An applicable formula for elastic buckling of rectangular plates under biaxial and shear loads

As thin plates have relatively big thickness ratios, their elastic buckling usually occurs before the yielding. From beginning of the previous century, many researchers have considered various in-plane loading states on thin plates and have strived to find simple equations to predict the buckling load. However, there are few valid equations with negligible errors for a thin plate, when it is under all of in-plane loads. In this paper, using energy method, an applicable formula is suggested for a simply supported rectangular plate, which is under biaxial and shear loads. The biaxial loads can be applied in the compressive/compressive, compressive/tensile, and tensile/tensile states on the plate. Generally, 15 129 examples are considered for this problem. The aspect ratio of plates varies from 1 to 5 and for each case and with the known load ratios, the plate buckling coefficient is calculated. Then, by using the regression techniques and interpolation, it is tried to estimate a simple equation with minimum error to predict the buckling load. The confirmed results show that for the biaxial compression and shear state, the maximum error is 8% and for the compression-tension-shear and biaxial tension and shear states, it increases until 20%.