Shear capacity model for FRP-beams: Database evaluation, three-stage particle swarm optimization, and experimental validation

Abstract

Abstract

Accurate prediction of the shear capacity of concrete beams reinforced with fiber-reinforced polymer (FRP) bars is hindered by large scatter and parameter-dependent bias in design models. This study compiles a database of 631 shear tests on FRP-reinforced concrete beams (499 without and 132 with FRP stirrups) and assesses nine design methods. The effects of effective depth, shear span-to-depth ratio, concrete compressive strength, and FRP stirrup ratio are quantified. Results reveal deficiencies in capturing size effects and modeling the coupling between concrete and FRP contributions, particularly for beams with small shear span-to-depth ratios and high-strength concrete. To improve predictive accuracy while retaining physical transparency, a three-stage particle swarm optimization (PSO) framework is developed to recalibrate coefficients and selected exponents of code-based shear equations. The optimized formulations substantially reduce prediction bias, coefficient of variation, and average absolute error, with the CSA S806-12-based model exhibiting the best overall performance among the formulations considered. A unified shear design equation for beams with and without FRP stirrups within the parameter ranges covered by the calibration database is proposed and examined against an independent seven-beam BFRP experimental program, providing preliminary external verification within the tested ranges and showing improved prediction consistency compared with existing design models.