Coupled finite element-finite difference formulation for long-term analysis of timber–concrete composite structures

• Development of a nonlinear frame finite element-finite difference model.
• Using force-based formulation with partial discrete connections.
• Derivation of all long-term effects of timber, concrete and connection.
• Implementation in a simple efficient step-by-step 1D FE model.
• Analysis of timber–concrete composite beams under long-term loads.

This paper focuses on development of a simple frame finite element model for nonlinear analysis of timber–concrete composite (TCC) beams under long-term loads. The element formulation within the context of the force interpolation and modified fibre element is derived in which the partial interaction between the layers can be captured by discrete nonlinear springs at ends of the element. Further, a finite difference scheme is also developed to analyse variation of diffusion within the timber section with respect to relative humidity changes. Different long-term effects of timber, concrete and connection are taken into account and their formulations within the total secant approach and efficient step-by-step analysis are derived. The implementation of the proposed model in a 1D FE model is discussed and the long-term behaviour of TCC components and beams is verified with available test results from literature.