Uniformly Stiffened Cantilever Plates under Bending

Abstract

A number of studies have shown that T-beams exhibit positive shear lag under bending; however, a detailed stress distribution profile of uniformly stiffened plates is rarely presented. The present study analyzes uniformly stiffened plates under bending. The stiffened plate model is discretized using an energy-based variational approach. In order to develop differential equations, the principle of minimum potential energy is applied. Based on simplified assumptions, simple, closed-form solutions are obtained for normal stress distributions. Unlike what has been reported for T-beams, stiffeners applied uniformly across the width of a plate change the direction of shear flow and thereby alter the normal stress distribution profile. It remains true that the peak stress of a cantilever stiffened plate remains on the centerline of the plate as that of a T-beam, but the stress distribution profile demonstrates a negative shear lag effect in this case. For a given aspect ratio (w/l) and a constant E/G ratio, the stress concentration is strongly influenced by the shear flow capacity of the stiffened plates contrary to T-beams where the stress concentration is determined by the relative stiffness of the flange. A high E/G ratio results in a higher stress concentration on the stiffened plate. In the case of an infinitely wide cantilever stiffened plate, peak stress factors converge to two. In the case of uniform and point loading, stiffened plates with a width four times the length (w/l=2) have a stress concentration approximately 8.57% and 11.31% lower than infinitely wide beams. In the case of w/l=4, this error is negligible. When the w/l ratio increases, the negative shear lag intensity increases, and the positive shear lag region decreases. The present research results have been verified by finite-element analysis (FEA) and are in close agreement with those reported in the literature.