Optimization of timber design values via reliability analysis considering the load ratio and resistance factor

Abstract The aim of this study was to investigate the relationship between the reliability index (β) and the resistance factor (∅) of structural timber to establish appropriate design values under the load and resistance factor design (LRFD) framework. Specifically, β is evaluated according to the bending and compression strengths, design values (allowable stress, format-converted value, and test-based lower 5th percentile (R 0.05 ) value), and dead-to-live load ratio (γ). The results show that β decreases uniformly with increasing ∅, while higher design values at a fixed ∅ lead to lower reliability. The sensitivity of β toward γ is smaller than that toward the design value and ∅. Among the types of design value, the test-based R0.05 value is the most suitable for LRFD calibration. To align with international standards, resistance factors of 0.85 and 0.90 are recommended for bending and compression, respectively. The corresponding optimized design values satisfying the target reliability of β = 2.4 are 31.2, 19.4, and 15.8 MPa for the bending of timber grades No. 1, 2, and 3, respectively, and 31.1 MPa for compression of grade No. 1. These findings provide a quantitative basis for transitioning timber design standards from allowable stress design (ASD) to LRFD, thereby reducing unnecessary conservatism, improving material efficiency, and harmonizing with global practices in sustainable structural materials.