Formulas for determining the critical buckling stress of I-shaped members under pure bending

Steel structures are widely used in construction, and the stability conditions for these structures are of greater concern due to their long and slender characteristics. When a plate element is subjected to axial compression, bending, shear, or a combination of these forces in its plane, the plate may buckle locally before the memberas a whole becomes unstable or before the yield stress of the material is reached. This local buckling behaviorcauses the plates in the cross-section of the steel member to interact with each other. Therefore, it is necessary to consider this interaction when calculating or checking for stability conditions. In this research, the proposed formulas determine the buckling coefficient as well as the local critical stress for I-shaped steel beams, accounting for the flange-web interaction when the flange-thickness to web-thickness ratio changes. Additionally, the buckling analysis results indicate that local buckling stress does not depend on the length-to-height ratio but is impacted by the height-to-width and thickness-to-width ratios. Comparisons between the proposed formulas and numerical results show that the suggested formulas have high reliability when the coefficient of variation is small and the coefficient of determination is very high.