Reliability analysis of timber structures considering variability in nonlinear joint behaviour

Doctoral thesis, 2025

In contemporary timber structures, joint behaviour is critical to overall performance and reliability. Yet joints are often idealised as pinned or rigid, despite their inherently nonlinear response. Current design rules prescribe a stiffness reduction ratio to account for the nonlinear behaviour. This simplification, coupled with the current component-based design checks, can misjudge structural reliability, leading to either unconservative or overly conservative design. This study aims to quantify the impact of the nonlinear behaviour of joints and related variability, specifically of steel-to-timber joints with self-tapping screws, on the reliability of statically indeterminate timber structures. A multi-level probabilistic framework was implemented, taking into account three levels: single-fastener, multi-screw, and structural level. First, an empirical probabilistic model of single-screw joints was developed based on experiments conducted with different load-to-screw axis angles. This model was then used as input for a semi-analytical multi-fastener model based on a displacement-controlled equilibrium, which captured the moment-rotation curve and related variability of the multi-fastener joints. Finally, employing the Monte Carlo simulation method, a reliability analysis was conducted on a statically indeterminate timber beam. Uncertainties in loads, material and joints nonlinear behaviour were considered. Results indicated that applying the currently prescribed stiffness ratio in the design of beams with joints with laterally loaded screws led to a probability of failure nearly twice the target value, whereas beams with joints with inclined screws required no stiffness reduction to meet the target probability of failure. An optimisation algorithm was used to calibrate the stiffness reduction ratio, restoring the target probability of failure. The probabilistic framework presented herein can be applied to other structural systems and joint typologies for a safer and more rational design of modern timber structures.