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FIGURE 6.9 Stress distribution in stiffened compression elements.

FIGURE 6.9 Stress distribution in stiffened compression elements.

FIGURE 6.10 Effective design width of stiffened compression elements: (a) actual element and (b) effective element, b and stress, f on effective elements.

For cold-formed steel members, a concept of''effective width'' has long been used for practical design. In this approach, instead of considering the nonuniform distribution of stress over the entire width of the plate w, it is assumed that the total load is carried by a fictitious effective width b, subjected to a uniformly distributed stress equal to the edge stress /max, as shown in Figure 6.9. The width b is selected so that the area under the curve of the actual nonuniform stress distribution is equal to the sum of the two parts of the equivalent rectangular shaded area with a total width b and an intensity of stress equal to the edge stress /max. Based on the research findings of von Karman, Sechler, Donnell, and Winter , the following equations have been developed in the AISI Specification for computing the effective design width, b, for stiffened elements under uniform compression .

max w w

6.5.2.1 Strength Determination

where b is the effective design width of uniformly compressed element for strength determination (Figure 6.10), w is the flat width of compression element, and p is the reduction factor determined from Equation 6.8:

p =(1 - 0.22/1)/1 < 1 (6.8) where 1 is the plate slenderness factor determined from Equation 6.9:

where k is equal to 4.0 is the plate buckling coefficient for stiffened elements supported by a web on each longitudinal edge as shown in Figure 6.10, t is the thickness of compression element, E is the modulus of elasticity, and fis the maximum compressive edge stress in the element without considering the factor of safety.

### 6.5.2.2 Serviceability Determination

For serviceability determination, Equations 6.6 through 6.9 can also be used for computing the effective design width of compression elements, except that the compressive stress should be computed on the basis of the effective section at the load for which serviceability is determined. The relationship between p and l according to Equation 6.8 is shown in Figure 6.11.

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