10-M.1    Scope

Steel structures checking according to the AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS 2010  and 2012 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:

 

6.8.2	Design of members for tension.
6.9.4	Design of members for compression.
6.12.2.2, A.6	Design of members for flexure.
6.10.9	Design of members for shear.
6.9.2.2,6.8.2.3	Design of members for combined forces

 

10-M.2    Checking Types

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

·         Checking of sections subjected to:

Tension	6.8.2
Flexure	6.12.2.2, A6
Shear Force	6.10.9
Flexure and axial force	6.9.2.2, 6.8.2.3
Bending plus axial force	6.9.2.2, 6.8.2.3

 

 

·         Buckling check:

Compression members subjected to flexure	6.9.4.1.2
Compression members subjected to flexure and torsion	6.9.4.1.3

 

10-M.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

 

10-M.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.

 

The cross-sections considered in the AASTHO LRFD BRIDGE DESIGN SPECIFICATIONS (2010 and 2012) code depend on the type of checking:

 

 

10-M.5    Data and Results used by CivilFEM

CivilFEM utilizes the following groups of data and results for checking according to AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS 2010 and 2012:

·         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.

10-M.5.1          Sections Data

AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS 2010 and 2012 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 AASHTO 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 article 6.9.4.2 of the code. This article classifies steel sections into three groups (compact, noncompact and slender) for flexure classification and into two groups (slender and non-slender) for compression classification, depending upon the width-thickness ratio and other mandatory limits.

The AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS 2010 and 2012  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 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 AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS 2010 and 2012 are shown in the following tables:

 

 

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

 

Table 10-M.5‑2 Gross section data

 

Table 10-M.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 10-M.5‑4 Net section data

 

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

 

10-M.5.2          Member Properties

For la AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS 2010 and 2012 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, RP, U, LV, of ~MEMBPRO command).

 

Table 10-M.5‑6 Member Properties

 

10-M.5.3          Material Properties

For AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS 2010 and 2012 checking, the following material properties are used:

 

Table 10-M.5‑7 Material properties

*th =thickness of plate

 

10-M.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.

 

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

Steel sections are classified for flexure as compact, noncompact or slender-element 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 l_p. If the width-thickness ratio of one or more compression elements exceeds l_p but does not exceed l_r, the section is noncompact. If the width-thickness ratio of any element exceeds l_r, the section is referred to as a slender-element compression section.  Compression classification is similar but with only one ratio to distinguish slender and non-slender sections

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 |Dy|<|Dz| (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.

 

10-M.6.1.1      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

10-M.6.1.2      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:

Flanges:

      

 

                      For hot rolled shapes

For welded sections     ,    

 

 = minimum of 0.7 , /_  y    but no less than  0.5. 

 

Web:

 

·         Section C

Flanges:

 

     

For hot rolled shapes

For welded sections   ,    

 = minimum of  y    but no less than  . 

Web:

 

·         Pipe section:

 

·         Box section:

Flanges of box section:

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

·         T section:

Flange:         

Web: No limits are included for flexure classification, so class section is only checked for flange limit.

10-M.6.2          Checking of Members for Tension    

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

The factored tensile resistance, _ , shall be taken as the lesser 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.

Values of R_p and U must be introduced by the user according article 6.8.2.1 with ~MEMBPRO command

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).

10-M.6.3          Checking of Members in Axial Compression

Axial compression check by la AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS 2010 and 2012 of the design compressive strength, _ , are determined as follows:

 

 

10-M.6.3.1      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,  :

 

(a) for

     

(b) for

 

Being:

 

Where:

	Gross area of member.
Q	Slender element reduction factor.
	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 ( exceed ratio given in 10-G.6.1.1 ) , the value of  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 calculated before is taken.

2)    With this value f = Q_sF_y   is calculated.

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

4)    With b_e the effective area is calculated.

5)    With the value of the effective area, Qa is calculated.

·                    For a box section

If

·                    For other sections

If

 

If it is not within those limits,

With the b_e values for each plate, the part that does not contribute [t·(b‑b_e)] 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.

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

 

 

10-M.6.3.2      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 normal axis:

 (6.9.4.1.3-7)

Where:

	Effective length factor for torsional buckling.
G	Shear modulus (MPa).
	Warping constant (mm6).
J	Torsional constant (mm4).
Â	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.

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

 

 

10-M.6.4          Checking of Members for Flexure     

Summary of the checks done by CivilFEM:

 

SECTION TYPE	YIELDING	LTB	FLB	WLB	Conditions
BOX	X (6.12.2.2.2)		X (6.12.2.2.2)	X (6.12.2.2.2)	Non-slender web
PIPE	X (6.12.2.2.3)		X(local buckling) (6.12.2.2.3)		Compact, non-compact and slender under the limit for flexure check.
T SECTION	X (6.12.2.2.4)	X (6.12.2.2.4)	X (6.12.2.2.4)	X (6.12.2.2.4)	Non-slender flange
I SECTION (FLEXUREABOUT STRONG AXIS)	X	X (A.6.3.3)	X (A.6.3.2)		Non-slender web and  Fy<70 ksi
DOUBLE T (FLEXURE ABOUT WEAK AXIS)	X		X (6.12.2.2.1)		Non-slender flanges
SECTION C (FLEXURE ABOUT STRONG AXIS)	X (6.12.2.2.5)	X (6.12.2.2.5)			Compact members
SECTION C (FLEXURE ABOUT WEAK AXIS)	X		X (6.12.2.2.5)		Non-slender flanges

 

The design flexural strength, f_f M_n, shall be determined as follows:

f_f  = 1.00

 

Where M_n is the lowest value of four checks:

a)    Yielding (Y)

b)    Lateral-torsional buckling (LTB)

c)    Flange local buckling (FLB)

d)    Web local buckling (WLB)

The checks done depends on the section:

·         Box   (non-slender webs)

·         Yielding

_ =

 

·         FLB

If _ 

                _  

                        If_  

                                                 _ 

·         WLB

If _ 

             _ 

 

·         Circular tubes   (compact, non-compact and slender under the ratio limit

 

)

 

1.    Yielding

 

2.    Local buckling

                      
If

 

 

If

 

                                                 

 

                                                  

 

·         T shape

1.    Yielding                                          

If stem is in tension, the limit on  is 1.6

If stem is in compression _ is limited to

 

2.    LTB

                             

 

                                             

(The plus sign for B shall apply when the stem is in tension and the minus sign shall apply when the stem is in compression)

3.    FLB

                        If 

                    

                         : Elastic section modulus with respect to the compression flange

                          is not provided because the limiting slenderness value  is larger than 12 (Eq. 6.10.2.2-1)

 

4.    Local buckling of the stem

                                         

·         I shape loaded on the strong axis   (non-slender web)

1.    Yielding

=

 

2.    LTB

 

 

Where:

 

_ 

  

 

 

                

 

 

=

 

 

3.    FLB

If

If

                          

                       

 is the web plastification factor for the compression flange determined as specified in Article A6.2.1 or Article A6.2.2:

 

If is compact web    

 

                                                   

                                                          

If is non-compact web,

                                                          

 is the hybrid factor and for sections that are checked in CivilFEM takes a value of 1.  

 

·          T shape loaded on weak axis (flanges compact or non-compact)

 

1.    Yielding:

_ =

2.    FLB

If

=

 

                        If 

                                                          
=

                                                         _ 

 

·         C shape loaded on the strong axis  ( web and flanges compact)

1.    Yielding

_ =

2.    LTB

                                                          

 

 

               

If <<

                   

                        If >

=

                              

                                                 

                                                 

                        Where:

                        = radius of gyration about the weak axis(in)

                        J = Torsional constant St. Venant (in⁴)

                        = Elastic section modulus about strong axis(in³)

                       

= distance between centroids of the flanges(in)

=warping constant(in⁶)

=Moment gradient modifier. Must be introduced by the user with ~MEMBPRO command.

 

·         C shape loaded on the weak axis  (flanges compact or non-compact)

1.    Yielding

 = min (, 1.6)

 

2.    FLB

If

                                                    _ =

                        If 

 

 

 

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

 

 

10-M.6.5          Checking of Members for Shear

The design shear strength, , shall be determined as follows:

For all provisions:

To calculate the nominal shear strength CivilFEM follows the provisions of the article 6.10.9.2 except for box-shaped (6.12.1.2.3b) and circular tubes (6.12.1.2.3c)

=

=, where D is total depth of the web.

C is the ratio of the shear-buckling resistance to the shear yield strength determined as:

a.    For                                    = 1.0          (AASHTO 6.10.9.3.2-4)

,

 

b.    For              (AASHTO 6.10.9.3.2-5)

 

c.    For                              (AASHTO 6.10.9.3.2-6)

 

The web plate buckling coefficient, Kv, will be calculated as a constant equal to 5.0.

For shape-box sections D is the clear distance between flanges less inside corner radius on each side. Both webs area shall be considered effective in resisting the shear.

For circular tubes the nominal shear strength will be taken as:

 , shear buckling resistance (ksi)taken as the larger of either:

                                                          

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

 

10-M.6.6          Checking of Members for Combined Forces

10-M.6.6.1      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 (M_n) 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  

    (6.8.2.3-2, 6.9.2.2-2)

 

(b)  For  

    (6.8.2.3-1, 6.9.2.2-1)

Where:

	Axial force resulting from factored loads.
	Factored resistance.
	Moment resulting from factored loads.
	Factored flexural resistance .
y	Strong axis bending.
z	Weak axis bending.

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.