A Beginner's Guide to the Steel Construction Manual, 13^th ed. (old)

Chapter 8 - Bending Members

© 2006, 2007, 2008 T. Bartlett Quimby

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:

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

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

V_n = 0.6F_yA_wC_v

Where:

• 0.6F_y is the shear yield strength of the steel,
• A_w is the shear are of a web, and
• C_v is a modifier that accounts for buckling behavior of the web.

Computing A_w

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

• For I shaped members including channels, A_w equals the overall depth times the web thickness, d t_w.
• The computation of A_w for single angle legs is found in SCM G4.  In this case A_w equals bt where b is the width, and t is the thickness, of the leg resisting the shear force.
• The computation of A_w for HSS and box members is found in SCM G5.  For these members, A_w 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 C_v

Since C_v accounts for buckling behavior of the web, it must account for the standard three ranges of the buckling curve.  The slenderness parameters, l_p and l_r, are found in G2.1(b).  The member slenderness, l, is h/t_w.

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

When l_p < l < l_r then the member is non-compact, is subject to inelastic buckling, and C_v 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 l_r < l then the member is slender, is subject to elastic buckling, and C_v is determined using the Euler style equation SCM Eq G2-5.

A part of the computation is the term k_v.  The specification for the computation of k_v 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 k_v increases the slenderness limits l_p and l_r, 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, V_n, for a typical W section. The input values are in the grey shaded cells and the result in the yellow highlighted cell.

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