Elastic Stability of Simply Supported Flat Rectangular Plates Under Critical Combinations of Longitudinal Bending, Longitudinal Compression, and Lateral Compression

Abstract

A theoretical investigation was made of the buckling of simply supported flat rectangular plates under critical combinations of longitudinal bending, longitudinal compression, and lateral compression. Interaction curves for these loadings are presented for various plate aspect ratios. Also included are curves of critical buckling constants for simply supported flat rectangular plates under combined unsymmetrical bending and lateral compression. The results indicate that the reduction in the allowable bending stress due to the addition of lateral compression is greatly magnified by the further addition of only a small longitudinal compressive load. INTRODUCTION IN THE DESIGN OF STRESSED-SKIN STRUCTURES, consideration must sometimes be given to the critical stress of a plate under combined longitudinal bending, longitudinal compression, and lateral compression. Box-beams webs, for example, are subjected to these loading conditions due to the bending moments alone. Also in beams having unsymmetrical distributions of cross-sectional area, the webs are subjected to unsymmetrical longitudinal bending stresses and lateral compression (crushing) stresses due to the applied moment. In the present paper, the critical stress coefficients are found for the plate loading shown in Fig. la. Critical stress coefficients have been calculated by other investigators for certain boundary values of the more general loading case assumed here. Some of these are: longitudinal bending and compression, Fig. lb ; longitudinal bending and lateral compression, Fig. lc; and compression in two directions,? 4 Fig. Id. The results of these papers were used to aid in the construction of the interaction curves presented herein. SYMBOLS a ~ length of plate in ^-direction an = Fourier coefficients b = width of plate in ^-direction D = plate flexural rigidity, Et/12(1 /x) E — Young's modulus of elasticity kb = critical longitudinal bending stress coefficient kbx = critical stress coefficient for longitudinal bending and compression combined kx = critical longitudinal compressive stress coefficient ky = critical lateral compressive stress coefficient m — number of half waves in x-direction Nb = longitudinal bending force per unit length acting on plate middle plane = maximum compressive value of Nb at edge of plate = longidutinal compressive force per unit length acting on plate middle plane = lateral compressive force per unit length acting on plate middle plane Nbx = sum of longitudinal loadings Nx and JV& R = stress ratio T = external work of applied forces t — thickness of plate V = internal energy of deformation w = deflection of buckled plate normal to middle plane iVo Nx Nv