Reliability-based assessment of knot impact and safety factor calibration for axial timber elements with knots

Abstract

Several timber design codes permit, under specific restrictions, the use of structural members containing knots to promote sustainability. However, the reduction factors currently applied to strength and stiffness properties in design are not commonly calibrated through structural reliability analyses. This gap motivated the present study, whose objective was to establish additional partial safety factors based on a reliability-based framework. To this end, tensile and compressive strengths parallel to the grain were assessed through 49,000 simulations, considering variations in knot content, strength classes of timber, and loading rates. The simulations employed the finite element method, the Monte Carlo method, and selected machine learning techniques. The proposed partial safety factors were subsequently calibrated against a target reliability index Bt = 3.10. Among various machine learning techniques, Gradient Boosting Regression achieved the highest accuracy (R2 = 0.97), enabling efficient reliability assessments. Monte Carlo simulations with 125,000 samples revealed a substantial reduction in the reliability index B as knot diameter increased. Knot-free members exhibited reliability indices of Bt = 3.61 in tension and Bc = 4.03 in compression, both exceeding Bt. In contrast, the presence of knots reduced reliability by up to 21.3% and 30.5% in tension and compression, respectively. These findings guided the calibration of additional partial safety factors based on reliability analysis, with Gw,knot values ranging from 1.05 to 1.20 in tension and 1.30 to 1.55 in compression, depending on the live to dead load ratio (L/D).