Efficient finite element modelling of timber beams strengthened with bonded fibre reinforced polymers

This paper presents development and application of a simple and efficient frame finite element (FE) able to estimate the load-carrying capacity of timber beams flexurally strengthened with externally bonded fibre reinforced polymer (FRP) strips and near-surface mounted FRP bars. The developed element is able to model collapse due to timber crushing under compression, timber fracture under tension and FRP rupture and it is developed in the framework of a flexibility-based fibre element formulation. Furthermore, a novel method based on central difference method in conjunction with composite Simpson’s integration scheme along the element axis is developed to take account of shear-slip. The developed model is employed to predict the loading capacity and the applied load-mid span deflection response of timber beams strengthened with FRP and the numerically simulated responses agree well with the corresponding experimental results. The major features of this frame FE are its simplicity and efficiency compared with more complex and computationally expensive FEs which makes it a suitable tool for practical use in design-oriented parametric studies.