Simplified Analysis of Negative Shear Lag in Laminated Composite Cantilever Beam

Abstract

In the present study, a composite cantilever beam subjected to shear loading has been analyzed. A simplified procedure is presented to examine the composite cantilever beam. The governing differential equations and boundary conditions are established by applying the principle of minimum potential energy, and solutions to the differential equation are given. A very simple and convenient formula to calculate the bending stresses consisting of shear lag in a composite cantilever beam is derived, which has a similar form as that of the bending stress in the elementary beam theory (EBT). A numerical example is illustrated to demonstrate the simplicity and accuracy of the proposed simplified method. For EsIs/EoIo=0.731, the stress factor (σx/σ), i.e., the ratio of actual flange stress to the stress calculated by EBT in the central line of the cover sheet at the clamped end, is computed as the following: 1.120, corresponding to the uniformly distributed load; 1.067, corresponding to the point load; 1.165, corresponding to the uniformly varied load increasing toward the support and 1.102 corresponding to the uniformly varied load decreasing toward the support. The results obtained by the simplified method have been verified by finite-element analysis (FEA). Further, the present methodology is compared with the Reissner box beam methodology. The theoretical results are found to compare well with test results and literature.