10-0.1         Scope

Steel structures checking according to the Steel Construction Manual of AISC 14^th Edition in CivilFEM includes the checking of structures composed of welded or rolled shapes under axial forces, shear forces and bending moments in 3D.

The calculations made by CivilFEM conform to the following sections of Part 16 Specifications and Codes:

 

D	Design of members for tension.
E	Design of members for compression.
F	Design of members for flexure.
G	Design of members for shear.
H	Design of members for combined forces and torsion.

 

10-0.2         Checking Types

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

·         Checking of sections subjected to:

Tension	D
Flexure	F
Shear Force	G
Flexure and axial force	H1
Bending plus axial force, shear & torsion	H3.3

 

 

·         Buckling check:

Compression members subjected to flexure	E3,E7
Compression members subjected to flexure and torsion	E4,E7

 

10-0.3         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”.

 

10-0.4         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 AISC 14TH EDITION code depend on the type of checking:

 

 

10-0.5         Data and Results used by CivilFEM

CivilFEM utilizes the following groups of data and results for checking according to AISC 14TH EDITION:

·         Data concerning 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.

Sections Data

AISC 14TH EDITION considers the following data set for the section:

·         Gross section data

·         Net section data

·         Effective section data

·         Data concerning to 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 AISC 14TH EDITION 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).

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 14TH EDITION module utilizes the gross section data in user units and the CivilFEM axis or section axis as initial data. The program calculates the effective section data and the class data, and stores them in CivilFEM’s results file, in user units and in CivilFEM or section axis. The data can be listed and plotted with the ~PLLSSTL and ~PRSTL commands.

the section data used in AISC 14TH EDITION are shown in the following tables:

 

 

Table 5‑1 Common data for gross, net and effective sections

 

Table 5‑2 Gross section data

 

Table 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; thus, the effective section is calculated for each element and each of the ends of the element.

 

Table 5‑4 Net section data

 

Table 5‑5 Data referred to the section plates

 

Member Properties

For AISC 14TH EDITION the checked data set used at member level is shown in the following table. All data is stored with the section data in user units and in the CivilFEM reference axis. (Parameters L, KY, KZ, KTOR, CB, LB, CHCKAXIS, of ~MEMBPRO command).

 

Table 5‑6 Member Properties

 

Material Properties

For AISC 14TH EDITION checking, the following material properties are used:

 

Table 5‑7 Material properties

*th =thickness of plate

 

10-0.6         Checking 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: (command ~CFMP)

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

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

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

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

e)    Results. In CivilFEM, checking results for each element end are 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.

    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:

Ra	Required strength (ASD)
Rn	Nominal strength.
Ω	Safety factor
Rn/ Ω	Allowable strength

 

General Processing of Sections. 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 14TH 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 14TH 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.

·    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:

           

 

 

Being:

	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).

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,

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

Output results are written in the CivilFEM results file (.RCV) as an alternative.

 

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,:

       (E4-1)

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

   (E4-6)

Where:

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

 

where:

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

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

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

Output results are written in the CivilFEM results file (.RCV) as an alternative.

 

 

Checking of Members for Flexure     (Chapter F)

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

Flexure Check

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:

Where M_n 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 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 . Nevertheless, the user may calculate this value and introduce it as a member property

 

• Flange local buckling

   (IS units)

where:

 

              and          

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

Output results are written in the CivilFEM results file (.RCV) as an alternative.

 

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

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.

Output results are written in the CivilFEM results file (.RCV) as an alternative.

 

Checking of Members for Combined Forces and Torsion (Chapter H)

Checking of Members Subject to Flexure and Axial Tension / Compression

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

1.    Yielding

2.    Lateral-torsional buckling

3.    Flange local buckling

4.    Web local buckling

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

(a)  For

    (H1-1a)

(b)  For

        (H1-1b)

If the axial force is tension:

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

 

If the axial force is compression:

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

 

The following checks are carried out by CivilFEM:

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

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

Output results are written in the CivilFEM results file (.RCV) as an alternative.

Checking of Members Subjected to Torsion, Flexure, Shear and/or Axial Force

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

  = 0.90 (LRFD)    = 1.67 (ASD)

 

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

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

·         For the limit state of buckling:

-          Where  is calculated

Output results are written in the CivilFEM results file (.RCV) as an alternative.