Code check for Structural Concrete Beams

Checking and reinforcement designing of reinforced concrete beams in CivilFEM ACT 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 Eurocode 2, from CivilFEM ACT, is the code from the checking and design post-processes are developed. The specified checks and designs will be determined ahead:

Code	Type of check
Eurocode 2	Bending + Axial
	Shear + Torsion
	Cracking

The necessary properties for each of these checks will be assigned in that Check properties section, being properly explained on chapters ahead.

2D Interaction Diagram

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 ACT 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 ACT, 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 ACT, 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

Diagram Construction Process

As stated in the previous section, CivilFEM ACT 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 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 ACT, 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.

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 ACT 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 ACT 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.

Axial Load and Biaxial Bending Checking

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.

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 ANSYS Workbench results file.

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.

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).

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.

Eurocode 2

If the active code is Eurocode 2, 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 (‰) =

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

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.

ACI 318-19

If the active code is ACI 318-19, 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 318-19) document. This value is taken from the member properties if the user has specified a constant value or is calculated according to the code as follows (if the member property is not defined or the value is set as 0.0):

Where:

with E = 29.000.000 psi

e_t is the maximum strain obtained at the reinforcement and is the strength reduction factor for compression controlled sections (21.2.2 of ACI 318 2019):

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 318-19) 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.

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

Figure 0‑1 ACI 349-01 strain limits

The theoretical values of the interaction diagram are affected by the strength reduction factor f (Chapter 9.3.2 of Code Requirements for Nuclear Safety-Related Concrete Structures (ACI 349-13) document). This value is taken from the member properties if the user has specified a constant value or is calculated according to the code as follows (if the member property is not defined or the value is set as 0.0):

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

Member with spiral reinforcement =0.75

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:

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.

GB50010

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

Figure 0‑2 GB50010 Strain Limits

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

Shear and Torsion

Previous considerations

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

Table 0‑1 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.

Shear and torsion code properties

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

EUROCODE 2

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.

ACI318 / ACI 349

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).

GB50010

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).
A_cor:	Area enclosed within the hoop reinforcements for torsion A_st1 (Art. 7.6.4).
A_cor1:	Area enclosed within the hoop reinforcements for torsion A_st1 (Art. 7.6.4) of branch 1(e. x. Flange).
A_cor2:	Area enclosed within the hoop reinforcements for torsion A_st1 (Art. 7.6.4) of branch 2(e. x. Flange).
U_cor:	Perimeter of the A_cor area (Art. 7.6.4).
U_cor1:	Perimeter of the A_cor1 area of branch 1 (Art. 7.6.4).
U_cor2:	Perimeter of the A_cor2 area of branch 2 (Art. 7.6.4).
W_t:	Plastic resistance of torsion moment (Art. 7.6.4).
W_t1:	Plastic resistance of torsion moment of branch 1 (Art. 7.6.4).
W_t2:	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).
ALF_h:	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.

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.

Rectangular Section Parameters

Where Tky Section width in Y.

Tkz Section width in Z.

Eurocode 2 and ITER






.

ACI 318 and ACI 349

GB50010

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

ACI 318 and ACI 349

GB50010

REC = 0.04 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

Circular Section Parameters

Where: OD Diameter of the section.

Eurocode 2

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 = 0.04 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

GB50010

REC = 0.04 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

Circular Hollow Section Parameters

Where: OD Diameter of the section.

TKWALL Thickness of the wall.

Eurocode 2

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 = 0.04 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

GB50010

REC = 0.04 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

Double T / I-Section Parameters

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

TW Web thickness.

Eurocode 2

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

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

T-Section Parameters

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

TW Web thickness.

Eurocode 2

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

GB50010

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

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

Shear Check:

Checking elements for shear according to Eurocode 2 (EN 1992-1-1:2004/AC:2008) 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)

Compressive mean stress

Tensile mean stress

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 ANSYS Workbench results file.

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):

Where :

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

Results are written for each end in the ANSYS Workbench 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

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.

Torsion Check:

The torsion checking according to Eurocode 2 (EN 1992-1-1:2004/AC:2008) 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)

Compressive mean stress

Tensile mean stress

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 ANSYS Workbench results file.

Moment Description

Design torsional moment

5) Calculating the angle  between the concrete compressive struts and the longitudinal axis of the member. Angle  is determined according to both the transverse and longitudinal torsion reinforcements with the expression below:

This angle must satisfy the following condition:

If the angle obtained does not satisfy this condition, the value of the nearest limit is adopted.

When evaluating , three reinforcement cases exist. For a section with no torsion reinforcement, cotanqis defined by the user within the previous limits. If the section only contains transverse reinforcement, cotanq =1.0, and if it contains only longitudinal reinforcement, cotanq = 2.5. Obviously, in these cases the section will not satisfy torsion checking.

6) 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 as the parameters:

TRDMAX	=
CRT_1	=

7) 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 ANSYS Workbench 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.

8) 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	=

9) 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 ANSYS Workbench results file for each end.

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

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)

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)

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.

Shear Design

Shear reinforcement design according to Eurocode 2 (EN 1992-1-1:2004/AC:2008) 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)

Compressive mean stress

Tensile mean stress

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 ANSYS Workbench results file.

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 ANSYS Workbench 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):

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 ANSYS Workbench 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 ANSYS Workbench results file as the following parameters:



DSG_CRT	=	Design criterion

Torsion Design

Torsion reinforcement design according to Eurocode 2 (EN 1992-1-1:2004/AC:2008) 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)

Compressive mean stress

Tensile mean stress

3) Obtaining forces and moments acting on the section. The torsional moment that acts on the section is obtained from the ANSYS Workbench 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 ANSYS Workbench 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 ANSYS Workbench 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 ANSYS Workbench 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.

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).

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).

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.

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.

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.

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).

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.

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:

VNàNominal 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.

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.

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.

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 for solid sections:

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.

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 318-14. 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.

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.

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.

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).

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).

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.

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.

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.

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 318-14.

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 318-14.

Shear and Torsion according to ACI 318-19

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 318-19) document.

Shear Checking

Shear checking according to ACI 318-19 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. Section geometrical requirements must be defined within CivilFEM database. 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 within the CivilFEM database. Required data:

web width or diameter of circular section, (parameter BW_VY or BW_VZ).

Ratio of tensile reinforcement to

4) Obtaining reinforcement data of the section. Data concerning reinforcements of the section must be included within the CivilFEM database. Required data are as follows:

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

area of the reinforcement per unit length (reinforcement ratio) in both the Y and Z directions, (These can be defined directly using the ASSY and ASSZ parameters).

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

total area of the reinforcement legs, (parameters ASY and ASZ ).

s spacing of the stirrups, (parameter S).

or with the following input:

s spacing of the stirrups, (parameter S).

f diameter of bars, (parameter PHI).

N number of reinforcement legs, (parameters NY or NZ).

5) Obtaining forces and moments acting on the section. The forces that act on the section are obtained from the CivilFEM results file.

Force Description

Factored design shear force

Factored axial force occurring simultaneously to the shear force (positive for compression).

6) Calculates Av,min as the greater value of:

7) 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, according to As defined and Av, min:

where:

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

ratio of tensile reinforcement defined by the user. Default value for is equal to

N is positive for compression and negative for tension

Size effect modification factor, determined as:

Limits for Vc are taken as:

Once Vc is calculated, the cross-sectional dimensions limit is checked. If end doesn´t fill the next equation, the end is not checked by CivilFEM

The calculation result for both element ends is stored in the CivilFEM results file as the parameter VC:

VC Shear strength provided by concrete.

8) 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:

VS Shear strength provided by transverse reinforcement.

9) Calculating the nominal shear strength of section. The nominal shear strength () is the sum 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.

10) Obtaining shear criterion. The section will be valid for shear if the following condition is fulfilled:

f 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.

Torsion Checking

The torsion checking according to ACI 318-19 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. Geometrical parameters used for torsion calculations must be defined within the CivilFEM database. The required data are as follows:

web width or diameter of circular section, (parameter BW_VY or BW_VZ).

area enclosed by outside perimeter of concrete cross section, (parameter ACP).

outside perimeter of the concrete cross section, (PCP).

area enclosed by center line of the outermost closed transverse torsional reinforcement, (parameter AOH).

perimeter of centerline of outermost closed transverse torsional reinforcement, (parameter PH).

gross area enclosed by shear flow path, (parameter AO).

3) Obtaining reinforcement data of the section. Data concerning reinforcements of the section must be included within the CivilFEM database.. Required data are as follows:

Transverse Reinforcement

area of transverse reinforcement per unit of length, (this can be defined directly using the ASST parameter as part of the commands).

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

closed stirrups area for torsion, (parameter AST).

s spacing of closed stirrups, (parameter S).

Or with the following data:

s spacing of closed stirrups, (parameter S).

diameter of the closed stirrups, (parameter PHIT).

Longitudinal Reinforcement

total area of the longitudinal reinforcement, (parameter ASL).

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

diameter of longitudinal bars, (parameter PHIL).

N number of longitudinal bars, (parameter N).

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

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:

a) Solid sections:

b) Hollow sections:

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:

a) Solid sections:

b) 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:

a) Solid sections:

b) Hollow sections:

Φ strength reduction factor of the section, (0.75 for shear and torsion).

Therefore, the validity torsion criterion is defined as follows for solid sections:

For hollow sections:

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 Φ value is stored in the CivilFEM results file for both element ends as the parameter TFI.

Combined Shear and Torsion Checking

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 318-19. 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 318-19. 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.

Shear Design

The shear designing according to ACI 318-19 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. Section geometrical requirements must be defined within the CivilFEM database. Required data for shear designing are the following ones:

area of concrete section.

3) Obtaining geometrical parameters depending on specified code. Geometrical parameters used for shear designing must be defined within the CivilFEM database. The Required data are as follows:

web width or diameter of the circular section, (parameter BW_VY or BW_VZ).

Ratio of tensile reinforcement to

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, (parameter ALPHA). If this angle is equal to zero or it is not defined, a = 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.

Force Description

Design shear force

Nu Axial force (positive for compression)

6) Calculates Av,min as the greater value of:

7) Calculating the shear strength provided by concrete assuming . The shear strength provided by concrete () is calculated with the following assumption

where:

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

ratio of tensile reinforcement defined by the user. Default value for is equal to

N is positive for compression and negative for tension

Limits for Vc are taken as:

Once Vc is calculated, the cross-sectional dimensions limit is checked. If end doesn´t fill the next equation, the end is not checked by CivilFEM

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:

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 60,000 psi). (Parameter FY).

If and is required ( ) then:

If and is not required Vc is recalculated using the formula for :

where:

Size effect modification factor, determined as:

Then step 7 and 8 are done again with the new value of Vc.

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).

Torsion Design

The torsion designing according to ACI 318-19 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. Geometrical parameters used for torsion designing must be defined within the CivilFEM database. The required data are as follows:

web width or diameter of the circular section, (parameter BW_VY or BW_VZ).

Area enclosed by outside perimeter of concrete cross section, (parameter ACP).

Outside perimeter of the concrete cross section, (PCP).

Area enclosed by centerline of the outermost closed transverse torsional reinforcement, (parameter AOH).

Perimeter of centerline of outermost closed transverse torsional reinforcement (parameter PH).

Gross area enclosed by shear flow path, (parameter AO).

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 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 solid sections:

In 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:

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.

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 (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 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 318-19.

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 318-19.

Shear and Torsion according to ACI 349-13

Strength reduction factor ϕ is taken as ϕ = 0.75 for shear and torsion according to Chapter 9.3.2 of Code Requirements for Nuclear Safety Related Concrete Structures (ACI 349-13) documents.

Shear Check

Shear checking according to ACI 349-13 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).

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.

Torsion Check

Torsion checking according to ACI349-13and 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.

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.

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

Shear Design

Shear design according to ACI 349-13 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).

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.

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).

Torsion Design

The design of torsion reinforcements according to ACI349-13 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.

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

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.

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 ACI349-13.

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 ACI349-13.

Shear and Torsion according to GB50010 -2010

Shear Checking

Shear checking for elements according to GB50010-2010 follows the steps below:

1) Obtaining materials 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 defined previously. 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. Section geometrical requirements must be defined within the CivilFEM database. Required data for shear checking are the following:

total cross-sectional area of the concrete section.

3) Obtaining geometrical parameters depending on specified code. Geometrical parameters used for shear calculations must be defined within the CivilFEM database. Required data are the following:

bminimum width of the section over the effective depth, (parameter BW_VY or BW_VZ)

effective height of the section, (parameter D_Y or D_Z).

the web height (parameter HW_VY).

4) Obtaining the reinforcement data of the section. The section reinforcement data should be defined in the database of CivilFEM. The necessary data are:

a Angle formed by the reinforcement with the longitudinal axis of the piece where they meet (ALPHA parameter).

Reinforcement area per length unit, (AS/S parameter).

Alternatively, the amount of reinforcement can be determined from:

total area in the reinforcement legs (AS parameter).

s spacing among stirrups, ( S parameter).

Or from the data below:

s spacing among stirrups ( S parameter).

f diameter among bars, (PHI parameter).

N reinforcement leg number, (N).

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.

Force Description

V Design shear force

N Axial force

Shear Checking 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 b_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.

Shear Checking with Seismic Action

Shear checking of elements according to GB50010-2010 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.

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 (parameter D_Y or D_Z )

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.

Torsion Checking

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. Section geometrical requirements must be defined within the CivilFEM database. 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. Geometrical parameters used for torsion calculations must be defined within the CivilFEM database. The required data are the following:

bminimum width of the section over the effective depth, (parameter BW_VY or BW_VZ), or section inner diameter for circular section.

height of the section, (parameter D_Y or D_Z), section outer diameter for circular section.

the web height (parameter HW_VY).

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 section reinforcement data must be defined in the database of CivilFEM. The required data are:

Transverse Reinforcement

transverse reinforcement area per length unit (AST/S parameter).

Alternatively, the amount of the reinforcement can be calculated from:

critical tensile zone, (AST parameter).

s spacing between stirrups, (ST).

Or from the data below:

s spacing between stirrups (ST).

diameter of the bar of the stirrup, (PHIT parameter).

Longitudinal Reinforcement

Total area of the longitudinal reinforcement, (ASL parameter).

Alternatively, the amount of the reinforcement can determined from:

Longitudinal bar diameter, (PHIL diameter).

N Longitudinal bar number, (N parameter).

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

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)

Combined Shear and Torsion Checking

1) Checking for whether section dimensions meet the requirements.

Where

If or 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.

Shear Design

Elements shear design according to GB50010-2010 follows the steps below:

1) Obtaining materials 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:

design compressive strength of concrete.

design tensile strength of concrete.

design tensile strength for of shear reinforcement.

2) Obtaining geometrical data of the section. Section geometrical requirements must be defined within the CivilFEM database. Required data for shear checking are the following:

total cross-sectional area of the concrete section.

3) Obtaining geometrical parameters depending on specified code. Geometrical parameters used for shear calculations must be defined within CivilFEM database, see ~SECMDF command. Required data are the following:

bminimum width of the section over the effective depth, (parameter BW_VY or BW_VZ)

effective height of the section, (parameter D_Y or D_Z).

the web height (parameter HW_VY).

4) Obtaining reinforcement data of the section. Data concerning reinforcements of the element section must be included within CivilFEM database. Required data are the following:

area of reinforcement per unit of length, (parameter AS/S).

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

Force Description

V Design shear force

N Axial force

Shear Designing 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), b_c =0.8,

· For concrete C55-75, a linear interpolation is made for b_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):

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.

Shear Designing with Seismic Action

Shear checking of elements according to GB50010-2010 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.

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 , 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.

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. Section geometrical requirements must be defined within CivilFEM database. Required data for shear checking are the following:

total cross-sectional area of the concrete section.

thickness of a box section (TWY)

bminimum width of the section over the effective depth, (parameter BW_VY or BW_VZ), or section inner diameter for circular section.

height of the section, (parameter D_Y or D_Z ), section outer diameter for circular section.

the web height (parameter HW_VY).

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.

4) Obtaining reinforcement data of the section. Data concerning reinforcements of the section must be included within the CivilFEM database. Required data are the following ones:

Transverse Reinforcement

Area of transverse reinforcement per unit length, (parameter AST/S).

Longitudinal Reinforcement

total area of the longitudinal reinforcement, (parameter ASL).

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

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. 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:

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. Section geometrical requirements must be defined within CivilFEM database. Required data for shear checking are the following ones:

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 database. Required data are the following:

bminimum width of the section over the effective depth, (parameter BW_VY or BW_VZ), or section inner diameter for circular section.

effective height of the section, (parameter D_Y or D_Z), section outer diameter for circular section.

the web height (parameter HW_VY).

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. Data concerning reinforcements of the element section must be included within the CivilFEM database. Required data are the following:

Shear Reinforcement

area of reinforcement per unit length, (parameter AS/S )

Transverse Torsion Reinforcement

area of reinforcement per unit length, (parameter AS/S).

Torsion Longitudinal Reinforcement

total area of the longitudinal reinforcement, (parameter ASL).

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.

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

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.

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.

Cracking Checking

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

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.

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.

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).

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.

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.

Reinforcement Stress Calculation

Checking results are stored in the corresponding alternative in the ANSYS Workbench 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.

Cracking according to ACI 318

Cracking Checking

Checking of the Cracking Limit State according to ACI 318-14 and ACI 318-19 consists of the following condition:

Where:

Reinforcement spacing closest to the fiber in tension

s Design reinforcement spacing

CivilFEM ACT 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

Reinforcement Stress Calculation

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

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.

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.

Code check for Concrete Shells

Reinforcement Directions

Three types 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

Interaction Diagram

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 ACT 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 ACT 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.

Axial + Bending Check and Design

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.

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 ANSYS Workbench results file.

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.

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%.

CEB-FIP Method

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).

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:

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)

Checking Outline

· 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:

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.

4. 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:

· Steel amount

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

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.

Required Parameters

· 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).

· Checking Requirements

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

Design according to the Orthogonal Directions Method

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

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:

3) Torsional moment and membrane shear force in tension/compression:

Then previous two cases are performed and selected the most unfavorable of both

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.

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.

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 ANSYS Workbench results file:

· Criterion for X direction.

· Criterion for Y direction.

7) Design results. Design results are stored in the ANSYS Workbench 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.

Out-of-Plane Shear Load according to EC2

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

Required Input Data

Shear check or design according to Eurocode 2 (EN 1992-1-1:2004/AC:2008) 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)

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 ANSYS Workbench results file.

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):

Out-of-Plane Shear Checking

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):

where:

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

Results are written for each end in the ANSYS Workbench 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

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.

Out-of-Plane Shear Design

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:

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.

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

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

Required Input Data

Shear checking or design according to ACI 318-14 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.

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).

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

Force Description

V_u Design out-of-plane shear force

N_u Axial force (positive for compression).

Out-of-Plane Shear Checking

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.

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:

This condition is reflected in the total criterion.

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.

Minimum Reinforcement

If reinforcement is required, the minimum allowable value is:

(ACI 318-14 Eqn.11-13)

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:

Out-of-Plane Shear Design

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.

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 318-14 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.

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).

Out-of-Plane Shear Loads according to ACI 318-19

Required Input Data

Shear checking or design according to ACI 318-19 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).

Out-of-Plane Shear Checking

Minimum Reinforcement

If minimum reinforcement is required, the minimum allowable is the greater value of:

Shear Strength Provided by Concrete

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

where:

b_w = 1 (unit length)

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

ratio of tensile reinforcement defined by the user. Value is taken as the greater of defined and the one that is equal to

N is positive for compression and negative for tension

Size effect modification factor, determined as:

Limits for Vc are taken as:

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.

Shear Strength Provided by Shear Reinforcement

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

(ACI 318-19)

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.

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.

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:

Where f is the strength reduction factor. 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 cross-sectional dimensions limit is checked. If end doesn´t fill the next equation, the criterion is equal to 2¹⁰⁰

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

The total checking criterion is defined as:

Out-of-Plane Shear Design

Minimum Reinforcement

If minimum reinforcement is required, the minimum allowable is the greater value of:

Shear Strength Provided by Concrete

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

where:

= 1 (unit length)

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

ratio of tensile reinforcement defined by the user. Value is taken as the greater of defined and the one that is equal to

N is positive for compression and negative for tension

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.

Required Reinforcement Contribution

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

where: is the strength reduction factor.

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.

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

If and is required ( ) then:

If and is not required Vc is recalculated using the formula for :

where:

Size effect modification factor, determined as:

Then is recalculated with the new value of Vc

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).

Out-of-Plane Shear Load according to ACI-349-13

Required Input Data

Shear checking or design according to ACI 349-13 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).

Out-of-Plane Shear Checking

Shear Strength Provided by Concrete

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

(ACI 349-13 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 349-13 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 349-13 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.

Shear strength provided by shear reinforcement

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

(ACI 349-13Eqn.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 349-13 Eqn.11.5.6.8)

This condition is reflected in the total criterion.

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.

Minimum reinforcement

If reinforcement is required, the minimum allowable value is:

(ACI 349-13 Eqn.11-13)

Shear criterion

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

(ACI 349-13 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:

Out-of-Plane Shear Design

Shear strength provided by concrete

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

(ACI 349-13 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 349-13 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 349-13 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.

Required reinforcement contribution

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

(ACI 349-13 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 349-13 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.

Required reinforcement

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

(ACI 349-13 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 349-13 Eqn.11-13)

The area of the designed reinforcement per unit of area is stored in the CivilFEM ACT checking 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).

In-Plane Shear Load according to ACI 349-13

Required Input Data

Shear checking or design according to ACI 349 13 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 is obtained from the ANSYS Workbench results file. 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 349-13 is divided into the three following types:

· Walls with non-seismic loads. Covers chapter 14 of ACI 349-13 for walls.

· Walls with seismic loads. Covers chapters 14 and 21 of ACI 349-13 for walls.

· Slabs with seismic loads. Covers chapter 21 of ACI 349-13 for slabs.

In-Plane Shear Checking for Walls

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 349-13 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 349-13 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.

Shear strength provided by shear reinforcement

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

(ACI 349-13 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.

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 349-13 Eqn: 11-1 and 11-2)

(ACI 349-13 11.10.3 and 11.10.4)

(ACI 349-13 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 ACT checking 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).

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 349-13 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 349-13 21.6.5.2)

(ACI 349-13 21.6.5.6)

(ACI 349-13 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 ACT checking results file as the parameter VPHI_# (# is the direction of the shell, X or Y).

In-Plane Shear Design for Walls

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 349-13 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 349-13 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 ACT checking results file as the parameter VC (# is the direction of the shell, X or Y):

VC_# Shear strength provided by concrete.

Required reinforcement contribution

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

(ACI 349-13 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.

Required reinforcement – Non seismic loads

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

(ACI 349-13 11.10.4 Eqn: 11-33)

The reinforcement amount has a minimum requirement of:

(ACI 349-13 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 ACT checking results file as:

Also, the following condition must be satisfied:

(ACI 349-13 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)

Required reinforcement – Seismic loads

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

(ACI 349-13 Eqn: 11-1 and 11-2)

With

(ACI 349-13 Eqn: 11-33)

and

(ACI 349-13 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 349-13 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 349-13 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)

In-Plane Shear Checking for Slabs (Seismic Loads)

In plane shear criterion

The nominal shear strength (V_n) is limited by:

(ACI 349-13 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 349-13 21.6.5.2)

(ACI 349-13 21.6.5.6)

(ACI 349-13 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).

In-Plane Shear Design for Slabs (Seismic Loads)

Required reinforcement

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

(ACI 349-13 21.6.5.2)

where A_cv is the area of concrete:

The reinforcement amount has a minimum requirement of:

(ACI 349-13 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 349-13 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:

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

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).

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.

Checking results

Checking results are stored in the corresponding ANSYS Workbench 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.

Cracking Checking according to ACI 318

Cracking Checking

Checking of the Cracking Limit State according to ACI 318-14 and ACI 318-19 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).

Reinforcement Stress Calculation

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

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.

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.