Development of an Enhanced Reduced Cross-Section Method for the Fire Design of Glulam Beams

Current international design standards for timber structures under fire exposure rely on simplified reduced cross-section methods (RCMs) that generally assume constant charring rates and a fixed zero-strength layer (ZSL) thickness, typically 7 mm. These assumptions do not account for the influence of timber density, moisture content, cross-sectional geometry, or fire exposure configuration on charring and thermal degradation. This study presents an enhanced reduced cross-section method (ERCM) for the fire design of Glulam beams by incorporating these parameters. The underlying numerical model was independently validated against experimental thermal and structural fire tests, demonstrating accurate predictions of both charring rates and structural deflection under fire exposure before conducting the 65 coupled thermal–structural simulations detailed in a companion manuscript. Analytical models for average charring rate and ZSL evolution were then formulated using nonlinear regression of this validated numerical dataset. The average charring-rate model incorporates timber density, moisture content, fire exposure duration, and number of fire-exposed faces. The ZSL model is formulated as the product of a Peak ZSL, which depends on density, moisture content, and cross-sectional geometry, and a time-dependent ZSL coefficient that depends on density, moisture content, fire exposure duration, and number of fire-exposed faces. The models yielded coefficients of determination (R2) of 0.982 for average charring rate, 0.973 for Peak ZSL, 0.914 for time-dependent ZSL coefficient, and 0.927 for time at Peak ZSL. The resulting analytical models were incorporated into the reduced cross-section framework and applied to four design examples representing 60 min residential and 90 min office applications, considering Glulam densities of 300 and 450 kg/m3. The ERCM was compared with Eurocode 5 Simplified Method (EC5, SM) and AS/NZS 1720.4 using consistent loading and material assumptions. The comparison demonstrates substantial differences between the design methods, particularly at low timber densities and longer fire exposure durations. The spread between the methods increases as density decreases and fire exposure duration increases, with the constant-parameter EC5 (SM) approach becoming non-conservative for low-density glulam at long fire exposure durations, while AS/NZS 1720.4 becomes overly conservative under the same conditions. The results illustrate the influence of density-dependent charring and ZSL evolution on the predicted residual cross-section and fire utilisation. The proposed ERCM provides a physically representative framework for evaluating fire resistance, though its application beyond the validated parameter ranges requires further experimental confirmation.