A Beginner's Guide to the Steel Construction Manual, 16^th ed.

Chapter 8 - Bending Members

© 2006, 2007, 2008, 2011, 2017, 2023 T. Bartlett Quimby

Section 8.3.2

Shear Strength Limit State

Last Revised: 06/22/2023

The computation for the shear strength of steel sections is found in SCM Chapter G. Section G2.1 investigates the pre-buckling strength of stiffened and unstiffened webs. Section G2.2 considers post buckling strength (or the strength related to tension field action). This text focuses of section G2.1 since G2.1 applies to the vast majority of situations found in practice.

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 G2-1:

V_n = 0.6F_yA_wC_v1

Where:

• 0.6F_y is the shear yield strength of the steel,
• A_w is the shear area of a web, and
• C_v1 is a modifier that accounts for the three ranges of 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 G3. 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 G4. 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 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, l_p and l_r, can be extracted from the various equations.

All rolled shapes, except those eight W shapes indicated in a user note in G2.1(a), satisfy the implied compactness criteria for F_y = 50 ksi. This means that in the overwhelming majority of typical shear calculations with rolled shapes, the buckling modifier C_v1 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 and the stiffeners on either side of the panel. Tension field action is considered principally in built-up girders with slender webs.

Prior to the 15th edition of the SCM, 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. While the handout includes reference to the tension field action sections, SCM G2.2 and SCM 2.3, those sections are not discussed in this introductory text.

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

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

When l_r < 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 k_v. The specification for the computation of k_v 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 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.

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

When considering tension field action in SCM G2.2 and G2.3, the shear modifiers become functions of C_v2 and a/h. These complex equations are rarely used as in most cases tension field action can be avoided. As this is a basic introductory text, tension field action is not discussed here.

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 F_y is less than 70 ksi and, therefore, the Buckling Modifier, C_v2, 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 = b_f/2t_f for I-shaped members or l = b_f/t_f for channels

l_p = 1.10*sqrt(1.2E/F_y)

C_v2 = l_p / l

Shear Area = b_ft_f

V_n = 0.6F_y(Shear Area)C_v2

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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