Inelastic Lateral Stability Under a Moment Gradient

The lateral stability of mild steel I beams simply supported on a single span and loaded beyond yield with a concentrated load at mid span is examined. The analysis uses the theorem of stationary potential energy and the tangent modulus. It compares certain approximations regarding the buckled shape, the variation of lateral, warping and torsional rigidities with moment beyond yield and the stress-strain properties of the steel and shows that assumed linear relations agree well with a set of experimental results from tests on small scale steel models. An approximate method for calculating the critical moment-length relations for standard I and WF beams under similar loading conditions is suggested.