Lateral Postbuckling Analysis of Beam Columns

Abstract

This paper contributes further to the knowledge of the postbuckling behavior of flexural members after flexural-torsional buckling by extending previous research on the postbuckling behavior of beams to beam columns. Early studies were carried out by Masur and Milbradt (1957) and subsequently by Woolcock and Trahair (1974, 1975, 1976). These studies included narrow rectangular and I-section members. The beams were statically determinate beams and cantilevers as well as redundant restrained beams and continuous beams. Theoretical predictions were verified by test results, and recently (Pi and Trahair 1994) by finite-element analysis. The findings of these early studies on beam postbuckling were the following: (1) flexural-torsional buckling of beams is of a stable symmetric nature; (2) the postbuckling path in statically determinate beams and cantilevers is very shallow; (3) the postbuckling of statically indeterminate beams may lead to significant .increases in strength after buckling, due to redistributions of the in-plane bending moments; and (4) the postbuckling increases in strength may be significant in redundant beams of narrow rectangular section, but appreciable increases are not realized in I-section members unless they are extremely slender. The studies of Woolcock and Trahair (1974, 1975, 1976) incorporated the effects of the prebuckling deflections on flexural-torsional buckling, which become more important for beams with high ratios of minor-to-major-axis flexural rigidity. Early research on this subject was reviewed by Trahair and Woolcock (1973) and later by Trahair (1993), with more recent research by Pi and Trahair (1992a, b). The authors have investigated the effects of postbuckling on the first yield of beam columns, possibly having in mind that this might have an application to design codes. However, their studies omit the effects of residual stresses, initial curvature and twist, and load eccentricity and inclination, each of which is likely to have greater influence on the strengths of real beams than the postbuckling behavior. The strengths of real beams have been reviewed by Trahair and Bradford (1991). The effects of large twist rotations have been considered by the authors by using better approximations than <p for sin <p. Pi and Trahair (1993), in a recent study of the large twist rotations undergone by I-section beams loaded in torsion by Farwell and Galambos (1969), have shown that the additional (Wagner) normal stresses developed at large twist rotations cause significant stiffening, thus explaining the experimental finding of Farwell and Galambos that I-sections in torsion fail after tensile rupture at the flange tips.