Optimized shear design equation for slender concrete beams reinforced with FRP bars and stirrups using Genetic Algorithm and reliability analysis

• A database of 162 tests on beams with FRP bar with and without stirrup was composed.
• The shear equations for FRP longitudinal bar and stirrup were optimized.
• The proposed equations offer higher accuracy in shear prediction compared to code equations.
• A Monte Carlo simulation was performed for the reliability analysis.
• Resistance factors were recommended for the design equations in order to achieve an acceptable level of safety.

A lack of confidence in the shear design of concrete beams reinforced with Fiber Reinforced Polymer (FRP) bars may lead to excessive reinforcement and thus increase the overall cost of construction. In order to improve the accuracy of the current guidelines, two databases of slender (shear span to depth ratio > 2.5) FRP reinforced concrete (RC) beams were developed from literature. The first set of data contains slender beams of 116 tests with only FRP rebar as longitudinal reinforcements whereas the second set contains 46 test beams reinforced with FRP as both longitudinal reinforcements and stirrups. The second database was used to evaluate the confinement effect of FRP rebar as stirrups. Thereafter a Genetic Algorithm was implemented to optimize the shear equations proposed in FRP design guidelines of ACI 440.1R-06, CSA S806-02, CSA S6-09, and Reineck’s tooth model. The optimized shear equations showed less scatter than the original equations as they could achieve an average Vtest/Vcalc close to 1.0 with a significant improvement in coefficient of variation (CoV) with the validation database compared to the original equations. It was observed that the concrete shear equation prediction could be improved if the concrete strength could be taken to a power value less than what is currently recommended in the guidelines. In the case of transverse shear equations, the inclusion of concrete strength improved the results of the optimized equations. The optimized shear equations were further calibrated by performing reliability analysis in order to use them for design purposes. The resistance factors for the shear design equations were calculated at a target reliability index, βT of 3.5 in order to achieve an acceptable level of structural safety.