A nonlinear modelling framework for unbonded post-tensioned timber members

Abstract

Post-tensioned timber elements have become a competitive alternative for long-span structures such as bridges or open-plan buildings. Post-tensioning can add an improved load-bearing capacity and enhanced deflection control to the well established structural efficiency and sustainability advantages of wood as a construction material. Despite of these improvements, the use of unbonded post-tensioning tendons introduces several complexities to the already intricate response of timber structures such as strain incompatibility and second-order effects that require careful consideration. In this study, a fibre-based finite element (FE) analysis framework for the simulation of the full nonlinear response of post-tensioned timber members up to their ultimate failure state is presented. In this framework, the exerted post-tensioning force is assessed using a constantly updated equivalent load which is dependent on member deformations. A description of the FE formulation, modelling assumptions and robust solution algorithms of the fibre-based framework within a corotational formulation is discussed first. Also, a robust numerical procedure is described to evaluate the initial state immediately after the post-tensioning operation. Then it is shown, with reference to available experimental and numerical results, that the approach adopted can simulate effectively the behaviour of post-tensioned timber elements with different post-tensioning layouts while complementary simulations on post-tensioned reinforced concrete (RC) beams demonstrate its versatility. Finally, a study on the influence of deviator spacing on the ultimate response of post-tensioned timber beams, that is known to be largely dependent on second order effects, is conducted. Besides the good agreement with experimental and numerical results, the proposal features promising adaptability, numerical robustness and computational efficiency. This study constitutes a first step towards the realistic simulation of the full global nonlinear response of post-tensioned timber members using an efficient non-linear FE model.