Failure-guided optimisation of castellated steel beams with circular and hexagonal openings

This study presents an analytical–numerical framework for the failure-guided assessment and design exploration of castellated beams with circular and hexagonal openings across six beam spans (300–800 cm). The framework uses five metaheuristic optimisation algorithms, applied individually and comparatively to these types of castellated beams within a unified design framework, with the objective of minimising construction cost while satisfying strength and serviceability constraints. The proposed framework simultaneously optimises the main cross-sectional parameters (bf, tf, tw, and dg) and investigates the relationship of these parameters to potential failure modes, complementing previous optimisation studies by explicitly linking cross-sectional decisions to the governing failure mechanisms for both opening types. The performance of the algorithms was evaluated using sensitivity analyses, processing time, standard deviation, and the coefficient of variation. Particular emphasis is placed on identifying the governing failure mechanisms associated with different optimised configurations. As an additional numerical check, finite element analysis was performed for selected critical and representative circular opening cases, including the weakest and strongest optimised configurations. This integration provides a practical framework that can be extended to other structural design problems.