Reliability-Based Shape Optimization of Timber-Steel Hybrid Roof Trusses Considering Material Uncertainty
The construction sector is increasingly pressured to reduce embodied carbon, and long-span roof trusses—heavy consumers of structural steel—represent a critical target for decarbonization. Replacing selected steel members with glued laminated timber offers a promising pathway, yet current practice simply substitutes materials while retaining the geometry optimized for all-steel trusses. This study questions whether such an approach is adequate and reveals a systematic carbon penalty that has been overlooked. Through parametric analysis of Warren and Pratt roof trusses across practical spans (24-80 m) and Monte Carlo simulation accounting for the inherent variability of timber properties, the study demonstrates that timber-steel hybrid trusses favor fundamentally different optimal geometries—taller with fewer panels—than their all-steel counterparts. Ignoring this divergence sacrifices roughly one-third of the achievable carbon savings, and the penalty is shown to be robust under realistic material uncertainty. A set of simplified design formulas is proposed to help engineers rapidly identify the correct hybrid geometry without running a full optimization, bridging the gap between research insights and everyday design practice.