Elasticity Solutions for Continuous Laminated Beams Subjected to Arbitrarily Distributed Loads

Discontinuous high-speed vehicle loads may induce highly localized stresses that can lead to cracking and delamination failure of simply supported composite girder bridges. An elasticity analytical method is proposed to predict the displacement and stress distributions of multi-span laminated beams under arbitrary static distributed loads. The reaction forces of the intermediate supports are considered to be unknown vertical external forces acting on the bottom surface of the continuous beam. Based on the basic equations of plane stress problems in theory of elasticity, the general solutions of displacements and stresses for each single layer are derived by adopting the Fourier series expansion method. Then, the elasticity analytical solutions of the laminated beam can be obtained by the continuity conditions of the interfaces and the boundary conditions of the top and bottom surfaces. The convergence and comparison studies of the solution are conducted through two numerical examples. And the numerical results using the present method are in good agreement with those by using the finite element software, thus effectively verifying the accuracy and correctness of the present method.