Elastic, lateral-torsional stability of beams: Moment modification factor

Abstract

Abstract An accurate estimate of the elastic buckling load is of fundamental importance in the design of beams. Whilst an exact closed-form solution is available for the uniform buckling moment of a simply supported beam, moment modification is a popular approach for estimating buckling strength of beams with unequal end moments. Presently available expressions for the moment modification factor were derived for an ideal case of a simply supported beam with zero warping rigidity, thus leading to unduly conservative estimates of buckling strength for end conditions other than simple supports. This paper presents a more accurate closed-form parametric expression for moment modification factor which incorporates the effects of beam slenderness, moment gradient and lateral end restraint in an explicit manner, and is more accurate than presently available expressions. In a departure from traditional methods, the problem is treated as the superposition of two hypothetical cases of beam buckling corresponding to zero warping and zero torsional rigidity. The effects of beam slenderness, moment gradient and lateral end restraints are considered independently on each mode and then superimposed to obtain the final expression for the moment modification factor. Classical and numerical solutions for some of the parameters related to the proposed expression are enumerated. The approximations involved in previous solutions are also highlighted and possible sources of discrepancies are traced. The present solution attempts to overcome the shortcomings of the existing solutions by providing a better interpretation of lateral-torsional failure.