AISC LRFD 1.pdf

Comm. C1.] SECOND ORDER EFFECTS 185The two kinds of first order moment M nt and M lt may both occur in sidesway framesfrom gravity loads. M nt is defined as a moment developed in a member with framesidesway prevented. If a significant restraining force is necessary to preventsidesway of an unsymmetrical structure (or an unsymmetrically loaded symmetricalstructure), the moments induced by releasing the restraining force will be M ltmoments, to be multiplied by B 2 . In most reasonably symmetric frames, this effectwill be small. If such a moment B 2 M lt is added algebraically to the B 1 M nt momentdeveloped with sidesway prevented, a fairly accurate value of M u will result. Endmoments produced in sidesway frames by lateral loads from wind or earthquakewill always be M lt moments to be multiplied by B 2 .When first order end moments in members subjected to axial compression are magnifiedby B 1 and B 2 factors, equilibrium requires that they be balanced by momentsin connected members (Figure C-C1.1). This can generally be accomplished satisfactorilyby distributing the difference between the magnified moment and the firstorder moment to any other moment-resisting members attached to the compressedmember (or members) in proportion to the relative stiffness of the uncompressedmembers. Minor imbalances may be neglected in the judgment of the engineer.However, complex conditions, such as occur when there is significant magnificationin several members meeting at a joint, may require a second order elastic analysis.Connections shall also be designed to resist the magnified end moments.The center-to-center member length is usually used in the structural analysis. Inbraced and unbraced frames, P n is governed by the maximum slenderness ratioregardless of the plane of bending. However, P e1 and P e2 are always calculated usingthe slenderness ratio in the plane of bending. Thus, when flexure is about the strongFig. C-C1.1. Moment amplification.LRFD Specification for Structural Steel Buildings, December 27, 1999AMERICAN INSTITUTE OF STEEL CONSTRUCTION