Simplified Stress Design of Helicoidal HSS Beams

To facilitate the initial stress design of three-dimensional (3D) curved hollow structural steel (HSS) steel (i.e., helicoidal) beams and rapid early-stage topology decisions, a series of design charts and closed-form equations are presented that incorporate the effects of coupled forces and helicoidal geometry on stresses. These design aids were motivated by structures with extreme curves, featuring nonprismatic structural systems and nonplanar facades, which increasingly require the design of helicoidal elements. To establish these design aids, a converged beam model was developed for parametric studies of 71 different cross sections and a range of plan angles, lead angles, and beam radii. The results were curve-fitted, providing simplified stress utilization design equations expressed in terms of beam cross section ($S_x$ and $S_y$). Results for the design equations and simplified design charts were within 1.5% and 5% of detailed finite-element analysis (FEA), respectively. The design aids were compared to two-dimensional (2D) projection methods and 3D helicoidal slab equations showing that the projection methods were able to be nonconservative by up to 34%, whereas the design aids were overconservative by up to 5% compared with the detailed FEA.