10-H.1      Scope

Steel structures checking according to Documento Básico de Seguridad Estructural de Acero, CTE DB SE-A (March 2006) in CivilFEM includes the checking of structures composed by welded or rolled shapes under axial forces, shear forces and bending moments in 3D.

The calculations made by CivilFEM correspond to the provisions of CTE DB SE-A, sections:

5.2.4   Classification of cross-sections

6.2      Resistance of cross-sections

6.3      Buckling resistance of members

 

10-H.2      Checking Types

With CivilFEM it is possible to accomplish the following checking and analysis types:

·         Checking of sections subjected to:

- Tension	CTE DB SE-A sect. 6.2.3
- Compression	CTE DB SE-A sect. 6.2.5
- Bending	CTE DB SE-A sect. 6.2.6
- Shear force	CTE DB SE-A sect. 6.2.4
- Bending and Shear	CTE DB SE-A sect. 6.2.8
- Bending and axial force	CTE DB SE-A sect. 6.2.8
- Bending, shear and axial force	CTE DB SE-A sect. 6.2.8

·         Checking to buckling:

- Compression members with constant cross-section	CTE DB SE-A sect. 6.3.2
- Lateral-torsional buckling of beams	CTE DB SE-A sect. 6.3.3
- Members subjected to bending and axial	CTE DB SE-A sect. 6.3.4.1
- Members subjected to bending and axial compression	CTE DB SE-A sect. 6.3.4.2

 

10-H.3      Valid Element Types

The valid element types supported by CivilFEM are the following 2D and 3D ANSYS link and beam elements:

2D Link	LINK1
3D Link	LINK8
3D Link	LINK10
2D Beam	BEAM3
3D Beam	BEAM4
3D Tapered Unsymmetrical Beam	BEAM44
2D Tapered Elastic Unsymmetrical Beam	BEAM54
2D Plastic Beam	BEAM23
3D Thin-walled Beam	BEAM24
3D Elastic Straight Pipe	PIPE16
3D Plastic Straight Pipe	PIPE20
3D Finite Linear Strain Beam	BEAM188
3D Quadratic Linear Strain Beam	BEAM189

 

Moreover, it is possible to check solid sections captured from 2D or 3D models if the cross section is classified as “structural steel”.

 

10-H.4      Valid Cross-Section Types

Valid cross-sections supported by CivilFEM for checking according to CTE DB SE-A are the following:

All the rolled shapes included in the program libraries (see the hot rolled shapes library and ~SSECLIB command)

The following welded beams: double T shapes, U or channel shapes, T shapes, box, equal and unequal legs angles and pipes. (~SSECDMS commands).

Structural steel sections defined by plates (command ~SSECPLT). Shapes from solid sections captured from 2D or 3D models which transverse cross section is classified as “structural steel”.

CivilFEM considers all these sections as sections composed by plates, for example, a double T section is composed by five plates: four flanges and one web. These cross sections are therefore adapted to the method of analysis of CTE DB SE-A. Obviously circular sections cannot be decomposed into plates, so these sections are analyzed differently.

 

 

10-H.5      Reference Axis

CivilFEM, for checking according to CTE DB SE-A, includes three different coordinate reference systems. All these systems are right-handed:

1.    CivilFEM Reference Axis. ().

2.    Cross-Section Reference Axis. ().

3.    CTE DB SE-A Reference Axis. (Code axis). ().

 

Figure 10-H.5‑1 Axis Orientation in Beam Sections

 

For the CTE DB SE-A axis system:

The system origin coincides with the CivilFEM axis origin.

 axis coincides with CivilFEM X-axis.

 axis is the relevant axis for bending and its orientation is defined by the user. (~MEMBPRO and ~CHKSTL commands).

 axis is perpendicular to the plane defined by the X and Y axis, to ensure a right-handed system.

To define this reference system, the user must indicate which of the CivilFEM axis (-Z, -Y, +Z or +Y) coincides with the relevant axis for positive bending. The user may define this reference system with the commands: ~MEMBPRO, when defining member properties for CTE DB SE-A and ~CHKSTL when checking according to this code. However, in case of any contradiction, the definition considered will be the one established with the ~MEMBPRO command, and the one introduced through ~CHKSTL command will be neglected. In conclusion, the code reference system coincides with that of CivilFEM, rotated a certain multiple of 90 degrees, as demonstrated below.

Table 10-H.5‑1

Relevant Axis for Bending in CivilFEM Reference System	Angle of Rotation (in clockwise) of CTE DB SE-A Reference System respect to the CivilFEM Reference System
	90 º  (Default option)
	180 º
	270 º
	0 º

 

10-H.6      Data and Results used by CivilFEM

CivilFEM uses the following data and result groups for checking according to CTE DB SE-A:

Data pertaining to sections: properties and dimensions of gross, net and effective sections, characteristics and dimensions of section plates.

Member properties.

Material properties.

Forces and moments in the section.

Checking results.

10-H.6.1           Sections Data

CTE DB SE-A considers the following data set for the section:

-          Gross section data

-          Net section data

-          Effective section data

-          Data concerning the section and plates class.

Gross section data correspond to the nominal properties of the cross-section.

From net section, only the area is considered. This area is calculated by subtracting the holes for screws, rivets and other holes from the gross section area. (The area of the holes is introduced through the parameter AHOLES in ~SECMDF command).

The effective section data and the section and plates class data are obtained in the checking process according to the effective width method (Sect. 5.2.5 of CTE DB SE-A). For class 4 cross-sections, this method subtracts the zones that do not contribute to local buckling resistance. For cross-sections of a lower class, this method does not reduce the section for local buckling.

The CTE DB SE-A module takes the gross section data in user units and CivilFEM axis or section axis as initial data. The program calculates the effective section data and the class data, and stores them in CivilFEM’s results file, in user units and in CivilFEM or section axis. All these data can be listed and plotted with the ~PLLSSTL and ~PRSTL commands.

In the following tables, the section data used in CTE DB SE-A are shown:

 

Table 10-H.6‑1 Common data for gross, net and effective sections

 

Table 10-H.6‑2 Gross section data

 

Table 10-H.6‑3 Net section data

* The section holes are introduced as a property at member level

The effective section depends on the section geometry and on the forces and moments that are applied to it. Consequently, for each element end, the effective section is calculated.

 

Table 10-H.6‑4 Effective section data

 

Table 10-H.6‑5 Data referred to the section plates

10-H.6.2           Member Properties

For CTE DB SE-A checking the data set used at member level is shown in the following table. All data is stored with the section data in user units and in the CivilFEM reference axis. (Parameters L, K, KW, C1, C2, C3, CMY, CMZ, CMLT, PSIVEC, CFBUCKXY and CFBUCKXZ of ~MEMBPRO command).

 

Table 10-H.6‑6 Member Properties

10-H.6.3           Material Properties

CTE DB SE-A checking uses the following material properties:

 

Table 10-H.6‑7 Material properties

*th =thickness of the plate

 

10-H.6.4           Forces and Moments

The forces and moments necessary for checking are obtained from the CivilFEM results file (.RCV) for the selected load step and substep. CivilFEM performs the necessary operations to convert the CTE DB SE-A units system, axis and criteria. The program also makes the necessary sign conversions to satisfy the code criterion (compressive forces and stresses are positive). Internally, CivilFEM works according to code prescriptions.

ANSYS forces and moments depend on the option selected by the user in the CLASSMOD argument of the ~CHKSTL command. If the selected option is partial, the calculation of the cross-section class is accomplished with the same forces and moments used in code checking (default option). Otherwise, if the selected option is full, all the forces and moments are considered in the calculation of the cross-section class, independently of the checking type.

The partial forces and moments sets, considered for each type of external load, are shown in the following table. The forces and moments represented at the top of the table refer to the CTE DB SE-A axis (relevant axis for bending YY) with the CTE DB SE-A signs criterion (in general, compressive force is positive, except for tension and bending + axial tension, where the tensile force is considered positive). All of these terms are the used by the code.

 

Table 10-H.6‑8 Forces and Moments

10-H.6.5           Checking Final Results

The ultimate objective is to check if the code conditions for each type of external load are fulfilled.

In general, for any type of external force, the condition required by the code for a section is the following:

The numerators of the condition are the forces and moments in the section: the axial force and the bending moments in Y and in Z axis. In some cases, these forces and moments are modified by correction factors that depend on the type of external load as well as the presence of shear forces.

The denominators include the design resistances to each of the forces and moments in the cross-section. These terms are calculated in a particular way for each type of external load and for each cross-section class. In addition, the section class depends on the cross-section type and on the internal forces and moments.

 

CivilFEM stores the results for each element end in an alternative in the CivilFEM results file (.RCV). These results can be retrieved with the corresponding alternative number using the command ~CFSET.

The available results data for each checking type are described within tables found in their corresponding sections within this manual.

10-H.7      Checking Process

The checking process evaluates the following expression:

Evaluation steps:

1.    Read the checking type requested by the user.

2.    Default checking type: Bending, shear and axial force.

3.    Read the CivilFEM axis to be considered as the relevant axis for bending so that it coincides with the Y axis of CTE DB SE-A.

In CivilFEM, by default, the relevant axis of bending that coincides with +Y axis of CTE DB SE-A is the –Z-axis.

4.    The following operations are necessary for each selected element:

a.    Obtain material properties of the element stored in the CivilFEM database and calculate the rest of the properties needed for checking:
Properties obtained from the CivilFEM database:

 

Elasticity modulus	E
Poisson’s ratio	n
Yield strength	Fy(th)
Ultimate strength	Fu(th)
Partial safety factors	and  (CTE DB SE-A Art.2.3.3)
Shear modulus	G
Thickness of the plate	th

 

Calculated properties:

Epsilon, material coefficient:                   

                        

b.    Obtain the cross-sectional data corresponding to the element.

c.    Initialize values of the effective cross-section.

d.    Initialize reduction factors of section plates and the rest of plate parameters necessary for obtaining the plate class.

e.    If necessary for the checking type (checking for buckling), calculate the critical forces and moments of the section for buckling: elastic critical forces for the XY and XZ planes and elastic critical moments for lateral-torsional buckling. (See section: Calculation of critical forces and moments).

f.     Obtain internal forces and moments (, , , _, , and ) within the section.

g.    Check a specific section according to the type of external load. The specific checking includes:

1.    If necessary, selecting the forces and moments considered for the determination of the section class and used for the checking process.

2.    Obtaining the cross-section class and calculating the effective section properties (See Section: General Processing of Sections).

3.    Checking the cross-section according to the external load and its class, by calculating the following criteria: Crt_TOT, Crt_N, Crt_Mx and Crt_My.

h.   Recording the results.

10-H.7.1           General Processing of Sections. Section Class and Reduction Factors Calculation.

Sections, according to CTE DB SE-A are made up by plates. These plates can be classified according to:

5.      Plate function: webs and flanges in Y and Z axis, according to the considered relevant axis of bending.

6.      Plate Union Condition: internal plates or outstand plates

For sections included in the program libraries, the information above is defined for each plate. CivilFEM classifies plates as flanges or webs according to their axis and provides the plate union condition for each end. Ends can be classified as fixed or free (a fixed end is connected to another plate and free end is not).

For checking the structure for safety, CTE DB SE-A classifies sections as one of four possible classes (Sect. 5.2.4):

Class 1	Cross-sections which can form a plastic hinge with the rotation capacity required for plastic analysis.
Class 2	Cross-sections which can reach their plastic moment resistance, but have limited rotation capacity.
Class 3	Cross-sections for which the stress in the extreme compression fiber of the steel member can reach its yield strength, but local buckling is liable to prevent development of the plastic moment resistance.
Class 4	Cross-sections for which it is necessary to make explicit allowances for the effects of local buckling when determining their moment resistance or compression resistance.

 

The cross-section class is the highest (least favorable) class of all of its elements: flanges and webs (plates). First, the class of each plate is determined according to the limits of Table 5.3 of CTE DB SE-A. According to this table, the plate class depends on:

1.    The geometric width to thickness ratio, with the plate width properly corrected according to the plate and shape type.

GeomRat = Corrected_Width / thickness

The width correction consists of subtracting the zone that does not contribute to buckling resistance in the fixed ends. This zone depends on the shape type of the section. Usually, the radii of the fillet in hot rolled shapes or the weld throats in welded shapes determine the zone to be deducted, (see Table 5.3 of CTE DB SE-A). The values of the corrected width that CivilFEM uses for each shape type include:

·    Welded Shapes:

Double T section:

Internal webs or flanges:

                       Corrected width = d

                       d          Web free depth

Outstand flanges:

Corrected width =

B         Flanges width

T section:

Internal webs or flanges:

                       Corrected width = d

Outstand flanges:

Corrected width =

C section:

Internal webs or flanges:

                       Corrected width = d

Outstand flanges:

                       Corrected width = B

L section:

Corrected width =

    Angle flange width

Box section:

Internal webs:

                       Corrected width = H

H         Height

Internal flanges:

                       Corrected width =

       Web thickness

Circular hollow section

                       Corrected width = H

·    Rolled Shapes:

Double T section:

Internal webs or flanges:

                       Corrected width = d

d         Web free depth

Outstand flanges:

Corrected width =

B         Flanges width

T Section:

Internal webs or flanges:

                       Corrected width = d

Outstand flanges:

Corrected width =

C Section:

Internal webs or flanges:

                       Corrected width = d

Outstand flanges:

                       Corrected width = B

L Section:

Corrected width =

     Angle flange width

Box section:

Internal webs:

                       Corrected width = d

Internal flanges:

                       Corrected width =

        Flanges thickness

Pipe section:

                       Corrected width = H

2.    The limit listed below for width to thickness ratio. This limit depends on the material parameter e  and the normal stress distribution in the plate section. The latter value is given by the following parameters: a, Y, and  , and the plate type, internal or outstand; the outstand case depends on if the free end is under tension or compression.

Limit (class) =

 

3.    Where:

 

	Compressed length / total length
	Buckling factor
	The higher stress in the plate ends.
	The lower stress in the plate ends.

 

A linear stress distribution in the plate is assumed.

The procedure to determine the section class is as follows:

1.    Obtain stresses for the first plate ends from the stresses applied on the section, properly filtered according to the checking type requested by the user.

2.    Calculate parameters:

  is obtained from formulas included in table 5.6 of CTE DB SE-A.

For internal plates:

                 For   

                                                          

 

For     

                                       

For     

                                       

For          

For outstand plates with an absolute value of the stress at the free end greater than the corresponding value at the fixed end:

For                

                                                                                                                                                        

For             

                           

For outstand plates with an absolute value of the stress at the free end lower than the corresponding value at the fixed end:

For                

For             

 

Cases in which  = infinite are not included in the CTE DB SE-A. With these cases, plate is considered to be practically in tension and it will not be necessary to determine the class. These cases have been included in program to avoid errors, and the value =infinite has been adopted because the resultant plate class is 1 and the plate reduction factor is r = 1 (the same values as if the whole plate was in tension). The reduction factor is used later in the effective section calculation.

3.    Obtain the limiting proportions as functions of: a, Y and  and the plate characteristics (internal, outstand: free end in compression or tension).

Internal plates:

 

	for a  ≥0.5
	for a £ 0.5
	for a  ≥0.5
	for a £ 0.5
	for y  ≥-1
	for y £ -1

 

Outstand plates, free end in compression:

 

 

Outstand plates, free end in tension:

 

	for welded shapes
	for welded shapes
	for welded shapes

 

Where:

  

     

 

Above is the general equation used by the program to obtain the limiting proportions for determining plate classes. This corresponds to tables 5.3 and 5.4. In addition, the user can check columns according to special cases.

For example:

For sections entirely under compression:

a = 1     y       Y = 1   for all plates

For sections under pure bending:

a = 0.5  y       Y= -1   for the web

a = 1     y       Y = 1 for compressed flanges

Etc.

4.    Obtain the plate class:

If		GeomRat	< Limit(1)	Plate Class = 1
If	Limit(1) £	GeomRat	< Limit(2)	Plate Class = 2
If	Limit(2) £	GeomRat	< Limit(3)	Plate Class = 3
If	Limit(3) £	GeomRat		Plate Class = 4

 

Repeat the steps above (1, 2, 3, and 4) for each section plate.

5.    Assign the highest class of the plates to the entire section.
In tubular sections, the section class is directly determined as if it were a unique plate, with GeomRat and the Limits calculated as follows:

                        GeomRat = d/t          d = outer diameter.

                                                           t = thickness.

For class 4 sections, the section resistance is reduced, using the effective width method of Section 5.2.5 of CTE DB SE-A.

For each section plate, the effective lengths at both ends of the plate and the reduction factors r₁ and r₂ are calculated. These factors relate the length of the effective zone for each plate end to its width.

 

            Effective_length_end1 = plate_width*r₁

            Effective_length_end 2 = plate_width*r₂

 

The formula included in table 5.6 of CTE DB SE-A has been implemented for this process:

y =  s₂/s₁

1. Internal plates:

For        (Both ends in compression)

Figure 10-H.7‑1 Internal plates

  = corrected plate width

plate_width = real plate width

For  (end 1 in compression and end 2 in tension)

Figure 10-H.7‑2

2. Outstand plates:

For     (Both ends in compression: end 1 fixed, end 2 free)

Figure 10-H.7‑3

For  (end 1 fixed and in tension, end 2 free and in compression)

Figure 10-H.7‑4

For  (end 1 fixed and in compression, end 2 free and in tension)

Figure 10-H.7‑5

 

 

 

If end 2 is the fixed end, the values   and  are switched.

The global reduction factor  is obtained by (Art. 5.2.5):

            For a plane element, simply supported at both ends:

            For a plane element, simply supported at one end:

is the plate slenderness given by:

Where:

    =                            corrected plate width

t      =                            relevant thickness

e      =                            material parameter

k    =                                      buckling factor

To determine the effective section properties, three steps are followed:

1.    Effective widths of flanges are calculated from factors a  and Y; these factors are determined from the gross section properties. As a result, an intermediate section is obtained with reductions taken in the flanges only.

2.      The resultant section properties are obtained and factors a  and Y are calculated again.

3.    Effective widths of webs are calculated so that the finalized effective section is determined. Finally, the section properties are recalculated once more.

The recalculated section properties are included in the effective section data table. Checking can be accomplished with the gross, net or effective section properties, according to the section class and checking type.

Each checking type follows a specific procedure that will be explained in the following sections.

10-H.7.2           Checking of Members in Axial Tension (Art. 6.2.5)

1.    Forces and moments selection.
The forces and moments considered for this checking type are:

            Design value of the axial force (positive if tensile,           element not

                           processed if compressive).

2.    Class definition and effective section properties calculation.
For this checking type, the section class is always 1 and the considered section is the either the gross or net section.

3.    Criteria calculation.
For members under axial tension, the general criterion Crt_TOT is checked at each section. This criterion coincides with the axial criterion Crt_N.

    à   

Where N_t.Rd is the design tension resistance of the cross-section, taken as the smaller value of:

	design plastic resistance of the gross cross-section
	design ultimate resistance of the net cross-section

 

4.    Output results are written in the CivilFEM results file (.RCV) as an alternative. Checking results: criteria and variables are described in the following table:

 

Table 10-H.7‑1 Art. 6.2.3 Checking of Members in Axial Tension

10-H.7.3           Checking of Members in Axial Compression (Art. 6.2.5)

1.    Forces and moments selection.
The forces and moments considered for this checking type are:

 = FX        Design value of the axial force (positive if compressive, element not processed if tensile).

2.    Class definition and effective section properties calculation.
For this checking type, the section class is always 1 and the considered section is the gross or the net section.

3.    Criteria calculation.
For members in axial compression, the general criterion Crt_TOT is checked at each section. This criterion coincides with the axial criterion Crt_N:

    à   

 

where  is the design compression resistance of the cross-section.

Class 1, 2, or 3 cross-sections:

  design plastic resistance of the gross section

Class 4 cross sections:

          design local buckling resistance of the cross-section

4.    Output results are written in the CivilFEM results file (.RCV) as an alternative. Checking results: criteria and variables are described in the following table.

 

Table 10-H.7‑2 Art. 6.2.5 Checking of Members in Axial Compression

 

10-H.7.4           Checking of Members under Bending Moment (Art. 6.2.6)

1.    Forces and moments selection.
The forces and moments considered for this checking type are:

     Design value of the bending moment along the relevant axis for bending.

2.    Class definition and effective section properties calculation.
The section class is determined by the general processing of the section with the previously selected forces and moments if the selected option is partial or with all the forces and moments if the option is full. These calculations are based on gross section properties.

3.    Criteria calculation.
For members subjected to a bending moment in the absence of shear force, the following condition is checked at each section:

   à  

where:

design value of the bending moment

design moment resistance of the cross-section

Class 1 or 2 cross-sections:

    
 

Class 3 cross sections:

Class 4 cross sections:

4.    Output results are written in the CivilFEM results file (.RCV) as an alternative. Checking results: criteria and variables are described in the following table.

 

Table 10-H.7‑3 Art. 6.2.6 Checking of Members under Bending Moment

10-H.7.5           Checking of Members under Shear Force (Art. 6.2.4)

1.    Forces and moments selection.
The forces and moments considered for this checking type are:

     Design value of the shear force perpendicular to the relevant axis of bending.

2.    Class definition and effective section properties calculation.
For this checking type, the section class is always 1 and the effective section is the gross section.

3.    Criteria calculation.
In members under shear force, the following condition at each section is checked:

    à   

where:

 

4.    Output results are written in the CivilFEM results file (.RCV) as an alternative. Checking results: criteria and variables are described in the following table.

 

Table 10-H.7‑4 Art. 6.2.4 Checking of Members under Shear Force

10-H.7.6           Checking of Members under Bending Moment and Shear Force (Art. 6.2.8)

1.    Forces and moments selection.
The forces and moments considered for this checking type are:

V_Ed = FZ or FY          Design value of the shear force perpendicular to the relevant axis of bending.

    Design value of the bending moment along the relevant axis of bending.

2.    Class definition and effective section properties calculation.
The section class is determined by the general processing of the section with the previously selected forces and moments if the selected option is partial, or with all the forces and moments if the option is full. The calculations are accomplished with gross section properties.

3.    Criteria calculation.
In members subjected to bending moment and shear force, the following condition is checked at each section:

    à   

Where:           design resistance moment of the cross-section, reduced by the presence of shear.

The reduction for shear is applied if the design value of the shear force exceeds 50% of the design plastic shear resistance of the cross-section. Written explicitly as:

The design resistance moment is obtained as follows:

a.    For cross-sections with equal flanges, bending about the major axis (rolled or welded double T sections, channel sections and tubular rectangular sections):

 

if 

if 

b.    For other cases:

Note: This is equivalent to a reduction of the yield strength fy applied to the whole section. CTE DB SE-A only requires the reduction to be applied to the shear area; therefore it is a conservative simplification.

For both cases  is the smaller value of either  or .

 is the design moment resistance of the cross-section, calculated according to the class.

Output results are written in the CivilFEM results file (.RCV) as an alternative. Checking results: criteria and variables are described in the following table.

 

Table 10-H.7‑5 Art. 6.2.8 Checking of Members under Bending Moment and Shear Force

10-H.7.7           Checking of Members under Bending Moment + Axial Force and Bi-axial Bending + Axial Force (Art. 6.2.8)

1.    Forces and moments selection.
The forces and moments considered for this checking type are:

	Design value of the axial force.
	Design value of the bending moment along the relevant bending axis.
	Design value of the bending moment about the secondary bending axis.

2.    Class definition and effective section properties calculation.
The section class is determined by the section’s general processing with the previously selected forces and moments if the selected option is partial or with all the forces and moments if the option is full. These calculations are accomplished with gross section properties.

3.    Criteria calculation.
For members subjected to bi-axial bending in absence of shear force, the same formula is implemented as explained above (Art 6.2.8).

For  I or H welded sections, the effect of the axial force is ignored if it less than half of the tension resistance of the web.

 

Class 1 and 2 sections:

Where:

                     

 

Condition equivalent to:

Crt_TOT = Crt_N + Crt_My + Crt_Mz £ 1

 

Where  is the plastic resistant modulus about y axis and  is the plastic resistant modulus about the z axis.

In absence of  the above criterion becomes:

Condition equivalent to:

Crt_TOT = Crt_N + Crt_My £ 1

 

Class 3 sections:

 

Where:

 

Condition equivalent to:

Crt_TOT = Crt_N + Crt_My + Crt_Mz £ 1

  

 

 

 

Where  is the elastic resistant modulus about y axis and   is the elastic resistant modulus about z axis.

In absence of , the above criterion becomes:

Which is equivalent to:

 

Crt_TOT = Crt_N + Crt_My £ 1

Class 4 sections:

 

Where:

 

Condition equivalent to:

 

Crt_TOT = Crt_N + Crt_My + Crt_Mz £ 1

 

 

 

Without , the above criterion becomes:

 

Which is equivalent to:

Crt_TOT = Crt_N + Crt_My £ 1

 

 

 

Where:                   

	effective area of the cross-section
	effective section modulus of the cross-section when subjected to a moment about the y axis
	effective section modulus of the cross-section when subjected to a moment about the z axis
	shift of the center of gravity along the y axis
	shift of the center of gravity along the z axis

 

 

4.    Output results are written in the CivilFEM results file (.RCV) as an alternative. Checking results: criteria and variables are described in the following table.

 

Table 10-H.7‑6 Art.6.2.8 Checking of Members under Bending Moment + Axial Force and Bi-axial Bending + Axial Force

10-H.7.8           Checking of Members under Bending, Shear and Axial Force (Art. 6.2.8)

1.    Forces and moments selection.
The forces and moments considered for this checking type are:

	Design value of the axial force.
	Design value of the shear force perpendicular to the secondary axis of bending.
	Design value of the shear force perpendicular to the relevant axis of bending.
	Design value of the bending moment about the relevant axis of bending.
	Design value of the bending moment about the secondary axis of bending.

2.    Class definition and effective section properties calculation.
The section class is determined by the section’s general processing with the previously selected forces and moments if the selected option is partial or with all the forces and moments if the option is full.  These calculations are accomplished with gross section properties.

3.    Criteria calculation.
In members subjected to bending, axial and shear forces, the same conditions for bending +axial force and bi-axial bending are checked at each section, reducing the design plastic resistance moment for the presence of shear force.
Shear force effects are taken into account when they exceed 50% of the design plastic resistance of the cross-section. For this case, both the axial and shear forces will be taken into account.

The axial force effects are included as described in the previous section, and the shear force effects are taken into account considering a yield strength for the cross-section, reduced by the factor (1-r):

where:

 

This yield strength reduction is selectively applied to the resistance of the cross-section along each axis, according to the previous conditions.

Note: The yield strength reduction is applied to the shear area; therefore, this is a conservative simplification.

4.    Output results are written in the CivilFEM results file (.RCV) as an alternative. Checking results: criteria and variables are described in the following table.

Table 10-H.7‑7 Art. 6.2.8 Checking of Members under Bending, Shear and Axial Force

10-H.7.9           Checking for Buckling of Compression Members (Art. 6.3.2)

1.    Forces and moments selection.
The forces and moments considered for this checking type are:

Design value of the axial force (positive if compressive, otherwise the element is not processed).

2.    Class definition and effective section properties calculation.
The section class is determined by the sections general processing with the previously selected forces and moments if the selected option is partial or with all the forces and moments if the option is full. These calculations are accomplished with gross section properties.

3.    Criteria calculation.
Criterion for checking for buckling of compression members is as follows:

    à   

where:

	Design value of the axial force.
	Design buckling resistance. Where A is the area of the lateral section for classes 1, 2 or 3 and Aeff  is the efficient area for class 4.
c	Reduction factor for the relevant buckling mode, the program does not consider the torsional or the lateral-torsional buckling, because in these cases, CTE DB SE-A refers to ENV 1993-1-3 CTE DB SE-A Part 1-3 (in elaboration process).

 

The c factor for members with constant cross-sections may be determined by:

    and

Where    is an imperfection factor that depends on the buckling curve. This curve depends on the cross-section type, buckling plane and steel type, producing the following values for  (figure 6.3 and table 6.3 from CTE DB SE-A):

 

Table 10-H.7‑1 Imperfection factor a

Section type		Limits	Buckling axis	Steel type	Buckling curve		a
Rolled I Rolled I		h/b>1.2 and t40mm	y – y	S235 to S355	a		0.21
				S450	a0		0.13
Rolled I Rolled I		h/b>1.2 and t40mm	z – z	S235 to S355	b		0.34
				S450	a0		0.13
Rolled I Rolled I		h/b>1.2 and 40mm<t100mm	y – y	S235 to S355	b		0.34
				S450	a		0.21
Rolled I Rolled I		h/b>1.2 and 40mm<t100mm	z – z	S235 to S355	c		0.49
				S450	a		0.21
Welded I Welded I		h/b1.2 and t100mm	y – y	S235 to S355	b		0.34
				S450	a		0.21
Welded I Welded I		h/b1.2 and t100mm	z – z	S235 to S355	c		0.49
				S450	a		0.21
Rolled I Rolled I		t>100mm	y – y	S235 to S355	d		0.76
				S450	c		0.49
Rolled I Rolled I		t>100mm	z – z	S235 to S355	d		0.76
				S450	c		0.49
Welded I		t40mm	y – y	all	b	0.34
Welded I		t40mm	z – z	all	c	0.49
Welded I		t >40mm	y – y	all	c	0.49
Welded I		t >40mm	z – z	all	d	0.76
Welded and laminated agroupated sections		---------	all	all	c	0.49
Pipes	Hot finished		all	S235 a S355	a	0.21
				S450	a0	0.13
	Cold formed		all	all	c	0.49
Reinforced box sections	Thick weld: a/t>0.5 b/t<30 h/tw<30		all	all	c	0.49
	In other case		all	all	b	0.34
U, T, plate		---------	all	all	c	0.49
L		---------	all	all	b	0.34

 

Where  is the elastic critical force for the relevant buckling mode. (See section, Critical Forces and Moments Calculation).

The elastic critical axial forces are calculated in the XY and XZ  planes and the corresponding values of  and  _,  taking the smaller one as the final value for c.

4.    Output results are written in the CivilFEM results file (.RCV) as an alternative. Checking results: criteria and variables are described in the following table.

 

Table 10-H.7‑8 Art. 6.3.2 Checking for Buckling of Compression Members

10-H.7.10       Checking for Lateral-Torsional Buckling of Beams Subjected to Bending (Art. 6.3.3)

This check is calculated for the   axis of double T and channel sections and for  the Y and  Z  axes of box sections.

1.    Forces and moments selection:

The forces and moments considered for this checking type are:

Design value of the bending moment about the relevant axis of bending.

2.    Class definition and effective section properties calculation.
The section class is determined by the sections general processing with the previously selected forces and moments if the selected option is partial or with all the forces and moments if the option is full. These calculations are accomplished with gross section properties.

3.    Criteria calculation.
The criterion checking for lateral-torsional buckling of beams shall be taken as:

    à   

where:

	Design value of the bending moment.
	Design buckling resistance moment of a laterally unrestrained beam. for class 1and 2 sections. for class 3 sections.   for class 4 sections.
	Reduction factor for lateral-torsional buckling.

 

The value of  may be calculated from:

Where:

 is the elastic critical moment for lateral-torsional buckling

  is the imperfection factor for lateral-torsional buckling and may be taken as:

 

 

5.    Output results are written in the CivilFEM results file (.RCV) as an alternative. Checking results: criteria and variables are described in the following table.

 

Table 10-H.7‑9 Art. 6.3.3 Checking for Lateral-Torsional Buckling of Beams Subjected to Bending

10-H.7.11       Checking Lateral-Torsional Buckling of Members Subjected to Combined Bending and Axial Tension (Art. 6.3.4.1)

1.    Forces and moments selection.
The forces and moments considered for this checking type are:

	Design value of the axial force (positive if tensile, element not processed if compressive).
	Design value of the bending moment about the relevant axis of bending.

2.    Class definition and effective section properties calculation.
The section class is determined by the sections general processing with the previously selected forces and moments if the selected option is partial or with all the forces and moments if the option is full. These calculations are accomplished with gross section properties.

3.    Criteria calculation.
When analyzing lateral-torsional buckling of members subjected to combined bending and axial tension, the value of the axial force is multiplied by a reduction factor in order to consider the axial force and bending moment as a vectorial effect.
The value of  depends on the country in which the code will be applied. This factor is introduced as a property at member level and is generally equal to:
The stress in the extreme compression fiber is calculated as follows:

Where
 is the elastic section modulus for the extreme compression fiber

 and  is the design value of the axial tension.

The verification equation is derived to:

   à   

Where  

 

4.    Output results are written in the CivilFEM results file (.RCV) as an alternative. Checking results: criteria and variables are described in the following table.

 

 

 

Table 10-H.7‑10 Art. 6.3.4.1 Checking Lateral-Torsional Buckling of Members Subjected to Combined Bending and Axial Tension

10-H.7.12       Checking for Lateral-Torsional Buckling of Members Subjected to Bending and Axial Compression (Art. 6.3.4.2)

1.    Forces and moments selection.
The forces and moments considered for this checking type are:

 

		Design value of the axial compression.
		Design value of the bending moment about the relevant bending axis.
		Design value of the bending moment about the secondary axis bending axis.

2.    Class definition and effective section properties calculation.
The section class is determined by the sections general processing with the previously selected forces and moments if the selected option is partial or with all the forces and moments if the option is full. These calculations are accomplished with gross section properties.

3.    Criteria calculation.

The following criterion will always be calculated:

à  Crt_1 = Crt_N1 + Crt_My1 + Crt_Mz1 £ 1

Elements without torsional buckling:

Elements that may have torsional buckling:

Where:   

	Axial force criterion 1.
	Bending moment criterion for principal axis 1.
	Bending moment criterion for secondary axis 1
Crt_TOT1	General criterion 1.
	Axial force criterion 2.
	Bending moment criterion 2 for principal axis without torsional buckling
	Bending moment criterion 2 for principal axis when torsional buckling is considered.
	Bending moment criterion 2 for secondary axis.
Crt_TOT2	Criterion 2
Crt_TOT=min (Crt_tot1, Crt_tot2 )	Global criterion.

 

Where:

            

 

             

 

.

and  are the reduction factors defined for the section corresponding to the check for Buckling of Compression Members.

lateral buckling factor, (Art 6.3.3). This value is equal to 1 for members not subjected to lateral torsional bucking.

and  are displacements of the center of gravity of the effective section with respect to the center of gravity of the gross section for class 4 members.

, and  are equivalent uniform moment factors for flexural bending. (See CTE DB SE-A Sect. 6.3.4.2 and table 6.14). These factors are member properties at member level. (See  and ).

Checking Parameters (Table 6.12):

Class	A
1	A			0.6	0.6	0	0
2	A			0.6	0.6	0	0
3	A			0.8	1	0	0
4				0.8	1	Depends on the members and stress	Depends on the members and stress

 

Interaction Coefficients (Table 6.13):

 

 

 

where:

= and  Limited slenderness values for y-y and z-z axes. Less than 1.

4.    Output results are written in the CivilFEM results file (.RCV) as an alternative. Checking results: criteria and variables are described in the following table.

 

Table 10-H.7‑11 Art. 6.3.4.2 Checking for Lateral-Torsional Buckling of Members Subjected to Bending and Axial Compression

10-H.7.13       Critical Forces and Moments Calculation

The critical forces and moments  and Mcr are necessary for the different types of buckling checks and are calculated with the following formulas:

Where:

	Elastic critical axial force in XY plane.
	Elastic critical axial force in XZ plane.
A	Gross area.
E	Elasticity modulus.
	Member slenderness in XY plane.
	Member slenderness in XZ plane.
	Radius of gyration of the member in XY plane.
	Radius of gyration of the member in XZ plane.
	Buckling length of member in XY plane.
	Buckling length of member in XZ plane.

The buckling length for both planes is the length between ends restrained against lateral movement and is obtained from member properties according to the following expressions:

Where:

Cfbuckxy	Buckling factor in XY plane.
Cfbuckxz	Buckling factor in XZ plane.

 

Elastic critical moment for lateral-torsional buckling is obtained according to article 6.3.3.3:

 

Where:

Where:

	Elastic critical moment for lateral-torsional buckling (Art. 6.35).
	component for uniform torsional resistance (Art. 6.36).
	component for non-uniform torsional resistance (Art. 6.37).
	Uniform torsional modulus.
	Moment of inertia about the Z axis.
	Length of the member between end restraints.
G	Shear modulus.
	Factor depending on the loading and end restraint conditions.
E	Modulus of Elasticity.
	Elastic modulus with respect to the axis of inertia of the extreme compression fiber.
	Radius of gyration with respect to the minor axis of inertia of the area defined by the compression flange and one third of the web’s compression zone.

Factor C₁ must be previously defined as a member property, according to CTE DB SE-A table 6.11.