Approximate flexural-extensional relations for steel structural members

Abstract

The object of this investigation is to propose approximate moment-curvature-axial load-mean strain relations for steel members loaded beyond the yield point by combined bending and axial load, accounting for initial residual stresses induced in the members during their formative hot-rolling or welding processes. Since no exact relations can be found, except for residual stress-free members, with rectangular cross sectional, numerical procedure has been developed for integrating stresses at certain points obtained by dividing the cross-section into small elements. A Newton-Raphson type iterative procedure has been developed for obtaining curvatures and mean strains, given moments and axial loads. Moment-curvature and axial load -mean strain relations, with axial load and moment, respectively held constant. A least-squares procedure has been developed to approximate the curves by simple mathematical functions A hyperbola was found to be the most valuable approximation.