Abstract: Taking into account the effects of bi-modulus for tension and compression of fiber reinforced polymer (FRP) layers and second order deformation and axial tension of the nonlinear bending of a timber beam, nonlinear bending of simply-supported FRP-strengthened timber beams under a uniform transversal load is investigated with the perturbation method. Asymptotic expressions of deflection and bending moments of the FRP-strengthened timber beam are obtained, and numerical results are presented. It is revealed that deflections and bending moments of nonlinear bending of the FRP-strengthened timber beam are smaller than those of linear bending. When the dimensionless load is less than 5, deflections and bending moments of nonlinear and linear bending are almost equal to each others, and there are no distinct differences. The difference between them increases when the load is increased. When the dimensionless load is greater than 20, the effect of nonlinear bending is remarkable, and a model of nonlinear bending of the FRP-strengthened timber beam should be used.

Key words:  fiber reinforced polymer (FRP), nonlinear bending, perturbation method, reinforcement, second order effect