Analytical approach to elastic stability problems of plates with different boundary conditions subjected to combined bending, shear and patch loading

Abstract

The elastic stability of plates with simply supported edges (SSSS) and with two edges clamped and two simply supported (CSCS) under combination of bending, shear and patch load is investigated.General analytical approach for elastic buckling analysis of plates with different boundary conditions, subjected to any combination of in-plane loads, is presented. Exact solutions for pre-buckling stress distributions and double Fourier series for deflection functions within Ritz energy method guarantees accuracy of results and enabled very complex stability analysis.Combined in-plane loads action is very common during incremental bridge lunching and different stress conditions can occur in web girders. All analyses conducted so far regarding such problems are related to simply supported plate (SSSS). However, web girder is elastically restrained to the certain point depending on flanges rigidity and authors considered interesting to investigate behavior of plate with two opposite edges restrained and other two simply supported (CSCS) under same load conditions as simply supported plate.First part of the paper deals with patch load problem for plates with two different boundary conditions and evaluation of input data for bending-patch load (M-F), shear-patch load (V-F) and bending-shear-patch load (M-V-F) interaction curves and surfaces definition. Second part is dedicated to presentation, analysis and comparison of the interaction curves and surfaces for the cases of simply supported plate (SSSS) and plate with two clamped and two simply supported edges (CSCS), in order to obtain realistic bucking load ratios in accordance with boundary conditions.