Structural Stability Theory and Practice

7Buckling of Plates

7.1 Introduction

Thin plates are considered as two-dimensional members and the bending takes place in two planes, whereas columns were one-dimensional members and the bending could be assumed in one plane. The deflections and bending moments in the columns were functions of one independent variable, whereas in plates these quantities are dependent on two independent variables. Hence, the governing equations in the columns were ordinary differential equations. In the case of plates, the behavior is governed by partial differential equations. Another difference between the behavior of columns and plates is that the columns cannot take additional forces beyond their buckling loads, and the critical load is the failure load for columns. Plates have additional capacity to resist forces beyond their buckling load and their failure load is much higher. The failure load for the plates can be found by considering their post-buckling behavior. Plates are used as elements of wide flange, channel, angles, and other column cross-sections. In such cases, the buckling of plates is responsible for the local buckling of the column cross-sections. In addition, the plates are used as flat surfaces in buildings, bridges, aircraft wings, plate girder webs, ship hulls, etc. Plates are of different shapes, and sizes, e.g. circular and rectangular plates, thin and thick plates. Plates are supported by different types of supports.

7.2 Theory of Plate Bending

It is customary to ...