Span-dependent comparative analysis of lateral torsional buckling and nonlinear load behaviour in castellated and solid I-beams using analytical and finite element approaches

Castellated beams (CB), widely employed in modern construction, offer an improved strength-to-weight ratio and enhanced structural efficiency due to their increased depth and moment of inertia. However, the presence of web openings and discontinuous geometry significantly alters their lateral-torsional stiffness, making them more susceptible to lateral-torsional buckling (LTB), particularly. This study investigates the buckling and ultimate load behaviour of CB compared to solid I-sections through analytical (T-section method), numerical (IS 800, Handbook SP6-1-based), and finite element approaches. A steel I-section was castellated to form IC 225 sections with hexagonal openings, maintaining a 50% increase in depth. Both parent and CB were analyzed for three spans: 2 m, 5 m, and 8 m under simply supported conditions and central point loading. Nonlinear static analysis and buckling analysis were conducted in ABAQUS (2024) using shell elements, incorporating initial geometric imperfections equal to depth/500. Results indicate that CB exhibit up to 24%–42% higher ultimate load capacity and up to 37% lower deflection than solid beams due to increased depth and moment of inertia. However, their buckling resistance decreases by 8%–31% due to a decrease in torsional rigidity, with LTB as the dominant failure mode in longer spans. In addition to these expected trends, the study highlights the post-buckling behaviour, for which the stress redistribution characteristics and modes of stability differed between the CB and parent beams. Nonlinear static analysis also showed that loads and deflection changes became almost constant for spans above 5 m, indicating span-dependent nonlinearity. Nonlinear FEM results closely matched numerical predictions, with an error of 7%–11%, confirming model reliability. This study concludes that CB provides superior load performance and stiffness but requires careful design to mitigate LTB and localized Vierendeel failures around web openings. Results reveal a nonlinear response dependence on span, for which the loading and deflection become stabilized beyond 5 m. In comparison with previous works, this study provides new insights into the stress redistribution mechanisms and stability mode transitions of CBs, which contribute to the understanding of design guidelines for long-span steel structures.