Analytical and Numerical Evaluation of Additional Deflection in Tapered Steel Beams with Variable Diameter Web Openings

This study presents an analytical formulation for predicting the additional elastic deflection of tapered steel beams with variable-diameter circular web openings, a configuration that is not addressed by existing analytical models or current design codes. The proposed formulation accounts for the coupled effects of cross-section tapering, progressive variation in opening diameter along the span, and shear–bending interaction within perforated regions. To the best of the authors’ knowledge, this is the first analytical model addressing such complex non-prismatic cellular beam configurations. The formulation is implemented in MATLAB R2019a, enabling fast and automated deflection calculations over a wide parametric range, including various loading cases, tapering ratios, beam spans, web-post widths, and opening dimensions. For prismatic configurations, the analytical predictions are benchmarked against Eurocode 3 and the SCI P355 design guide, both originally developed for beams with constant cross-sections and regular openings. The results demonstrate the improved accuracy and broader applicability of the proposed approach. For tapered configurations with variable-diameter openings, the formulation is assessed against finite element simulations performed in Abaqus/CAE 2017, with the numerical model previously validated against experimental results available in the literature. The proposed method provides a reliable and practical analytical tool for the serviceability assessment of tapered perforated steel beams in structural engineering applications.