Generalized Strength Prediction Model for Timber Beams Strengthened Using NSM FRP Bars and FRP Sheets

Existing analytical models for Fiber-Reinforced Polymer (FRP)-strengthened timber beams are generally limited to individual strengthening techniques and cannot readily accommodate hybrid reinforcement systems. This study develops a generalized analytical model to predict the flexural capacity of timber beams strengthened with near-surface-mounted (NSM) FRP bars, externally bonded FRP sheets, or their hybrid combination within a unified theoretical framework. The model is formulated based on internal force equilibrium and strain compatibility, incorporating a constitutive model for timber with linear elastic tensile behavior and a bilinear compressive stress–strain relationship including post-peak softening. The generalized formulation can be readily adapted to different strengthening configurations through appropriate simplifications. The proposed model was validated against experimental results obtained from four-point bending tests on small-scale timber beams strengthened with NSM GFRP bars and externally bonded GFRP sheets. The analytical predictions showed good agreement with the experimental results, with differences generally ranging from 2% to 23%, demonstrating satisfactory predictive accuracy. The experimental results further showed that the hybrid strengthening system increased the flexural capacity of the timber beams by up to 84% compared with the unstrengthened control beams, while also improving stiffness, ductility, and overall structural response. Failure was primarily due to timber tensile rupture and longitudinal splitting, whereas the GFRP reinforcement remained effective without rupture, indicating efficient utilization of the strengthening system. The proposed generalized analytical model provides a practical and reliable design tool for predicting the flexural strength of timber beams strengthened with various FRP reinforcement configurations, thereby supporting the structural rehabilitation and sustainable retrofitting of timber structures.