Simplified Approach for Determining Buckling Load in Portal Frames: Elastic Stability Analysis

Abstract The stability of portal frames is a critical aspect of structural engineering, significantly influencing their safety and performance. It refers to their ability to resist buckling or collapse under compressive forces, ensuring structural integrity and safety under various loading conditions. This study aims to provide design charts, created from closed-form solutions, on the probability of forming four different failure modes depending upon stiffness and axial load ratios. These charts provide a simplified and efficient method for quickly and easily assessing the elastic stability of a portal frame without the need for complex analyses or numerical simulations. The results indicate that in most cases, the governing failure mode is the sway-without-shear mode. However, upon further analysis, it is found that when the stiffness ratio (EI 2 /EI 1 ) exceeds 2 and the force ratio (P 2 /P 1 ) exceeds 1.33, the observed failure mode typically shifts to the symmetrical failure mode. Moreover, of the concluded results, the study discloses that the stiffer the beam, the higher the critical load ratio, and subsequently, the higher the buckling load. This is due to the fact that the beam behaves more like a rigid element, which prevents joint rotation, as in the fixed-end condition.