PSI - Issue 64

1002 Amir Mofidi et al. / Procedia Structural Integrity 64 (2024) 999– 1008 Mofidi et al./ Structural Integrity Procedia 00 (2019) 000 – 000 CFRP, is the orientation of the shear failure crack, and stands for the inclination of the CFRP laminates with respect to the beam axis. 2.4. Perera et al. (2014) In this research study, an optimization problem was defined to obtain a multi-objective NSM FRP shear design equation as presented in Eq. 8. The objectives were to minimize the difference between the measured shear strength of RC beams and their calculated values. The objective functions were constructed as a measure of how well the model’s predicted output agrees with the experimentally measured data. (8) where, is the FRP Young’s modulus , is the web width, is the distance from the extreme compression fibre of the cross-section to the centroid of the longitudinal reinforcement, is the angle for FRP reinforcement fibre direction in relation to the beam’s longitudinal axis , is the FRP cross-section, is the spacing between adjacent strips, is concrete average compressive strength, and accounts for the FRP reinforcement ratio. Meanwhile, 5 , 6 , 7 and 8 are unknown coefficients to be determined. After solving the optimization problem, final parameter values were obtained from the best ones in the 10 times solving of the problem as 5 =0.983, 6 =1.735, 7 =1.549, and 8 =1.119. 2.5. Bianco et al. (2014) This model proposed a comprehensive design formulation with 27 equations to predict the NSM FRP strips' shear strength derived from a previously developed numerical model with certain simplifications. Eq. 9 presents the actual NSM shear strength contribution, , and the design value . max ,int , 1 1 (2 sin ) l fd f f fi eff Rd Rd V V N V    = = (9) where, is the partial safety factor. . , . , and are the minimum integer number of strips effectively crossing the critical diagonal crack, the maximum effective capacity and the FRP strip inclination angle with respect to the beam longitudinal axis, respectively. 2.6. Modified Mofidi et al. (2016) In this article, a modified version of Mofidi et al. (2016) model is provided that leads to superior accuracies. Similar to the original Mofidi et al. (2016), the modified version, benefits from a truss analogy to obtain the FRP contribution to the shear resistance using Eq. 10. ( ) cot cot sin f fe f v f f A E d V S     +  = (10) where is the FRP cross-sectional area on both sides of the beam, is the FRP rod or laminate modulus of elasticity, is the diagonal crack inclination angle, is the angle for NSM FRP material direction with respect to the beam’s longitudinal axis , is the effective shear depth of the cross-section and stands for the spacing between the NSM FRP rods or laminates. The effective shear depth can be taken as the greater of 0.72 ℎ and 0.9 , where ℎ is the 4 7         8 6 5 sin (cot cot 45) C c c f cm f f w V C E b d = f f w f f  f A f b s E           +