Stress recovery from one dimensional models for tapered bi-symmetric thin-walled I beams: Deficiencies in modern engineering tools and procedures

Abstract

This paper highlights several issues of the procedures nowadays adopted for the recovery of cross-sections stress distribution within tapered thin-walled I beams. In particular, deficiencies are evident even considering bi-symmetric structural elements behaving under the assumption of plane stress. In fact, analytical results available in the literature since the first half of the past century highlight that the continuous variation of the height of a infinite long wedge induces shear stress distributions substantially different from the ones occurring in prismatic beams. Unfortunately, this peculiarity of non-prismatic beams is neglected or treated with coarse approaches by most of the modern engineering tools and procedures, leading to inaccurate descriptions (and also severe underestimations) of the real stress magnitude. After a comprehensive literature review on this specific topic, the paper compares most common stress-recovery procedures with a new, simple, and effective tool derived from a recently proposed non-prismatic planar beam model. The numerical examples reported in the paper highlight that the approaches available in the literature and widely used in practice estimate the parameters of interest for practitioners with errors bigger than 50% leading therefore to unreliable results. Conversely, the herein proposed tool leads to errors smaller than 5% in all the considered cases, paving the way to a new generation of effective tools that practitioners can use for the design of such structural elements.