A Technical Note: Derivation of the LRFD Column Design Equations

Since the publication of the first Load and Resistance Factor Design (LRFD) Specification by the American Institute of Steel Construction, Inc. (AISC, 1986) the column design equations have been presented by the Euler buckling equation in the elastic range and an exponential equation in the inelastic range. Background information, including accumulated test data, for these equations was presented at a Structural Stability Research Council (SSRC) meeting held in Cleveland, Ohio in 1985 (Tide, 1985). However, the actual derivation of the design equations relative to the accumulated test data has not been documented. The purpose of this paper is to document the derivation of the LRFD column design equations. LRFD column equations were derived to represent a lower bound to the available test data and to satisfy the philosophical requirements of nearly all of the AISC Specification committee members at the time. Slight numerical differences occur at the common point for the two equations for both the non-dimensional stress and slope.