AISC LRFD 1.pdf

186 SECOND ORDER EFFECTS [Comm. C1.axis only, two different values of slenderness ratio may be involved in solving agiven problem.When second order analysis is used, it must account for the interaction of the factoredload effects, that is, combinations of factored loads must be used in analysis.Superposition of forces obtained from separate analyses is not adequate.When bending occurs about both the x and the y axes, the required flexural strengthcalculated about each axis is adjusted by the value of C m and P e1 or P e2 correspondingto the distribution of moment and the slenderness ratio in its plane of bending, and isthen taken as a fraction of the design bending strength, b M n , about that axis, with dueregard to the unbraced length of the compression flange where this is a factor.Equations C1-2 and C1-3 approximate the maximum second order moments incompression members with no relative joint translation and no transverse loadsbetween the ends of the member. This approximation is compared to an exact solution(Ketter, 1961) in Figure C-C1.2. For single curvature, Equation C1-3 is slightlyunconservative, for a zero end moment it is almost exact, and for double curvature itis conservative. The 1978 AISC ASD Specification imposed the limit C m 0.4which corresponds to a M 1 /M 2 ratio of 0.5. However, Figure C-C1.2 shows that if,for example, M 1 /M 2 = 0.8, the C m = 0.28 is already very conservative, so the limithas been removed. The limit was originally adopted from Austin (1961), which wasintended to apply to lateral-torsional buckling, not second-order in-plane bendingstrength. The AISC Specifications, both in the 1989 ASD and LRFD, use a modificationfactor C b as given in Equation F1-3 for lateral-torsional buckling. C b isapproximately the inverse of C m as presented in Austin (1961) with a 0.4 limit. InFig, C-C1.2. Second-order moments for beam-columns in braced frames.LRFD Specification for Structural Steel Buildings, December 27, 1999AMERICAN INSTITUTE OF STEEL CONSTRUCTION