Strength distribution predictions of glued laminated timber beams: Influence of size, load configuration, and strength class described by the finite weakest-link theory

Abstract

In structural engineering, assessing the probability of failure is crucial for reliability considerations in design codes. Most experimental studies on glued laminated timber (GLT) beams have focused on small-scale beams, leaving a gap in understanding the failure probabilities of large-scale structures up to 3 m. Despite the use of various probability distribution functions (PDFs) to characterize GLT beam strength, a comprehensive mechanics-based approach that accounts for beam size, load configurations, and strength classes remains absent. To address this, we applied the finite weakest-link theory to model the PDFs of GLT beams with homogeneous layup according to European standards. This study details the parameter identification process, compares model predictions with experimental data, explores trends for large-scale beams, and discusses the implications for structural reliability. Our model predictions showed strong agreement with data from nine experimental studies involving 556 beams. For large-scale beams, where no experimental data was available, the predicted trends aligned with an independent numerical study. The characteristic bending and tensile strengths were successfully modeled in accordance with European standards, and an exemplary structural reliability analysis revealed diverging trends when comparing the Weibull-Gaussian distribution with the commonly used log-normal distribution. In conclusion, this statistical mechanics-based model effectively characterizes the PDFs of homogeneous GLT beams based on size, load configuration, and strength class. The left tail of strength distributions is essential for assessing structural reliability. While this tail has been characterized through simulations, detailed experimental investigations will be required to validate these findings.