Stability of a Doubly Symmetric Web-Tapered I-Beam Cantilever

Introduction. The current paper examines the stability of cantilevered symmetrical web-tapered I-beams under end point load and uniformly distributed load. Elastic lateral-torsional buckling solutions are given in closed form and based on an energy approach with alternative trial functions for twist rotation. The aim of the paper is to refine and rectify bifurcation solutions of the cantilevered beams and present them in alternative formulations. Results are given in new terms that include lateral-torsional beam parameter ψ0 and load height parameter η. Theoretical work has been done with respect to the current state and philosophy of steel design code CP 16.13330.2017. Unified simple formulae for the lateral-torsional buckling capacities of cantilevered beams can be addressed for solving not only non-prismatic cases but prismatic cases too. Simplicity achieved by minimizing the number of terms in trial functions and subsidized with different and closed ones to real behavior of the beam under transverse loads.

Materials and methods. Refined lateral-torsional buckling solution and an energy method were used in the work.

Results. Based on given refinements, a closed form of elastic lateral-torsional buckling solution of a linear non-prismatic member was obtained. As a result of the theoretical work evaluated, a lateral-torsional buckling formula was introduced.

Conclusions. The current theoretical work shows that the solution of lateral-torsional buckling problem of web-tapered cantilevered I-beam with thin-walled open cross sections can be rectified by introducing alternative trial function for twist rotation and given in closed form with additional coefficients. The solution stays relevant for prismatic cases.

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