Probability-Modeling of FRP Reinforced Beams

Solid-sawn wood or wood composite beams may be reinforced with Fiber Reinforced Polymers (FRPs) on the tension side to increase their bending strength, stiffness and ductility. This paper describes results of an extensive full-scale physical testing program designed to verify the accuracy of a probabilistic model of reinforced glued laminated (glulam) beams. The testing program evaluated 90 glulam beams 130 mm wide x 305 mm deep x 6.7 m long reinforced in tension with E-glass FRP (GFRP). The beams were made using a random layup of L2 and better grade of Douglas Fir and Western Hemlock lamstock and were tested in four-point bending according to ASTM D198. The numerical model, called ReLAM (for Reinforced LAMinated beams), predicts the probability density functions (PDFs) of the Modulus of Rupture (MOR) and Modulus of Elasticity (MOE) for a selected layup of reinforced glulam beams. The model utilizes a moment-curvature mechanics approach, Monte Carlo simulations, and internally calculates the volume effect in reinforced glulam beams from basic statistical mechanics principles. Both the laboratory testing and ReLAM showed that for the Douglas Fir layup tested, a GFRP tension reinforcement ratio of 3.3% increased the allowable bending strength F_b by 119%. ReLAM was found to be an accurate tool for predicting the bending strength and stiffness PDFs of reinforced glulams. These PDFs can be used in reliability-based design of FRP-glulams.