A Beginner's Guide to the Steel Construction Manual, 14th ed.

Chapter 8 - Bending Members

2006, 2007, 2008, 2011 T. Bartlett Quimby

Introduction


Flexure


Shear


Deflection


Misc. Limit States


Beam Design

Chapter Summary

Example Problems

Homework Problems

References


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Section 8.3.2

Shear Strength Limit State

Last Revised: 11/04/2014

The computation for the shear strength of steel sections is found in SCM Chapter G.  Section G2 investigates the pre-buckling strength of stiffened and unstiffened webs.  Section G3 considers post buckling strength (or the strength related to tension field action).  This text focuses of section G2.

The Limit State

The basic limit state follows the standard form.  The statement of the limit states and the associated reduction factor and factor of safety are given here:

LRFD ASD
Vu < fvVn Va < Vn/Wv
Req'd Vn = Vu / fv < Vn Req'd Vn = Va Wv < Vn
Vu / (fvVn< 1.00 Va / (Vn/Wv) < 1.00
fv = 0.90 Wv = 1.67

The values of Vu and Va are the LRFD and ASD factored shears, respectively, applied to the member. 

In this case Vn is the nominal shear strength of the member is computed using SCM equation J3-1:

Vn = 0.6FyAwCv

Where:

  • 0.6Fy is the shear yield strength of the steel,
  • Aw is the shear area of a web, and
  • Cv is a modifier that accounts for buckling behavior of the web.

Computing Aw

The computation of Aw is dependent on the type of member and the direction of the shear on the cross section.

  • For I shaped members including channels, Aw equals the overall depth times the web thickness, d tw.
  • The computation of Aw for single angle legs is found in SCM G4.  In this case Aw equals bt where b is the width, and t is the thickness, of the leg resisting the shear force.
  • The computation of Aw for HSS and box members is found in SCM G5.  For these members, Aw equals 2ht, where h is the distance between the toe of the fillets, and t is the thickness, of the plate elements resisting the shear.

Computing Cv

Since Cv accounts for buckling behavior of the web, it must account for the standard three ranges of the buckling curve.  The general slenderness parameters, lp and lr, can be extracted from equations found in SCM G2.1(b): 

 and 

The general member slenderness, l, is h/tw.

When l < lp then the member is compact, is not subject to shear buckling, and Cv = 1 (SCM Eq G2-3).

When lp < l < lr then the member is non-compact, is subject to inelastic buckling, and Cv is determined using the linear transition equation SCM Eq G2-4.  This equation is a linear interpolation between the limits of the inelastic region.

When lr < l then the member is slender, is subject to elastic buckling, and Cv is determined using the Euler style equation SCM Eq G2-5.

A part of the computation is the term kv.  The specification for the computation of kv is found in SCM G2.1(b)(i & ii).  For angles and rectangular HSS & box members this factor is further specified in SCM G4 and G5.  This factor accounts for the presence of stiffeners.  It is a function of the clear distance between stiffeners, a, and h.  Note that increasing kv increases the slenderness limits lp and lr, thus increasing the shear strength of non-compact and slender webs by shifting the buckling curve to the right.

Sample Spreadsheet Calculation

The following spreadsheet example computes the shear capacity, Vn, for a typical W section. The input values are in the grey shaded cells and the result in the yellow highlighted cell.

 

Beam Shear          
SCM G2            
           
Section W12x65          
Steel: A992          
Fy 50 ksi        
a 0 in (enter "0" if no stiffeners)    
             
Tabulated Section Properties   Computed Section Quantities
h/tw 24.9     kv 5.000  
tw 0.39 in    h 9.71 in
d 12.1 in   Aw 4.72 in2
           
Computations        
  l 24.90        
  lp 59.2        
  lr 73.8        
  Cv 1.00        
  Vn 142 k <---- Answer  

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