Theoretical derivation of elastic local buckling load formulae of I-shaped steel girders considering web-flange interaction

The objective of this study is to develop formulae for the elastic local buckling loads of I-shaped steel girders subjected to uniform bending and pure shear stress, considering the interaction between the web and flange plate elements. In conventional design standards for steel structures, various limitations for width-to-thickness ratios have been published, most of which are based on equations that treat the web and flanges as independent plate elements. In practical I-shaped steel girders, local buckling occurs due to the interaction between the web and flanges. However, the current design standards do not incorporate this plate element interaction into the design equations for local buckling or the width-to-thickness ratio limitations. Previous studies have attempted to derive the elastic local buckling load of I-shaped steel girders by considering plate element interaction. However, the design equations for local buckling loads proposed in these studies are regression equations based on experimental and analytical results and do not explicitly formulate the plate element interaction. In contrast, the methodology proposed in this study introduces a series of displacement functions that accurately approximate the local buckling deformations of the web and flange in the cross-sections, explicitly formulating the plate element interaction. Specifically, a two-term displacement function is used for the web, and the displacement function for the flange is dependent on the displacement function of the web. The formulae for the elastic local buckling loads under uniform bending and pure shear stress are derived using the energy method. To validate the proposed formulae, buckling eigenvalue analyses using the finite element method are performed for I-shaped steel girders with various cross-sectional profiles. By comparing the analysis results with the derived formulae, it is verified that the proposed formulae accurately predict the elastic local buckling loads.