Efficient Numerical Modelling Technology of Timber Post-and-Beam Frame Robustness

The structural strength requirements for timber buildings have been significantly tightened in the second generation of Eurocodes (EN 1990:2023, EN 1991-1-7), which poses a particular challenge for solid timber frames with a beam-and-column structure, where the transfer of tensile forces via dowel connections is inherently limited. Existing multiscale frameworks for timber post-and-beam robustness lack operational detail at each scale, and no validated workflow currently bridges joint-level continuum damage mechanics and frame-level progressive failure analysis in compliance with the second-generation Eurocodes. This paper addresses this gap by proposing an effective two-scale finite element method (FEM) modelling framework for assessing the strength of such frames during column removal. Existing multiscale models describing the strength of timber structures with beam-and-column systems lack the operational details necessary to integrate failure mechanics at the joint level and progressive failure modelling at the frame level within a single, validated workflow. In this paper, this gap is addressed through three specific contributions: a physically modified quadratic Hashin-type failure criterion for timber, which eliminates the non-physical increase in shear strength under combined stress states perpendicular to the grain; a two-scale structure based on the finite element method (FEM), in which the results of continuous damage mechanics at the joint level directly parameterise non-linear joint elements with six degrees of freedom at the frame level, taking into account coupled directional wear and erosion of the elements; and quantitative validation of both scales against experimental data and the conversion factors for characteristic values of the second generation of Eurocode 5 (prEN 1995-1-1:2023). At the connection level, the simulated strength and stiffness values agree with the experiments to within an error of no more than 5%. At the frame level, the model correctly reproduces the non-linear ‘load–displacement’ relationship, the sequence of joint failure, and the axial forces in the chain line for vertical displacements up to 390 mm, which corresponds to experimental observations.