Evaluation of flexural and distortional elastic stability of mono-symmetric box girders with simply supported conditions using Vlasov theory and power series approach

Abstract

Mono-symmetric box girders are widely used in bridge construction for their strength, durability, and design flexibility. Traditional single-variable analysis methods, such as trigonometric series under simply supported (SS) conditions, often oversimplify and converge slowly. This study addresses these limitations using Vlasov theory combined with a multi-variable power series approach. Varbanov's modified generalized displacement functions were applied to derive the governing Vlasov differential equations, simplifying strain fields through the unit displacement method at the pole and shear center. Enhanced product integrals computed critical section properties, and power, trigonometric, and Taylor-Maclaurin series shape functions solved the reduced equations, enabling detailed analysis of flexural and distortional behaviors. The results revealed significant deformation patterns and rapid convergence. In the power series, maximum deflections occurred at 5 m and 45 m, attributed to localized bending moments caused by eccentric loading. Minimum distortion points were observed away from load concentrations, with reduced cross-sectional warping. Taylor-Maclaurin series deflections peaked at mid-span, consistent with beam theory predictions, while distortional curves showed linear trends with deformation neutralization at mid-span due to opposing end constraints. Trigonometric series displayed cyclic deformation patterns, reflecting the effects of fluctuating loads, and distortional curves stabilized at mid-span. These findings emphasize the ability of mono-symmetric box girders to mitigate torsional moments and improve structural efficiency. The proposed multi-variable power series approach provides precise deformation analysis and insights into localized bending, shear forces, and distortional effects. This study validates the methodology and demonstrates its potential to enhance bridge design practices through accurate and efficient structural analysis, addressing critical performance factors and advancing the understanding of mono-symmetric girder behavior under various loading conditions