Simplified calculation method for the critical load bearing of market-based profile emergency steel pier

A novel emergency steel pier, assembled from market-available profiles, has been developed to address the challenges associated with the "regular stockpiling and rapid emergency deployment" of bridge pier repair equipment. These challenges often involve significant labor and financial costs for manufacturing and maintenance. The buckling modes of the columns and pier-girder connections were considered. Using energy methods and plate-shell theory, an analytical formula for the critical load-bearing capacity of the steel pier under emergency conditions was derived. Numerical simulations were conducted for comparison and validation, resulting in an optimized and simplified method for calculating the critical load capacity, which is suitable for engineering applications. The study shows that the critical load-bearing capacity of the emergency steel pier exhibits distinct patterns under the influence of column buckling modes and pier-girder connection methods. In cases where the column is fixed at one end and hinged at the other, or fixed at both ends, the critical load for axisymmetric buckling is affected by factors such as elastic modulus, Poisson's ratio, height, radius, wall thickness, and the number of buckling waves. When considering non-axisymmetric buckling, the number of circumferential buckling waves becomes an additional factor. A simplified method for calculating the critical load-bearing capacity was developed. The simplified formula depends only on a correction factor, modified buckling stress, the number of columns, and cross-sectional area. This makes it highly practical for emergency engineering applications.