z CivilFEM

4: -Y CivilFEM

Kcx

Kcy
KLtx

Klty

Cfbuckx, Cfbucky

CteRob

mlt

d/a

CHCKAXIS

Section 4.7.3

Section 4.7.3
Section 4.3.5

Section 4.3.5

Appendix C.2

Section 4.8.3

Section 4.3.6.6

Section 4.3.6.7

Section 4.4.5

7.3.6 Checking Process

The steps for the checking process are the following ones:

4. Read the checking type requested by the user.

5. Read the CivilFEM axis to be considered as the principal axis for bending, so that it coincides with the X-axis of BS5950. In CivilFEM, by default, the principal axis for bending that coincides with the +X axis of BS 5950:2000 is the –Z-axis.

6. The following operations are carried out for each selected element:

a. Obtain material properties corresponding to the element, stored in CivilFEM database, and calculate the rest of the properties needed for checking:
Properties obtained from CivilFEM database:

Elasticity modulus	E
Poisson’s ratio	
Yield strength
Ultimate strength
Design strength
Ke parameter
Safety factor

Calculated properties:

Shear Modulus:

Epsilon, material coefficient:

( in)

b. Obtain the cross-section data corresponding to the element.

c. Determination of section class.

d. There are two calculation procedures for slender cross sections (class 4) that may be may chosen by the user:

1. Initialize reduction factors of section plates and the effective cross section properties calculation.

2. Calculate a reduced design strength that should be used in place of the nominal design strength (section 3.6.5 of the code).

e. Obtain forces acting on the section (FX,).

f. Specific section checking according to the type of external load.

g. Writing of results, which will be stored in the results file .CRCF

7.3.7 Section Class and Reduction Factor Calculation.

According to BS 5950:2000, the sections are made up of different elements, which can be classified according to:

a) The way they work:

Webs and flanges in the X and Y axes, depending on which is the principal bending axis.

b) Their relation to the other elements:

Internal or outside elements

The sections of the shapes included in the program libraries contain this information for each element. CivilFEM classifies elements as either flange or web according to each axis and gives the element union condition at each end. The ends can be classified as fixed or free (i.e. an end is called fixed if it is in contact with another plate and free if it is not).

For checking the structure for safety, BS 5950:2000 classifies cross sections into four different classes to determine whether local buckling influences their capacity (section 3.5.2):

Class 1	Plastic cross sections are those in which a plastic hinge can be developed with sufficient rotation capacity to allow redistribution of moments within the structure.
Class 2	Compact cross sections are those in which the full plastic moment capacity can be developed but local buckling may prevent development of a plastic hinge with sufficient rotation capacity to permit plastic design.
Class 3	Semi-compact sections are those in which the stress at the extreme fibers can reach the design strength but local buckling may prevent the development of the full plastic moment.
Class 4	Slender sections are those which contain slender elements subject to compression due to moment or axial load. Local buckling may prevent the stress in a slender section from reaching the design strength.

The cross-section class is the highest (least favorable) class of its elements: flanges and webs. The class of each element is first determined according to the limits of tables 11 and 12 of BS 5950:2000. According to these tables, the class of an element depends on:

1. The width to thickness ratio. The dimensions of the elements (b, d, t, T) should be
taken as shown in Figure 5 of the code.

Rd = Width / Thickness

2. The limits of this ratio, according to the type of section, element (flange or web) and position (internal or outside). Elements that do not meet the limits for class 3 semi-compact are classified as class 4. The limits are the following (refer to figure 5 of the code for dimensions):

· Sections other than circular hollow sections (CHS) and rectangular hollow section (RHS):

Compression element	Class 1	Class 2	Class 3
Outstand rolled flange Angle, compression due to bending
Angle, axial compression	0	0	y
Outstand welded flange
Internal flange, compression due to bending
Internal flange, axial compression	0	0
Web of an I, H or box section, compression due to bending		For For but
Web of an I, H or box section, axial compression	0	0
Web of a channel
Stem of a T section, rolled or cut from a rolled I or H section

· Circular hollow sections (CHS):

Circular hollow sections are classified as having only one element and the width to thickness ratio () is determined as follows:

D = Diameter.

t = Wall thickness.

	Class 1	Class 2	Class 3
Compression due to bending
Axial compression	0	0

· Rectangular hollow sections hot finished (HF RHS):

Compression element	Class 1	Class 2	Class 3
Flange, compression due to bending
Flange, axial compression	0	0
Web, compression due to bending
Web, axial compression	0	0

· Rectangular hollow sections cold formed (CF RHS):

Compression element	Class 1	Class 2	Class 3
Flange, compression due to bending
Flange, axial compression	0	0
Web, compression due to bending
Web, axial compression	0	0

* The dimensions b and t are defined in figure 5 of the code.

Notes:

1. The classification of the elements according to the way they work (webs or flanges) is included in the program section library. In other cases the user can specify it or, by default, the program will automatically determine it as a function of the angle a with respect to the principal axis of bending, following the below criterion:

ForaWeb

ForaFlange

2. Apart from the type of section, type and position of the element, the limits of the width to thickness ratio also depend on the material parameter  and on the parameters and, which translates into the following relationships

a) For I or H-sections with equal flanges:

with

b) For I or H-sections with unequal flanges:

The program deals with this type of sections as generic sections for which the values of r₁ and are the following:

= 1

c) Rectangular hollow sections or welded box sections with equal flanges:

with

Where:

	Gross section area.
	Width of the compression flange.
	Width of the tension flange.
d	Web depth.
	Axial compression (negative for tension).
	Maximum compressive stress in the web (figure 7 of the code).
	Minimum compressive stress in the web (figure 7 of the code).
	Design strength of the flanges.
	Design strength of the web (but ).
	Thickness of the compression flange.
	Thickness of the tension flange.
t	Web thickness.

3. The webs are also classified for shear buckling resistance according to the following criteria:

a. For rolled sections with Rd

b. For welded sections with Rd

In these cases, the shear buckling resistance should be checked according to the section 4.4.5 of the BS 5950:2000.

4. Class 3 semi-compact sections are designed using the effective plastic modulus
according to section 3.5.6 and followings of BS 5950:2000.

7.3.7.1 Procedures for Slender Sections (Class 4)

BS 5950:2000 accepts two different procedures for designing slender cross sections.

a) Effective section properties calculation (Sections 3.6.2, 3.6.3, 3.6.4)

The local buckling resistance of class 4 slender cross sections is performed by adopting effective section properties. The width of the compression elements are reduced in such way that the effective width of a class 4 section will be the same as the maximum width for a class 3 section.

For outstand elements, the reduction is applied to its free end, and for internal elements, the reduction is applied to the non-effective zone, comprised of the central portion of the element with two equal portions of effective zone at the ends.

For each section element, the program calculates two reduction factors
and to determine the effective width at each element end. These factors relate the width of the effective zone at each end with the width of the plate.

Effective_width_end1 = plate_

Effective_ width _end 2 = plate_

Effective area calculation ()

The effective area is determined from the effective cross section as shown in Figure 8a of the code (section 3.6.2.2).

Effective modulus calculation ()

The effective modulus is determined from the effective cross section as shown in Figure 8b of the code (section 3.6.2.3).

For cross sections with slender webs, the effective modulus is determined from the effective cross section as shown in Figure 9 of the code (section 3.6.2.4).

Circular Hollow Sections

For circular hollow sections, the effective modulus and the effective area is determined according to the section 3.6.6 of BS 5950:2000.

b) Alternative Method (section 3.6.5)

As an alternative to the method previously described, a reduced design strength r_yr is calculated as if the cross section were a class 3 semi-compact. This reduced design strength is used in place of r_y in the checks of section capacity and member buckling resistance. The reduction factor f_r is calculated for each section 4 element according to the below expression:

Where:

b₃	Limiting value for a class 3 section according to the tables 11 and 12 of the code.
b	Width to thickness ratio for each element.

7.3.8 Checking of Bending Moment and Shear Force (BS Article 4.2)

1. Forces and moments selection
The forces and moments considered for this checking type are:

= FZ or FY	Design value of the shear force perpendicular to the relevant axis of bending.
= MY or MZ	Design value of the bending moment along the relevant axis of bending.

2. Class determination and calculation either of the effective section properties or the design strength reduction factor for slender sections (depending on the selected method).

3. Criteria calculation

In members subjected to bending moment and shear force, three conditions should be checked:

3.1. Shear checking (Article 4.2.3 of BS 5950:2000)

The first condition to be checked is the shear criteria at each section:

Where:

Design value of the shear capacity:

Design strength of the material.

Shear area.

Shear Area Calculation ()

According to section 4.2.3 the shear area is calculated as follows:

Shape	Shear Area
Rolled I, H and channel sections, load parallel to web.
Welded I sections, load parallel to web.
Solid bars and plates.
Rectangular hollow sections, load parallel to webs.
Welded box sections.
Circular hollow sections.
Any other case.

where:

t	Total web thickness.
B	Breadth.
D	Overall depth.
d	Depth of the web.
A	Area of the section.
	Area of the rectilinear element of the section which has the largest dimension in the direction parallel to the load:

In the case of biaxial bending, it is necessary to consider both shear areas, perpendicular to both the Standard’s X- and Y-axis.

3.2. Shear buckling resistance of thin webs (Article 4.4.5)

The shear buckling resistance should be checked if the ratio d/t of the web exceeds 70·e for a rolled section or 62·e for welded sections. It should satisfy the following criterion:

Where:

	Shear buckling resistance (summation extended to all section webs).
	Critical shear strength.
d	Depth of the web.
t	Thickness of the web.

The critical shear strength is obtained following the Appendix H.1 of the code

where and a is the distance between stiffeners. The ratio

d/a may be introduced by the user. By default, d/a = 1.

If the web of the section is not slender (d/t < 70·e for rolled sections and
d/t < 62·e for welded sections):

Crt_PV = 0

3.3. Bending moment check

Besides the shear checking, the following condition at each section is checked (Article 4.2.5 of BS 5950:2000):

Where:

Moment capacity.

Stress reduction factor (only for the alternative method for slender sections).

Bending resistant modulus.

The reduction of the bending resistant modulus due to the effect of shear load is only applied if the shear load is above 60% of shear capacity of the section:

The bending resistant modulus is obtained by the following expressions:

1. If

a. For plastic or compact sections:

b. For semi-compact sections:

c. For slender sections:

2. If

a. For plastic or compact sections:

b. For semi-compact sections:

c. For slender sections:

Where:

Z	Elastic resistant modulus of the section.
	Effective elastic modulus.
S	Plastic resistant modulus of the section.
	Effective plastic modulus.
	Plastic reduced modulus due to the effect of shear force.

Sv Parameter Calculation

The calculation is done following the expression below:

Where:

Plastic resistant modulus of the section: S

Plastic modulus of the section remaining after deduction

of the shear area:

4. Calculation of the total criterion:

CRT_TOT = Max (Crt_V, Crt_PV, Crt_M)

5. Output results are written in the CivilFEM results file (.CRCF). Checking results: criteria and variables are described in the following table:

Result	Concepts	Articles	Description
MX			Design value of the bending moment
MC		4.2.5	Moment capacity
FV			Design value of the shear force
PV		4.2.3	Design value of the shear capacity
CRT_V		4.2.3	Shear criterion
CRT_PV		4.4.5	Buckling web criterion
CRT_M		4.2.5	Bending criterion
CRT_TOT			BS Global criterion
CLASS		3.5.2	Section class
WEBCLASS		3.5.2	Webs' Class
MDF		4.2.5	Plastic or elastic modulus of the section
VW		4.4.5	Shear buckling resistance

7.3.9 Checking of Lateral Torsional Buckling Resistance (BS Article 4.3)

1. Forces and moments selection.
The forces and moments considered in this check are:

= MY or MZ

Design value of the bending moment about the relevant axis of bending.

2. Class determination.

3. Criteria calculation.

Resistance to lateral-torsional buckling need not be checked separately for the following cases:

· Bending about the minor axis

· Circular hollow sections (CHS), square RHS or circular or square solid bars

· I, H, Channel or Box sections, if equivalent slenderness does not exceed the limiting equivalent slenderness

· RHS, unless the slenderness exceeds the limiting value given in Table 15 of the code for the relevant value D/B.

D/B Depth / Width	Limiting value of λ
1.25
1.33
1.4
1.44
1.5
1.67
1.75
1.8
2
2.5
3
4

When checking for lateral torsional buckling of beams, the criterion shall be taken as:

Where:

	Lateral torsional buckling resistance moment.
	Equivalent uniform moment factor for lateral torsional buckling. This can be introduced according to the table 18 of the code
	Maximum major axis bending moment.

3.1 Determination of the buckling resistance moment Mb (Article 4.3.6.4)

The value of may be determined from the following:

· For plastic and compact sections:

· For semi-compact sections:

· For slender sections:

Where is the bending strength.

If the equivalent slenderness is less than or equal to the limiting slenderness for the relevant design strength given in the tables 16 and 17 of the code, then should be taken as equal to and no considerations for lateral torsional buckling will be necessary.

Otherwise the bending strength is obtained from the formula given in Appendix B.2.1 of the code:

For

Where h_LT is the Perry coefficient

The Perry coefficient for lateral torsional buckling should be taken as follows:

a) For rolled sections:

con

b) For welded sections:

If
If
If
If

Where:

	Limiting equivalent slenderness:
	Robertson constant, taken as 0.007.
	Equivalent slenderness.

A. Equivalent Slenderness for I, H and Channel Sections

The equivalent slenderness is taken as follows:

The ratio depends on the section class:

· For class 1 or 2 sections:

· For class 3 sections:

· For class 4 sections:

The buckling parameter u and the torsional index x are calculated as follows:

· For I and H sections

· For Channel sections

Where:

J	Torsion constant (mechanical property of the section).
	Thickness of the compression flange.
	Thickness of the tension flange.
	Plastic modulus about the major axis.
	Moment of inertia about the major axis (mechanical property of the section).
	Moment of inertia about the minor axis (mechanical property of the section).
A	Cross sectional area (mechanical property of the section).
H	Warping constant (mechanical property of the section).

The slenderness factor (v parameter) is given by:

Where:

	Moment of area of the compression flange about the minor axis of the section.
	Moment of area of the tension flange about the minor axis of the section.
	Monosymmetry index, for I and T sections with lipped flanges.

The monosymmetry index is calculated as follows:

for

Where:

D	Overall depth of the section (mechanical property of the section).
DL	Depth of the lip. By default DL=0.

B. Equivalent slenderness determination for Box Sections including RHS (Appendix B.2.6)

The equivalent slenderness, , for box sections is taken directly from the expression below:

C. Equivalent slenderness determination for T sections (Appendix B.2.8)

The equivalent slenderness, , for T sections is obtained from the following:

a) If = : Lateral torsional buckling does not occur and

b) If : Lateral torsional buckling occurs about the x-x axis and is given by:

c) If: Lateral torsional buckling occurs about the x-x axis and is given by:

D. Equivalent slenderness determination for Equal Angle sections (Appendix B.2.9.1)

The equivalent slenderness, , for equal angle sections is obtained from the following:

E. Equivalent slenderness determination for Unequal Angle sections (Appendix B.2.9.2)

The equivalent slenderness, , for unequal angle sections is obtained from the following:

The monosymmetry index for an unequal angle is taken as positive when the short leg is in compression and negative when the long leg is in compression.

is the coordinate of the shear center along the v-v axis.

Result	Concepts	Articles	Description
MB		4.3.6	Buckling resistance moment
UMLT		4.3.6	Equivalent uniform moment
M	m		Equivalent uniform moment factor
LAMBDA	Lambda	B.2	Slenderness
LAMBDALT	LambdaLT	B.2	Equivalent slenderness
LAMBDALO	LambdaLO	B.2	Limiting equivalent slenderness
CRT_TOT		4.3.6	Global criterion
CLASS		3.5.2	Section class
WEBCLASS		3.5.2	Web class

7.3.10 Checking of Members in Axial Tension (BS Article 4.6)

1. Forces and moments selection.
The forces and moments considered for this checking type are:

F = FX

Design value of the axial force (positive if tensile, element not processed if compressive).

2. Class determination.

3. Criteria calculation.
For members under axial tension, the general criterion Crt_TOT is checked at each section. This criterion coincides with the axial criterion Crt_N:

Where Pt is the tension capacity:

4. Output results are written in the CivilFEM results file (.CRCF). Checking results: criteria and variables are described in the following table:

Result	Concepts	Articles	Description
F	F	4.6.1	Tension Force
PT		4.6.1	Tension capacity
CRT_TOT		4.6.1	Global criterion

7.3.11 Checking of Members in Axial Compression (BS Article 4.7)

1. Forces and moments selection.
The forces and moments considered for this checking type are:

F = FX

Design value of the axial force (negative if it is compressive). If it is tensile, the element is not processed.

2. Class determination.

3. Criteria calculation.
For members under axial compression, the general criterion Crt_TOT is checked at each section. This criterion coincides with the axial compression criterion Crt_CB:

Where:

F	Axial compression force.
	Compressive strength for buckling.

The compressive strength is determined according to the article 4.7.4 of BS 5950:2000:

· For class 1, 2 or 3 sections:

· For class 4 sections:

Where:

	Gross sectional area.
	Effective cross sectional area.
	Compressive strength.
	Compressive strength for a reduced slenderness of .

The compressive strength may be obtained from (See Appendix C):

Where:

	Design strength (reduced by 20N/mm² for welded I, H or box sections).
	Euler strength:
E	Material elasticity modulus.
	Slenderness:
	Radius of gyration about the relevant axis.
	Effective buckling length:
L	Actual length of the member.
and	Correction factors of buckling lengths for planes XZ and YZ.

The Perry coefficient η for flexural buckling under load should be taken as follows (Appendix C.2):

Where is the limiting slenderness:

The constant a (Robertson constant) is determined by the program from the type of section and buckling axis, according to the table 23 of the BS 5950:2000. Therefore, if the user introduces a value for this constant in member properties, the program will give precedence to the user’s value.

a=	2.0 for curve (a)
a=	3.5 for curve (b)
a=	5.5 for curve (c)
a=	8.0 for curve (d)

To distinguish between I and H shapes the program follows the criteria below:

I shapes if

H shapes if

4. Output results are written in the CivilFEM results file (.CRCF). Checking results: criteria and variables are described in the following table.

Result	Concepts	Articles	Description
F	F	4.7	Compression Force
PC		4.7.4	Compression capacity
RHOC		4.7.5	Compression Resistance
LAMBDA	Lambda	4.7.2	Slenderness
LAMBDA0	Lambda0	C.2	Limiting slenderness
PERRYFCT	NU	C.2	Perry factor
ROBERSTS	a	C.2	Robertson constant
CRT_TOT		4.7	Global criterion
WEBCLASS		3.5.2	Web class
CLASS		3.5.2	Section class

7.3.12 Tension Members with Moments (BS Article 4.8.2)

1. Forces and moments selection.
The forces and moments considered for this checking type are:

F = FX	Design value of the axial force.
= MY or MZ	Design value of the bending moment along the primary bending axis.
= MZ or MY	Design value of the bending moment about the secondary bending axis.

2. Class determination.

3. Criteria calculation.

For members subjected to an axial tension force and bending moments, each section should be checked according the same conditions for members subjected to a shear force and bending moments (see section 9.8.3 of this manual).

Therefore, for this type of checking, the following conditions are checked:

3.1 Shear checking in both directions

Where and are the shear forces about X and Y axis, and and the shear capacity about X and Y axis.

3.2 Shear buckling resistance of shear webs

Where Vwx and Vwy are the shear buckling resistance about X and Y axis, respectively.

3.3 Checking of axial force and bending moments

Each section is checked according to the following condition:

Equivalent to:

Crt_CMP = Crt_AXL + Crt_Mx + Crt_My £ 1

Where:

F	Axial force.
	Bending moment about major axis.
	Bending moment about minor axis.
	Effective net area of the section.
	Design strength of the material.
	Moment capacity about major axis.
	Moment capacity about minor axis.

and are calculated according to the Article 4.2.5 of BS 5950:2000.

For this checking type (moments on both directions), the shear area, the plastic modulus and the parameter are calculated with respect to both directions (X and Y axis).

3.3 Checking of global criterion

CRT_TOT = Max (Crt_CMP, Crt_VX, Crt_VPX, Crt_VY, Crt_VPY)

4. Output results are written in the CivilFEM results file (.CRCF). Checking results: criteria and variables are described in the following table.

Result	Concepts	Articles	Description
F	F		Axial tension force
MX		4.2.5	Bending moment about major axis
MY		4.2.5	Bending moment about minor axis
FVX			Shear force about major axis
FVY			Shear force about minor axis
PVX		4.2.3	Shear capacity about major axis
PVY		4.2.3	Shear capacity about minor axis
PT		4.6.1	Axial Tension Capacity
MCX		4.2.5	Moment capacity about major axis
MCY		4.2.5	Moment capacity about minor axis
CRT_AXL		4.6.1	Axial Criterion
CRT_VX		4.2.3	Shear Criterion about major axis
CRT_VY		4.2.3	Shear Criterion about minor axis
CRT_MX		4.2.5	Bending Criterion about major axis
CRT_MY		4.2.5	Bending Criterion about minor axis
CRT_PVX		4.4.5	Buckling web Criterion about major axis
CRT_PVY		4.4.5	Buckling web Criterion about minor axis
CRT_CMP	Crt_AXL + Crt_MX + Crt_MY	4.8.2	Axial + moments Criterion
SVX		4.2.6	Sv parameter for major axis
SVY		4.2.6	Sv parameter for minor axis
CRT_TOT		4.8.2	Global criterion
AVX		4.2.3	Shear Area for major axis
AVY		4.2.3	Shear Area for minor axis
VWX		4.4.5	Shear buckling resistant for major axis
VWY		4.4.5	Shear buckling resistant for minor axis
MDFX		4.2.6	Resistant modulus for major axis
MDFY		4.2.6	Resistant modulus for minor axis
ZX		4.2.6	Elastic Modulus about major axis
SX		4.2.6	Plastic Modulus about major axis
ZY		4.2.6	Elastic Modulus about minor axis
SY		4.2.6	Plastic Modulus about minor axis
CLASS		3.5.2	Sections class
WEBCLASS		3.5.2	Web’s class

7.3.13 Compression Members with Moments (BS Article 4.8.3)

1. Forces and moments selection.
The forces and moments considered for this checking type are:

F = FX	Design value of the axial force.
= FY or FZ	Design value of the shear force perpendicular to the primary bending axis.
= FZ or FY	Design value of the shear force perpendicular to the secondary bending axis.
= MY or MZ	Design value of the bending moment along the primary bending axis.
= MZ or MY	Design value of the bending moment about the secondary bending axis.

2. Class determination.

3. Criteria calculation.

Compression members are checked for local capacity at the points of greatest bending and axial load. This capacity may be limited by either yielding or local buckling, depending on the section properties. The member is then checked for global buckling.
Therefore, for this type of checking, the following conditions are checked:

3.1 Local Capacity Check

3.1.1 Axial Criterion

Where:

Axial load

Compression capacity:

For class 1, 2 or 3 sections:

For class 4 sections:

3.1.2 Local criteria as for Tension Members with Moments

Bending criterion (major axis)= Crt_MX_L

Bending criterion (minor axis)= Crt_MY_L

Shear criterion about major axis= Crt_VX

Shear criterion about minor axis = Crt_VY

Buckling web Criterion about major axis = Crt_PVX

Buckling web Criterion about minor axis = Crt_PVY

3.1.3 Component Local Criterion

3.2 Overall Buckling Check

3.2.1 Axial Criterion (Buckling)

Where:

F	Design value of the axial compressive force.
	Compression resistance.
	Compresion resistance, considering buckling about the minor axis only: For class 1, 2 or 3 sections: For class 4 sections:
	Gross sectional area.
	Compressive strength obtained according article 4.7.5 of the code.

3.2.2 Bending Moment Criterion (primary axis)

Where:

	Equivalent uniform moment factor. By default .
	Equivalent uniform moment factor for lateral torsional buckling. By default .
	Bending moment about major axis.
	Buckling resistance moment according the article 4.3 of the code.
	Maximum major axis moment .

3.2.3 Bending Moment Criterion (secondary axis)

Where:

	Equivalent uniform moment factor. By default .
	Bending moment about minor axis.
	Elastic modulus about the minor axis (for slender class 4 sections is taken).

3.2.4 Component Global Criterion

3.3 Total Criterion

Crt_TOT=Max(Crt_CM_L,Crt_CM_O,Crt_VX, Crt_VPX, Crt_VY,Crt_VPY)

4. Output results are written in the CivilFEM results file (.CRCF). Checking results: criteria and variables are described in the following table.

TABLE	Concepts	Articles	Description
F	F		Design value of the axial compressive force
PC		4.7.4	Compression resistance
FVX			Shear force about major axis
MX			Bending moment about major axis
ZX		4.2.5	Elastic Modulus about major axis
SX		4.2.5	Plastic Modulus about major axis
SVX		4.2.5	Sv parameter for major axis
AVX		4.2.3	Shear Area for major axis
VWX		4.4.5	Shear buckling resistant for major axis
MDFX		4.2.5	Resistant modulus for major axis
PVX		4.2.3	Shear capacity about major axis
MCX		4.2.5	Moment capacity about major axis
FVY			Shear force about minor axis
MY			Bending moment about minor axis
ZY		4.2.5	Elastic Modulus about minor axis
SY		4.2.5	Plastic Modulus about minor axis
SVY		4.2.5	Sv parameter for minor axis
AVY		4.2.3	Shear Area for minor axis
VWY		4.4.5	Shear buckling resistant for minor axis
MDFY		4.2.5	Resistant modulus for minor axis
PVY		4.2.3	Shear capacity about minor axis
MCY		4.2.5	Moment capacity about minor axis
M	M	4.8.3.3	Equivalent uniform moment factor
LAMBDA	Lambda	4.3.7.5	Slenderness
LAMBDA0	Lambda0	C.2	Limiting slenderness
LAMBDALT	LambdaLT	4.3.7.5	Equivalent slenderness
LAMBDAL0	LambdaL0	B.2.4	Limiting equivalent slenderness
PERRYFCT	NU	C.2	Perry Factor
MB		4.3.7	Buckling resistance moment capacity
CRT_TOT	Max(Crt_CM_L, Crt_CM_O, Crt_VX, Crt_VY, ...)	4.8.3	Total Criterion
CRT_CM_L	Crt_AX_L + Crt_MX_L + Crt_MY_L	4.8.3	Local Axial + moments Criterion
CRT_CM_O	Crt_AX_O + Crt_MX_O + Crt_MY_O	4.8.3	Global Axial + moments Criterion
CRT_AX_L		4.8.3	Local axial criterion
CRT_MX_L		4.2.5	Local bending moment criterion about X axis
CRT_MY_L		4.2.5	Local bending moment criterion about Y axis
CRT_AX_O		4.8.3	Global axial criterion
CRT_MX_O		4.8.3	Global bending moment criterion about X axis
CRT_MY_O		4.8.3	Global bending moment criterion about Y axis
CRT_VX		4.2.3	Shear criterion about X axis
CRT_PVX		4.4.5	Buckling web Criterion about major axis
CRT_VY		4.2.3	Shear criterion about Y axis
CRT_PVY		4.4.5	Buckling web Criterion about minor axis
CLASS	Class	3.5.2	Section Class
WEBCLASS	Webclass	3.5.2	Web’s Class

7.4. Steel Structures According to ASME BPVC III Sub. NF

Steel structures checking according to ASME BPVC III Subsection NF in CivilFEM includes the checking of structures composed of welded or rolled shapes under axial forces, shear forces and bending moments in 3D.

The calculations performed by CivilFEM correspond to the provisions of this code according to the following sections:

1	Allowable Stresses
2	Stability and Slenderness and Width-Thickness Ratios

7.4.1 Checking Types

With CivilFEM it is possible to accomplish the following checking and analysis types:

Checking of sections (ASME NF-3322.1) subjected to:

Stress in Tension

Stress in Shear

Stress in Compression

Stress in Bending

Axial Compression and Bending

Axial Tension and Bending

Stability check (ASME NF-3322.2):

Maximum Slenderness Ratios

Width Ratios

7.4.2 Material Properties

The following material properties are used for checking according to ASME BPVC III Subsection NF:

Description	Property
Steel yield strength	(th)
Ultimate strength	(th)
Modulus of Elasticity	E

*th = plate thickness

Furthermore, although austenitic stainless steel is an intrinsic material property, it can be modified by changing the material property.

7.4.3 Section Data

The section data of the element must be included in the CivilFEM database. All geometrical and mechanical properties are automatically obtained when defining the cross section or capturing the solid section. The section data required for checking according to this code are listed below:

Data	Description
A	Area of the cross-section
	Moment of inertia about Y axis
	Moment of inertia about Z axis
	Product of inertia about YZ
Y	Coordinate Y of the considered fiber
Z	Coordinate Z of the considered fiber
	Radius of gyration about Y axis
	Radius of gyration about Z axis
	Shear area in Y
	Shear area in Z

From the net section, only the area is considered. This area is calculated by subtracting the holes for screws, rivets and other holes from the gross sectional area. The user should be aware that the code indicates the diameter used to calculate the area of holes is greater than the real diameter. The area of holes is introduced within the structural steel code properties.

In order to determine the effective net area of axially loaded tension members, the reduction coefficient Ct must be set (parameter). By default, Ct=0.75.

7.4.4 Structural Steel Properties

For ASME BPVC III Subsection NF, the data set checked at member level is shown in the following table.

Description

Data

Chapter

1.- Unbraced length of the member

2.- Buckling length factor in Y axis

3.- Buckling length factor in Z axis

4.- Bending coefficient dependent upon moment gradient in Y axis

5.- Bending coefficient dependent upon moment gradient in Z axis

6.- Coefficient applied to bending term in interaction equation and dependent upon column curvature caused by applied moments in Z axis

7.- Coefficient applied to bending term in interaction equation and dependent upon column curvature caused by applied moments in Y axis

8.- Pin-connected members:

0: No (default)

1: Yes

9.- Member type:

0: Beam (default)

1: Column

9.- Laterally braced in the region of compression:

0: No (default)

1: Yes

CBY

CBZ

CMY

CMZ

COLUMN

BRACED

3322

7.4.5 Checking Process

Necessary steps to conduct the different checks in CivilFEM are as follows:

a) Obtain the cross-sectional data corresponding to the element.

b) Specific section checking according to the type of external load.

c) Results. In CivilFEM, checking results for each element end are stored in the results file .CRCF

The required data for the different types of checking can be found in tables within the corresponding sections in this manual.

7.4.6 Tension Checking

In CivilFEM, elements subjected to tension are checked according to ASME BPVC III Subsection NF code for each end of the selected elements and solid sections of the model with a structural steel cross section. The check for tension adheres to the following steps:

7.4.6.1 Calculation of the Allowable Stress

The allowable stress in tension shall be as given in the equations below:

Except for pin-connected and threaded members, F_t shall be:

(*) on the effective net area

For pin-connected members, using the net area:

7.4.6.2 Calculation of the Stress Criterion

The obtained equivalent stress is divided by the steel design strength in order to obtain a value that is stored as the CRT_STR parameter in the corresponding alternative. This value must be between 0.0 and 1.0 for the element to be valid according to the ASME BPVC III Subsection NF code; consequently, the equivalent stress must be less than the steel design strength.

7.4.6.3 Slenderness Ratio

The maximum slenderness ratio l/r for tension members is obtained and stored as SLD_RT. This slenderness ratio is divided by 240 (SLD_RT shall not exceed 240) and stored as the CRT_SLD. Therefore, this value must be between 0.0 and 1.0 for the element to be valid according this code.

7.4.6.4 Calculation of the Total Criterion

The Total Criterion is obtained from the maximum value between the stress criterion and the slender criterion; this criterion is stored as the CRT_TOT parameter in the corresponding alternative in CivilFEM’s results file for each element end. This value must be between 0.0 and 1.0 for the element to be valid according the ASME BPVC III Subsection NF code.

CRT_TOT=MAX(CRT_STR,CRT_SLD)

7.4.7 Shear Checking

In CivilFEM the elements subjected to a shear force are checked according to ASME BPVC III Subsection NF code is done for each element end of those selected elements or solid sections of the model with a structural steel cross section.

7.4.7.1 Calculation of the Allowable Stress

The allowable stress for shear resistance of the effective section is as follows:

7.4.7.2 Calculation of the Total Criterion

The equivalent stress obtained is divided by the steel design strength in order to obtain a value that is stored as the CRT_TOT parameter in the active alternative in the CivilFEM’s results file for each element end. This value must be between 0.0 and 1.0 so that the element will be valid according to the ASME BPVC III Subsection NF code; consequently, the equivalent stress must be less than the steel design strength.

This equivalent stress f_v is the maximum value obtained in both directions:

7.4.8 Compression Checking

In CivilFEM, elements subjected to compression are checked of according to ASME BPVC III Subsection NF for each element end of the selected elements or solid sections of the model with a structural steel cross section.

7.4.8.1 Calculation of the Allowable Stress

The allowable stress in compression shall be determined as described below:

1- Gross sections of columns, except those fabricated from austenitic stainless steel:

where

2- Gross sections of columns fabricated from austenitic stainless steel:

if kI/r

if kI/r 120

3- Member elements other than columns:

7.4.8.2 Slenderness Ratio

The maximum slenderness ratio l/r for tension members is obtained and stored as SLD_RT. This slenderness ratio is divided by 200 (SLD_RT shall not exceed 200) and stored as the parameter CRT_SLD. Consequently, this value must be between 0.0 and 1.0 for that the element to be valid according this code.

7.4.8.3 Stress Reduction Factor

The ASME BPVC III Subsection NF code decreases the efficiency of a section through reduction factors when axially loaded members contain elements subjected to compression and have a width-thickness ratio above the limit below:

7.4.8.4 Unstiffened Compression Elements

Unstiffened compression elements have one free edge parallel to the direction of the compressive stress. Stress on these elements shall be decreased by the reduction factor Qs when the width-thickness ratio exceeds the limits below. The flange width will be the distance from the free edge to the web.

1- For Single Angles,

when

Qs = 1.0

when

when b/t 155/

2- For Stems of Tees,

when

3- For other Compression Members,

when

where Sy is the yield strength, in ksi.

Furthermore, proportions of unstiffened elements of channels and tees that exceed the limits above are checked for the following limits:

Shape	Ratio of Flange Width to Profile Depth	Ratio of Flange Thickness to Web or Stem Thickness
Built-up Channels
Rolled Channels
Built-up Tees
Rolled Tees

Table NF-3322.2(e)(2)-1

This proportion checking result is defined in the CivilFEM results file (.CRCF) as CTR_W with a value of 0.0 if the proportional limits are fulfilled and 2¹⁰⁰ if they are not.

7.4.8.5 Stiffened Compression Elements

Stiffened compression elements have lateral support along both edges which are parallel to the direction of the compressive stress. If the width-thickness ratio of these elements exceeds the limit below, a reduced effective width b_e shall be used:

1- For the flanges of square and rectangular sections of uniform thickness:

when

2- For other uniform compressed elements:

when

Where f is the axial compressive stress on the member based on the effective area, in ksi.

If unstiffened elements are included in the total cross section, f must be such that the maximum compressive stress in the unstiffened elements does not exceed . Therefore, the calculation of the effective width of stiffened elements adheres to the following iterative process:

a) The axial compressive stress f is obtained.

b) An initial value of the effective width is calculated.

c) A new axial compressive stress f’ of the effective area is obtained

d) If f’ exceeds , a new axial compressive stress f’’ is obtained by increasing the last axial compressive stress f’.

This process is repeated until the axial compressive stress does not exceed or until the effective area is equal to the total area.

Using the effective width , the form factor is then calculated by the ratio of the effective area to the total area.

7.4.8.6 Calculation of the Stress Criterion

The allowable stress for axially loaded compression members shall not exceed:

After verifing the equation above, the equivalent stress obtained is divided by the steel design strength to obtain a value stored as the CRT_STR parameter in the active alternative in CivilFEM’s results file for each element end. This value must be between 0.0 and 1.0 so that the element will be valid according to ASME BPVC III Subsection NF; therefore, the equivalent stress must be lower than the steel design strength.

7.4.8.7 Calculation of the Total Criterion

The Total Criterion is obtained from the maximum value between the stress criterion and the slender criterion and is stored as the CRT_TOT parameter in the active alternative in the CivilFEM’s results file for each element end. This value must be between 0.0 and 1.0 for the element to be valid according to the ASME BPVC III Subsection NF.

7.4.9 Bending Checking

In CivilFEM, elements subjected bending are checked according to ASME BPVC III Subsection NF for each element end of the selected elements or solid sections of the model with a structural steel cross section.

7.4.9.1 Calculation of the Allowable Stress

First, the section is classified as a compact section, member with a high flange width-thickness ratio or miscellaneous member:

(a) Compact sections: For a section to qualify as compact, its flanges must be continuously connected to the web or webs and the width-thickness ratios of its compression elements must not exceed the limiting ratios below:

1- The width-thickness ratio of the compression flanges shall not exceed:

a. for unstiffened elements

b. for stiffened elements

2- Depth-thickness ratio of webs

3- Moreover, the compression flanges shall be braced laterally at intervals not exceeding nor . This property is set by the user as a structural steel code property. If the cross section has no compression flanges, the member will be taken into account as braced laterally.

(b) Members with a high flange width-thickness ratio: members shall satisfy the requirements above, except unstiffened flanges shall satisfy:

(c) Miscellaneous members: limit ratios above do not apply to these members.

Next, the allowable bending stress is determined by the equations below:

1- I Sections:

a. Compact sections bent about their minor axis of inertia shall not exceed a bending stress of:

b. Members with a high flange width-thickness ratio bent about their minor axis of inertia shall not exceed a bending stress of:

c. Compact sections bent about their major axis of inertia shall not exceed:

d. Members with a high flange width-thickness ratio bent about their major axis of inertia shall not exceed a bending stress of:

e. Miscellaneous member sections bent about their major axis of inertia shall not exceed the larger value below:

when

where is the radius of the section, comprising of the area of the compression flange plus one-third of the area of the compression web.

When the area of the compression flange is greater than or equal to the area of the tension flange:

f. Members not included above which are braced laterally in the region of the compressive stress shall not exceed a bending stress of:

If these members are not braced laterally in the region of the compressive stress, the section will be not checked.

2- Tubular Square Box Sections:

a. Compact sections bent about their minor axis of inertia, but not necessarily braced laterally, shall not exceed a bending stress of:

b. Members not included shall not exceed a bending stress of:

However, this section strength can be decreased through reduction factors.

3- Pipe Sections:

a. If the diameter-thickness ratio of hollow, circular sections does not exceed , the bending stress shall not exceed:

If the diameter-thickness ratio is greater than the value above, the section will be not checked.

4- U channel Sections:

a. If the section is bent about its major axis of inertia, the bending stress shall not exceed the larger value below:

when

where is the radius of the section, comprising of the area of the compression flange plus one-third of the area of the compression web.

When the area of the compression flange is greater than or equal to the area of the tension flange,

b. Members not included above which are braced laterally in the region of the compressive stress shall not exceed a bending stress of:

If these members are not braced laterally in the region of the compressive stress, the section will be not checked.

5- Tees Sections:

a. Compact sections loaded in the direction of the web which coincides with the minor axis of inertia, shall not exceed a bending stress of:

b. Members with a high flange width-thickness ratio which are loaded in the direction of the web coinciding with the minor axis of inertia shall not exceed a bending stress of:

c. Miscellaneous member sections loaded in the direction of the web coinciding with the minor axis of inertia, shall not exceed the larger bending stress below:

when

When

where is the radius of a section comprising the area of the compression flange plus one-third of the area the of compression web

When the compression flange area is greater than or equal to the tension flange area:

d. Members not included above which are braced laterally in the region of the compressive stress shall not exceed a bending stress of:

If these members are not braced laterally in the region of the compressive stress, the section will be not checked.

6- All other sections:

a. Members braced laterally in the region of the compressive stress shall not exceed a bending stress of:

If these members are not braced laterally in the region of compressive stress, the section will be not checked.

7.4.9.2 Stress Reduction Factor

ASME BPVC III Subsection NF Code decreases the efficiency of a section through reduction factors for flexural members containing elements subject to compression with a width-thickness ratio in excess of the limits below:

7.4.9.3 Unstiffened Compression Elements

Unstiffened compression elements have one free edge parallel to the direction of the compressive stress. When the width-thickness ratio exceeds the limits below, the stress calculation will include a reduction of factor Qs. The width of flanges is taken from distance from the free edge to the weld.

1- For Single Angles:

when

2- For Stems of Tees:

when

3- For Other Compression Members:

when

where Sy is the yield strength, in ksi.

Furthermore, unstiffened elements of channels and tees with proportions that exceed the limits above are checked for the following limits:

Shape	Ratio of Flange Width to Profile Depth	Ratio of Flange Thickness to Web or Stem Thickness
Built-up channels
Rolled channels
Built-up tees
Rolled tees

Table NF-3322.2(e)(2)-1

This proportion checking result is written in the CivilFEM results file (.CRCF) as CTR_W with a value of 0.0 if the proportion limits are satisfied and 2¹⁰⁰ if they are not.

7.4.9.4 Stiffened Compression Elements

Stiffened compression elements have lateral support along both edges which are parallel to the direction of the compressive stress. When the width-thickness ratio of these elements exceeds the applicable limit below, a reduced effective width shall be used:

1- For the flanges of square and rectangular sections of uniform thickness,

when

2- For other uniform compressed elements,

When

Where f is the compressive stress on member based on the effective area, in ksi.

If unstiffened elements are included in the total cross section, f must have a value such that the maximum compressive stress in the unstiffened elements does not exceed . Therefore, the calculation of the effective width of stiffened elements adheres to the following iterative process:

a) The maximum compressive stress f of the element is obtained

b) An initial value of the effective width is calculated in all the compressive elements.

c) A new axial compressive stress f’ is obtained of the effective area.

d) If f’ exceeds , a new effective width ’ is obtained by increasing the previous effective width .

This iteration is repeated until the axial compressive stress is less than or the effective area is equal to the total area.

Using the effective width , the form factor is then calculated by the ratio of the effective area to the total area.

7.4.9.5 Calculation of the Total Criterion

When reduction factors are required, the maximum allowable bending stress shall not exceed 0.6 or the value as provided above.

The computed bending stress , obtained from the effective area, is divided by the steel design strength in order to obtain a value that is stored as the CRT_TOT parameter in the active alternative in CivilFEM’s results file for each element end. This value must be between 0.0 and 1.0 so that the element will be valid according to ASME BPVC III Subsection NF; therefore, the equivalent stress must be less than the steel design strength.

7.4.10 Axial Compression & Bending Checking

In CivilFEM the checking of elements under bending and axial compression forces according to ASME BPVC III Subsection NF code are done for each element end of those selected elements or solid sections of the model whose cross section type is structural steel.

7.4.10.1 Calculation of the Total Criterion

For members subjected to both axial compression and bending, stresses shall satisfy the requirements of the following equations:

When evaluating both primary and secondary stresses:

When evaluating primary stresses:

The Total Criterion will be the maximum value of the equations below and will be stored as the CRT_TOT parameter in the active alternative in CivilFEM’s results file for each element end. This value must be between 0.0 and 1.0 for the element to be valid according to ASME BPVC III Subsection NF; therefore, the equivalent stress must be less than the steel design strength.

7.4.10.2 Axial Tension & Bending Checking

In CivilFEM, elements subjected bending and axial tension forces are checked according to ASME BPVC III Subsection NF for each element end of the selected elements or solid sections of the model with a structural steel cross section.

7.4.10.3 Calculation of the Total Criterion

Members subject to both axial tension and bending stresses shall satisfy the requirements of the following equation:

Where f_b is the computed bending tensile stress. However, the computed bending compressive stress, taken alone, shall not exceed the allowable compressive stress F_a.

Therefore, the total criterion will be:

Where f_bc is the computed bending compressive stress.

The total criterion is stored as the CRT_TOT parameter in the active alternative in CivilFEM’s results file for each element end. This value shall be between 0.0 and 1.0 for the element to be valid according to ASME BPVC III Subsection NF; consequently, the equivalent stress must be less than the steel design strength.

7.5. Steel Structures According to GB50017

Steel structures checking according to the Chinese Steel Design Code GB50017 in CivilFEM includes the checking of structures composed of welded or rolled shapes subjected to axial forces, shear forces and bending moments in 3D.

The calculations made by CivilFEM correspond to the provisions of GB50017 from the following sections:

Section 4	Bending element calculations
Section 5	Axially loaded structures and calculation of compression and bending

7.5.1 Checking Types

For checks within CivilFEM according to GB50017, it is possible to accomplish the following checking and analysis types:

Checking of sections subjected to:

- Bending force	GB50017 Art. 4.1.1
- Shear force	GB50017 Art. 4.1.2
- Bending and shear force	GB50017 Art. 4.1.4
- Axial force	GB50017 Art. 5.1.1
- Bending and axial force	GB50017 Art. 5.2.1
- Compression buckling	GB50017 Art. 5.1.2

7.5.2 Material Properties

In GB50017 checking, the following material properties are used:

Description	Property
Steel yield strength	(th)
Ultimate strength	(th)
Shear strength	(th)
Elasticity modulus	E

*th = plate thickness

7.5.3 Section Data

The section data of the element must be included in the CivilFEM database. All geometrical and mechanical properties are automatically obtained defining the cross section or capturing the solid section. Below, the section data necessary for checking according to GB50017 are listed:

Data	Description
A	Area of the cross-section
	Moment of inertia about Y axis
	Moment of inertia about Z axis
	Product of inertia about YZ
Y	Coordinate Y of the considered fiber
Z	Coordinate Z of the considered fiber
	Radius of gyration about Y axis
	Radius of gyration about Z axis
	Shear area in Y
	Shear area in Z
	Torsional modulus

From net section, only the area is considered. This area is calculated by subtracting the holes for screws, rivets and other holes from the gross section area. The user should be aware that LRFD indicates the diameter from which to calculate the area of holes is greater than the real diameter. The area of holes is introduced within the structural steel code properties.

7.5.4 Structural steel code properties

For LRFD, the checked data set used at member level is shown in the following table. All data is stored with the section data in user units and in CivilFEM reference axis.

Description

Data

Chapter

Input data:

1.- Plastic developing coefficient in Y axis

0.0: not defined (default)

2.- Plastic developing coefficient in Z axis

0.0: not defined (default)

3.- Cross section type in Y axis:

0: not defined (default)

1: Type a

2: Type b

3: Type c

4: Type d

4.- Cross section type in Z axis:

0: not defined (default)

1: Type a

2: Type b

3: Type c

4: Type d

5.- Unbraced length of the member

6.- Buckling length factor in Y axis

7.- Buckling length factor in Z axis

GAMMAy

GAMMAz

TSECy

TSECz

5.2

Table 5.1.2-1 &

Table 5.1.2-2

Table 5.1.2-1 &

Table 5.1.2-2

5.1.2

7.5.5 Cross Section Type Classification

The cross section type is defined by values introduced in TSECY and TSECZ structural steel code properties. Otherwise they will be computed from the following table 5‑3:

CROSS SECTION TYPE			Y	Z
I Section	Rolled Section	If	b	a
	Rolled Section	If	b	b
	Welded Section		b	b
	Welded Section		b	b
Channel	Rolled or Welded		b	b
Pipe	Rolled		a	a
Pipe	By dimensions		b	b
L angle	Rolled		b	b
Square Tubing or Box	Rolled or Welded if		c	c
Standard T	Rolled or Welded		b	b

CROSS SECTION TYPE			Y	Z
I Section	Rolled	If	c	b
		If	d	c
	Welded (default)		b	b
Square Tubing or Box	Rolled or Welded if		b	b
	Rolled or Welded if		c	c

7.5.6 Checking Process

Required steps to conduct the different checks in CivilFEM are as follows:

a) Obtain the cross-section data corresponding to the element.

b) Specific section checking according to the type of external load.

c) Results. Checking results are stored in the results file .CRCF.

In sections corresponding to the different types of checking, the necessary data corresponding to the each type of solicitation is described.

7.5.7 Bending Checking

In CivilFEM the checking of elements under bending according to GB50017 code is done for each element end of those selected elements or solid sections of the model with a cross section type of structural steel. For this check, the program follows the steps below:

7.5.7.1. Calculation of the Maximum Normal Stress

The maximum normal stress is calculated with the general equation for sections subjected to bending moments according to axes, not necessarily principal of inertia:

Where:

	Bending moment in Y direction
	Bending moment in Z direction
	Moment of inertia in Y direction
	Moment of inertia in Z direction
	Product of inertia about YZ

Plastic development coefficients
are obtained from the associated structural steel code properties. Otherwise they should be defined according to 11.5.4.

CROSS SECTION TYPE
	1.20	1.05
		1.05
		1.05
	1.15	1.15
	1.05	1.05
	1.20
	1.20
Otherwise	1.00	1.00

7.5.7.2. Calculation of GB50017 Criterion

The equivalent stress previously obtained is then divided by the steel design strength
in order to obtain a value that is stored as the CRT_TOT parameter in the active alternative in CivilFEM’s results file for each element end. This value shall be between 0.0 and 1.0 so that the element will be valid according to the GB50017 code; therefore, the equivalent stress must be lower than the steel design stress.

7.5.8 Shear Checking

In CivilFEM, the checking of elements under shear force according to the GB50017 code is performed for each element end of those selected elements or solid sections of the model with a cross section type of structural steel.

7.5.8.1. Calculation of the Maximum Tangential Stress

The maximum tangential shear and torsion stresses for each element end are calculated from shear forces and section mechanical properties in the following equation:

Where:

	Shear Force in Y direction
	Shear Force in Z direction
	Shear area about Y axis.
	Shear area about Z axis.

7.5.8.2. Calculation of GB50017 Criterion

The equivalent stress obtained is divided by the steel design strength in order to obtain a value that is stored as the CRT_TOT parameter in the active alternative in CivilFEM’s results file for each element end. This value shall be between 0.0 and 1.0 so that the element will be valid according to the GB50017 code; consequently, the equivalent stress must be lower than the steel design stress.

7.5.9 Bending & Shear Checking

In CivilFEM the checking of elements under bending and shear forces according to GB50017 code is done for each element end of those selected elements or solid sections of the model with a cross section type of structural steel. The following steps:

7.5.9.1. Calculation of the Maximum Normal Stress

The maximum normal stress is calculated with the general equation for sections subjected to bending moments according to axes, not necessarily the principal axes of inertia:

Where:

	Bending moment in Y direction
	Bending moment in Z direction
	Moment of inertia in Y direction
	Moment of inertia in Z direction
	Product of inertia about YZ

7.5.9.2. Calculation of the Maximum Tangential Stress

The maximum tangential shear and torsion stresses for each element end are calculated from shear forces and section mechanical properties in the following equation:

Where:

	Shear Force in Y direction
	Shear Force in Z direction
	Shear area about Y axis.
	Shear area about Z axis.

7.5.9.3. Calculation of the Maximum Equivalent Stress

The maximum equivalent stress in the section is calculated by using:

The maximum equivalent stress for each element end is stored in the active alternative in CivilFEM’s results file with the parameter named SCEQV.

7.5.9.4. Calculation of GB50017 Criterion

The equivalent stress obtained is divided by the steel design strength s_u in order to obtain a value that is stored as the CRT_TOT parameter in the active alternative in CivilFEM’s results file for each element end. This value shall be between 0.0 and 1.0 so that the element will be valid according to the GB50017 code; thus, the equivalent stress must be lower than the steel design stress.

Where is the amplifying factor for the combined design strength. If and have different sign = 1.2, otherwise = 1.1.

7.5.10 Axial Force Checking

In CivilFEM, the checking of elements under axial forces (without considering buckling) according to the GB50017 code is done for each element end of those selected elements or solid sections of the model with a cross section type of structural steel.

7.5.10.1. Calculation of the Maximum Axial Stress

The maximum tangential shear and torsion stresses for each element end are calculated from shear forces and section mechanical properties in the following equation:

Where:

	Axial force
	Net area of the cross section
	Number of high-strength frictional bolts
	Number of bolts at the calculated section

In CivilFEM coefficient is given by RTB factor which can be modified in the structural steel code properties.

7.5.10.2. Calculation of GB50017 Criterion

The equivalent stress obtained is then divided by the steel design strength in order to obtain a value that is stored as the CRT_TOT parameter in the active alternative in the CivilFEM’s results file for each element end. This value shall be between 0.0 and 1.0 so that the element will be valid according to the GB50017 code; therefore, the equivalent stress must be lower than the steel design stress.

7.5.11 Bending & Axial Checking

In CivilFEM, checking elements subjected to bending and axial forces according to GB50017 code is conducted for each element end of those selected elements or solid sections of the model with a cross section type of structural steel.

7.5.11.1. Calculation of the Maximum Equivalent Stress

The maximum equivalent stress in the section is calculated by using:

Where:

		Bending moment in Y direction
		Bending moment in Z direction
		Moment of inertia in Y direction
		Moment of inertia in Z direction
		Product of inertia about YZ

Plastic development coefficients are obtained from the associated in the structural steel code properties.

7.5.11.2. Calculation of GB50017 Criterion

The equivalent stress obtained is then divided by the steel design strength in order to obtain a value that is stored as the CRT_TOT parameter in the active alternative in CivilFEM’s results file for each element end. This value shall be between 0.0 and 1.0 so that the element will be valid according to the GB50017 code; therefore, the equivalent stress must be lower than the steel design stress.

7.5.12 Compression Buckling Checking

In CivilFEM the checking of elements considering buckling according to GB50017 code is done for each element end of those selected elements or solid sections of the model with a cross section type of structural steel and subjected to a compressive force.

7.5.12.1. Calculation of the Maximum Equivalent Stress

The maximum equivalent stress in the section is calculated by using:

Where   is the stability coefficient for axially compressed members. The stability coefficient  is calculated from the slenderness ratio:

Where:

L	Unbraced length of member
	Buckling length factors in Y axis
	Buckling length factors in Z axis
	Rotational radius to Y axis
	Rotational radius to Z axis

In non symmetric sections, the axes are defined as the directions of principal inertia.

To compute:

a) If then

b) Otherwise:

Where are chosen according to the following table:

CROSS SECTION
a	0.410	0.986	0.152
b	0.650	0.965	0.300
c	0.730	0.906	0.595
c	0.730	1.216	0.302
d	1.350	0.868	0.915
d	1.350	1.375	0.432

The cross section type is determined from tables of chapter 7.5.5.

7.5.12.2. Calculation of GB50017 Criterion

The equivalent stress obtained is then divided by the steel design strength in order to obtain a value that is stored as the CRT_TOT parameter in the active alternative in CivilFEM’s results file for each element end. This value shall be between 0.0 and 1.0 so that the element will be valid according to the GB50017 code; consequently, the equivalent stress must be lower than the steel design stress.

7.6. Steel Structures According to IS800-07

Checking steel structures according to Indian Standard IS 800 (2007) is implemented in CivilFEM. It is possible to check structures composed by welded or rolled shapes under axial forces, shear forces and bending moments in 3D.

The calculations made by CivilFEM correspond to the recommendations of Indian Standard General Construction in Steel – Code of Practice (Third Revision).

7.6.1 Checking types

With CivilFEM it is possible to accomplish the following check and analysis types:

- Tension	Section 6.2
- Compression	Section 7.1
- Bending	Section 8.2.1
- Shear force	Section 8.4
- Bending and Shear	Section 9.2
- Lateral Torsional Buckling	Section 8.2.2
- Axial Force with Moments	Section 9.3

7.6.2 Material Properties

For IS 800:2007 checking, the following material properties are used:

Description	Properties, symbol
Yield strength	fy
Ultimate tensile strength	fu
Partial safety factor for material	Resistance, governed by yielding
	Resistance of member to buckling
	Resistance, governed by ultimate stress
Modulus of elasticity	E = 200 kN/mm2
Shear Modulus
Poisson’s ratio	n = 0.3
Coefficient of linear thermal expansion	a = 12×10-6 °C-1
Constant є

7.6.2 Section Data

IS 800:2007 considers the following data set for the section:

- Gross section data

- Net section data

- Effective section data

- Data pertaining to the section and plates class.

Gross section data correspond to the nominal properties of the cross-section.

For the net section, only the area is considered. This area is calculated by subtracting the holes for screws, rivets and other holes from the gross section area.

The initial required data for the IS 800:2007 module includes the gross section data in user units and the CivilFEM or section axis. In the following tables, the section data used in IS 800:2007 are shown:

Common data for gross, net and effective sections

Description

Data

Input data:

1.- Height

2.- Web thickness

3.- Flanges thickness

4.- Flanges width

5.- Distance between flanges

6.- Radius of fillet (Rolled shapes)

7.- Toe radius (Rolled shapes)

8.- Weld throat thickness (Welded shapes)

9.- Web free depth

r₁

r₂

Output data

(None)

Gross section data

Description

Data

Reference axis

Input data:

1.- Depth in Y

2.- Depth in Z

3.- Cross-section area

4.- Moments of inertia for torsion

5.- Moments of inertia for bending

6.- Product of inertia

7.- Elastic resistant modulus

8.- Plastic resistant modulus

9.- Radius of gyration

10.- Gravity center coordinates

11.- Extreme coordinates of the perimeter

12.- Distance between GC and SC in Y and in Z

13.- Warping constant

14.- Shear resistant areas

15.- Torsional resistant modulus

16.- Moments of inertia for bending about U, V

17.- Angle Y->U or Z->V

Tky

tkz

Iyy, Izz

Izy

Wely, Welz

Wply, Wplz

iy, iz

Ycdg, Zcdg

Ymin, Ymax,

Zmin, Zmax

Yms, Zms

Yws, Zws

Xwt

Iuu, Ivv

CivilFEM

Section

CivilFEM

Principal

CivilFEM

Output data:

(None)

Net section data

Description

Data

Input data:

1.- Gross section area

2.- Area of holes

Agross

Aholes

Output data:

1.- Net Cross-section area

Anet

The effective section depends on the section geometry and on the forces and moments that are applied to it. Consequently, for each element end, the effective section is calculated.

Effective section data

Description

Data

Reference axis

Imput data:

(None)

Output data:

1.- Cross-section area

2.- Moments of inertia for bending

3.- Product of inertia

4.- Elastic resistant modulus

5.- Gravity center coordinates

6.- Distance between GC and SC in Y and in Z

7.- Warping constant

8.- Shear resistant areas

Aeff

Iyyeff, Izzeff

Izyeff

Wyeff, Wzeff

Ygeff, Zgeff

Ymseff, Zmseff

Yws, Zws

CivilFEM

Section

CivilFEM

Data referred to the section plates

Description

Data

Input data:

1.- Plates number

2.- Plate type: flange or web (for the relevant axis of bending)

3.- Union condition at the ends: free or fixed

4.- Plate thickness

5.- Coordinates of the extreme points of the plate (in Section axis)

Pltype

Cp1, Cp2

Yp1, Yp2,

Zp1, Zp2

Output data:

6.- Reduction factors of the plates at each end

7.- Plates class

Rho1, Rho2

7.6.3 Structural steel code properties

For IS 800:2007 checking, the data set used at member level are shown in the following table. All the data are stored with the section data in user units and in the CivilFEM reference axis. This data is defined as the parameters:

L, K, KW, C1, C2, C3, CMY, CMZ, CMLT, CFBUCKXY and CFBUCKXZ.

Note that CFBUCKXY and CFBUCKXZ are used for simple buckling calculations and K, KW, C1, C2, C3, CMY, CMZ, CMLT are used for lateral and torsional buckling. This is important for understanding the way CivilFEM obtains buckling length. In simple buckling, buckling effective length (K*L according to 7.2.1) is obtained as CFBUCKXZ*L or CFBUCKXY*L. Lateral buckling effective length (L_LT according to 8.3) is obtained using K*L (this K is the one entered in the Member Properties pane).

Member Properties

Description	IS800-07
Input data:
1.- Unbraced length of member (global buckling). Length between lateral restraints (lateral-torsional buckling)	L
2.- Effective length factors	k, kw
3.- Lateral buckling factors, depending on the load and restraint conditions	C1, C2, C3
4.- Equivalent uniform moment factors for flexural buckling	CMy, CMz
5.- Equivalent uniform moment factors for lateral-torsional buckling	CMLt
6.- Reduction factor for vectorial effects	N/A
7.- Buckling factors for planes XZ and YZ (Effective buckling length for plane XY =LCfbuckxy ) (Effective buckling length for plane XZ =LCfbuckxz )	Cfbuckxy, Cfbuckxz

7.6.4 Check process

The checking process includes the evaluation of the following expression:

Evaluation steps:

1. Read the checking type requested by the user.

2. Default checking type: Bending, shear and axial force.

3. Read the CivilFEM axis to be considered as the relevant axis for bending so that it coincides with the Y axis of IS 800:2007. In CivilFEM, by default, the principle bending axis that coincides with the +Y axis of IS 800:2007 is the –Z.

4. The following operations are necessary for each selected element:

a. Obtain material properties of the element stored in CivilFEM database and calculate the rest of the properties needed for checking:
Properties obtained from CivilFEM database:

Calculated properties:

Epsilon, material coefficient:

( in N/mm²)

b. Obtain the cross-section data corresponding to the element.

c. Initialize values of the effective cross-section.

d. Initialize reduction factors of section plates and the rest of plate parameters necessary for obtaining the plate class.

f. Obtain internal forces and moments (T_d, P_d, V_y.d, V_z.d, M_x.d, M_y.d, M_z.d within the section.

g. Specific section checking according to the type of external load. The specific check includes:

1. If necessary, selecting the forces and moments considered for the determination of the section class and used for the checking process.

2. Obtaining the cross-section class and calculating the effective section properties (See Section: General Processing of Sections).

3. Checking the cross-section according to the external load and its class by calculating the following criteria: Crt_TOT, Crt_N, Crt_Mx and Crt_My.

h. Recording the results.

7.6.5 Section Class and Reduction Factors Calculation

Sections, according to IS 800:2007, are made up by plates. These plates can be classified according to:

Plate function: webs and flanges in Y and Z axis, according to the considered relevant axis of bending.

Plate union condition: internal plates or outstand plates.

For checking the structure for safety, IS 800:2007 classifies sections as one of four possible classes:

Class 1 (Plastic)	Cross-sections, which can develop plastic hinges and have the rotation capacity required for failure of the structure by formation of plastic mechanism.
Class 2 (Compact)	Cross-sections, which can develop plastic moment of resistance, but have inadequate plastic hinge rotation capacity for formation of plastic mechanism, due to local buckling.
Class 3 (Semi-Compact)	Cross-sections, in which the extreme fiber in compression can reach yield stress, but cannot develop the plastic moment of resistance, due to local buckling.
Class 4 (Slender)	Cross-sections in which the elements buckle locally even before reaching yield stress.

The cross-section class is the highest (least favorable) class of all of its elements: flanges and webs (plates). First, the class of each plate is determined according to the limits of IS 800:2007. The plate class depends on the following:

- The geometric width to thickness ratio with the plate width properly corrected according to the plate and shape type.

GeomRat = Corrected_Width / thickness

· Welded Shapes:

Double T section:

Internal webs or flanges:

Corrected width = d

d Web free depth

Outstand flanges:

Corrected width

Where:

B	Flanges width
	Web thickness
	Radius of fillet

T section:

Internal webs or flanges:

Corrected width = d

Outstand flanges:

Corrected width =

C section:

Internal webs or flanges:

Corrected width = d

Outstand flanges:

Corrected width

L section:

Corrected width =

Angle flange width

Box section:

Internal webs:

Corrected width = H

H Height

Internal flanges:

Corrected width =

Web thickness

Circular hollow section

Corrected width = H

· Rolled Shapes:

Double T section:

Internal webs or flanges:

Corrected width = d

d Web free depth

Outstand flanges:

Corrected width =

B Flanges width

T Section:

Internal webs or flanges:

Corrected width = d

Outstand flanges:

Corrected width =

C Section:

Internal webs or flanges:

Corrected width = d

Outstand flanges:

Corrected width = B

L Section:

Corrected width =

Angle flange width

Box section:

Internal webs:

Corrected width = d

Internal flanges:

Corrected width =

Flanges thickness

Pipe section:

Corrected width = H

The limit listed below for width to thickness ratio. This limit depends on the material parameter  and the normal stress distribution in the plate section. The latter value is given by the following parameters: , , and k₀, and the plate type, internal or outstand; the outstand case depends on if the free end is under tension or compression.

Limit (class) =

where:

	Compressed length / total length
y
	Buckling factor
_	The higher stress in the plate ends.
_	The lower stress in the plate ends.

A linear stress distribution on the plate is assumed.

The procedure to determine the section class is as follows:

Obtain stresses at first plate ends from the stresses applied on the section, properly filtered according to the check type requested by the user.

Calculate the parameters: ,  and

For internal plates:



	= infinite

For outstand plates with an absolute value of the stress at the free end greater than the corresponding value at the fixed end:

For

= infinite

For outstand plates with an absolute value of the stress at the free end lower than the corresponding value at the fixed end:

For

= infinite

Cases in which = infinite are not included in IS 800:2007. With these cases, the plate is considered to be practically in tension and it will not be necessary to determine the class. These cases have been included in the program to avoid errors, and the value =infinite has been adopted because the resultant plate class is 1 and the plate reduction factor is r = 1 (the same values as if the whole plate was in tension). The reduction factor is used later in the effective section calculation.

- Obtain the limiting proportions as functions of: ,  and k₀ and the plate characteristics (internal, outstand: free end in compression or tension).

Internal plates:

	for < 0.5
	for < 0.5
	for ≥ 0.5
	for <0.5
	for > -1
	for  -1

Outstand plates, free end in compression:

Outstand plates, free end in tension:

Above is the general equation used by the program to obtain the limiting proportions for determining plate classes. In addition, plates of IS 800:2007 may be checked according to special cases.

For example:

In sections totally compressed:

 = 1;  = 1 for all plates

In sections under pure bending:

 = 0.5; = -1 for the web

 = 1;  = 1 for compressed flanges

Obtain the plate class:

If		GeomRat	< Limit(1)	Plate Class = 1
If	Limit(1) 	GeomRat	< Limit(2)	Plate Class = 2
If	Limit(2) 	GeomRat	< Limit(3)	Plate Class = 3
If	Limit(3) 	GeomRat		Plate Class = 4

Repeat these steps (1,2,3,4) for each section plate.

Assign of the highest class of the plates to the entire section.
In tubular sections, the section class is directly determined as if it were a unique plate, with GeomRat and the Limits calculated as follows:

GeomRat = outer diameter/ thickness.

For class 4 sections, the section resistance is reduced, using the effective width method.

For each section plate, the effective lengths at both ends of the plate and the reduction factors ₁ and ₂ are calculated. These factors relate the length of the effective zone at each plate end to its width.

Effective_length_end1 = plate_width*_

Effective_length_end 2 = plate_width*_

The following formula from IS 800:2007 has been implemented for this process:

1. Internal plates:

For (Both ends compressed)

ec3_1

Internal plates

= corrected plate width

plate_width = real plate width

For (end 1 in compression and end 2 in tension)

ec3_2

2. Outstand plates:

For (Both ends in compression: end 1 fixed, end 2 free)

ec3_3

For (end 1 fixed and in tension, end 2 free and in compression)

ec3_4

For (end 1 fixed and in compression, end 2 free and in tension)

ec3_5

If end 2 is the fixed end, the values and are switched.

The global reduction factor r is obtained by as follows:

For internal compression elements

For

For outstands compression elements:

For

is defined as the plate slenderness given by:

where:

= corrected plate width

t = relevant thickness

 = material parameter

= buckling factor

To determine effective section properties, three steps are followed:

- Effective widths of flanges are calculated from factors  and these factors are determined from the gross section properties. As a result, an intermediate section is obtained with reductions taken in the flanges only.

- The resultant section properties are obtained and factors and  are calculated again.

- Effective widths of webs are calculated so that the finalized effective section is determined. Finally, the section properties are recalculated once more.

Each checking type follows a specific procedure that will be explained in the following sections.

7.6.6 Checking of Members in Axial Tension

Corresponds to chapter 6 in IS-800-2007.

- Forces and moments selection.
The forces and moments considered for this checking type are:

T = FX

Design value of the axial force (positive if tensile, element not processed if compressive).

- Class determination.

- Criteria calculation.
For members under axial tension, the general criterion Crt_TOT is checked at each section.

à Crt_TOT =

Where is the design strength of the member.

If we only take into account the design strength due to yielding of gross section (article 6.2, IS800:2007):

If we take into account the design strength in tension of a plate, ,as governed by rupture of net cross-sectional area:

is the net cross-sectional area and it will be calculated as

should be included by the user according to the IS 800:2007

- Output results are written in the CivilFEM results file as an alternative. Checking results: criteria and variables are described in the following table:

Checking of Members in Axial Tension

Result	Concepts	Description
T	T	Tension Force.
TD	Td	Design strength of the member.
TDG	Tdg	Design strength due to yielding of gross section.
TDN	Tdn	Design strength in tension of a plate, as governed by rupture of net cross-sectional area.
CRT_TOT	T/T_d	Global criterion.

7.6.7 Checking of Members under Bending Moment

Corresponds to chapter 8 in IS-800-2007.

- Forces and moments selection.
The forces and moments considered for this checking type are:

Design value of the bending moment along the relevant axis for bending. Represented as M_d in IS-800-2007.

- Class definition and effective section properties calculation.
The section class is determined by the general processing of the section with the previously selected forces and moments if the selected option is partial or with all the forces and moments if the selected option is full. The entire calculation process is accomplished with the gross section properties.

- Criteria calculation.
For members subjected to a bending moment in the absence of shear force, the following condition is checked at each section:

where:

design value of the bending moment

design moment resistance of the cross-section

Class 1 or 2 cross-sections:

Class 3 cross sections:

Class 4 cross sections:

- Output results are written in the CivilFEM results file as an alternative. Checking results: criteria and variables are described in the following table.

Checking of Members under Bending Moment

Result	Concepts	Description
MED		Design value of the bending moment.
MCRD		Design moment resistance of the cross-section.
CRT_M		Bending criterion.
CRT_TOT		IS 800:2007 global criterion.
CLASS		Section Class.
W		Used section modulus (Elastic, Plastic or Effective).

7.6.8 Checking of Members under Shear Force

Corresponds to chapter 8.4 in IS-800-2007.

- Forces and moments selection.
The forces and moments considered for this checking type are:

Design value of the shear force perpendicular to the relevant axis of bending.

- Class definition and effective section properties calculation.
For this checking type, the section class is always 1 and the effective section is the gross section.

- Criteria calculation.
With members under shear force, the following condition is checked at each section:

where:

	design value of the shear force
	design plastic shear resistance:
	shear area.

IS800-07 specifies additional cases for the calculation of :

· I and channel sections:

· Rectangular hollow sections of uniform thickness

Loaded parallel to depth (h) — A h / (b + h)

Loaded parallel to width (b) — A b / (b + h)

· Circular: 2A/π

- Output results are written in the CivilFEM results file as an alternative. Checking results: criteria and variables are described in the following table.

Checking of Members under Shear Force

Result	Concepts	Description
VED		Design value of the shear force.
VPLRD		Design plastic shear resistance.
CRT_S		Shear criterion.
CRT_TOT		IS 800:2007 global criterion.
CLASS		Section Class.
S_AREA		Shear area.

7.6.9 Checking of Members under Bending Moment and Shear Force

Corresponds to chapter 9.2 in IS-800-2007.

- Forces and moments selection.
The forces and moments considered for this checking type are:

Design value of the shear force perpendicular to the relevant axis of bending.

Design value of the bending moment along the relevant axis of bending.

- Class definition and effective section properties calculation.
The section class is determined by the general processing of the sections with the previously selected forces and moments if the selected option is partial or with all the forces and moments if the selected option is full. The entire calculation is accomplished with gross section properties.

- Criteria calculation.
For members subjected to bending moment and shear force, the following condition is checked at each section:

Where:

design resistance moment of the cross-section, reduced by the presence of shear.

The reduction for shear is applied if the design value of the shear force exceeds 50% of the design plastic shear resistance of the cross-section; written explicitly as:

The design resistance moment is obtained as follows:

- For double T cross-sections with equal flanges, bending about the major axis:

- For other cases the yield strength is reduced as follows:

Note: This reduction of the yield strength fy is applied to the entire section. IS 800:2007 only requires the reduction to be applied to the shear area, and therefore, it is a conservative simplification.

For both cases, is the smaller value of either or .

is the design moment resistance of the cross-section, calculated according to the class.

- Output results are written in the CivilFEM results file as an alternative. Checking results: criteria and variables are described in the following table.

Checking of Members under Bending Moment and Shear Force

Result	Concepts	Description
MED		Design value of the bending moment.
VED		Design value of the shear force.
MVRD		Reduced design resistance moment of the cross-section.
CRT_BS		Bending and Shear criterion.
CRT_TOT		IS 800:2007 global criterion.
CLASS		Section Class.
S_AREA		Shear area.
W		Used section modulus (Elastic, Plastic or Effective).
VPLRD		Design plastic shear resistance.
RHO	ρ	Reduction factor.

7.6.10 Checking of Members under Bending Moment + Axial Force and Bi-axial Bending + Axial Force

Corresponds to chapter 9.3 in IS-800-2007.

- Forces and moments selection.
The forces and moments considered for this checking type are:

	Design value of the axial force..
	Design value of the bending moment along the relevant axis of bending.
	Design value of the bending moment about the secondary axis of bending.

- Class definition and effective section properties calculation.
The section class is determined by the general processing of the sections with the previously selected forces and moments if the selected option is partial, or with all the forces and moments if the selected option is full. These calculations are accomplished with the gross section properties.

- Criteria calculation.
For members subjected to bi-axial bending and in absence of shear force, the following conditions at each section are checked:

Class 1 and 2 sections:

This condition is equivalent to:

Where and are the design moment resistance of the cross-section, reduced by the presence of the axial force:

Where a and b are constants, which may take the following values:

For I and H sections:

For circular tubes:

For rectangular hollow sections:

but

For solid rectangles and plates (the rest of sections):

In absence of , the previous check can be reduced to:

Condition equivalent to:

Class 3 sections (without holes for fasteners):

Condition equivalent to:

Crt_TOT = Crt_N + Crt_My + Crt_Mz £ 1

Where is the elastic resistant modulus about the y axis and is the elastic resistant modulus about the z axis.

In absence of , the above criterion becomes:

Which is equivalent to:

Crt_TOT = Crt_N + Crt_My £ 1

Class 4 sections:

Condition equivalent to:

Crt_TOT = Crt_N + Crt_My + Crt_Mz £ 1

Where:

	effective area of the cross-section
	effective section modulus of the cross-section when subjected to a moment about the y axis
	effective section modulus of the cross-section when subjected to a moment about the z axis
	shift of the center of gravity along the y axis
	shift of the center of gravity along the z axis

Without , the above criterion becomes:

which is equivalent to:

Crt_TOT = Crt_N + Crt_My + Crt_Mz £ 1

- Output results are written in the CivilFEM results file as an alternative. Checking results: criteria and variables are described in the following table.

Checking of Members under Bending Moment + Axial Force and Bi-axial Bending + Axial Force

Result	Concepts	Description
NED		Design value of the axial force.
MYED		Design value of the bending moment about Y axis.
MZED		Design value of the bending moment about Z axis.
NCRD	,	Design compression resistance of the cross-section
MNYRD	,,	Reduced design moment resistance of the cross-section about Y axis
MNZRD	,,	Reduced design moment resistance of the cross-section about Z axis
CRT_N		Axial criterion
CRT_MY		Bending criterion along Y
CRT_MZ		Bending criterion along Z
ALPHA	α	Alpha constant
BETA	β	Beta constant
CRT_TOT	Crt_tot £ 1	IS 800:2007 global criterion
CLASS		Section Class
AREA		Area of the section utilized (Gross or Effective)
WY		Used section Y modulus (Elastic, Plastic or Effective)
WZ		Used section Z modulus (Elastic, Plastic or Effective)
SIGXED		Maximum longitudinal stress
ENY		Shift of the Z axis in Y direction
ENZ		Shift of the Y axis in Z direction
USE_MY		Modified design value of the bending moment about Y axis
USE_MZ		Modified design value of the bending moment about Z axis
PARM_N	n	Parameter n

7.6.11 Checking for Buckling of Compression Members

Corresponds to chapter 8 in IS-800-2007.

- Forces and moments selection.
The forces and moments considered in this checking type are:

Design value of the axial force (positive if compressive, otherwise element is not processed). Represented as P_d .

- Class definition and effective section properties calculation.
The section class is determined by the sections general processing with the previously selected forces and moments if the selected option is partial, or with all the forces and moments if the selected option is full. The entire calculation is accomplished with the gross section properties.

- Criteria calculation.
When checking the buckling of compression members, the criterion is given by:

where:

Design buckling resistance.

= 1 for class 1, 2 or 3 sections.

= /A for class 4 sections.



Reduction factor for the relevant buckling mode, the program does not consider the torsional or the lateral-torsional buckling.

The c calculation in members of constant cross-section may be determined from:

where a is an imperfection factor that depends on the buckling curve. This curve depends on the cross-section type, producing the following values for a:

Imperfection factor a for IS-800-2007

Section type	Limits	Buckling axis	Buckling curve	a
Rolled I	h/b>1.2 and tf40mm	y – y	a	0.21
Rolled I	h/b>1.2 and tf40mm	z – z	b	0.34
Rolled I	h/b>1.2 and 40mm<t100mm	y – y	b	0.34
Rolled I	h/b>1.2 and 40mm<tf100mm	z – z	c	0.49
Rolled I	h/b1.2 and tf100mm	y – y	b	0.34
Rolled I	h/b1.2 and tf100mm	z – z	c	0.49
Rolled I	tf>100mm	y – y	d	0.76
Rolled I	tf>100mm	z – z	d	0.76

Welded I	tf40mm	y – y	b	0.34
Welded I	tf40mm	z – z	c	0.49
Welded I	tf >40mm	y – y	c	0.49
Welded I	tf >40mm	z – z	d	0.76

Rolled box and pipe	-	Any	a	0.21
Welded box and pipe (Using fyb)	-	Any	b	0.34

Welded box in other case	-	Any	b	0.34
Welded box	b/tf <30	y – y	c	0.49
Welded box	h/tw <30	z – z	c	0.49
U, L and T	-	Any	c	0.49

Where is the elastic critical force for the relevant buckling mode. (See section for Critical Forces and Moments Calculation).

The elastic critical axial forces are calculated in the planes XY () and XZ () and the corresponding values of and _, taking the smaller one as the final value for c.

- Output results are written in the CivilFEM results file as an alternative. Checking results: criteria and variables are described in the following table.

Checking for Buckling of Compression Members

Result	Concepts	Description
NED		Design value of the compressive force.
NBRD		Design buckling resistance of a compressed member.
CRT_CB		Compression buckling criterion.
CRT_TOT		IS 800:2007 global criterion.
CHI		Reduction factor for the relevant buckling mode.
BETA_A		Ratio of the used area to gross area.
AREA	A	Area of the gross section.
CHI_Y		Reduction factor for the relevant My buckling mode.
CHI_Z		Reduction factor for the relevant Mz buckling mode.
CLASS		Section Class.
PHI_Y		Parameter Phi for bending My.
PHI_Z		Parameter Phi for bending Mz.
LAM_Y		Non-dimensional reduced slenderness for bending My.
LAM_Z		Non-dimensional reduced slenderness for bending Mz.
NCR_Y		Elastic critical force for the relevant My buckling mode.
NCR_Z		Elastic critical force for the relevant Mz buckling mode.
ALP_Y		Imperfection factor for bending My.
ALP_Z		Imperfection factor for bending Mz.

7.6.12 Checking Lateral-Torsional Buckling of Members Subjected to Combined Bending and Axial Tension

Corresponds to chapter 9.3 in IS-800-2007.

- Forces and moments selection.
The forces and moments considered for this checking type are:

	Design value of the axial force (positive if tensile, otherwise element not processed if compressive).
	Design value of the bending moment about the relevant bending axis.

- Class definition and effective section properties calculation.
The section class is determined by the general processing of sections with the previously selected forces and moments if the selected option is partial, or with all the forces and moments if the selected option is full. The entire calculation is accomplished with the gross section properties.

- Criteria calculation.
With checking lateral-torsional buckling of members subjected to combined bending and axial tension, the value of the axial force is multiplied by a reduction factor
in order to consider the axial force and bending moment as a vector magnitude.
The value of depends on the country where the code will be applied. That factor is introduced as a property at member level, and typically its value is equal to: = 0.8
The stress in the extreme compression fiber is calculated as follows:

Where is the elastic section modulus for the extreme compression fiber and is the design value of the axial tension.

The verification equation is derived to:

Where:

- Output results are written in the CivilFEM results file as an alternative. Checking results: criteria and variables are described in the following table.

Checking Lateral-Torsional Buckling of Members Subjected to Combined Bending and Axial Tension

Results	Concepts	Description
NTSD		Design value of the axial tension.
MSD		Design value of the bending moment.
MEFFSD		Effective design internal moment.
MBRD		Buckling resistance moment of a laterally unrestrained beam.
CRT_LT		Lateral-torsional buckling criterion.
CRT_TOT		IS 800:2007 global criterion.
CLASS		Section Class.
WCOM		Elastic section modulus for the extreme compression fiber.
SCOMED		Net calculated stress in the extreme compression fiber.
CHI_LT		Reduction factor for lateral-torsional buckling.
BETA_W		Ratio of the used modulus to plastic modulus.
WPL		Plastic modulus.
PHI_LT		Parameter Phi for lateral-torsional buckling.
LAM_LT		Esbeltez adimensional reducida.
MCR		Elastic critical moment for lateral-torsional buckling.
ALP_LT		Non-dimensional reduced slenderness.

7.6.13 Checking for Lateral-Torsional Buckling of Members Subjected to Bending and Axial Compression

Corresponds to chapter 9.3 in IS-800-2007.

- Forces and moments selection.
The forces and moments considered in this checking type are:

	Design value of the axial compression (positive if compressive, otherwise element not processed if tensile).
	Design value of the bending moment about the relevant axis of bending.
	Design value of the bending moment about the secondary axis of bending.

- Criteria calculation.

When checking the lateral-torsional buckling of members subjected to combined bending and axial compression, the criterion to satisfy is as follows:

à Crt_TOT = Crt_N + Crt_My + Crt_Mz £ 1

where:

Crt_TOT	IS 800:2007 global criterion.
	Axial criterion.
	Bending criterion (principal axis).
	Bending criterion (secondary axis).
	Design buckling resistance for compression.
	Design buckling resistance moment (principal axis)
	Design buckling resistance moment (secondary axis).

The member resistances depend on the cross-section class and on the possibility that the lateral-torsional buckling is a potential failure mode for the structure.

Members with class 1 and 2 cross-sections shall satisfy:

where:

Where:

and	are the reduction factors defined at the section corresponding to Checking for Buckling of Compression Members.
and	are equivalent uniform moment factors for flexural bending. These factors are entered as properties at member level. (See section Data at Member Level, factors BetaMy and BetaMz).

Members with Class 1 and 2 cross-sections for which lateral-torsional buckling is a potential failure mode shall satisfy:

where:

where is an equivalent uniform moment factor for lateral-torsional buckling. This factor, as the precedent factors CMy and CMz.

Members with Class 3 cross-sections shall satisfy:

where k_y, k_z and c_minare as for Class 1 and 2 cross-sections.

Members with Class 3 cross-sections for which lateral-torsional buckling is a potential failure mode shall satisfy:

Members with Class 4 cross-sections shall satisfy:

where:

	are the same as for class 1 and 2 cross-sections, but use the effective area , instead of the gross area A.
	are the same as for class 3 cross-sections, but add the moment that appears by the shift of the center of gravity in the effective cross-section, when determining and .
	are defined in the section corresponding to Checking of members under bending and axial force and bi-axial bending.

Members with Class 4 cross-sections for which lateral-torsional buckling is a potential failure mode shall satisfy:

where:

	is similar to class 1 and 2 cross-sections, but uses the effective area A_eff, instead of the gross area A.
	is similar to class 2 cross-sections, but adds the moment that appears by the shift of the center of gravity in the effective cross-section, when determining _.

Checking Parameters:

Class	A
1	A	0.6	0.6	0	0
2	A	0.6	0.6	0	0
3	A	0.8	1	0	0
4		0.8	1	Depending on members and stresses	Depending on members and stresses

Interaction Factors:

Class	Section type
1 y 2	I, H
1 y 2	RHS
3 y 4	All sections

where:

y Limited slenderness values for y-y and z-z axes, less than 1.

- Output results are written in the CivilFEM results file as an alternative. Checking results: criteria and variables are described in the following table.

Checking for Lateral-Torsional Buckling of Members Subjected to Bending and Axial Compression

Result	Concepts	Description
NED		Design value of the axial compression force.
MYED		Design value of the bending moment about Y axis.
MZED		Design value of the bending moment about Z axis.
NBRD1		Design compression resistance of the cross-section.
MYRD1		Reduced design moment resistance of the cross-section about Y axis.
MZRD1		Reduced design moment resistance of the cross-section about Z axis.
NBRD2		Design compression resistance of the cross-section.
MYRD2		Reduced design moment resistance of the cross-section about Y axis.
MZRD2		Reduced design moment resistance of the cross-section about Z axis.
K_Y		Parameter K_y.
K_Z		Parameter K_z.
K_LT		Parameter K_LT.
CRT_N1		Axial criterion.
CRT_MY1		Bending Y criterion.
CRT_MZ1	·· ()/	Bending Z criterion.
CRT_1	CRT_N1+CRT_MY1 +CRT_MZ1	Criterion 1
CRT_N2	/	Axial criterion.
CRT_MY2	(+·)/	Bending Y criterion. K=K_yLT if torsion exists and if not present K=a_yK_y
CRT_MZ2	(+·)/	Bending Z criterion.
CRT_2	CRT_N2+CRT_MY2 +CRT_MZ2	Criterion 2
CRT_TOT	Crt_tot £ 1	IS 800:2007 global criterion.
CLASS		Section Class.
CHIMIN		Reduction factor for the relevant buckling mode.
CHI_Y		Reduction factor for the relevant My buckling mode.
CHI_Z		Reduction factor for the relevant Mz buckling mode.
CHI_LT		Reduction factor for lateral-torsional buckling.
AREA		Used area of the section (Gross or Effective).
WY		Used section Y modulus (Elastic, Plastic or Effective).
WZ		Used section Z modulus (Elastic, Plastic or Effective).
ENY		Shift of the Z axis in Y direction.
ENZ		Shift of the Y axis in Z direction.
NCR_Y		Elastic critical force for the relevant My buckling mode.
NCR_Z		Elastic critical force for the relevant Mz buckling mode.
MCR		Elastic critical moment for lateral-torsional buckling.
LAM_Y		Non-dimensional reduced slenderness for bending My.
LAM_Z		Non-dimensional reduced slenderness for bending Mz.
LAM_LT		Non-dimensional reduced slenderness for lateral-torsional buckling.

7.6.14 Critical Forces and Moments Calculation

The critical forces and moments, and , are needed for the different types of buckling checks. They are calculated based on the following formulation:

where:

	Elastic critical axial force in plane XY.
	Elastic critical axial force in plane XZ.
A	Gross area.
E	Elasticity modulus.
	Member slenderness in plane XY.
	Member slenderness in plane XZ.
	Radius of gyration of the member in plane XY.
	Radius of gyration of the member in plane XZ.
	Buckling length of member in plane XY.
	Buckling length of member in plane XZ.

The buckling length in both planes is the length between the ends restrained against lateral movement and it is obtained from the member properties, according to the following expressions:

where:

Cfbuckxy	Buckling factor in plane XY.
Cfbuckxz	Buckling factor in plane XZ.

For the calculation of the elastic critical moment for lateral-torsional buckling, Mcr, the following equation shall be used. This equation is only valid for uniform symmetrical cross-sections about the minor axis (Annex E, IS 800:2007). IS 800:2007 does not provide a method for calculating this moment in nonsymmetrical cross-sections or sections with other symmetry plane (angles, channel section, etc.).

where:

	Elastic critical moment for lateral-torsional buckling.
,	Factors depending on the loading and end restraint conditions.
k,	Effective length factors.
E	Elasticity modulus.
	Moment of inertia about the principal axis.
	Moment of inertia about the minor axis.
L	Length of the member between end restraints.
G	Shear modulus.
	–
	Coordinate of the point of load application. ANSYS always considers that the load is applied at the center of gravity, therefore: = 0.
	Coordinate of the shear center.
A	Cross-section area.

Factors C and k are read from the properties at member level.

The integration of the previous equation is calculated as a summation extending to each plate. This calculation is accomplished for each plate according to its ends coordinates:

, and , and its thicknesses.

where:

= thickness of plate i

= plate width

7.7. Steel Structures According to AASHTO LRFD (2012)

7.7.1. Checking Types

With CivilFEM it is possible to perform the following checking and analysis types:

- Tension	Section 6.8.2
- Flexure	6.12.2.2, A6
- Shear Force	6.10.9
- Flexure and axial force	6.9.2.2, 6.8.2.3
- Bending plus axial force	6.9.2.2, 6.8.2.3
- Compression members	6.9.4.1.2
- Compression members	6.9.4.1.3

7.7.2. Material Properties

For AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS 2010 checking, the following material properties are used:

Description	Property
Steel yield strength	Fy(th)
Ultimate strength	Fu(th)
Elasticity modulus	E
Poisson coefficient	n
Shear modulus	G

*th =thickness of plate

7.7.3. Check process

Necessary steps to conduct the different checks in CivilFEM are as follows:

a) Obtain material properties corresponding to the element stored in CivilFEM database and calculate the rest of the properties needed for checking:

Properties obtained from CivilFEM database:

Elasticity modulus E

Poisson’s ratio : ν

Yield strength: Fy (th)

Ultimate strength Fu (th)

Shear modulus G

Thickness of corresponding plate th

b) Obtain the cross-sectional data corresponding to the element.

c) Initiate the values of the plate’s reduction factors and the other plate’s parameters to determine its class.

d) Perform a check of the section according to the type of external load.

e) Results. In CivilFEM.

The required data for the different checking types are provided within tables found in their corresponding section of this manual.

7.7.4. Section Class and Reduction Factors Calculation

Steel sections are classified for flexure as compact, noncompact or slender-element sections. For a section to qualify as compact its flanges must be continuously connected to the web or webs and the width-thickness ratios of its compression elements must not exceed the limiting width-thickness ratios l_p. If the width-thickness ratio of one or more compression elements exceeds l_p but does not exceed l_r, the section is noncompact. If the width-thickness ratio of any element exceeds l_r, the section is referred to as a slender-element compression section. Compression classification is similar but with only one ratio to distinguish slender and non-slender sections

Therefore, the code suggests different lambda values depending on if the element is subjected to compression, flexure or compression plus flexure.

a) Length of elements:

The program will define the element length (b or h) as the length of the plate (distance between the extreme points), except when otherwise specified.

b) Flange or web distinction:

To distinguish between flanges or webs, the program follows the criteria below:

Once the principal axis of bending is defined, the program will examine the plates of the section. Fields Pty and Ptz of the plates indicate if they behave as flanges, webs or undefined, choosing the correct one for the each axis. If undefined, the following criterion will be used to classify the plate as flange or web: if |Dy|<|Dz| (increments of end coordinates) and flexure is in the Y axis, it will be considered a web; if not, it will be a flange. The reverse will hold true for flexure in the Z-axis.

· Hot rolled Steel Shapes:

Section I and C:

The length of the plate h will be taken as the value d for the section dimensions.

Section Box:

The length of the plate will be taken as the width length minus three times the thickness.

7.7.5. Members Subjected to Compression

In order to check for compression it is necessary to determine if the element is stiffened or unstiffened.

- For stiffened elements:

Pipe sections

Box sections

- Unstiffened elements:

Angular sections

Stem of T sections

7.7.6. Members Subjected to Bending

The bending check is only applicable to very specific sections. Therefore, the slenderness factor is listed for each section:

· Section I:

Flanges:

For hot rolled shapes

For welded sections ,

= minimum of 0.7 , / y but no less than 0.5.

Web:

· Section C

Flanges:

For hot rolled shapes

For welded sections ,

= minimum of y but no less than .

Web:

· Pipe section:

· Box section:

Flanges of box section:

Webs: the program distinguishes between the flange and web upon the principal axis chosen by the user.

· T section:

Flange:

Web: No limits are included for flexure classification, so class section is only checked for flange limit.

7.7.7. Members Subjected to Tension

The axial tension force must be taken as positive (if the tension force has a negative value, the element will not be checked)

The factored tensile resistance, _,shall be taken as the lesser of :

a) yielding in the gross section:

b) rupture in the net section:

Being:

	Effective net area.
	Gross area.
	Minimum yield stress.
	Minimum tensile strength.

Values of R_p and U must be introduced by the user according article 6.8.2.1.

The effective net area will be taken as A_g – AHOLES. The user will need to enter the correct value for AHOLES (the code indicates that the diameter is 1/16^th in. (2 mm) greater than the real diameter).

7.7.8. Members Subjected to Axial Compression

Axial compression check by la AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS 2010 of the design compressive strength, , are determined as follows:

Compressive Strength for Flexural Buckling

(a) for

(b) for

Being:

Where:

	Gross area of member.
Q	Slender element reduction factor.
	Governing radius of gyration about the buckling axis.
K	Effective length factor.
l	Unbraced length.

Factor Q for compact and noncompact sections is always 1. Nevertheless, for slender sections ( exceed ratio given in 10-G.6.1.1 ) , the value of has a particular procedure. Such procedure is described below:

Factor Q for slender sections:

For circular sections, there is a particular procedure of calculating Q. Such procedure is described below:

· For circular sections, Q is:

Factor Qs:

If there are several plates free, the value of Qs is taken as the biggest value of all of them. The program will check the slenderness of the section in the following order:

· Angular

If
If

· Stem of T

If
If

· Rolled shapes

If
If

· Other sections

If
If

Where l is the element slenderness and

	For hot rolled I sections
	for other sections

Factor Qa:

The calculation of factor Qa is an iterative process. Its procedure is the following:

7) An initial value of Q equal to Qs calculated before is taken.

8) With this value f = Q_sF_y is calculated.

9) For elements with stiffened plates, the effective width b_e is calculated.

10) With b_e the effective area is calculated.

11) With the value of the effective area, Qa is calculated.

· For a box section

· For other sections

If it is not within those limits,

With the b_e values for each plate, the part that does not contribute [t·(b‑b_e)] is subtracted from the area (where t is the plate thickness). Using this procedure, the effective area is calculated.

Finally, with Qs and Qa, Q is calculated.

Output results are written in the CivilFEM results file.

Compressive Strength for Flexural-Torsional Buckling

This type of check can be carried out for compact sections as well as for noncompact or slender sections. The steps for these three cases are as follows:

Nominal compressive strength, :

(a) for

(b) for

Where:

Factor Q for compact and noncompact sections is 1. Nevertheless, for slender sections, the Q factor has a particular procedure of calculation. Such procedure is equal to the one previously described.

(6.9.4.1.3-7)

Where:

	Effective length factor for torsional buckling.
G	Shear modulus (MPa).
	Warping constant (mm⁶).
J	Torsional constant (mm⁴).
	Moments of inertia about the principal axis (mm⁴).
	Coordinates of shear center with respect to the center of gravity (mm).

where:

A	Cross-sectional area of member.
l	Unbraced length.
	Effective length factor, in the z and y directions.
	Radii of gyration about the principal axes.
	Polar radius of gyration about the shear center.

In this formula, CivilFEM principal axes are used. If the CivilFEM axes are the principal axes ±5º sexagesimal degrees, Ky and Kz are calculated with respect to the Y and Z-axes of CivilFEM. If this is not the case (angular shapes, for example) axes U and V will be used as principal axes, with U as the axis with higher inertia.

Output results are written in the CivilFEM results file.

7.7.9. Members Subjected to Flexure

Summary of the checks done by CivilFEM:

SECTION TYPE	YIELDING	LTB	FLB	WLB	Conditions
BOX	X (6.12.2.2.2)		X (6.12.2.2.2)	X (6.12.2.2.2)	Non-slender web
PIPE	X (6.12.2.2.3)		X(local buckling) (6.12.2.2.3)		Compact, non-compact and slender under the limit for flexure check.
T SECTION	X (6.12.2.2.4)	X (6.12.2.2.4)	X (6.12.2.2.4)	X (6.12.2.2.4)	Non-slender flange
I SECTION (FLEXUREABOUT STRONG AXIS)	X	X (A.6.3.3)	X (A.6.3.2)		Non-slender web and Fy<70 ksi
DOUBLE T (FLEXURE ABOUT WEAK AXIS)	X		X (6.12.2.2.1)		Non-slender flanges
SECTION C (FLEXURE ABOUT STRONG AXIS)	X (6.12.2.2.5)	X (6.12.2.2.5)			Compact members
SECTION C (FLEXURE ABOUT WEAK AXIS)	X		X (6.12.2.2.5)		Non-slender flanges

The design flexural strength, f_f M_n, shall be determined as follows:

f_f = 1.00

Where M_nis the lowest value of four checks:

e) Yielding (Y)

f) Lateral-torsional buckling (LTB)

g) Flange local buckling (FLB)

h) Web local buckling (WLB)

The checks done depends on the section:

· Box (non-slender webs)

· Yielding

· FLB

· WLB

· Circular tubes (compact, non-compact and slender under the ratio limit

)

1. Yielding

2. Local buckling

· T shape

1. Yielding

If stem is in tension, the limit on is 1.6

If stem is in compression is limited to

2. LTB

(The plus sign for B shall apply when the stem is in tension and the minus sign shall apply when the stem is in compression)

3. FLB

: Elastic section modulus with respect to the compression flange

is not provided because the limiting slenderness value is larger than 12 (Eq. 6.10.2.2-1)

4. Local buckling of the stem

· I shape loaded on the strong axis (non-slender web)

1. Yielding

2. LTB

Where:

3. FLB

is the web plastification factor for the compression flange determined as specified in Article A6.2.1 or Article A6.2.2:

If is compact web

If is non-compact web,

is the hybrid factor and for sections that are checked in CivilFEM takes a value of 1.

· T shape loaded on weak axis (flanges compact or non-compact)

1. Yielding:

2. FLB

· C shape loaded on the strong axis ( web and flanges compact)

1. Yielding

2. LTB

If <<

If >

Where:

= radius of gyration about the weak axis(in)

J = Torsional constant St. Venant (in⁴)

= Elastic section modulus about strong axis(in³)

= distance between centroids of the flanges(in)

=warping constant(in⁶)

=Moment gradient modifier. Must be introduced by the user.

· C shape loaded on the weak axis (flanges compact or non-compact)

1. Yielding

= min (, 1.6)

2. FLB

Output results are written in the CivilFEM results file.

7.7.10. Members Subjected to Shear

The design shear strength, , shall be determined as follows:

For all provisions:

To calculate the nominal shear strength CivilFEM follows the provisions of the article 6.10.9.2 except for box-shaped (6.12.1.2.3b) and circular tubes (6.12.1.2.3c)

=, where D is total depth of the web.

C is the ratio of the shear-buckling resistance to the shear yield strength determined as:

a. For = 1.0 (AASHTO 6.10.9.3.2-4)

b. For (AASHTO 6.10.9.3.2-5)

c. For (AASHTO 6.10.9.3.2-6)

The web plate buckling coefficient, Kv, will be calculated as a constant equal to 5.0.

For shape-box sections D is the clear distance between flanges less inside corner radius on each side. Both webs area shall be considered effective in resisting the shear.

For circular tubes the nominal shear strength will be taken as:

, shear buckling resistance (ksi)taken as the larger of either:

Output results are written in the CivilFEM results file.

7.7.11. Members Subjected to Combined Forces

Checking of Members Subject to Flexure and Axial Tension / Compression

For this check, it is first necessary to determine the value of Mn. This value comes into play in the checking of formulas. The value of Mn, will be calculated in the same way as members subjected to flexure; thus, the nominal flexure strength (M_n) is the minimum of four checks:

1. Yielding

2. Lateral-torsional buckling

3. Flange local buckling

4. Web local buckling

In the case of having bending plus tension or bending plus compression, the interaction between flexure and axial force is limited by the following equations:

(6.8.2.3-2, 6.9.2.2-2)

(d) For

(6.8.2.3-1, 6.9.2.2-1)

Where:

	Axial force resulting from factored loads.
	Factored resistance.
	Moment resulting from factored loads.
	Factored flexural resistance .
y	Strong axis bending.
z	Weak axis bending.

The following checks are carried out by CivilFEM:

Axial force and flexural buckling
Bending moment Z direction
Bending moment Y direction

If one of these checks do not meet the code requirements, it will not be possible to check the member under flexure plus tension / compression.

Output results are written in the CivilFEM results file

7.8. Steel Structures According to AISC ASD/LRFD 14^thEd.

7.8.1. Material properties

For AISC 13^th Edition checking, the following material properties are used:

Description	Property
Steel yield strength	Fy(th)
Ultimate strength	Fu(th)
Elasticity modulus	E
Poisson coefficient	n
Shear modulus	G

*th =thickness of the plate

7.8.2. Section data

AISC 14^th Edition considers the following data set for the section:

- Gross section data

- Net section data

- Effective section data.

- Data belonging to the section and plates class.

Gross section data correspond to the nominal properties of the cross-section. For the net section, only the area is considered. This area is calculated by subtracting the holes for screws, rivets and other holes from the gross section area. (The area of holes is introduced within the structural steel code properties).

The AISC 14^TH Edition module utilizes the gross section data in user units and the CivilFEM axis or section axis as initial data. The program calculates the effective section data and the class data, and stores them in CivilFEM’s results file, in user units and in CivilFEM or section axis.

The section data used in AISC 14^TH Edition are shown in the following tables:

Description

Data

Input data:

1.- Height

2.- Web thickness

3.- Flanges thickness

4.- Flanges width

5.- Distance between flanges

6.- Radius of fillet (Rolled shapes)

7.- Toe radius (Rolled shapes)

8.- Weld throat thickness (Welded shapes)

9.- Web free depth

r₁

r₂

Output data

(None)

Description

Data

Reference axes

Input data:

1.- Depth in Y

2.- Depth in Z

3.- Cross-section area

4.- Moments of inertia for torsion

5.- Moments of inertia for bending

6.- Product of inertia

7.- Elastic resistant modulus

8.- Plastic resistant modulus

9.- Radius of gyration

10.- Gravity center coordinates

11.- Extreme coordinates of the perimeter

12.- Distance between GC and SC in Y and in Z

13.- Warping constant

14.- Shear resistant areas

15.- Torsional resistant modulus

16.- Moments of inertia for bending about U, V

17.- Angle Y->U or Z->V

Tky

tkz

Iyy, Izz

Izy

Wely, Welz

Wply, Wplz

iy, iz

Ycdg, Zcdg

Ymin, Ymax,

Zmin, Zmax

Yms, Zms

Yws, Zws

Xwt

Iuu, Ivv

CivilFEM

Section

CivilFEM

Principal

CivilFEM

Output data:

(None)

Description

Data

Input data:

1.- Gross section area

2.- Area of holes

Agross

Aholes

Output data:

1.- Cross-section area

Anet

The effective section depends upon the geometry of the section; thus, the effective section is calculated for each element and each of the ends of the element.

Description

Data

Input data:

(None)

Output data:

1.- Reduction factor

2.- Reduction factor

3.- Reduction factor

7.8.3. Structural steel code properties

For AISC 14^th Edition checking, besides the section properties, more data are needed for bucling checks. These data are shown in the following table.

Description

Data

Input data:

1.- Unbraced length of member (global buckling)

2.- Effective length factors Y direction

3.- Effective length factors Z direction

4.- Effective length factors for torsional buckling

5.- Flexural factor relative to bending moment

6.- Length between lateral restraints

KTOR

Output data:

1.- Compression class

2.- Bending class

CLS_COMP

CLS_FLEX

7.8.4. Check Process

Necessary steps to conduct the different checks in CivilFEM are as follows:

f) Obtain material properties corresponding to the element stored in CivilFEM database and calculate the rest of the properties needed for checking:
Properties obtained from CivilFEM database (materials):

Elasticity modulus	E
Poisson’s ratio	v
Yield strength	Fy (th)
Ultimate strength	Fu (th)
Shear modulus	G
Thickness of corresponding plate	th

g) Obtain the cross-sectional data corresponding to the element.

h) Initiate the values of the plate’s reduction factors and the other plate’s parameters to determine its class.

i) Perform a check of the section according to the type of external load.

j) Results. In CivilFEM, checking results for each element end are stored in the results file .CRCF

7.8.5. Design requirements

7.8.5.1. Design for Strength Using Load and Resistance Factor Design (LRFD)

Design shall be performed in accordance with:

Where:

	Required strength (LRFD).
	Nominal strength.
	Resistance factor.
	Design strength

7.8.5.2. Design for Strength Using Allowable Strength Design (ASD)

Design shall be performed in accordance with:

Where:

	Required strength (ASD)
	Nominal strength.
	Safety factor
	Allowable strength

Section Class and Reduction Factors Calculation.

Steel sections are classified as compact, noncompact or slender-element sections for bending sections and slender or non slender for compression sections. For a section to qualify as compact its flanges must be continuously connected to the web or webs and the width-thickness ratios of its compression elements must not exceed the limiting width-thickness ratios (see table B4.1 of AISC 14^th Edition). If the width-thickness ratio of one or more compression elements exceeds but does not exceed, the section is noncompact. If the width-thickness ratio of any element exceeds, (see table B4.1 of AISC 14^th Edition), the section is referred to as a slender-element compression section.

Therefore, the code suggests different lambda values depending on if the element is subjected to compression, flexure or compression plus flexure.

a) Length of elements:

The program will define the element length (b or h) as the length of the plate (distance between the extreme points), except when otherwise specified.

b) Flange or web distinction:

To distinguish between flanges or webs, the program follows the criteria below:

If (increments of end coordinates) and flexure is in the Y axis, it will be considered a web; if not, it will be a flange. The reverse will hold true for flexure in the Z-axis.

· Hot rolled Steel Shapes:

Section I and C:

The length of the plate h will be taken as the value d for the section dimensions.

Section Box:

The length of the plate will be taken as the width length minus three times the thickness.

7.8.5.3. Members subjected to compression

In order to check for compression it is necessary to determine if the element is stiffened or unstiffened.

- For stiffened elements:

Pipe sections

Box sections

- Unstiffened elements:

Angular sections

Stem of T sections

7.8.5.4. Members subjected to bending

The bending check is only applicable to very specific sections. Therefore, the slenderness factor is listed for each section:

· Section I and C:

=	69 MPa for hot rolled shapes (10 ksi)
	114 MPa for welded sections (16.5 ksi)

= minimum of () and () where and are the of flange and web respectively.

Flanges of rolled sections:

Flanges of welded sections:

Flange:

Always:

is the compression axial force (taken as positive). If in tension, it will be taken as zero.

· Pipe section:

Box section:

Flanges of box section:

Flanges: the program distinguishes between the flange and web upon the principal axis chosen by the user.

Always:

· T section:

Stem:

Flanges:

7.8.6. Checking of Members for Tension (Chapter D)

The axial tension force must be taken as positive (if the tension force has a negative value, the element will not be checked)

Design tensile strength and the allowable tensile strength , of tension members, shall be the lower value of :

c) yielding in the gross section:

d) rupture in the net section:

= 2.00 (ASD)

Being:

	Effective net area.
	Gross area.
	Minimum yield stress.
	Minimum tensile strength.

7.8.7. Checking of Members in Axial Compression (Chapter E)

The design compressive strength, ,and the allowable compressive strength, , are determined as follows:

The nominal compressive strength, , shall be the lowest value obtained according to the limit states of flexural buckling, torsional buckling and flexural-torsional buckling.

7.8.8. Compressive Strength for Flexural Buckling

This type of check can be carried out for compact sections as well as for noncompact or slender sections. These three cases adhere to the following steps:

Nominal compressive strength, :

(E3-1)

d) For :

e) for

Where:

	Gross area of member.
r	Governing radius of gyration about the buckling axis.
K	Effective length factor.
l	Unbraced length.
	Elastic critical buckling stress

Factor Q for compact and noncompact sections is always 1. Nevertheless, for slender sections, the value of Q has a particular procedure. Such procedure is described below:

Factor Q for slender sections:

For circular sections, there is a particular procedure of calculating Q. Such procedure is described below:

· For circular sections, Q is:

Factor Qs:

If there are several plates free, the value of Qs is taken as the biggest value of all of them. The program will check the slenderness of the section in the following order:

· Angular

If
If

· Stem of T

If
If

· Rolled shapes

If
If

· Other sections

If
If

Where l is the element slenderness and

	for I sections
	for other sections

Factor Qa:

The calculation of factor Qa is an iterative process. Its procedure is the following:

12) An initial value of Q equal to Qs is taken.

13) With this value is calculated.

14) This value is taken to calculate

15) For elements with stiffened plates, the effective width b_e is calculated.

16) With b_e the effective area is calculated.

17) With the value of the effective area, Qa is calculated, and the process starts again.

· For a box section

· For other sections

If it is not within those limits, = b

With the values for each plate, the part that does not contribute [t·(b‑)] is subtracted from the area (where t is the plate thickness). Using this procedure, the effective area is calculated.

Finally, with Qs and Qa, Q is calculated, and is obtained.

Output results are written in the CivilFEM results file (.CRCF).

7.8.9. Compressive Strength for Flexural-Torsional Buckling

This type of check can be carried out for compact sections as well as for noncompact or slender sections. The steps for these three cases are as follows:

Nominal compressive strength,:

f) for

(b) for

Where:

Factor Q for compact and noncompact sections is 1. Nevertheless, for slender sections, the Q factor has a particular procedure of calculation. Such procedure is equal to the one previously described.

Where:

	Effective length factor for torsional buckling.
G	Shear modulus (MPa).
	Warping constant (mm⁶).
J	Torsional constant (mm⁴).
	Moments of inertia about the principal axis (mm⁴).
	Coordinates of shear center with respect to the center of gravity (mm).

where:

A	Cross-sectional area of member.
l	Unbraced length.
	Effective length factor, in the z and y directions.
	Radii of gyration about the principal axes.
	Polar radius of gyration about the shear center.

Output results are written in the CivilFEM results file (.CRCF).

7.8.10. Compressive Strength for Flexure

Chapter F is only applicable to members subject to simple bending about one principal axis.

The design flexural strength,, and the allowable flexural strength, , shall be determined as follows:

For all provisions: = 0.90 (LRFD) = 1.67 (ASD)

Where is the lowest value of four checks according to sections F2 through F12:

i) Yielding

j) Lateral-torsional buckling

k) Flange local buckling

l) Web local buckling

The value of the nominal flexural strength with the following considerations:

For compact sections, if Lb < Lp only yielding of steel will be checked.
For T sections, and other compact sections, only yielding and torsional buckling will be checked.
The case of lateral-torsional buckling does not apply to sections loaded on the minor axis of inertia nor box or square sections.
The case of lateral-torsional buckling only applies for sections with double symmetry, channel and T sections. Therefore the rest of sections will be checked for torsion plus combined loads and will not be checked under flexure.
For slender sections, the code contemplates the following cases:

Shape	Limit State	Mr	Fcr	l	lp	lr
I, C loaded in the axis of higher inertia.	LTB
	FLB		rolled welded		Class B4.1	Class B4.1
	WLB		N.A.		Class B4.1	Class B4.1

Shape	Limit State	Mr	Fcr	l	lp	lr
I, C loaded in the axis of lower inertia.	LTB	N.A.	N.A.	N.A.	N.A.	N.A.
	FLB				Class B4.1	Class B4.1
	WLB	N.A.	N.A.	N.A.	N.A.	N.A.

Shape	Limit State	Mr	Fcr	l	lp	lr
Box	LTB
	FLB				Class B4.1	Class B4.1
	WLB		N.A.		Class B4.1	Class B4.1

Shape	Limit State	Mr	Fcr	l	lp	lr	Notes
Pipe	LTB	NA	NA	NA	NA	NA	Limited by Class B4.1
	FLB	Slender: Non-compact:			Class B4.1	Class B4.1
	WLB	NA	NA	NA	NA	NA

Shape	Limit State	Mr	Fcr	l	lp	lr
T, loaded in web plane	LTB		N.A.	N.A.	N.A.	N.A.
	FLB	N.A.	N.A.	N.A.	N.A.	N.A.
	WLB	N.A.	N.A.	N.A.	N.A.	N.A.

Where:

(positive sign if the stem is under tension, negative if it is under compression)

In T sections: stem in tension; stem in compression.

For slender webs the nominal flexural strength is the minimum of the following checks:

tension-flange yield
compression flange buckling

The first check uses the following formula:

where:

	Section modulus referred to tension flange.
	Yield strength of tension flange.

The second check uses the following formula:

where:

The critical stress depends upon different slenderness parameters such as l, , and in the following way:

For
For
For

The slenderness values have to be calculated for the following limit states:

Lateral torsional buckling

(International System units)

is the radius of gyration of compression flange plus one third of the compression portion of the web (mm).

By default, the program takes a conservative value of .

Flange local buckling

(IS units)

where:

and

Between these two slenderness, the program will choose values the value that produces a lower critical stress.

Output results are written in the CivilFEM results file (.CRCF).

7.8.11. Checking of Members for Shear (Chapter G)

The design shear strength, , and the allowable shear strength, , shall be determined as follows:

For all provisions: = 0.90 (LRFD) = 1.67 (ASD)

According to the limit states of shear yielding and shear buckling, the nominal shear strength, , of unstiffened webs is:

For webs of rolled I-shaped members with :

= 1.00 (LRFD) = 1.50 (ASD)

= 1.0 (web shear coefficient)

For webs of all other doubly symmetric shapes and singly symmetric shapes and channels is determined as follows:

= 1.0

Where is the overall depth times the web thickness.

It is assumed that there are no stiffeners; therefore, the web plate buckling coefficient will be calculated as a constant equal to 5.0.

Output results are written in the CivilFEM results file (.CRCF).

7.8.12. Checking of Members for Combined Flexure and Axial Tension / Compression (Chapter H)

5. Yielding

6. Lateral-torsional buckling

7. Flange local buckling

8. Web local buckling

In the case of having bending plus tension or bending plus compression, the interaction between flexure and axial force is limited by the following equations:

(e) For

(H1-1a)

(f) For

(H1-1b)

If the axial force is tension:

	Required tensile strength (N).
	Available tensile strength (N): (LRFD) or (ASD)
	Required flexural strength (N·mm).
	Available flexural strength (N·mm): Design: (LRFD) or Allowable: (ASD)
y	Strong axis bending.
z	Weak axis bending.
	Resistance factor for tension (Sect.D2)
	Resistance factor for flexure = 0.90
	Safety factor for tension (Sect D2)
	Safety factor for flexure = 1.67

If the axial force is compression:

	Required compressive strength (N).
	Available compressive strength (N): Design: (LRFD) or Allowable: (ASD)
	Required flexural strength (N·mm).
	Available flexural strength (N·mm): Design: (LRFD) or Allowable: (ASD)
Y	Strong axis of bending.
Z	Weak axis of bending.
	Resistance factor for compression =0.90
	Resistance factor for flexure = 0.90
	Safety factor for compression =1.67
	Safety factor for flexure = 1.67

The following checks are carried out by CivilFEM:

Axial force and flexural buckling
Bending moment Z direction
Bending moment Y direction

If one of these checks do not meet the code requirements, it will not be possible to check the member under flexure plus tension / compression.

Output results are written in the CivilFEM results file (.CRCF).

7.8.13. Checking of Members for Combined Torsion, Flexure, Shear and/or Axial Force (Chapter H)

= 0.90 (LRFD) = 1.67 (ASD)

· For the limit state of yielding, under normal stress:

· For the limit state of yielding, under shear stress:

· For the limit state of buckling:

- Where is calculated

Output results are written in the CivilFEM results file (.CRCF).

7.9. Steel Structures According to Structural Code (Spanish code)

For checking steel structures according to Structural code (Annex 22) in CivilFEM, it is possible to check structures composed by welded or rolled shapes under axial forces, shear forces and bending moments in 3D.

With CivilFEM it is possible to accomplish the following check and analysis types:

Check steel sections subjected to
- Tension	Art. 6.2.3
- Compression	Art. 6.2.4
- Bending	Art. 6.2.5
- Shear force	Art. 6.2.6
- Bending and Shear	Art. 6.2.8
- Bending and axial force	Art. 6.2.9
- Bending, shear and axial force	Art. 6.2.10
Check for buckling
- Compression members with constant cross-section	Art. 6.3.1
- Lateral-torsional buckling of beams	Art. 6.3.2
- Members subjected to bending and axial tension	N/A
- Members subjected to bending and axial compression	Art. 6.3.3

Valid cross-sections supported by CivilFEM for checks according to Structural code are the following:

All rolled shapes included in the program libraries (see the hot rolled shapes library).

The following welded beams: double T shapes, U or channel shapes, T shapes, box, equal and unequal legs angles and pipes.

Structural steel sections defined by plates.

CivilFEM considers the above sections as sections composed of plates; for example, an I-section is composed by five plates: four flanges and one web. These cross sections are therefore adapted to the method of analysis of Structural code. Obviously circular sections cannot be decomposed into plates, so these sections are analyzed separately.

7.1.1. Reference axis

With checks according to Structural code (Annex 22), CivilFEM includes three different coordinate reference systems. All of these systems are right-handed:

1. CivilFEM Reference Axis. (X_CF, Y_CF, Z_CF).

2. Cross-Section Reference Axis. (X_S, Y_S, Z_S).

3. Structural code Reference Axis. (Code axis). (X_code, Y_code, Z_code).

For the Structural code axes system:

The origin matches to the CivilFEM axes origin.

X_code axis coincides with CivilFEM X-axis.

Y_code axis is the relevant axis for bending and its orientation is defined by the user (in steel check process).

Z_code axis is perpendicular to the plane defined by X and Y axis, to ensure a right-handed system.

Relevant Axis for Bending in CivilFEM Reference System	Angle of Rotation (clockwise) of Structural Code Reference System respect to the CivilFEM Reference System
- Z_CF	90 º (Default value)
- Y_CF	180 º
+ Z_CF	270 º
+ Y_CF	0 º

7.1.2. Material properties

For Structural code checking, the following material properties are used:

Description	Property
Steel yield strength	Fy(th)
Ultimate strength	Fu(th)
Partial safety factors	g_M0 g_M1 g_M2
Elasticity modulus	E
Poisson coefficient	n
Shear modulus	G

*th =thickness of the plate

7.1.3. Section data

Structural code considers the following data set for the section:

Gross section data

Net section data

Effective section data

Data belonging to the section and plates class.

In the following tables, the section data used in Structural code are shown:

Description

Data

Input data:

1.- Height

2.- Web thickness

3.- Flanges thickness

4.- Flanges width

5.- Distance between flanges

6.- Radius of fillet (Rolled shapes)

7.- Toe radius (Rolled shapes)

8.- Weld throat thickness (Welded shapes)

9.- Web free depth

r₁

r₂

Output data

(None)

Description

Data

Reference axis

Input data:

1.- Depth in Y

2.- Depth in Z

3.- Cross-section area

4.- Moments of inertia for torsion

5.- Moments of inertia for bending

6.- Product of inertia

7.- Elastic resistant modulus

8.- Plastic resistant modulus

9.- Radius of gyration

10.- Gravity center coordinates

11.- Extreme coordinates of the perimeter

12.- Distance between GC and SC in Y and in Z

13.- Warping constant

14.- Shear resistant areas

15.- Torsional resistant modulus

16.- Moments of inertia for bending about U, V

17.- Angle Y->U or Z->V

Tky

tkz

Iyy, Izz

Izy

Wely, Welz

Wply, Wplz

iy, iz

Ycdg, Zcdg

Ymin, Ymax,

Zmin, Zmax

Yms, Zms

Yws, Zws

Xwt

Iuu, Ivv

CivilFEM

Section

CivilFEM

Principal

CivilFEM

Output data:

(None)

The effective section depends on the section geometry and on the forces and moments that are applied to it. Consequently, for each element end, the effective section is calculated.

Description

Data

Reference axis

Imput data:

(None)

Output data:

1.- Cross-section area

2.- Moments of inertia for bending

3.- Product of inertia

4.- Elastic resistant modulus

5.- Gravity center coordinates

6.- Distance between GC and SC in Y and in Z

7.- Warping constant

8.- Shear resistant areas

Aeff

Iyyeff, Izzeff

Izyeff

Wyeff, Wzeff

Ygeff, Zgeff

Ymseff, Zmseff

Yws, Zws

CivilFEM

Section

CivilFEM

7.1.4. Structural steel code properties

For Structural code checking, besides the section properties, more data are needed for buckling checks. These data are shown in the following table.

Description	Structural code
Input data:
1.- Unbraced length of member (global buckling). Length between lateral restraints (lateral-torsional buckling).	L
2.- Buckling effective length factors in XY, XZ planes YZ (Effective buckling length for plane XY =LK XY ) (Effective buckling length for plane XZ =LK XZ ).	K XY, K XZ
3.- Lateral buckling factors, depending on the load and restraint conditions.	C1, C2, C3
4.- Equivalent uniform moment factors for flexural buckling.	CMy, CMz
5.- Equivalent uniform moment factors for lateral-torsional buckling.	CMLt
6.- Effective length factor regarding the boundar conditions.	K
7.- Warping effective factor.	KW

7.1.5. Check Process

The checking process includes the evaluation of the following expression:

Evaluation steps:

1. Read the loading check requested by the user.

2. Read the CivilFEM axis to be considered as the relevant axis for bending so that it coincides with the Y axis of Structural code. In CivilFEM, by default, the principle bending axis that coincides with the +Y axis of Structural code is the –Z.

3. The following operations are necessary for each selected element:

a. Obtain material properties of the element stored in CivilFEM database and calculate the rest of the properties needed for checking:
Properties obtained from CivilFEM database:

Calculated properties:

Epsilon, material coefficient:

b. Obtain the cross-section data corresponding to the element.

c. Initialize values of the effective cross-section.

d. Initialize reduction factors of section plates and the rest of plate parameters necessary for obtaining the plate class.

f. Obtain internal forces and moments: , , , _, , within the section.

g. Specific section checking according to the type of external load. The specific check includes:

1. If necessary, selecting the forces and moments considered for the determination of the section class and used for the checking process.

2. Obtaining the cross-section class and calculating the effective section properties.

3. Checking the cross-section according to the external load and its class by calculating the check criterion.

h. Store the results.

7.1.6. Section Class and Reduction Factors Calculation

Sections, according to Structural code, are made up by plates. These plates can be classified according to:

4. Plate function: webs and flanges in Y and Z axis, according to the considered relevant axis of bending.

5. Plate union condition: internal plates or outstand plates.

For checking the structure for safety, Structural code classifies sections as one of four possible classes:

Class 1	Cross-sections which can form a plastic hinge with the rotation capacity required for plastic analysis.
Class 2	Cross-sections which can reach their plastic moment resistance, but have limited rotation capacity.
Class 3	Cross-sections for which the stress in the extreme compression fiber of the steel member can reach the yield strength, but local buckling is liable to prevent the development of the plastic moment resistance.
Class 4	Cross-sections for which it is necessary to make explicit allowances for the effects of local buckling when determining their moment resistance or compression resistance.

The cross-section class is the highest (least favorable) class of all of its elements: flanges and webs (plates). First, the class of each plate is determined according to the limits of Structural code. The plate class depends on the following:

1. The geometric width to thickness ratio with the plate width properly corrected according to the plate and shape type.

GeomRat = Corrected_Width / thickness

· Welded Shapes:

Double T section:

Internal webs or flanges:

Corrected width = d

d Web free depth

Outstand flanges:

Corrected width

Where:

B	Flanges width
T_w	Web thickness
	Radius of fillet

T section:

Internal webs or flanges:

Corrected width = d

Outstand flanges:

Corrected width = B/d

C section:

Internal webs or flanges:

Corrected width = d

Outstand flanges:

Corrected width

B – –

L section:

Corrected width =

Angle flange width

Box section:

Internal webs:

Corrected width = H

H Height

Internal flanges:

Corrected width

Web thickness

Circular hollow section

Corrected width = H

· Rolled Shapes:

Double T section:

Internal webs or flanges:

Corrected width = d

d Web free depth

Outstand flanges:

Corrected width = B/2

B Flanges width

T Section:

Internal webs or flanges:

Corrected width = d

Outstand flanges:

Corrected width = B/2

C Section:

Internal webs or flanges:

Corrected width = d

Outstand flanges:

Corrected width = B

L Section:

Corrected width =

Angle flange width

Box section:

Internal webs:

Corrected width = d

Internal flanges:

Corrected width

Flanges thickness

Pipe section:

Corrected width = H

Limit (class)

where:

a	Compressed length / total length
y
	Buckling factor
	The higher stress in the plate ends.
	The lower stress in the plate ends.

A linear stress distribution on the plate is assumed.

The procedure to determine the section class is as follows:

1. Obtain stresses at first plate ends from the stresses applied on the section, properly filtered according to the check type requested by the user.

2. Calculate the parameters: a, and k₀

For internal plates:




	= infinite

For outstand plates with an absolute value of the stress at the free end greater than the corresponding value at the fixed end:

For

= infinite

For outstand plates with an absolute value of the stress at the free end lower than the corresponding value at the fixed end:

For

= infinite

Cases in which infinite are not included in Structural code. With these cases, the plate is considered to be practically in tension and it will not be necessary to determine the class. These cases have been included in the program to avoid errors, and the value has been adopted because the resultant plate class is 1 and the plate reduction factor is r = 1 (the same values as if the whole plate was in tension). The reduction factor is used later in the effective section calculation.

3. Obtain the limiting proportions as functions of: a, and k₀and the plate characteristics (internal, outstand: free end in compression or tension).

Internal plates:

	for
	for
	for
	for
	for
	for

Outstand plates, free end in compression:

Outstand plates, free end in tension:

Above is the general equation used by the program to obtain the limiting proportions for determining plate classes. In addition, plates of Structural code may be checked according to special cases.

For example:

In sections totally compressed:

a= 1; = 1 for all plates

In sections under pure bending:

a = 0.5; = -1 for the web

a = 1; = 1 for compressed flanges

4. Obtain the plate class:

If		GeomRat	< Limit(1)	Plate Class = 1
If	Limit(1) ≤	GeomRat	< Limit(2)	Plate Class = 2
If	Limit(2) ≤	GeomRat	< Limit(3)	Plate Class = 3
If	Limit(3) ≤	GeomRat		Plate Class = 4

Repeat these steps (1,2,3,4) for each section plate.

6. GeomRat = outer diameter/ thickness.

For class 4 sections, the section resistance is reduced, using the effective width method.

Effective_length_end 1 =

Effective_length_end 2 =

The following formula from Structural code has been implemented for this process:

1. Internal plates:

For (Both ends compressed)

ec3_1

corrected plate width

plate_width = real plate width

For (end 1 in compression and end 2 in tension)

ec3_2

2. Outstand plates:

For (Both ends in compression: end 1 fixed, end 2 free)

ec3_3

For (end 1 fixed and in tension, end 2 free and in compression)

ec3_4

For (end 1 fixed and in compression, end 2 free and in tension)

ec3_5

If end 2 is the fixed end, the values and are switched.

The global reduction factor r is obtained by as follows:

For internal compression elements

For

For outstands compression elements:

For

The plate slendernesss given by:

where:

= corrected plate width

t = relevant thickness

e = material parameter

= buckling factor

To determine effective section properties, three steps are followed:

2. The resultant section properties are obtained and factors α and are calculated again.

3. Effective widths of webs are calculated so that the finalized effective section is determined. Finally, the section properties are recalculated once more.

Each checking type follows a specific procedure that will be explained in the following sections.

7.1.7. Checking of Members in Axial Tension

Corresponds to chapter 6.2.3 in Structural Code (Annex 22).

1. Forces and moments selection.
The forces and moments considered for this checking type are:

= FX Design value of the axial force (positive if tensile, element not processed if compressive).

2. Class definition and effective section properties calculation.
For this checking type, the section class is always 1 and the considered section is either the gross or net section.

3. Criteria calculation.
For members under axial tension, the general criterion Crt_TOT is checked at each section. This criterion coincides with the axial criterion Crt_N.

where is the design tension resistance of the cross-section, taken as the smaller value of:

plastic design strength

of the gross cross-section

ultimate design strength

of the net cross-section

4. Output results are written in the CivilFEM results file (.CRCF). Checking results: criteria and variables are described in the following table:

Result	Concepts	Description
NED		Design value of the tensile force.
NTRD		Design tensile strength of the cross-section.
CRT_N		Axial criterion.
CRT_TOT		Structural Code global criterion.
NPLRD		Design plastic strength of the gross cross-section.
NURD		Ultimate design strength

7.1.8. Checking of Members in Axial Compression

Corresponds to chapter 6.2.4 in Structural Code (Annex 22).

1. Forces and moments selection.
The forces and moments considered for this checking type are:

= FX Design value of the axial force (positive if compressive, element not processed if tensile).

2. Class definition and effective section properties calculation.
For this check type, the section class is always 1 and the considered section is the gross or net section.

3. Criteria calculation.
For members in axial compression, the general criterion Crt_TOT is checked at each section. This criterion coincides with the axial criterion Crt_N:

where is the design compression resistance of the cross-section

Class 1,2 or 3 cross-sections:

design plastic resistance of the gross section

Class 4 cross sections:

4. Output results written in the CivilFEM results file (.CRCF) . Checking results: criteria and variables are described at the following table.

Result	Concepts	Description
NED		Design axial force.
NCRD		Design compression strength of the cross-section.
CRT_N		Axial criterion.
CRT_TOT		Structural global criterion.
CLASS		Section Class.
AREA		Area of the section (Gross or Effective).

7.1.9. Checking of Members under Bending Moment

Corresponds to chapter 6.2.5 in Structural Code (Annex 22).

1. Forces and moments selection.
The forces and moments considered for this checking type are:

Design value of the bending moment along the relevant axis for bending.

3. Criteria calculation.
For members subjected to a bending moment in the absence of shear force, the following condition is checked at each section:

where:

design value of the bending moment

design moment resistance of the cross-section

Class 1 or 2 cross-sections:

Class 3 cross sections:

Class 4 cross sections:

4. Output results are written in the CivilFEM results file (.CRCF). Checking results: criteria and variables are described in the following table.

Result	Concepts	Description
MED		Design value of the bending moment.
MCRD		Design moment resistance of the cross-section.
CRT_M		Bending criterion.
CRT_TOT		Structural Code global criterion.
CLASS		Section Class.
W		Used section modulus (Elastic, Plastic or Effective).

7.1.10. Checking of Members under Shear Force

Corresponds to chapter 6.2.6 in Structural Code (Annex 22)..

1. Forces and moments selection.
The forces and moments considered for this checking type are:

Design value of the shear force perpendicular to the relevant axis of bending.

2. Class definition and effective section properties calculation.
For this checking type, the section class is always 1 and the effective section is the gross section.

3. Criteria calculation.
With members under shear force, the following condition is checked at each section:

where:

	design value of the shear force
	design plastic shear resistance:
	shear area, obtained subtracting from the gross area the summation of the flanges areas:

Modifications to the previous computation of are as follows:

· Rolled I and H sections, load parallel to web:

· Rolled channel sections, load parallel to web:

· Rolled I and H sections with load parallel to web:

but not less than η

· Rolled T shaped sections with load parallel to web:

Where:

η = 1.2 for steels with fy = 460 MPa

η= 1.0 for steels with fy > 460 MPa

Web depth

Web thickness

4. Output results are written in the CivilFEM results file (.CRCF). Checking results: criteria and variables are described in the following table.

Result	Concepts	Description
VED		Design value of the shear force.
VPLRD		Design plastic shear resistance.
CRT_S		Shear criterion.
CRT_TOT		Structural Code global criterion.
CLASS		Section Class.
S_AREA	Av	Shear area.

7.1.11. Checking of Members under Bending Moment and Shear Force

Corresponds to chapter 6.2.8 in Structural Code (Annex 22).

1. Forces and moments selection.
The forces and moments considered for this checking type are:

Design value of the shear force perpendicular to the relevant axis of bending.

Design value of the bending moment along the relevant axis of bending.

3. Criteria calculation.
For members subjected to bending moment and shear force, the following condition is checked at each section:

Where:

design resistance moment of the cross-section, reduced by the presence of shear.

The reduction for shear is applied if the design value of the shear force exceeds 50% of the design plastic shear resistance of the cross-section; written explicitly as:

The design resistance moment is obtained as follows:

a. For double T cross-sections with equal flanges, bending about the major axis:

b. For other cases the yield strength is reduced as follows:

Note: This reduction of the yield strength fy is applied to the entire section. Structural code only requires the reduction to be applied to the shear area, and therefore, it is a conservative simplification.

For both cases, is the smaller value of either or .

is the design moment resistance of the cross-section, calculated according to the class.

4. Output results are written in the CivilFEM results file (.CRCF). Checking results: criteria and variables are described in the following table.

Result	Concepts	Description
MED		Design value of the bending moment.
VED		Design value of the shear force.
MVRD		Reduced design resistance moment of the cross-section.
CRT_BS		Bending and Shear criterion.
CRT_TOT		Structural code global criterion.
CLASS		Section Class.
S_AREA		Shear area.
W		Used section modulus (Elastic, Plastic or Effective).
VPLRD		Design plastic shear resistance.
RHO		Reduction factor.

7.1.12. Checking of Members under Bending Moment and Axial Force

Corresponds to chapter 6.2.9 in Structural Code (Annex 22).

1. Forces and moments selection.
The forces and moments considered for this checking type are:

	Design value of the axial force.
	Design value of the bending moment along the relevant axis of bending.
	Design value of the bending moment about the secondary axis of bending.

2. Class definition and effective section properties calculation.
The section class is determined by the general processing of the sections with the previously selected forces and moments if the selected option is partial, or with all the forces and moments if the selected option is full. These calculations are accomplished with the gross section properties.

3. Criteria calculation.
For members subjected to bi-axial bending and in absence of shear force, the following conditions at each section are checked:

Class 1 and 2 sections:

This condition is equivalent to:

Where and are the design moment resistance of the cross-section, reduced by the presence of the axial force:

Where a and b are constants, which may take the following values:

For I and H sections:

a = 2 and b =5n

For circular tubes:

a = 2 and b =2

For rectangular hollow sections:

but

For solid rectangles and plates (the rest of sections):

(if it does not reach half the tension strength of the web)

The same is applicable for bending around the z-z axis due to the axial force. There is no reduction when the following condition is fulfiled:

In absence of , the previous check can be reduced to:

Condition equivalent to:

Class 3 sections (without holes for fasteners):

Condition equivalent to:

Crt_TOT = Crt_N + Crt_My + Crt_Mz £ 1

Where is the elastic resistant modulus about the y axis and is the elastic resistant modulus about the z axis.

In absence of , the above criterion becomes:

Which is equivalent to:

Crt_TOT = Crt_N + Crt_My £ 1

Class 4 sections:

Condition equivalent to:

Crt_TOT = Crt_N + Crt_My + Crt_Mz £ 1

Where:

	effective area of the cross-section
	effective section modulus of the cross-section when subjected to a moment about the y axis
	effective section modulus of the cross-section when subjected to a moment about the z axis
	shift of the center of gravity along the y axis
	shift of the center of gravity along the z axis

Without , the above criterion becomes:

which is equivalent to:

Crt_TOT = Crt_N + Crt_My + Crt_Mz £ 1

4. Output results are written in the CivilFEM results file (.CRCF). Checking results: criteria and variables are described in the following table.

Result	Concepts	Description
NED		Design value of the axial force.
MYED		Design value of the bending moment about Y axis.
MZED		Design value of the bending moment about Z axis.
NCRD		Design compression resistance of the cross-section
MNYRD		Reduced design moment resistance of the cross-section about Y axis
MNZRD		Reduced design moment resistance of the cross-section about Z axis
CRT_N		Axial criterion
CRT_MY		Bending criterion along Y
CRT_MZ		Bending criterion along Z
ALPHA	α	Alpha constant
BETA	β	Beta constant
CRT_TOT	Crt_tot £ 1	Structural Code global criterion
CLASS		Section Class
AREA		Area of the section utilized (Gross or Effective)
WY		Used section Y modulus (Elastic, Plastic or Effective)
WZ		Used section Z modulus (Elastic, Plastic or Effective)
SIGXED		Maximum longitudinal stress
ENY		Shift of the Z axis in Y direction
ENZ		Shift of the Y axis in Z direction
USE_MY		Modified design value of the bending moment about Y axis
USE_MZ		Modified design value of the bending moment about Z axis
PARM_N	n	Parameter n

7.1.13. Checking of Members under Bending, Shear and Axial Force

Corresponds to chapter 6.2.10 in Structural Code (Annex 22)..

1. Forces and moments selection. The forces and moments considered for this checking type are:

	Design value of the axial force.
	Design value of the shear force perpendicular to the secondary axis of bending.
	Design value of the shear force perpendicular to the relevant axis of bending.
	Design value of the bending moment about the relevant axis of bending.
	Design value of the bending moment about the secondary axis of bending.

2. Class definition and effective section properties calculation.
The section class is determined by the general processing of the sections with the previously selected forces and moments if the selected option is partial, or with all the forces and moments if the selected option is full. The entire calculation is accomplished with the gross section properties.

where:

for

	for

This yield strength reduction is selectively applied to the resistance of the cross-section along each axis, according to the previous conditions.

Note: The yield strength reduction is applied to the entire cross-section; however, Structural code only requires the reduction to be applied to the shear area. Thus, it is a conservative simplification.

4. Output results are written in the CivilFEM results file (.CRCF). Checking results: criteria and variables are described in the following table.

Result	Concepts	Description
NED		Design value of the axial force.
VZED		Design value of the shear force.
VYED		Design value of the shear force.
MYED		Design value of the bending moment about Y axis.
MZED		Design value of the bending moment about Z axis.
NCRD		Design compression resistance of the cross-section.
MNYRD		Reduced design moment Y resistance of the cross-section.
MNZRD		Reduced design moment Z resistance of the cross-section.
CRT_N		Axial criterion.
CRT_MY		Bending Y criterion.
CRT_MZ		Bending Z criterion.
ALPHA	α	Alpha constant.
BETA	β	Beta constant.
RHO_Y	ρ	Reduction factor for MNYRD.
RHO_Z	ρ	Reduction factor for MNZRD.
CRT_TOT	Crt_tot £ 1	Structural code global criterion.
AREA		Used area of the section (Gross or Effective).
WY		Used section Y modulus (Elastic, Plastic or Effective).
WZ		Used section Z modulus (Elastic, Plastic or Effective).
SIGXED		Maximum longitudinal stress.
ENY		Shift of the Z axis in Y direction.
ENZ		Shift of the Y axis in Z direction.
USE_MY		Modified design value of the bending moment about Y axis.
USE_MZ		Modified design value of the bending moment about Z axis.
SHY_AR		Shear Y area.
SHZ_AR		Shear Z area.
PARM_N	n	Parameter n.

7.1.14. Checking for Buckling of Members in Compression

Corresponds to chapter 6.3.1 in Structural Code (Annex 22)..

1. Forces and moments selection.
The forces and moments considered in this checking type are:

Design value of the axial force (positive if compressive, otherwise element is not processed).

3. Criteria calculation.
When checking the buckling of compression members, the criterion is given by:

where:

Design buckling resistance.

b = 1 for class 1, 2 or 3 sections.

b = for class 4 sections.

Reduction factor for the relevant buckling mode, the program does not consider the torsional or the lateral-torsional buckling.

The c calculation in members of constant cross-section may be determined from:

where a is an imperfection factor that depends on the buckling curve. This curve depends on the cross-section type, producing the following values for a:

Section type	Limits	Buckling axis	Steel f_y	Buckling curve		a
Rolled I	h/b>1.2 and t40mm	y – y	< 460 MPa	a		0.21
			≥ 460 MPa	a0		0.13
Rolled I	h/b>1.2 and t40mm	z – z	< 460 MPa	b		0.34
			≥ 460 MPa	a0		0.13
Rolled I	h/b>1.2 and 40mm<t100mm	y – y	< 460 MPa	b		0.34
			≥ 460 MPa	a		0.21
Rolled I	h/b>1.2 and 40mm<t100mm	z – z	< 460 MPa	c		0.49
			≥ 460 MPa	a		0.21
Welded I	h/b1.2 and t100mm	y – y	< 460 MPa	b		0.34
			≥ 460 MPa	a		0.21
Welded I	h/b1.2 and t100mm	z – z	< 460 MPa	c		0.49
			≥ 460 MPa	a		0.21
Rolled I	t>100mm	y – y	< 460 MPa	d		0.76
			≥ 460 MPa	c		0.49
Rolled I	t>100mm	z – z	< 460 MPa	d		0.76
			≥ 460 MPa	c		0.49

Welded I	t40mm	y – y	all	b	0.34
Welded I	t40mm	z – z	all	c	0.49
Welded I	t >40mm	y – y	all	c	0.49
Welded I	t >40mm	z – z	all	d	0.76

Pipes	Hot finished	all	< 460 MPa	a	0.21
			≥ 460 MPa	a0	0.13
	Cold formed	all	all	c	0.49
Reinforced box sections	Thick weld: a/t>0.5 b/t<30 h/tw<30	all	all	c	0.49
	In other case	all	all	b	0.34

U, T, plate	-	all	all	c	0.49

L	-	all	all	b	0.34

Where is the elastic critical force for the relevant buckling mode. (See section for Critical Forces and Moments Calculation).

In the case of angular sections, the buckling length will be taken as the highest among the buckling lengths on the Y and Z axis.

5. Output results are written in the CivilFEM results file (.CRCF). Checking results: criteria and variables are described in the following table.

Result	Concepts	Description
NED		Design value of the compressive force.
NBRD		Design buckling resistance of a compressed member.
CRT_CB		Compression buckling criterion.
CRT_TOT		Structural code global criterion.
CHI		Reduction factor for the relevant buckling mode.
BETA_A		Ratio of the used area to gross area.
AREA	A	Area of the gross section.
CHI_Y		Reduction factor for the relevant My buckling mode.
CHI_Z		Reduction factor for the relevant Mz buckling mode.
CHI_V		Reduction factor for the principal axis V.
CHI_U		Reduction factor for the principal axis U.
CLASS		Section Class.
PHI_Y		Parameter Phi for bending My.
PHI_Z		Parameter Phi for bending Mz.
PHI_V		Parameter Phi for the principal axis V.
PHI_U		Parameter Phi for the principal axis U.
LAM_Y		Non-dimensional reduced slenderness for bending My.
LAM_Z		Non-dimensional reduced slenderness for bending Mz.
LAM_V		Non-dimensional reduced slenderness for the principal axis V.
LAM_U		Non-dimensional reduced slenderness for the principal axis U.
NCR_Y		Elastic critical force for the relevant My buckling mode.
NCR_Z		Elastic critical force for the relevant Mz buckling mode.
NCR_V		Elastic critical force for the principal axis V.
NCR_U		Elastic critical force for the principal axis U.
ALP_Y		Imperfection factor for bending My.
ALP_Z	αz	Imperfection factor for bending Mz.

7.1.15. Checking for Lateral-Torsional Buckling of Beams Subjected to Bending

Corresponds chapter 6.3.2 in EN Structural Code (Annex 22)..

1. Forces and moments selection.
The forces and moments considered for this checking type are:

Design value of the bending moment about the relevant axis of bending.

3. Criteria calculation.
When checking for lateral-torsional buckling of beams, the criterion shall be taken as:

where:

Design buckling resistance moment of a laterally unrestrained beam.

b_w = 1 for class 1and 2 sections.

b_w = for class 3 sections.

b_w = for class 4 sections.

c_LT

Reduction factor for lateral-torsional buckling.

The value of c_LT is calculated as:

Where:

is the imperfection factor for lateral-torsional buckling:

Section type	Limits	Buckling curve	α
Rolled I	h/b≤2 h/b>2	a b	0.21 0.34
Welded I	h/b≤2 h/b>2	c d	0.49 0.76
Others			0.76

is the elastic critical moment for lateral-torsional buckling.

4. Output results are written in the CivilFEM results file (.CRCF). Checking results: criteria and variables are described in the following table.

Result	Concepts	Description
MED		Design value of the bending moment.
MBRD		Buckling resistance moment of a laterally unrestrained beam.
CRT_LT		Lateral-torsional buckling criterion.
CRT_TOT		Structural code global criterion.
CLASS		Section Class.
CHI_LT		Reduction factor for lateral-torsional buckling.
BETA_W		Ratio of the used modulus to plastic modulus.
WPL		Plastic modulus.
PHI_LT		Parameter Phi for lateral-torsional buckling.
LAM_LT		Non-dimensional reduced slenderness.
MCR	Mcr	Elastic critical moment for lateral-torsional buckling.
ALP_LT		Imperfection factor for lateral-torsional buckling.

7.1.16. Checking for Lateral-Torsional Buckling of Members Subjected to Bending and Axial Compression

Corresponds to chapter 6.3.3 in Structural Code (Annex 22).

1. Forces and moments selection.
The forces and moments considered in this checking type are:

= FX	Design value of the axial compression (positive if compressive, otherwise element not processed if tensile).
= MY or MZ	Design value of the bending moment about the relevant axis of bending.
= MZ or MY	Design value of the bending moment about the secondary axis of bending.

3. Criteria calculation.

The following criterion will always be calculated:

Crt_1 = Crt_N1 + Crt_My1 + Crt_Mz1 £ 1

Elements without torsional buckling:

Elements which may have torsional buckling:

à Crt_2 = Crt_N2 + Crt_My2 + Crt_Mz2 £ 1

à Crt_TOT = Max (Crt_1, Crt_2)

Where:

	Axial force criterion 1.
	Bending moment criterion for principal axis 1.
	Bending moment criterion for secondary axis 1
Crt_TOT1	General criterion 1.
	Axial force criterion 2.
	Bending moment criterion 2 for principal axis without torsional buckling
	Bending moment criterion 2 for principal axis when torsional buckling is considered.
	Bending moment criterion 2 for secondary axis.
Crt_TOT2	Criterion 2
Crt_TOT=max (Crt_TOT1, Crt_TOT2 )	Global criterion.

Where:

( when torsional buckling is not considered).

and are the reduction factors defined for the section corresponding to the check for Buckling of Compression Members.

lateral buckling factor according to 6.3.2.2. Assumes the value of 1 for members not susceptible to torsional deformations.

and shifts of the centroid of the effective area relative to the centre of gravity of the gross section in class 4 members for y, z axes.

, and are equivalent uniform moment factors for flexural bending. These factors are entered as member properties at member level. (See and ).

Checking Parameters:

Class	A
1	A	0.6	0.6	0	0
2	A	0.6	0.6	0	0
3	A	0.8	1	0	0
4		0.8	1	Depending on members and stresses	Depending on members and stresses

Interaction Factors:

Class	Section type
1 y 2	I, H
1 y 2	RHS
3 y 4	All sections

where:

Limited slenderness values for y-y and z-z axes, less than 1.

4. Output results are written in the CivilFEM results file (.CRCF). Checking results: criteria and variables are described in the following table.

Result	Concepts	Description
NED		Design value of the axial compression force.
MYED		Design value of the bending moment about Y axis.
MZED		Design value of the bending moment about Z axis.
NBRD1		Design compression resistance of the cross-section.
MYRD1		Reduced design moment resistance of the cross-section about Y axis.
MZRD1		Reduced design moment resistance of the cross-section about Z axis.
NBRD2		Design compression resistance of the cross-section.
MYRD2		Reduced design moment resistance of the cross-section about Y axis.
MZRD2		Reduced design moment resistance of the cross-section about Z axis.
K_Y		Parameter _.
K_Z		Parameter _.
K_LT		Parameter _.
CRT_N1		Axial criterion.
CRT_MY1		Bending Y criterion.
CRT_MZ1		Bending Z criterion.
CRT_1	CRT_N1+CRT_MY1+CRT_MZ1	Criterion 1
CRT_N2	/	Axial criterion.
CRT_MY2		Bending Y criterion. K= if torsion exists and if not present K=
CRT_MZ2		Bending Z criterion.
CRT_2	CRT_N2+CRT_MY2+CRT_MZ2	Criterion 2
CRT_TOT	Crt_tot £ 1	Structural code global criterion.
CLASS		Section Class.
CHIMIN		Reduction factor for the relevant buckling mode.
CHI_Y		Reduction factor for the relevant My buckling mode.
CHI_Z		Reduction factor for the relevant Mz buckling mode.
CHI_LT		Reduction factor for lateral-torsional buckling.
AREA		Used area of the section (Gross or Effective).
WY		Used section Y modulus (Elastic, Plastic or Effective).
WZ		Used section Z modulus (Elastic, Plastic or Effective).
ENY		Shift of the Z axis in Y direction.
ENZ		Shift of the Y axis in Z direction.
NCR_Y		Elastic critical force for the relevant My buckling mode.
NCR_Z		Elastic critical force for the relevant Mz buckling mode.
MCR		Elastic critical moment for lateral-torsional buckling.
LAM_Y		Non-dimensional reduced slenderness for bending My.
LAM_Z		Non-dimensional reduced slenderness for bending Mz.
LAM_LT		Non-dimensional reduced slenderness for lateral-torsional buckling.

7.1.17. Critical Forces and Moments Calculation

The critical forces and moments, and M_cr, are needed for the different types of buckling checks. They are calculated based on the following formulation:

where:

	Elastic critical axial force in plane XY.
	Elastic critical axial force in plane XZ.
A	Gross area.
E	Elasticity modulus.
	Member slenderness in plane XY.
	Member slenderness in plane XZ.
	Radius of gyration of the member in plane XY.
	Radius of gyration of the member in plane XZ.
	Buckling length of member in plane XY.
	Buckling length of member in plane XZ.

The buckling length in both planes is the length between the ends restrained against lateral movement and it is obtained from the member properties, according to the following expressions:

where:

Cfbuckxy	Buckling factor in plane XY.
Cfbuckxz	Buckling factor in plane XZ.

where:

	Elastic critical moment for lateral-torsional buckling.
	Factors depending on the loading and end restraint conditions.
	Effective length factors.
E	Elasticity modulus.
	Moment of inertia about the principal axis.
	Moment of inertia about the minor axis.
L	Length of the member between end restraints.
G	Shear modulus.

	Coordinate of the point of load application. By default the load is applied at the center of gravity, therefore:.
	Coordinate of the shear center.
A	Cross-section area.

Factors C and k are read from the properties at structural element level.

where:

= thickness of plate i

dA = * dl

= plate width

c_nj	is the participation factor for mode n in the j^th direction.
	is the eigenvector value for mode n and degree of freedom i.
	is the mass matrix.
	Defines the magnitude of the rigid body response of degree of freedom i to impose rigid body motion in the jth direction and takes the following form:

X, Y, and Z	are the coordinates of the respective node.
	are the coordinates of center of rotation.
	is the unit vector (carrying 1 for row j and the rest being zeros)

MARC EXIT 13	Input data errors were detected by the program.
MARC EXIT 2004	Operator matrix (for example, stiffness matrix in stress analysis) has become non-positive definite and the analysis terminated.
MARC EXIT 3002	Convergence has not occurred within the allowable number of iterations.
EXIT 3015	If the minimum time step is reached and the analysis still fails to converge.

NODAL RESULTS
UT	Displacements
UR	Rotations
RF	Reaction forces
RM	Reaction moments
CPRESS	Contact normal stress
CSHEAR	Contact shear stress
CNORMF	Contact normal force
CSHEARF	Contact shear force
CSTATUS	Contact status

TRUSS/BEAM/SHELL/SOLID RESULTS
S	Stresses
E	Total strain
EE	Elastic strain
PE	Plastic strain
PEEQ	Equivalent plastic strain
MISES	Von Mises equivalent stress
PRESS	Equivalent pressure stress
SF	Forces (O.BS.)
SM	Moments (O.BS.)
SE	Generalized strains (O.BS.)
SK	Curvatures (O.BS.)
CE	Cracking strain (N.B.)
SP	Principal stresses (O.S.)

AG	Design ground acceleration for the reference return period [a_g].
SPTYPE	Spectrum type defined. Elastic or Design.
C	Ground type coefficient [S].
QH	Horizontal behavior factor [q_h].
QV	Vertical behavior factor [q_v].
DMPRAT	Ratio of viscous damping ratio of the structure [] (in %).

Subsoil types for Type 1 Elastic	A	B	C	D	E
S	1.00	1.20	1.15	1.35	1.40
b₀	2.50	2.50	2.50	2.50	2.50
T_B(s)	0.15	0.15	0.20	0.20	0.15
T_C(s)	0.40	0.50	0.60	0.80	0.50
T_D(s)	2.0	2.0	2.0	2.0	2.0
T_E(s)	3.50	3.50	3.50	3.50	3.50
K_d1	2/3	2/3	2/3	2/3	2/3
K_d2	5/3	5/3	5/3	5/3	5/3
K₁	1.00	1.00	1.00	1.00	1.00
K₂	2.00	2.00	2.00	2.00	2.00

Subsoil types for Type 2 Elastic	A	B	C	D	E
S	1.00	1.35	1.50	1.80	1.60
b₀	2.50	2.50	2.50	2.50	2.50
T_B(s)	0.05	0.05	0.10	0.10	0.05
T_C(s)	0.25	0.25	0.25	0.30	0.25
T_D(s)	2.0	2.0	2.0	2.0	2.0
T_E(s)	3.50	3.50	3.50	3.50	3.50
K_d1	2/3	2/3	2/3	2/3	2/3
K_d2	5/3	5/3	5/3	5/3	5/3
K₁	1.00	1.00	1.00	1.00	1.00
K₂	2.00	2.00	2.00	2.00	2.00

q	=	behavior factor. The values for this factor differ for the horizontal seismic action and for the vertical seismic action. Therefore, this factor assumes two different values q_h and q_v depending on the material type.
K_d1, K_d2	=	exponents which influence the shape of the design spectrum for a vibration period greater than T_C, T_D respectively.

Subsoil types	Type 1	Type 2
	0.90	0.45
T_B(s)	0.05	0.05
T_C(s)	0.15	0.15
T_D(s)	1.0	1.0

AB	Ratio of the basic seismic acceleration to the gravity acceleration.
SPTYPE	Spectrum type to be calculated (Linear or Simplified).
RO	Dimensionless risk coefficient [ρ].
C	Coefficient of the ground type.
K	Coefficient of contribution.
OMEGA	Structure type [W].
MU	Ductility coefficient [m].

	Parameter
area	A
circle area	Ac
box number 3	box_3
steel thermal expansion	α_steel

Predefined constants
Constant Name	Value	Description
π	3.1415926	The ratio of a circle’s circumference to its diameter.
PI, pi	3.1415926	The ratio of a circle’s circumference to its diameter.
e	2.71828	Euler‘s constant.
g_SI	9.80665	Earth’s gravity in the International System of Units.
g_ft	32.174	Earth’s gravity in Imperial Units (feet per square second).

Parameters	Input	Output	Unit
B	35	35	deg
C	sin (B)	0.5735	-
D	cos (B)	0.8191	-
E	tan (B)	0.7002	-

	Parameter	Magnitude	Unit entered by the User
Rectangle side 1	R1	Length	cm
Rectangle side 2	R2	Undefined	?
Rectangle perimeter	Rp	Undefined	?
Triangle side A	tA	Length	in
Triangle side B	tB	Length	ft
Triangle side C	tC	Length	in
Triangle perimeter	tPer	Length	in

	Parameters	Input	Units
Rectangle side 1	R1	5	cm
Rectangle side 2	R2	6	? (m)
Rectangle perimeter	Rp	2*(R1 + R2)	? (m)
Triangle side A	tA	3	in
Triangle side B	tB	7	ft
Triangle side C	tC	4	in
Triangle perimeter	tPer	tA + tB + tC	in

	Param	Input	Consistent values	Output
Rectangle side 1	R1	5 cm	0.05 m	5 cm
Rectangle side 2	R2	6 (m)	6	6 (m)
Rect. perimeter	Rp	2*(R1 + R2)	12.1	12.1 (m)
Triangle side A	tA	3 in	0.0762 m	3 in
Triangle side B	tB	7 ft	2.1336 m	7 ft
Triangle side C	tC	4 in	0.1016 m	4 in
Tri. perimeter	tPer	tA + tB + tC	2.3114 m	91 in

Chapter 2 Loading

Chapter 3 Solution

3.3.1.1. Modal stresses and reactions

3.3.1.2. Participation factors and effective modal masses

3.3.2. Harmonic Analysis

3.3.2.1. Small amplitude vibration problem

3.3.2.2. Performing a Harmonic Response Analysis

3.3.3. Spectrum Analysis

3.3.4.1. Direct Integration

3.3.4.2. Time Step Definition

3.4.4. Convergence Controls

3.4.4.1. Residual Checking

3.4.4.2. Displacement Checking

3.5.2. Pardiso Direct Sparse method

3.5.3. Parallel processing

3.6.3. Output results

Chapter 4 Results

4.2.5. Forces and moments in beams

4.2.6. Generalized strains in beams and trusses

4.4. Combining Result Files

5.1.1. Forces and Moments Sign Criteria

5.1.4. Axial + Bending Check and Design

9.1.4.3 Reinforcement Design

5.2.3.2 Calculation Hypothesis

5.2.3.2 Calculation Process

5.3.4.1. Cases

5.3.4.2. Steel amount

5.3.6.1. General Requirements

5.3.6.2. Checking Requirements

5.5.2.1. Checking whether shear reinforcement is required

5.5.2.2. Shear Criterion

5.5.3.1. Checking whether shear reinforcement is required

5.5.3.2. Maximum Design Shear Force Resisted Without Crushing of the Concrete Compressive Struts

5.5.3.3. Ratio of Reinforcement Required

5.5.2.3. Checking whether shear reinforcement is required

5.5.2.4. Shear Criterion

5.5.3.4. Checking whether shear reinforcement is required

5.5.3.5. Maximum Design Shear Force Resisted Without Crushing of the Concrete Compressive Struts

5.5.3.6. Ratio of Reinforcement Required

5.6.2.1. Shear Strength Provided by Concrete

5.6.2.2. Shear Strength Provided by Shear Reinforcement

5.6.2.3. Nominal Shear Strength

5.6.2.4. Minimum Reinforcement

5.6.2.5. Shear Criterion

5.6.3.1. Shear Strength Provided by Concrete

5.6.3.2. Required Reinforcement Contribution

5.6.3.3. Required Reinforcement

5.7.2.1. Shear Strength Provided by Concrete

5.7.2.2. Shear Strength Provided by Shear Reinforcement

5.7.2.3. Nominal Shear Strength

5.7.2.4. Minimum Reinforcement

5.7.2.5. Shear Criterion

5.7.3.1. Shear Strength Provided by Concrete

5.7.3.2. Required Reinforcement Contribution

5.7.3.3. Required Reinforcement

5.8.2.1. Shear Strength Provided by Concrete

5.8.2.2. Shear strength provided by shear reinforcement

5.8.2.3. Nominal shear strength

5.8.2.4. Minimum reinforcement

5.8.2.5. Shear criterion

5.8.3.1. Shear strength provided by concrete

5.8.3.2. Required reinforcement contribution

5.8.3.3. Required reinforcement

5.9.2.1. Checking Failure by Compression

5.9.2.2. Checking Failure by Tension in the Web

5.9.2.3. Shear Criterion

5.9.3.1. Checking Compression Failure in the Web

5.9.3.2. Checking If the Shell Requires Shear Reinforcement

Chapter 2
Loading

Chapter 3
Solution

Chapter 4
Results