Simplified Design Methods for HSS Helicoidal Steel Beams

The coupling of modern architectural designs with digital parametric tools has resulted in non-planar structures and facades with extreme curves. As a result, structural engineers are routinely designing elements that are curved in 2 or 3 dimensions. While these structural elements can often be discretized into a series of straight elements that approximate the curve, or analyzed using detailed finite element models, it is often necessary to design curved structural elements to accurately account for combined stress behavior due to coupled forces. As a result, it is desirable to provide practicing engineers with a series of design charts and closed-form equations to facilitate early-stage topology decisions with accurate and convenient tools. The closed form solution for 2D beams curved in-plan is well known and readily found in most undergraduate mechanics texts. However, the topic of 3D curved beams (i.e., helicoidal beams) has not been addressed in the literature for applications involving steel beams and girders. As a result, engineers typically design helicoidal beams by considering only the strong-axis moment through the vertical projection of the beam and resolve it into a fixed ended, 2D curved beam. However, this approach is approximate and not necessarily conservative since it neglects the coupled effects of stresses due to geometry. This research presents a numerical model for converged discretization of a helicoidal beam and subsequent use of the convergence criteria for a series of parametric studies. The results are plotted and curve-fitted to provide simplified design equations for a variety of different cross-sections and stair geometry. The results of individual stresses show good agreement (within 6%) with analytical models and resulting design values.