Probabilistic Models for Temperature-Dependent Compressive and Tensile Strengths of Timber

Abstract

Reliable reduction factors for timber mechanical properties at elevated temperaturas are needed to design timber structures for fire safety as well as to assess the safety of historic timber structures against fire hazards. In this paper, a compilation of the available data on the compressive and tensile strengths of timber at elevated temperatures is carried out. Then, a probabilistic modeling approach to predict the temperature-dependent reduction factors applicable to fire design is proposed. The collected data cover both solid and engineered timber at temperatures from 20°C to 300°C, with a variety of sample sizes, wood species, test protocol, and moisture content used in the experiments. The data reveal a large scatter in elevated temperature strengths, and a large conservativeness of the relationships of the current Eurocode 5 - Part 1-2 (EN 1995-1-2), which is the standard commonly used for the advanced design of timber structures under fire. To address this variability, multiple probability density functions are calibrated across the temperature range, quantifying the goodness of fit with statistical criteria. Two-parameter Weibull functions provide the best fit and continuous temperature-dependent relationships are derived for the parameters of the distribution. The proposed probabilistic models can be implemented in a numerical code, facilitating their use in analytical and computational approaches, and can be applied to the probabilistic assessment of the structural performance and reliability of timber structures against fire.