Shape optimization of tapered I-beams with lateral-torsional buckling, deflection and stress constraints

Built-up tapered I-beams, which are mostly loaded so as to be under bending about their strong axis for the economical use of the structural material, are commonly used in wide span steel structures. Lateral-torsional buckling, excessive deflection and partial or complete yielding of the material are the important failure modes, which should be considered in design of these members. However, today's “modern design” concept not only requires the satisfaction of certain constraints but also a lightweight structure. This study presents the shape optimization of flange and/or web tapered doubly-symmetric I-beams and discusses the contribution of flange and/or web tapering and inflection point location to the economical design. The optimization procedure is constructed by slightly modifying the Big Bang - Big Crunch algorithm, which is a simple and effective population-based metaheuristic, and installing the Deb's constraint handling method. Four beam configurations with various loading and restraint conditions are optimized and final designs are validated by finite element analysis software. It is shown that tapering, and therefore the inflection point location may not have a significant effect on the material economy in certain conditions.