10-E.1      Scope

Steel structures checking according to LRFD, December 27 of 1999 in CivilFEM is included in 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 LRFD (Load and Resistance Factor Design) for the following sections:

 

D	Tension members.
E	Columns and other compression members.
F	Beams and other flexural members.
G	Plate girders.
H	Members under combined forces and torsion.

 

 

10-E.2      Checking Types

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

·         Checking of sections subjected to:

- Tension	LRFD apt. D-1
- Flexure	LRFD apt. F-1
- Shear force	LRFD apt. F-2
- Bending and axial force	LRFD apt. H-1
- Bending plus axial force, shear and torsion	LRFD apt. H-2

·         Buckling check:

- Compression members subjected to flexure	LRFD apt. E-2
- Compression members subjected to flexure and torsion	LRFD apt. E-3
- Plate girders	LRFD apt. G

 

10-E.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 with a transversal cross section classified as “structural steel”.

 

10-E.4      Valid Cross-Section Types

The steel type cross-sections used by CivilFEM can be classified as:

• All the rolled shapes (I shapes, U or channel shapes, etc.) included in the program libraries (see the hot rolled shapes library and ~SSECLIB command)
• The following welded beams: I shapes, U or channel shapes, T shapes, box, equal and unequal legs angles and pipes. (~SSECDMS commands). These sections are considered as a generic shape.
• Structural steel sections defined by plates (command ~SSECPLT). These sections are considered as a generic shape.
• Shapes from solid sections captured from 2D or 3D models which transverse cross section is classified as “structural steel” (command ~SLDSEC).

 

The cross-sections considered in the LRFD code depend on the type of checking:

 

 

10-E.5      Data and Results used by CivilFEM

CivilFEM works with the following groups of data and results for checking according to LRFD:

·         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 over the sections.

·         Checking results.

10-E.5.1           Sections Data

LRFD 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 user should be aware that LRFD indicates the diameter from which to calculate the parameter AHOLES is greater than the real diameter (the total calculated area is introduced in the parameter AHOLES with the command ~SECMDF).

Effective section data and section and plates class data are obtained in the checking process according to chapter B, section B5 of the code. This chapter, classifies steel sections into three groups, compact, noncompacts and slender, depending upon the width-thickness ratio and some mandatory limits.

The LRFD module utilizes the gross section data in user units and the CivilFEM axis or section axis as initial data. The program calculates the effective section data and the class data and stores them in CivilFEM’s results file, in user units and in CivilFEM or section axis. All these data can be listed and plotted with the ~PLLSSTL, ~PLCSEC3 and ~PRSTL commands.

The section data used in LRFD are shown in the following tables:

 

 

Table 10-E.5‑1 Common data for gross, net and effective sections

 

Table 10-E.5‑2 Gross section data

 

Table 10-E.5‑3 Net section data

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

 

The effective section depends upon the geometry of the section and therefore, the effective section is calculated for each element and end.

 

Table 10-E.5‑4 Net section data

 

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

 

10-E.5.2           Member Properties

The checked data set for LRFD 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, KY, KZ, KTOR, CB, LB, CHCKAXIS, of ~MEMBPRO command).

 

Table 10-E.5‑6 Member Properties

 

10-E.5.3           Material Properties

For LRFD checking, the following material properties are used:

 

Table 10-E.5‑7 Material properties

*th =thickness of plate

 

10-E.6      Checking Process

Steps necessary to conduct the different checks in CivilFEM are the following:

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: (command ~CFMP)

Elasticity modulus	E
Poisson’s ratio	n
Yield strength
Ultimate strength
Shear modulus	G
Thickness of corresponding plate	th

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

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

d)    Specific section checking according to the type of external load.

e)    Results. In CivilFEM , checking results for each element end are grouped into alternatives in the results file .RCV so that the user may access them by indicating the number of the alternative using the CivilFEM command ~CFSET.

The required data for the different checking types are provided within tables found in their corresponding section of this manual.

10-E.6.1           General Processing of Sections. Section Class and Reduction Factors Calculation.

Steel sections are classified as compact, noncompact or slender-element sections. For a section to qualify as compact its flanges, it 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 B5.1 of LRFD). 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 B5.1 of LRFD), 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 its plates. Therefore, the class is calculated for each plate with the exception of pipe sections, which have their own equation because they cannot be decomposed into plates. The classification will take into account the following parameters:

a) Length of elements:

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

b) Flange or web distinction:

To distinguish between flanges or webs, the programs follow 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. In the case of undefined, the following criterion will be taken into account to classify the plate as a flange or a web: if |Dy|<|Dz| (increments of end coordinates) and flexure is in the Y axis, it is considered as 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 of the section dimensions.

Section Box:

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

 

10-E.6.1.1       Members Subjected to Compression

In order to check a member under compression it is necessary to determine if the particular element is stiffened or unstiffened.

- For stiffened elements:

Pipe Sections

Box sections

 

- Unstiffened elements:

        

Angular sections

 

Stem of T sections

 

10-E.6.1.2       Members Subjected to Bending

Checking for bending is only applicable to very specific sections. Therefore the slenderness factor is indicated 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 flange and web upon the principal axis chosen by the user.

If: :   

If:     

Always:

·         T section:

    

Stem:

Flanges :

10-E.6.2           Checking of Members in Axial Tension (Chapter D of LRFD)

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

Design strength of tension members:  shall be the lower value of:

a)    Yielding in the gross section:

b)    Fracture in the net section:

Where:

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

 

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

 

Table 10-E.6‑1 Chapter D Checking of Members in Axial Tension

 

10-E.6.3           Checking of Members in Axial Compression (Chapter E and Appendix B of LRFD)

Among the checks for members subjected to axial compression, the LRFD includes the following checks:

10-E.6.3.1       Compressive Strength for Flexural Buckling 

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

Axial compression design strength:  (E2)

 = 0.85

  (E2-1)

(a) for

     (E2-2) (A-B5-15)

(b) for

       (E2-3) (A-B5-16)

Where:

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

Factor Q for compact and noncompact sections is always 1. Nevertheless, for slender sections, 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, the particular procedure for calculating Q is described below:

·                    For circular sections, Q is:

·                     

 

Factor Qs:

If there are several plates free, the value of Qs is taken as the largest 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 :

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

1)    An initial value of Q equal to  is taken

2)    With this value  is calculated

3)    This  value is taken to calculate

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

5)    With be the effective area is calculated

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

 

·                    For a box section

If

·                    For other sections

If

 

If it is not within those limits,

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

 

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

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-E.6‑2 Chapter E Checking of Members Subjected to Compression

 

10-E.6.3.2       Compressive Strength for Flexural-Torsional Buckling

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

 

Axial design strength:  (E3)

       (E3-1)

(a) for

(A-E3-2)

(b) for

           (A-E3-3)

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 F_e is calculated as the lowest root of the following third degree equation, in which the axis have been changed to adapt to CivilFEM normal axis:

(A-E3-7)

Where:

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

 

where:

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

In these expressions, CivilFEM principal axes are used. If the CivilFEM axes are the principal axes ±5º sexagesimal, 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 LRFD) is calculated for CivilFEM sections, but not for captured sections. Therefore the user will have to introduce this parameter into the mechanical properties of CivilFEM.

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-E.6‑3 Chapter E Checking of elements subjected to compression for flexural-torsional buckling

 

10-E.6.4           Checking of Members Under Bending Moment (Chapter F of LRFD)

Chapter F is only applicable for compact and noncompact sections subjected to bending moment and shear.

10-E.6.4.1       Flexure Check

The nominal flexural strength  will be the lowest value of four checks:

a)    Yielding

b)    Lateral-torsional buckling

c)    Flange local buckling

d)    Web local buckling

I sections with slender webs (plate girders), are checked according to Appendix G.

The value of the nominal flexural strength taking 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, as well as box or square sections.
• The case of lateral-torsional buckling only applies for sections with double symmetry, channel and T sections. For other sections, the code uses Appendix F1. Therefore the rest of the sections will be checked for torsion plus combined loads and will not be checked under flexure.
• For non-compact sections, the code uses Appendix F1, which contemplates the following cases (Table A-F1.1 of LRFD) summarized herein:

 

 

 

 

 

 

 

Where:

            

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

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

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-E.6‑4 Chapter F Checking of Members Subjected to Flexure

 

10-E.6.4.2       Shear Check

Shear check applies to shapes I and C loaded in the plane of the web and non slender web (for slender webs look at 10-E.6.4.3). The calculation procedure is as follows:

                       

           

           

Where  is the web area.

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-E.6‑5 Chapter F Checking of memebers Subjected to Shear

 

10-E.6.4.3       Plate Girders

This type of section is addressed by LRFD in Appendix G. From this Appendix, only I shapes loaded in the plane of the web are checked. The web will be considered slender if the height-thickness ratio satisfies the following expressions:

 and also

The nominal flexural strength M_n is the minimum of the following checks:

• Tension-flange yield
• Compression flange buckling

The first check uses the following formula:

  (A-G2-1)

where:

	Section modulus referring to tension flange.
	1.0
	Yield strength of tension flange.

 

The second check uses the following formula:

 (A-G2-2)

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 . Nevertheless, the user may calculate this value according to section F1.2 and introduce it as a member property.

 

• Flange local buckling

   (IS units)

where:

      and          

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

It also checks for shear, by calculating  as the value from the following formula:

where the value of the shear coefficient  (A-G3-5 and 6), is calculated in the following way:

• For     

• For     

where the K_v value is taken as 5.0 if a/h exceeds 3.0 or [260 / (h/tw)]²

Also, CivilFEM provides the interaction criterion between flexure and shear. This criterion is calculated using the following formula:

The global criterion is the maximum of the three criteria.

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-E.6‑6 Appendix G Plate Girders

 

10-E.6.5           Checking of Members Under Combined Forces and Torsion (Chapter H)

 

10-E.6.5.1       Checking of Members Subjected to Flexure and Axial Tension / Compression

For this check, it is necessary to know first the value of Mn. This value comes into play in the checking formulas. The value of Mn, will be calculated in the same way as members subjected to flexure, that is, 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 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).
	Nominal tensile strength (N).
	Required flexural strength (N·mm).
	Nominal flexural strength (N·mm).
y	Strong axis of bending.
z	Weak axis of bending.
f	Resistance factor for tension.
	Resistance factor for flexure = 0.90

If the axial force is compression:

Pu	Required compressive strength (N).
Pn	Nominal compressive strength (N).
Mu	Required flexural strength (N·mm).
Mn	Nominal flexural strength (N·mm).
y	Strong axis of bending.
z	Weak axis of bending.
f	Resistance factor for compression= 0.85
fb	Resistance factor for flexure = 0.90

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 code requirements, it will not be possible to check the member under flexure plus tension / compression.

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

 

Table 10-E.6‑7 Chapter H Checking of Members Subjected to Flexure plus Tension / Compression

 

10-E.6.5.2       Checking of Members Subjected to Torsion, Flexure, Shear and/or Axial Force

This code check is based upon a check of stress (normal and tangential) and buckling, following the next procedure:

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

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

·         For the limit state of buckling:

o

Where Fcr is calculated as for:

_-           Elements subjected to compression with flexural buckling, for the case of .

-          Elements subjected to compression with lateral-torsional buckling, for the case of .

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-E.6‑8 Chapter H Checking of Members Subjected to Torsion, Flexure, Shear and/or Axial Force