## Rwu

Region of failure

FIGURE 6.27 Loading conditions for web crippling tests: (a) EOF loading, (b) IOF loading, (c) ETF loading, and (d) ITF loading (courtesy of Yu, W.W. 1991).

The nominal web crippling strength of webs without holes for a given loading condition can be determined from the following AISI equation [7] on the basis of the thickness of web element, design yield point, the bend radius to thickness ratio, the depth to thickness ratio, the bearing length to thickness ratio, and the angle between the plane of the web and the plane of the bearing surface:

where Pn is the nominal web crippling strength, C is the coefficient, Ch is the web slenderness coefficient, CN is the bearing length coefficient, CR is the inside bend radius coefficient, Fy is the design yield point, h is the flat portion of web measured in the plane of the web, N is the bearing length (4 in. [19 mm] minimum), R is the inside bend radius, t is the web thickness, and 6 is the angle between the plane of the web and the plane of the bearing surface, 45° < 6 < 90°. Values of C, CR, CN, Ch, factor of safety, and resistance factor are listed in separate tables of the AISI Specification [7] for built-up sections, single web channel and C-sections, single web Z-sections, single hat sections, and multiweb deck sections.

For C-section webs with holes, the web crippling strength determined in accordance with the above equation should be reduced by using a reduction factor as given in the Specification [7].

### 6.6.4.5 Combined Bending and Web Crippling

For combined bending and web crippling, the design of beam webs should be based on the interaction equations provided in the AISI Specification [7]. These equations are presented in Table 6.4.

### 6.6.4.6 Bracing Requirements

In cold-formed steel design, braces should be designed to restrain lateral bending or twisting of a loaded beam and to avoid local crippling at the points of attachment. When C-sections and Z-sections are used as beams and loaded in the plane of the web, the AISI Specification [7] provides design requirements to restrain twisting of the beam under the following two conditions: (1) the top flange is connected to deck or sheathing material in such a manner as to effectively restrain lateral deflection of the connected flange and (2) neither flange is connected to sheathing. In general, braces should be designed to satisfy the strength and stiffness requirements. For beams using symmetrical cross-sections such as I-beams, the AISI Specification does not provide specific requirements for braces. However, the braces may be designed for a capacity of 2% of the force resisted by the compression portion of the beam. This is a frequently used rule of thumb but is a conservative approach, as proven by a rigorous analysis.

### 6.6.5 Concentrically Loaded Compression Members

Axially loaded cold-formed steel compression members should be designed for the following limit states: (1) yielding, (2) overall column buckling (flexural buckling, torsional buckling, or torsional-flexural buckling), and (3) local buckling of individual elements. The governing failure mode depends on the configuration of the cross-section, thickness of material, unbraced length, and end restraint. For distorsional buckling of compression members, see Section 6.9 on Direct Strength Method.

TABLE 6.4 Interaction Equations for Combined Bending and Web Crippling

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