Application of Vlasov theory and multi-variable power series for elastic stability analysis of mono-symmetric box girder

This study employs a combination of Vlasov’s thin-walled beam theory and a multi-variable power series approach to analyze the elastic stability of mono-symmetric box girders, a class of thin-walled structural elements widely used in bridge engineering, subjected to eccentric transverse loading. The primary objective is to investigate the discrepancy between the shear center and the center of gravity, which induces complex coupled deformation modes, particularly flexural and distortional effects. Using Varbanov’s modified generalized displacement functions, the governing differential equation of equilibrium were derived based on section properties evaluated at the pole and shear center, through a unit displacement approach. Essential cross-sectional parameters were obtained using enhanced product integrals (diagram multiplications). Given the complexity of the governing equation and boundary conditions, exact closed-form solutions were not attainable. To address this, three analytical methods, power series, trigonometric series, and Taylor-Maclaurin series, were applied to solve the reduced equations, enabling a comprehensive evaluation of flexural and distortional behaviors. Among these, the power series method proved most effective, accurately capturing the multi-variable interactions required to model realistic deformation patterns. Under eccentric loading, maximum flexural deformation occurred at 10 and 40 meters, while distortional deformation peaked at 40 meters and diminished near 45 meters. The Taylor-Maclaurin series showed maximum flexural deformation at 30 meters and distortional deformation at 9 meters. The trigonometric series revealed cyclic deformation patterns indicative of fluctuating load effects but lacked the precision needed for complex geometries. This study addresses a notable gap in the literature by providing a robust analytical framework for mono-symmetric girders and emphasizes the importance of advanced multi-variable analytical techniques in structural design and engineering education.