AISC LRFD 1.pdf

194 FRAME STABILITY [Comm. C2.where Q is the axial load in the girder and Q cr is the in plane buckling load of thegirder based on K = 1.0. Tensile axial load in the girders can be ignored when determiningG.Sidesway instability of an unbraced frame is a story phenomenon involving thesum of the sway resistances of each column in the story and the sum of the factoredgravity loads in the columns in that story. If each column in a story of anunbraced frame is designed to support its own P and P moment, then all the columnswill buckle simultaneously (assumption 8). Under this condition, there is nointeraction among the columns in the story; column sway instability and frameinstability occur at the same time. Framing systems can be used that redistributethe story P to the columns in that story in proportion to their individualstiffnesses. In an unbraced frame that contains columns that contribute little ornothing to the sway stiffness of the story, such columns can be designed using K =1.0 (leaning columns), but the other columns in the story must be designed to supportthe destabilizing P moments developed from the loads on such columns.Similarly, more highly loaded columns in a story will redistribute some of theirP moments to more lightly loaded columns.Two methods for evaluating story frame stability are recognized, the story stiffnessmethod (LeMessurier, 1976 and 1977) and the story buckling method (Yura, 1971)as reflected in Equations C1-4 and C1-5, respectively. For an individual column inthe sway-resisting system,2P2 ( KL)ylc=2 AFg y=p EI PTo account for the redistribution of the P moments within a story, determine P n foran individual column in the sway-resisting system by substituting c for c , wheree2KL ¢lc¢=prFyEand K is given below.For the story stiffness methodKPDeoh¢ = åPu0.822Pçèuå HL÷øæö(C-C2-5)whereEIPe = π2 .2LThe 0.822 factor is the ratio of the lateral column shear force per radian of drift tothe buckling load of a sway permitted column with large end restraint, G = 0. Thisfactor will approach 1.0 for more flexible systems or systems with a large percent-LRFD Specification for Structural Steel Buildings, December 27, 1999AMERICAN INSTITUTE OF STEEL CONSTRUCTION