Ultimate Strength and Effective Width Formulations for Ship Plating Subject to Combined Axial Load, Edge Shear, and Lateral Pressure

Abstract

The aim of the present study is to develop closed-form formulations for the ultimate strength of simply supported steel plating subject to a combination of longitudinal axial load, edge shear, and lateral pressure. The post-weld initial imperfections (initial deflections and residual stresses) are included in the strength formulations as parameters of influence. By solving the equilibrium and compatibility governing differential equations of large-deflection plate theory, the membrane stress distribution inside the plating under axial and lateral pressure loads is formulated in closed form. The ultimate strength formulation for plating under axial load and lateral pressure is then derived under the assumption that the ultimate limit state is reached if the plate edges yield. An empirical formula for the plate ultimate shear strength is suggested based on numerical FE solutions. A relevant ultimate strength relationship between axial load and edge shear is then proposed by combining the two sets of the ultimate strength formulations. As another contribution, the effective width formulation for plating under combined axial compression and edge shear which allows for the shear lag effect caused by lateral pressure as well as the influence of post-weld initial imperfections is developed. The validity of the proposed ultimate strength formulations is shown by comparing with experimental results and nonlinear finite-element analyses. Modeling uncertainty of the developed plate ultimate strength formula against the experimental and numerical results is studied in terms of bias and coefficients of variation.