ACT Structural Steel Manual

Table of Contents

 

ACT Theory Manual 1

Table of Contents. 2

Code Check for Structural Steel Members. 5

Steel Structures according to Eurocode 3. 6

Reference axis. 7

Material properties. 9

Section data  9

Structural steel code properties. 12

Check Process. 12

Section Class and Reduction Factors Calculation. 13

Checking of Members in Axial Tension. 25

Checking of Members in Axial Compression. 26

Checking of Members under Bending Moment 27

Checking of Members under Shear Force. 28

Checking of Members under Bending Moment and Shear Force. 30

Checking of Members under Bending Moment  and Axial Force. 32

Checking of Members under Bending, Shear and Axial Force. 38

Checking for Buckling of Members in Compression. 41

Checking for Lateral-Torsional Buckling of Beams Subjected to Bending. 45

Checking for Lateral-Torsional Buckling of Members Subjected to Bending and Axial Compression  47

Critical Forces and Moments Calculation. 53

Steel Structures According to AISC ASD/LRFD 14th Ed. 57

Material properties. 57

Section data  57

Structural steel code properties. 59

Check Process. 60

Design requirements. 60

Checking of Members for Tension (Chapter D) 65

Checking of Members in Axial Compression (Chapter E) 66

Compressive Strength for Flexural Buckling. 66

Compressive Strength for Flexural-Torsional Buckling. 69

Compressive Strength for Flexure. 71

Checking of Members for Shear (Chapter G) 76

Checking of Members for Combined Flexure and Axial Tension / Compression (Chapter H) 77

Checking of Members for Combined Torsion, Flexure, Shear and/or Axial Force (Chapter H) 79

Steel Structures According to AISC ASD/LRFD 15th Ed. 80

Material properties. 80

Section data  80

Structural steel code properties. 82

Check Process. 82

Design requirements. 83

Checking of Members for Tension (Chapter D) 87

Checking of Members in Compression (Chapter E) 88

Checking of Members for Flexure (Chapter F) 91

Checking of Members for Shear (Chapter G) 98

Checking of Members for Combined Flexure and Axial Tension / Compression (Chapter H) 99

 

Code Check for Structural Steel Members

Structural steel members are referred to steel beams structural element. These steel members are managed to be checked according to:

·         Eurocode 3

·         AISC 14^th Edition

·         AISC 15^th Edition

The different checking types will be assigned on the Check properties from the Details window. The available checking types in CivilFEM ACT are:

Code	Type of check
Eurocode 3	Tension	Bending + Axial Force
	Compression	Bending + Shear + Axial Force
	Bending	Compressing Buckling
	Shear	Bending Buckling
	Bending + Shear	Bending + Compression buckling
AISC 14th Edition	Tension	Shear
	Compression flexural buckling	Plate girder
	Compression flexural torsional buckling	Bending + Axial Force
	Bending
AISC 15th Edition	Tension (Section D)	Shear (Section G)
	Compression (Section E)	Bending (Section F)
	Bending + Axial Force (Section H)

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

Steel Structures according to Eurocode 3

For checking steel structures according to Eurocode 3 in CivilFEM ACT, it is possible to check structures composed by welded or rolled shapes under axial forces, shear forces and bending moments in 3D. The calculations made by CivilFEM ACT correspond to the recommendations of Eurocode 3: Design of steel structures Part 1-1: General rules and rules for buildings (EN 1993-1-1:2005).

 

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

Check steel sections subjected to
- Tension	Art. 6.2.3
- Compression	Art. 6.2.4
- Bending	Art. 6.2.5
- Shear force	Art. 6.2.6
- Bending and Shear	Art. 6.2.8
- Bending and axial force	Art. 6.2.9
- Bending, shear and axial force	Art. 6.2.10
Check for buckling
- Compression members with constant cross-section	Art. 6.3.1
- Lateral-torsional buckling of beams	Art. 6.3.2
- Members subjected to bending and axial tension	N/A
- Members subjected to bending and axial compression	Art. 6.3.3

 

Valid cross-sections supported by CivilFEM ACT for checks according to Eurocode 3 are the following:

·         All rolled shapes included in the program libraries (see the hot rolled shapes library).

·         The following welded beams: double T shapes, U or channel shapes, T shapes, box, equal and unequal legs angles and pipes.

·         Structural steel sections defined by plates.

CivilFEM ACT considers the above sections as sections composed of plates; for example, an I 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 Eurocode 3. Obviously circular sections cannot be decomposed into plates, so these sections are analyzed separately.

Reference axis

With checks according to Eurocode 3, CivilFEM ACT includes three different coordinate reference systems. All of these systems are right-handed:

CivilFEM ACT Reference Axis. (X_CF, Y_CF, Z_CF).

Cross-Section Reference Axis. (X_S, Y_S, Z_S).

Eurocode 3 Reference Axis. (Code axis). (X_EC3, Y_EC3, Z_EC3).

For the Eurocode 3 axes system:

·         The origin matches to the CivilFEM axes origin.

·         X_EC3 axis coincides with CivilFEM X-axis.

·         Y_EC3 axis is the relevant axis for bending and its orientation is defined by the user (in steel check process).

·         Z_EC3 axis is perpendicular to the plane defined by X and Y axis, to ensure a right-handed system.

To define this reference system, the user must indicate which direction of the CivilFEM axis (-Z, -Y, +Z or +Y) coincides with the relevant axis for positive bending. The user may define this reference system when checking according to this code. In conclusion, the code reference system coincides with that of CivilFEM.

 

Material properties

For Eurocode 3 checking, the following material properties are used:

*th =thickness of the plate

Section data

Eurocode 3 considers the following data set for the section:

·         Gross section data

·         Net section data

·         Effective section data

·         Data belonging to the section and plates class.

 

Gross section data correspond to the nominal properties of the cross-section. For the net section, only the area is considered. This area is calculated by subtracting the holes for screws, rivets and other holes from the gross section area. The area of holes is introduced within the structural steel code properties.

Effective section data and section and plates class data are obtained in the checking process according to the effective width method. For class 4 cross-sections, this method subtracts the non-resistance zones for local buckling. However, for cross-sections of a lower class, the sections are not reduced for local buckling.

In the following tables, the section data used in Eurocode 3 are shown:

 

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.

 

 

Structural steel code properties

For Eurocode 3 checking, besides the section properties, more data are needed for buckling checks. These data are shown in the following table.

 

Check Process

The checking process includes the evaluation of the following expression:

                                         

Evaluation steps:

1.      Read the loading check requested by the user.

2.      Read the CivilFEM axis to be considered as the relevant axis for bending so that it coincides with the Y axis of Eurocode 3. In CivilFEM, by default, the principle bending axis that coincides with the +Y axis of Eurocode 3 is the +Y.

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

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

Calculated properties:

Epsilon, material coefficient:

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

c.      Initialize values of the effective cross-section.

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

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

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

g.      Specific section checking according to the type of external load. The specific check includes:

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

2.  Obtaining the cross-section class and calculating the effective section properties.

3.  Checking the cross-section according to the external load and its class by calculating the check criterion.

h.      Store the results.

 

Section Class and Reduction Factors Calculation

Sections, according to Eurocode 3, are made up by plates. These plates can be classified according to:

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

2.      Plate union condition: internal plates or outstand plates.

 

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

For checking the structure for safety, Eurocode 3 classifies sections as one of four possible classes:

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

The cross-section class is the highest (least favorable) class of all of its elements: flanges and webs (plates). First, the class of each plate is determined according to the limits of Eurocode 3. The plate class depends on the following:

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

                                  GeomRat = Corrected_Width / thickness

The width correction consists of subtracting the zone that does not contribute to buckling resistance in the fixed ends. This zone depends on the shape type of the section. Usually, the radii of the fillet in hot rolled shapes or the weld throats in welded shapes determine the deduction zone. The values of the corrected width that CivilFEM uses for each shape type include:

·    Welded Shapes:

Double T section:

Internal webs or flanges:

             Corrected width = d

             d          Web free depth

 

Outstand flanges:

Corrected width

Where:

B	Flanges width
Tw	Web thickness
	Radius of fillet

T section:

Internal webs or flanges:

             Corrected width = d

Outstand flanges:

Corrected width = B/d

C section:

Internal webs or flanges:

             Corrected width = d

Outstand flanges:

            

Corrected width

B –  –

L section:

Corrected width =

      Angle flange width

Box section:

Internal webs:

             Corrected width = H

H          Height

Internal flanges:

             Corrected width

        Web thickness

Circular hollow section

             Corrected width = H

·    Rolled Shapes:

Double T section:

Internal webs or flanges:

             Corrected width = d

d           Web free depth

Outstand flanges:

Corrected width = B/2

B           Flanges width

T Section:

Internal webs or flanges:

             Corrected width = d

Outstand flanges:

Corrected width = B/2

C Section:

Internal webs or flanges:

             Corrected width = d

Outstand flanges:

             Corrected width = B

L Section:

Corrected width =

       Angle flange width

Box section:

Internal webs:

             Corrected width = d

Internal flanges:

             Corrected width

         Flanges thickness

Pipe section:

             Corrected width = H

2.      The limit listed below for width to thickness ratio. This limit depends on the material parameter e and the normal stress distribution in the plate section. The latter value is given by the following parameters: a,  and k₀, and the plate type, internal or outstand; the outstand case depends on if the free end is under tension or compression.

Limit (class) 

 

where:

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

A linear stress distribution on the plate is assumed.

The procedure to determine the section class is as follows:

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

2.      Calculate the parameters: a,  and k₀

For internal plates:

	ENV 1993-1-1:1992	EN 1993-1-1:2005
	= infinite

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

For      

 

For      

= infinite

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

For      

For      

 

For      

= infinite

Cases in which  infinite are not included in Eurocode 3. With these cases, the plate is considered to be practically in tension and it will not be necessary to determine the class. These cases have been included in the program to avoid errors, and the value  has been adopted because the resultant plate class is 1 and the plate reduction factor is r = 1 (the same values as if the whole plate was in tension). The reduction factor is used later in the effective section calculation.

3.      Obtain the limiting proportions as functions of: a,  and k₀ and the plate characteristics (internal, outstand: free end in compression or tension).

EN 1993-1-1:2005:

Internal plates:

	for
	for
	for
	for
	for
	for

Outstand plates, free end in compression:

Outstand plates, free end in tension:

Above is the general equation used by the program to obtain the limiting proportions for determining plate classes. In addition, plates of Eurocode 3 may be checked according to special cases.

For example:

In sections totally compressed:

a= 1;            = 1 for all plates

In sections under pure bending:

a = 0.5;        = -1 for the web

a = 1;           = 1 for compressed flanges

4.      Obtain the plate class:

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

Repeat these steps (1,2,3,4) for each section plate.

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

6.      GeomRat = outer diameter/ thickness.

For class 4 sections, the section resistance is reduced, using the effective width method.

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

            Effective_length_end 1 =

            Effective_length_end 2 =

The following formula from Eurocode 3 has been implemented for this process:

1. Internal plates:

For         (Both ends compressed)

  corrected plate width

plate_width = real plate width

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

2. Outstand plates:

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

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

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

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

The global reduction factor r is obtained by as follows:

 

EN 1993-1-1:2005:

For internal compression elements

   For        

   For        

For outstands compression elements:

   For        

   For        

 

 Both Eurocode define as the plate given by:

where:

       =     corrected plate width

t        =     relevant thickness

e        =     material parameter

           =     buckling factor

To determine effective section properties, three steps are followed:

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

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

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

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

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

Checking of Members in Axial Tension

Corresponds to chapter 6.2.3 in EN 1993-1-1:2005.

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

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

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

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

where  is the design tension resistance of the cross-section, taken as the smaller value of:

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

4.     Output results are written in the ANSYS Workbench results file. Checking results: criteria and variables are described in the following table:

 

Checking of Members in Axial Compression

Corresponds to chapter 6.2.4 in EN 1993-1-1:2005.

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

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

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

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

where  is the design compression resistance of the cross-section

Class 1,2 or 3 cross-sections:

 design plastic resistance of the gross section

Class 4 cross sections:

EN 1993-1-1:2005:

4.     Output results written in the CivilFEM ACT checked file. Checking results: criteria and variables are described at the following table.

 

Checking of Members under Bending Moment

Corresponds to chapter 6.2.5 in EN 1993-1-1:2005.

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

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

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

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

where:

 design value of the bending moment

 design moment resistance of the cross-section

Class 1 or 2 cross-sections:

Class 3 cross sections:

Class 4 cross sections:

EN 1993-1-1:2005:

4.     Output results are written in the CivilFEM ACT checked file. Checking results: criteria and variables are described in the following table.

Checking of Members under Shear Force

Corresponds to chapter 6.2.6 in EN 1993-1-1:2005.

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

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

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

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

       

where:

	design value of the shear force
	design plastic shear resistance:
	shear area, obtained subtracting from the gross area the summation of the flanges areas:

 

 

 

 

Modifications to the previous computation of are as follows:

a.      Rolled I and H sections, load parallel to web:

b.      Rolled channel sections, load parallel to web:

EN 1993-1-1:2005 specifies additional cases for the calculation of :

·         Rolled I and H sections with load parallel to web:

 
      but not less than  η

·         Rolled T shaped sections with load parallel to web:

  

Where:

η	η = 1.2 for steels with fy = 460 MPa η= 1.0 for steels with fy > 460 MPa
	Web depth
	Web thickness

4.     Output results are written in the CivilFEM ACT checked file. Checking results: criteria and variables are described in the following table.

Checking of Members under Bending Moment and Shear Force

Corresponds to chapter 6.2.8 in EN 1993-1-1:2005.

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

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

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

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

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

 

Where:

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

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

The design resistance moment is obtained as follows:

EN 1993-1-1:2005:

a.  For double T cross-sections with equal flanges, bending about the major axis:

b.  For other cases the yield strength is reduced as follows:

 

Note: This reduction of the yield strength fy is applied to the entire section. Eurocode 3 only requires the reduction to be applied to the shear area, and therefore, it is a conservative simplification.

For both cases,  is the smaller value of either  or .

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

 

4.     Output results are written in the CivilFEM ACT checked file. Checking results: criteria and variables are described in the following table.

 

 

Checking of Members under Bending Moment  and Axial Force

Corresponds to chapter 6.2.9 in EN 1993-1-1:2005.

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

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

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

3.     Criteria calculation. For members subjected to bi-axial bending and in absence of shear force, the following conditions at each section are checked:

Class 1 and 2 sections:

This condition is equivalent to:

Where  and  are the design moment resistance of the cross-section, reduced by the presence of the axial force:

 

Where a and b are constants, which may take the following values:

For I and H sections:

a = 2   and b =5n   

For circular tubes:

a = 2  and b =2

For rectangular hollow sections:

   

 

  but     

For solid rectangles and plates (the rest of sections):

Furthermore, the code specifies that in the case of rolled shapes for I or H sections or other sections with flanges, it is not necessary to reduce the design plastic strength for bending around the y-y axis due to the axial force if the following two conditions are fulfilled:

(if it does not reach half the tension strength of the web)

The same is applicable for bending around the z-z axis due to the axial force. There is no reduction when the following condition is fulfiled:

In absence of , the previous check can be reduced to:

Condition equivalent to:

Class 3 sections (without holes for fasteners):

 

Condition equivalent to:

Crt_TOT = Crt_N + Crt_My + Crt_Mz £ 1

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

In absence of , the above criterion becomes:

Which is equivalent to:

Crt_TOT = Crt_N + Crt_My £ 1

Class 4 sections:

Condition equivalent to:

Crt_TOT = Crt_N + Crt_My + Crt_Mz £ 1

Where:                    

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

Without , the above criterion becomes:

which is equivalent to:

Crt_TOT = Crt_N + Crt_My + Crt_Mz £ 1

 

4.     Output results are written in the CivilFEM ACT checked file. Checking results: criteria and variables are described in the following table.

Checking of Members under Bending, Shear and Axial Force

Corresponds to chapter 6.2.10 in EN 1993-1-1:2005.

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

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

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

3.     Criteria calculation. For members subjected to bending, axial and shear force, the same conditions of the bending +axial force and bi-axial bending are checked at each section, reducing the design plastic resistance moment for the presence of shear force. The shear force effect is taken into account when it exceeds 50% of the design plastic resistance of the cross-section. In this case, both the axial and the shear force are taken into account.

 

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

where:

       for  

for

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

Note: The yield strength reduction is applied to the entire cross-section; however, Eurocode only requires the reduction to be applied to the shear area. Thus, it is a conservative simplification.

4.     Output results are written in the CivilFEM ACT checked file. Checking results:  criteria and variables are described in the following table.

 

Checking for Buckling of Members in Compression

Corresponds to chapter 6.3.1 in EN 1993-1-1:2005.

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

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

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

3.     Criteria calculation. When checking the buckling of compression members, the criterion is given by:

   

where:

	Design buckling resistance. b = 1 for class 1, 2 or 3 sections. b = for class 4 sections.
	Reduction factor for the relevant buckling mode, the program does not consider the torsional or the lateral-torsional buckling.

The c calculation in members of constant cross-section may be determined from:

where a is an imperfection factor that depends on the buckling curve. This curve depends on the cross-section type, producing the following values for a:

 

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

In the case of angular sections, the buckling length will be taken as the highest among the buckling lengths on the Y and Z axis.

The elastic critical axial forces are calculated in the planes XY (Ncr_xy) and XZ (Ncr_xz) and the corresponding values of c_xy and c_{xz ,} and the correspondent to the principal axis Ncr_u and Ncr_v and the values for c_u and c_v taking the smaller one as the final value for c.

4.     Output results are written in the CivilFEM ACT checked file. Checking results: criteria and variables are described in the following table.

 

Checking for Lateral-Torsional Buckling of Beams Subjected to Bending

Corresponds to chapter 6.3.2 in EN 1993-1-1:2005.

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

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

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

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

    à   

 

where:

	Design buckling resistance moment of a laterally unrestrained beam. bw = 1 for class 1and 2 sections. bw = for class 3 sections. bw = for class 4 sections.
cLT	Reduction factor for lateral-torsional buckling.

The value of c_LT is calculated as:

Where:

is the imperfection factor for lateral-torsional buckling: Section type Limits Buckling curve α Rolled I h/b≤2 h/b>2 a b 0.21 0.34 Welded I h/b≤2 h/b>2 c d 0.49 0.76 Others     0.76

 

is the elastic critical moment for lateral-torsional buckling.

4.     Output results are written in the CivilFEM ACT checked file. Checking results: criteria and variables are described in the following table.

 

Checking for Lateral-Torsional Buckling of Members Subjected to Bending and Axial Compression

Corresponds to chapter 6.3.3 in EN 1993-1-1:2005.

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

= FX	Design value of the axial compression (positive if compressive, otherwise element not processed if tensile).
= MY or MZ	Design value of the bending moment about the relevant axis of bending.
= MZ or MY	Design value of the bending moment about the secondary axis of bending.

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

3.     Criteria calculation.

EN 1993-1-1:2005 and Annex B (method 2)

The following criterion will always be calculated:

Crt_1 = Crt_N1 + Crt_My1 + Crt_Mz1 £ 1

Elements without torsional buckling:

Elements which may have torsional buckling:

 

à Crt_2 = Crt_N2 + Crt_My2 + Crt_Mz2 £ 1

à Crt_TOT = Max (Crt_1, Crt_2)

 

Where:

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

Where:

 ( when torsional buckling is not considered).

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

 

lateral buckling factor according to 6.3.2.2. Assumes the value of 1 for members not susceptible to torsional deformations.

and  shifts of the centroid of the effective area relative to the centre of gravity of the gross section in class 4 members for y, z axes.

,  and are equivalent uniform moment factors for flexural bending. These factors are entered as member properties at member level. (See and ).  These factors may be taken from Table B.3 from Annex B of code EN 1993-1-1:2005.

Checking Parameters:

Interaction Factors:

 

 

where:

Limited slenderness values for y-y and z-z axes, less than 1.

4.     Output results are written in the CivilFEM ACT checked file. Checking results: criteria and variables are described in the following table.

 

Critical Forces and Moments Calculation

The critical forces and moments, and M_cr, are needed for the different types of buckling checks. They are calculated based on the following formulation:

 

where:

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

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

 

where:

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

For the calculation of the elastic critical moment for lateral-torsional buckling, Mcr, the following equation shall be used. This equation is only valid for uniform symmetrical cross-sections about the minor axis (Annex F, ENV 1993-1-1:1992). Eurocode 3 does not provide a method for calculating this moment in nonsymmetrical cross-sections or sections with other symmetry plane (angles, channel section, etc.).

where:

	Elastic critical moment for lateral-torsional buckling.
	Factors depending on the loading and end restraint conditions.
	Effective length factors.
E	Elasticity modulus.
	Moment of inertia about the principal axis.
	Moment of inertia about the minor axis.
L	Length of the member between end restraints.
G	Shear modulus.
	Coordinate of the point of load application. By default the load is applied at the center of gravity, therefore:.
	Coordinate of the shear center.
A	Cross-section area.

Factors C and k are read from the properties at structural element level.

The integration of the previous equation is calculated as a summation extending to each plate. This calculation is accomplished for each plate according to its ends coordinates: and  and its thicknesses.

where:

= thickness of plate i

dA =  * dl

 =  plate width

 

 

 

Steel Structures According to AISC ASD/LRFD 14th Ed.

Material properties

For AISC 14^th Edition checking, the following material properties are used:

*th =thickness of the plate

Section data

AISC 14^th Edition considers the following data set for the section:

-          Gross section data

-          Net section data

-          Effective section data.

-          Data belonging to the section and plates class.

 

Gross section data correspond to the nominal properties of the cross-section. For the net section, only the area is considered. This area is calculated by subtracting the holes for screws, rivets and other holes from the gross section area. (The area of holes is introduced within the structural steel code properties).

The effective section data and the section and plates class data are obtained in the checking process according to chapter B, section B4 of the code. This chapter classifies steel sections into three groups (compact, noncompact and slender), depending upon the width-thickness ratio and other mandatory limits.

The AISC 14^TH Edition module uses the gross section data in user units and the CivilFEM ACT’s axis or section axis as initial data. The program calculates the effective section data and the class data, and stores them in ANSYS Workbench results file, in user units and in CivilFEM ACT or section axis.

 

The section data used in AISC 14^TH Edition are shown in the following tables:

 

 

The effective section depends upon the geometry of the section; thus, the effective section is calculated for each element and each of the ends of the element.

Structural steel code properties

For AISC 14^th Edition checking, besides the section properties, more data are needed for buckling checks. These data are shown in the following table.

Check Process

Necessary steps to conduct the different checks in CivilFEM are as follows:          

a)      Obtain material properties corresponding to the element stored in CivilFEM database and calculate the rest of the properties needed for checking:
Properties obtained from CivilFEM database (materials):

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

c)      Initiate the values of the plate’s reduction factors and the other plate’s parameters to determine its class.

d)      Perform a check of the section according to the type of external load.

Design requirements

·         Design for Strength Using Load and Resistance Factor Design (LRFD)

Design shall be performed in accordance with:

Where:

	Required strength (LRFD).
	Nominal strength.
	Resistance factor.
	Design strength

·         Design for Strength Using Allowable Strength Design (ASD)

Design shall be performed in accordance with:

Where:

	Required strength (ASD)
	Nominal strength.
	Safety factor
	Allowable strength

·         Section Class and Reduction Factors Calculation.

Steel sections are classified as compact, noncompact or slender-element sections for bending sections and slender or non-slender for compression sections. For a section to qualify as compact its flanges must be continuously connected to the web or webs and the width-thickness ratios of its compression elements must not exceed the limiting width-thickness ratios  (see table B4.1 of AISC 14^th Edition). If the width-thickness ratio of one or more compression elements exceeds  but does not exceed, the section is noncompact. If the width-thickness ratio of any element exceeds, (see table B4.1 of AISC 14^th Edition), the section is referred to as a slender-element compression section.

Therefore, the code suggests different lambda values depending on if the element is subjected to compression, flexure or compression plus flexure.

The section classification is the worst-case scenario of all of its plates. Therefore, the class is calculated for each plate with the exception of pipe sections, which have their own formulation because it cannot be decomposed into plates. This classification will consider the following parameters:

a)  Length of elements:

The program will define the element length (b or h) as the length of the plate (distance between the extreme points), except when otherwise specified.

b)  Flange or web distinction:

To distinguish between flanges or webs, the program follows the criteria below:

Once the principal axis of bending is defined, the program will examine the plates of the section. Fields Pty and Ptz of the plates indicate if they behave as flanges, webs or undefined, choosing the correct one for the each axis. If undefined, the following criterion will be used to classify the plate as flange or web:

If (increments of end coordinate) and flexure is in the Y axis, it will be considered a web; if not, it will be a flange. The reverse will hold true for flexure in the Z-axis.

·    Hot rolled Steel Shapes:

Section I and C:

The length of the plate h will be taken as the value d for the section dimensions.

Section Box:

The length of the plate will be taken as the width length minus three times the thickness.

·         Members subjected to compression

In order to check for compression it is necessary to determine if the element is stiffened or unstiffened.

- For stiffened elements:

                     

 

Pipe sections

    

Box sections

 

 

- Unstiffened elements:

         

Angular sections

         

Stem of T sections

 

·         Members subjected to bending

The bending check is only applicable to very specific sections. Therefore, the slenderness factor is listed for each section:

·         Section I and C:

 

=	69 MPa for hot rolled shapes (10 ksi)
	114 MPa for welded sections (16.5 ksi)

 

= minimum of () and () where and  are the  of flange and web respectively.

Flanges of rolled sections:

             

 

 

Flanges of welded sections:

Flange:

If   

If   

Always:

 is the compression axial force (taken as positive). If in tension, it will be taken as zero.

·         Pipe section:

 

                                                                                    

·         Box section:

Flanges of box section:

Flanges: the program distinguishes between the flange and web upon the principal axis chosen by the user.

If   

If                 

Always:  

·         T section:

   

Stem:

Flanges:

Checking of Members for Tension (Chapter D)

The axial tension force must be taken as positive (if the tension force has a negative value, the element will not be checked)

Design tensile strength and the allowable tensile strength , of tension members, shall be the lower value of :

a)      yielding in the gross section:

    

b)      rupture in the net section:

           

     = 2.00 (ASD)

Being:

	Effective net area.
	Gross area.
	Minimum yield stress.
	Minimum tensile strength.

The effective net area will be taken as  – A_HOLES. The user will need to enter the correct value for A_HOLES (the code indicates that the diameter is 1/16^th in. (2 mm)  greater than the real diameter).

Checking of Members in Axial Compression (Chapter E)

The design compressive strength, ,and the allowable compressive strength,  , are determined as follows:

The nominal compressive strength, , shall be the lowest value obtained according to the limit states of flexural buckling, torsional buckling and flexural-torsional buckling.

   

Compressive Strength for Flexural Buckling

This type of check can be carried out for compact sections as well as for noncompact or slender sections. These three cases adhere to the following steps:

Nominal compressive strength,  :

       (E3-1)

a)      For :

=                              

b)      for

                                         

 

 

Where:

	Gross area of member.
r	Governing radius of gyration about the buckling axis.
K	Effective length factor.
l	Unbraced length.
	Elastic critical buckling stress

Factor Q for compact and noncompact sections is always 1. Nevertheless, for slender sections, the value of Q has a particular procedure. Such procedure is described below:

Factor Q for slender sections:

For unstiffened plates, Qs must be calculated and for stiffened plates, Qa must be determined.  If these cases do not apply (box sections or angular sections, for example), a value of 1 for these factors will be taken.

For circular sections, there is a particular procedure of calculating Q. Such procedure is described below:

·                     For circular sections, Q is:

              

Factor Qs:

If there are several plates free, the value of Qs is taken as the biggest value of all of them. The program will check the slenderness of the section in the following order:

·                     Angular

If
If

 

 

·                     Stem of T

If
If

·                     Rolled shapes

If
If

·                     Other sections

If
If

Where l is the element slenderness and

Factor Qa:

The calculation of factor Qa is an iterative process. Its procedure is the following:

1)      An initial value of Q equal to Qs is taken.

2)      With this value is calculated.

3)      This value is taken to calculate

4)      For elements with stiffened plates, the effective width b_e is calculated.

5)      With b_e the effective area is calculated.

6)      With the value of the effective area, Qa is calculated, and the process starts again.

·                     For a box section

If

·                     For other sections

If

 

If it is not within those limits, = b

With the values for each plate, the part that does not contribute [t·(b‑)] is subtracted from the area (where t is the plate thickness). Using this procedure, the effective area is calculated.

Finally, with Qs and Qa, Q is calculated, and is obtained.

Compressive Strength for Flexural-Torsional Buckling

This type of check can be carried out for compact sections as well as for noncompact or slender sections. The steps for these three cases are as follows:

Nominal compressive strength,:

           

a)      for

                              

b)  for

                                         

Where:

Factor Q for compact and noncompact sections is 1. Nevertheless, for slender sections, the Q factor has a particular procedure of calculation. Such procedure is equal to the one previously described.

The elastic stress for critical torsional buckling or flexural-torsional buckling  is calculated as the lowest root of the following third degree equation, in which the axis have been changed to adapt to the CivilFEM ACT normal axis:

  

Where:

	Effective length factor for torsional buckling.
G	Shear modulus (MPa).
	Warping constant (mm6).
J	Torsional constant (mm4).
	Moments of inertia about the principal axis (mm4).
	Coordinates of shear center with respect to the center of gravity (mm).

where:

A	Cross-sectional area of member.
l	Unbraced length.
	Effective length factor, in the z and y directions.
	Radii of gyration about the principal axes.
	Polar radius of gyration about the shear center.

In this formula, CivilFEM principal axes are used. If the CivilFEM axes are the principal axes ±5º sexagesimal degrees, and are calculated with respect to the Y and Z-axes of CivilFEM. If this is not the case (angular shapes, for example) axes U and V will be used as principal axes, with U as the axis with higher inertia.

The torsional inertia (Ixx in CivilFEM, J in AISC 14^TH Edition) is calculated for CivilFEM sections, but not for captured sections. Therefore the user will have to introduce this parameter in the mechanical properties of CivilFEM.

Compressive Strength for Flexure

Chapter F is only applicable to members subject to simple bending about one principal axis.

The design flexural strength,, and the allowable flexural strength, , shall be determined as follows:

For all provisions:  = 0.90 (LRFD)   = 1.67 (ASD)

Where is the lowest value of four checks according to sections F2 through F12:

a)      Yielding

b)      Lateral-torsional buckling

c)      Flange local buckling

d)      Web local buckling

The value of the nominal flexural strength with the following considerations:

• For compact sections, if Lb < Lp only yielding of steel will be checked.
• For T sections, and other compact sections, only yielding and torsional buckling will be checked.
• The case of lateral-torsional buckling does not apply to sections loaded on the minor axis of inertia nor box or square sections.
• The case of lateral-torsional buckling only applies for sections with double symmetry, channel and T sections. Therefore the rest of sections will be checked for torsion plus combined loads and will not be checked under flexure.
• For slender sections, the code contemplates the following cases:

 

 

 

 

 

Where:

(positive sign if the stem is under tension, negative if it is under compression)

In T sections:  stem in tension;  stem in compression.

For slender webs the nominal flexural strength  is the minimum of the following checks:

• tension-flange yield
• compression flange buckling

The first check uses the following formula:

where:

	Section modulus referred to tension flange.
	Yield strength of tension flange.

 

The second check uses the following formula:

where:

The critical stress depends upon different slenderness parameters such as l, ,  and  in the following way:

For
For
For

The slenderness values have to be calculated for the following limit states:

• Lateral torsional buckling

   (International System units)

 is the radius of gyration of compression flange plus one third of the compression portion of the web (mm).

By default, the program takes a conservative value of .

• Flange local buckling

   (IS units)

where:

and

Between these two slenderness, the program will choose values the value that produces a lower critical stress.

Checking of Members for Shear (Chapter G)

The design shear strength, , and the allowable shear strength, , shall be determined as follows:

For all provisions:  = 0.90 (LRFD)    = 1.67 (ASD)

According to the limit states of shear yielding and shear buckling, the nominal shear strength,  , of unstiffened webs is:

For webs of rolled I-shaped members with  :

  = 1.00 (LRFD)         = 1.50 (ASD)

 = 1.0 (web shear coefficient)

For webs of all other doubly symmetric shapes and singly symmetric shapes and channels is determined as follows:

1. For

= 1.0

2. For

3. For    

Where is the overall depth times the web thickness.

It is assumed that there are no stiffeners; therefore, the web plate buckling coefficient  will be calculated as a constant equal to 5.0.

Checking of Members for Combined Flexure and Axial Tension / Compression (Chapter H)

For this check, it is first necessary to determine the value of Mn. This value comes into play in the checking of formulas. The value of M_n, will be calculated in the same way as members subjected to flexure; thus, the nominal flexure strength () is the minimum of four checks:

1.  Yielding

2.  Lateral-torsional buckling

3.  Flange local buckling

4.  Web local buckling

 

In the case of having bending plus tension or bending plus compression, the interaction between flexure and axial force is limited by the following equations:

(a)   For

    (H1-1a)

(b)   For

        (H1-1b)

If the axial force is tension:

	Required tensile strength (N).
	Available tensile strength (N): (LRFD) or (ASD)
	Required flexural strength (N·mm).
	Available flexural strength (N·mm): Design:      (LRFD) or Allowable:   (ASD)
y	Strong axis bending.
z	Weak axis bending.
	Resistance factor for tension  (Sect.D2)
	Resistance factor for flexure = 0.90
	Safety factor for tension  (Sect D2)
	Safety factor for flexure = 1.67

If the axial force is compression:

	Required compressive strength (N).
	Available compressive strength (N): Design:       (LRFD) or Allowable:   (ASD)
	Required flexural strength (N·mm).
	Available flexural strength (N·mm): Design:       (LRFD) or Allowable:   (ASD)
Y	Strong axis of bending.
Z	Weak axis of bending.
	Resistance factor for compression =0.90
	Resistance factor for flexure = 0.90
	Safety factor for compression =1.67
	Safety factor for flexure = 1.67

The following checks are carried out by CivilFEM:

• Axial force and flexural buckling
• Bending moment Z direction
• Bending moment Y direction

If one of these checks do not meet the code requirements, it will not be possible to check the member under flexure plus tension / compression.

Checking of Members for Combined Torsion, Flexure, Shear and/or Axial Force (Chapter H)

The design torsional strength, f_TT_n , and the allowable torsional strength, T_n/Ω_T , shall be the lowest value obtained according to the limit states of yielding under normal stress, shear yielding under shear stress or buckling, determined as follows:

  = 0.90 (LRFD)         = 1.67 (ASD)

·         For the limit state of yielding, under normal stress:

·         For the limit state of yielding, under shear stress:

·         For the limit state of buckling:

-          Where  is calculated

 

 

Steel Structures According to AISC ASD/LRFD 15th Ed.

Material properties

For AISC 15^th Edition checking, the following material properties are used:

*th =thickness of the plate

Section data

AISC 15^th Edition considers the following data set for the section:

-          Gross section data

-          Net section data

-          Effective section data.

-          Data belonging to the section and plates class.

 

Gross section data correspond to the nominal properties of the cross-section. For the net section, only the area is considered. This area is calculated by subtracting the holes for screws, rivets and other holes from the gross section area. (The area of holes is introduced within the structural steel code properties).

The effective section data and the section and plates class data are obtained in the checking process according to chapter B, section B4 of the code. This chapter classifies steel sections into three groups (compact, noncompact and slender), depending upon the width-thickness ratio and other mandatory limits.

The AISC 15^TH Edition module uses the gross section data in user units and the CivilFEM ACT’s axis or section axis as initial data. The program calculates the effective section data and the class data, and stores them in ANSYS Workbench results file, in user units and in CivilFEM ACT or section axis.

 

The section data used in AISC 15^TH Edition are shown in the following tables:

 

 

The effective section depends upon the geometry of the section; thus, the effective section is calculated for each element and each of the ends of the element.

Structural steel code properties

For AISC 15^th Edition checking, besides the section properties, more data are needed for bucling checks. These data are shown in the following table.

Check Process

Necessary steps to conduct the different checks in CivilFEM are as follows:          

a)      Obtain material properties corresponding to the element stored in CivilFEM database and calculate the rest of the properties needed for checking:
Properties obtained from CivilFEM database (materials):

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

c)      Initiate the values of the plate’s reduction factors and the other plate’s parameters to determine its class.

d)      Perform a check of the section according to the type of external load.

Design requirements

·         Design for Strength Using Load and Resistance Factor Design (LRFD)

Design shall be performed in accordance with:

Where:

	Required strength (LRFD).
	Nominal strength.
	Resistance factor.
	Design strength

·         Design for Strength Using Allowable Strength Design (ASD)

Design shall be performed in accordance with:

Where:

	Required strength (ASD)
	Nominal strength.
	Safety factor
	Allowable strength

·         Section Class and Reduction Factors Calculation.

Steel sections are classified as compact, noncompact or slender-element sections for bending sections and slender or non slender for compression sections. For a section to qualify as compact its flanges must be continuously connected to the web or webs and the width-thickness ratios of its compression elements must not exceed the limiting width-thickness ratios  (see table B4.1 of AISC 15TH EDITION). If the width-thickness ratio of one or more compression elements exceeds but does not exceed , the section is noncompact. If the width-thickness ratio of any element exceeds , (see table B4.1 of AISC 15TH EDITION), the section is referred to as a slender-element compression section.

Therefore, the code suggests different lambda values depending on if the element is subjected to compression, flexure or compression plus flexure.

The section classification is the worst-case scenario of all of its plates. Therefore, the class is calculated for each plate with the exception of pipe sections, which have their own formulation because it cannot be decomposed into plates. This classification will consider the following parameters:

a)  Length of elements:

The program will define the element length (b or h) as the length of the plate (distance between the extreme points), except when otherwise specified.

b)  Flange or web distinction:

To distinguish between flanges or webs, the program follows the criteria below:

Once the principal axis of bending is defined, the program will examine the plates of the section. Fields Pty and Ptz of the plates indicate if they behave as flanges, webs or undefined, choosing the correct one for the each axis. If undefined, the following criterion will be used to classify the plate as flange or web: if (increments of end coordinates) and flexure is in the Y axis, it will be considered a web; if not, it will be a flange. The reverse will hold true for flexure in the Z-axis.

·    Steel Shapes dimensions:

Section I and C:

The length of the plate h will be taken as the value d for the section dimensions.

 

Rectangular HSS:

The length of the plate will be taken as the width length minus three times the design thickness (=0.93*nominal thickness).

Box by dimensions:

The length of the plate will be taken as the width length minus two times the thickness.

Round HSS:

The length of the plate will be taken as the external diameter. Thickness will be taken as the design thickness (=0.93*nominal thickness).

Pipe by dimensions:

The length of the plate will be taken as the external diameter. Thickness will be taken as the thickness of the section.

·         Members subjected to compression

In order to check for compression it is necessary to determine if the element is stiffened or unstiffened.

- For stiffened elements:

                      

Pipe sections

    

Box sections

 

 

- Unstiffened elements:

Angular sections

         

Stem of T sections

 

·         Members subjected to bending

The bending check is only applicable to very specific sections. Therefore, the slenderness factor is listed for each section:

·         Section I and C:

Flanges of rolled sections:

             

Flanges of welded sections:

       = 0.7Fyf.

 

 

Web:

         

 

·         Pipe section:

                    

·         Box section:

Flanges of box section:

Flanges: the program distinguishes between the flange and web upon the principal axis chosen by the user.

                

 

·         T section:

Stem:

             

 

Flanges:

             

Checking of Members for Tension (Chapter D)

The axial tension force must be taken as positive (if the tension force has a negative value, the element will not be checked)

Design tensile strength and the allowable tensile strength , of tension members, shall be the lower value of :

a)      yielding in the gross section:

    

b)      rupture in the net section:

           

     = 2.00 (ASD)

Being:

	Effective net area.
	Gross area.
	Minimum yield stress.
	Minimum tensile strength.

The effective net area will be taken from the net section properties (by default as  – A_HOLES). It is important to notice that the shear leg factor U is not included so the user must modify the default effective net area Aeff =(A_g – AHOLES)*U. Net section properties can be modified in the beam structural element window (edit->Mechanical Properties->Sttel Net)

Checking of Members in Compression (Chapter E)

The design compressive strength, , and the allowable compressive strength,  , are determined as follows:

The nominal compressive strength, , shall be the lowest value obtained according to the limit states of flexural buckling and flexural-torsional buckling.

   

Nominal compressive strength,  :

       (E3-1)

(a) If 

  

(b) If   

 

Compressive Strength for Flexural Buckling

Calculation of elastic critical buckling stress is performed for each axis and is calculated as the lowest of both:

This type of check can be carried out for compact sections as well as for noncompact or slender sections. These three cases adhere to the following steps:

 

The value Fe will be taken as the minimum of Fe for flexural buckling (about both axis) and Fe for flexural-torsional buckling.

 

Where:

r	Governing radius of gyration about the buckling axis.
K	Effective length factor.
L	Unbraced length.

Compressive Strength for Flexural-Torsional Buckling

The elastic stress for critical torsional buckling or flexural-torsional buckling F_e is calculated as (formulas are referred to CivilFEM axis):

I shape sections:

T shape sections:

                                                                 

C shape sections:

                                                                 

Other sections: the lowest root of the following third degree equation, in which the axis have been changed to adapt to the CivilFEM normal axis:

   (E4-4)

Where:

	Effective length factor for torsional buckling.
G	Shear modulus (MPa).
	Warping constant (mm6).
J	Torsional constant (mm4).
	Moments of inertia about the principal axis (mm4).
	Coordinates of shear center with respect to the center of gravity (mm).

 

where:

A	Cross-sectional area of member.
L	Unbraced length.
	Effective length factor, in the z and y directions.
	Radio of gyration about the principal axes.
	Polar radius of gyration about the shear center.

In this formula, CivilFEM principal axes are used. If the CivilFEM axes are the principal axes ±5º sexagesimal degrees, Ky and Kz are calculated with respect to the Y and Z-axes of CivilFEM. If this is not the case (angular shapes, for example) axes U and V will be used as principal axes, with U as the axis with higher inertia.

The torsional inertia (Ixx in CivilFEM, J in AISC 15TH EDITION) is calculated for CivilFEM sections. The user can modify this parameter in the mechanical properties of CivilFEM.

Checking of Members for Flexure (Chapter F)

Chapter F is only applicable to members subject to simple bending about one principal axis.

The design flexural strength,, and the allowable flexural strength, , shall be determined as follows:

For all provisions:  = 0.90 (LRFD)  = 1.67 (ASD)

Where M_n is the lowest value of four checks according to sections of chapter F:

a)      Yielding

b)      Lateral-torsional buckling

c)      Flange local buckling

d)      Web local buckling

The value of the nominal flexural strength with the following considerations:

Shape: I-shaped members and channels bent about their major axis with compact web

Limit state:

·         Yielding:

 

·         LTB (Lp<Lb<=Lr):

·         LTB (Lb>Lr):

 

 = Value introduced by user in member properties

 = Critical stress 

 = = elastic section modulus

  = distance between the flange centroids

 

·         FLB (noncompact flanges):

 

·         FLB (slender flanges):

     

Shape: I-shaped members bent about their major axis with noncompact web.

Limit state:

·         Yielding:

 = elastic section modulus referred to compression flange

= web plastification factor, determined in accordance with Section F4.2(c)(6)

·         LTB (Lp<Lb<=Lr):

·         LTB (Lb>Lr):

 

 = Value introduced by user in member properties

 = Critical stress 

= web plastification factor

 

·         FLB (noncompact flanges):

 

·         FLB (slender flanges):

     

Shape: I-shaped members bent about their major axis with slender web.

Limit state:

·         Yielding:

 = elastic section modulus referred to compression flange

= Bending strength reduction factor (F5-6)

·         LTB (Lp<Lb<=Lr):

·         LTB (Lb>Lr):

 

 = Value introduced by user in member properties

 = Critical stress 

= Bending strength reduction factor (F5-6)

 

·         FLB (noncompact flanges):

 

·         FLB (slender flanges):

     

Shape: I-shaped members and channels bent about their minor axis.

Limit state:

·         Yielding:

 

·         FLB (noncompact flanges):

 

·         FLB (slender flanges):

Shape: Box.  

Limit state:

·         Yielding:

 

 

·         LTB (Lp<Lb<=Lr):

·         LTB (Lb>Lr):

 

·         FLB (noncompact flanges):

 

·         FLB (slender flanges):

 = effective section modulus determined with the effective width, be, of the compression flange (F7-4 o F7-5)

 

·         WLB (noncompact web):

 

·         WLB (slender web): Value is taken as the lowest for compression flange yielding (F7-7) and compression flange local buckling (F7-8)

 = elastic section modulus referred to compression flange

= Bending strength reduction factor (F5-6)

 

 

Shape: Tubular

Limit state:

·         Yielding:

 

 

·         FLB (noncompact):

·         FLB (slender):

Shape:Tees loaded in the plane of symmetry

Limit State:

·         Yielding (tee stems in tension):

·         Yielding (tee stem in compression):

 

·         LTB (Lp<Lb<=Lr):

·         LTB (Lb>Lr):

 

                                       

(positive sign if the stem is under tension, negative if it is under compression)

Checking of Members for Shear (Chapter G)

The design shear strength, , and the allowable shear strength, , shall be determined as follows:

For all provisions:  = 0.90 (LRFD)   = 1.67 (ASD)

Except for webs of rolled I-shaped members with .

In this case:  = 1.00 (LRFD)            = 1.50 (ASD)

According to the limit states of shear yielding and shear buckling, the nominal shear strength,  , is calculated following the next considerations:

Shape: I-shaped and Channels with shear forcé in the web plane.

For webs of rolled I-shaped members with ->

For all other I-shaped members and channels:

            If          ->

            If          ->

It is assumed that there are no stiffeners; therefore, the web plate buckling coefficient  will be calculated as a constant equal to 5.34.

Shape: Tubular

Because the Lv value (distance from maximum cutting force to zero) is unknown, Fcr is calculated as:

 

Shape: Other sections

yis calculated following chapters G3,G4 y G6

Checking of Members for Combined Flexure and Axial Tension / Compression (Chapter H)

For this check, it is first necessary to determine the value of Mn. This value comes into play in the checking of formulas. The value of Mn, will be calculated in the same way as members subjected to flexure; thus, the nominal flexure strength () is the minimum of four checks:

1-      Yielding

2-      Lateral-torsional buckling

3-      Flange local buckling

4-      Web local buckling

 

In the case of having bending plus tension or bending plus compression, the interaction between flexure and axial force is limited by the following equations:

(a)   For

    (H1-1a)

(b)   For

        (H1-1b)

If the axial force is tension:

	Required tensile strength (N).
	Available tensile strength (N): (LRFD) or (ASD)
	Required flexural strength (N·mm).
	Available flexural strength (N·mm): Design:      (LRFD) or Allowable:   (ASD)
y	Strong axis bending.
z	Weak axis bending.
	Resistance factor for tension  (Sect.D2)
	Resistance factor for flexure = 0.90
	Safety factor for tension  (Sect D2)
	Safety factor for flexure = 1.67

 

If the axial force is compression:

	Required compressive strength (N).
	Available compressive strength (N): Design:       (LRFD) or Allowable:   (ASD)
	Required flexural strength (N·mm).
	Available flexural strength (N·mm): Design:       (LRFD) or Allowable:   (ASD)
Y	Strong axis of bending.
Z	Weak axis of bending.
	Resistance factor for compression =0.90
	Resistance factor for flexure = 0.90
	Safety factor for compression =1.67
	Safety factor for flexure = 1.67

 

The following checks are carried out by CivilFEM:

• Axial force and flexural buckling
• Bending moment Z direction
• Bending moment Y direction

If one of these checks do not meet the code requirements, it will not be possible to check the member under flexure plus tension / compression.