10-P.1        Scope

Steel structures checking according to the Steel Construction Manual of AISC 15^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 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-P.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

 

 

·         Buckling check:

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

 

10-P.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-P.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 15TH EDITION code depend on the type of checking:

 

 

10-P.5        Data and Results used by CivilFEM

CivilFEM utilizes the following groups of data and results for checking according to AISC 15TH 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 15TH 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 of the provisions made on section B4-3 of AISC 15TH EDITION to calculate the parameter AHOLES (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 15TH 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 15TH 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 15TH 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,  of ~MEMBPRO command).

 

Table 5‑6 Member Properties

 

Material Properties

For AISC 15TH EDITION checking, the following material properties are used:

 

Table 5‑7 Material properties

*th =thickness of plate

 

10-P.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.

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:

           

 

 

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_g – AHOLES). 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 using the command ~SECMDF.

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 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:

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.
	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 15TH 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.

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

Estado Límite:

·         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)

 

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)

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

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.