Chapter 8 - Bending Members
© 2006, 2007, 2008, 2011 T. Bartlett Quimby
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 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
The computation of Aw is dependent on the type of member and the direction of the shear on the cross section.
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):
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.