A Beginner's Guide to the Steel Construction Manual, 15th ed.

Chapter 8 - Bending Members

© 2006, 2007, 2008, 2011, 2017 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: 04/19/2021

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 = 0.6FyAw[Buckling Modifier]

Where:

  • 0.6Fy is the shear yield strength of the steel,
  • Aw is the shear area of a web, and
  • [Buckling Modifier}] is a modifier that accounts for buckling behavior of the web. The modifier takes the form Cv1, Cv2, or a function of shear panel size and Cv2, depending on the situation.

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 G3. 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 G4. 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 the Buckling Modifier

Since the Buckling Modifier 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 the various equations.

For all rolled shapes, except those 8 W shapes indicated in a user note in G2.1(a), satisfy the implied compactness criteria for Fy = 50 ksi. This means that in the overwhelming majority of typical shear calculations with rolled shapes, the buckling modifier will be 1.0.

For I-Shaped Members and Channels (SCM G2) there is a choice to consider shear strength with or without tension field action. Tension field action is a post shear buckling shear strength for a section reinforced with web stiffeners. After shear buckling, the shear panel tends to act like a tension diagonal in a truss and the stiffeners act as compression verticals, hence the name "Tension Field Action" refers to the truss strength carried by the tension diagonal in the shear panel. Tension field action is considered principally in built-up girders with slender webs.

In previous additions of the specification, tension field action had its own section in Chapter G. With the 15th edition, it has been included in SCM G2 with some upgrades to the equations.

In an effort to summarize the strong axis shear strength requirements of SCM G2 through SCM G4, a downloadable handout has been created: ShearStrengthSummary.pdf. It would be useful for you to download that now.

The handout follows this text's trend of expressing strength in terms of the three buckling ranges. It will be noticed, however, that elastic buckling in shear is generally discouraged unless tension field behavior is to be considered.

The general member slenderness, l, is the ratio of the width to thickness for the member under consideration.

When l < lp then the member is compact, is not subject to shear buckling, and the Buckling Modifier equals 1.0.

When lp < l < lr then the member is non-compact, is subject to inelastic buckling, and the Buckling Modifier is generally a linear transition.

When lr < l then the member is slender, is subject to elastic buckling, and the Buckling Modifier is determined using an Euler style equation.

A part of the computation is the term kv. The specification for the computation of kv is found in SCM G2.1(b)(2). For angles and rectangular HSS & box members this factor is further specified in SCM G3 and G4. This factor accounts for the presence of stiffeners. It is a function of the clear distance between stiffeners, a, and effective height, 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.

In the provided summary handout, the specified constant kv terms have been incorporated directly into the equations.

Weak-axis Shear Strength

SCM G6 addresses the computation of weak-axis shear strength. A means for computing strength for non-compact and slender sections, however the user note in this section points out that all rolled I-shapes meet the compact criteria when Fy is less than 70 ksi and, therefore, the Buckling Modifier, Cv2, is equal to 1.0. The buckling modifier will only be less than 1.0 for built-up sections with slender flanges.

In the event that there is a slenderness issue, using the nomenclature of the handout, you can compute the shear strength by:

l = bf/2tf for I-shaped members or l = bf/tf for channels

lp = 1.10*sqrt(1.2E/Fy)

Cv2 = lp / l

Shear Area = bftf

Vn = 0.6Fy(Shear Area)Cv2

 

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        
  Cv1 1.00        
  Vn 142 k <---- Answer  

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