Inverse interaction of shear between steel-stirrups and externally bonded carbon fiber-reinforced polymers in shear-strengthened reinforced concrete beams: Analytical and numerical models

Shear failure in reinforced concrete (RC) beams have always been a serious concern due to its brittle fracture mode. In addition, many questions are raised about the accuracy of current design guidelines for predicting the shear resistance contribution of externally bonded carbon fiber-reinforced polymers (EB-CFRPs) to the ultimate shear strength of strengthened RC beams, particularly with regard to the inverse interaction of the shear contribution between steel-stirrups and EB-CFRPs. The main objective of the present study is to implement experimental and numerical tests to develop analytical and numerical models for RC beams strengthened in shear using EB-CFRPs. Emphasis is placed on the negative inverse interaction between the steel-stirrups and the EB-CFRPs as the ratio of EB-CFRP-to-steel-stirrups increases with increasing the CFRP rigidity (CFRP thickness and CFRP width). The inverse interaction is not included in the design models proposed by most current guidelines, although it has a considerable effect on shear resistance as predicted by the guidelines. In fact, the shear contribution associated with EB-CFRP decreases as the ratio of EB-CFRP-to-steel-stirrups increases. Therefore, proposing reliable effective strains by including these parameters improve the calculated shear contribution of EB-CFRPs. First, an analytical model is proposed for CFRP effective strain considering the inverse interaction between EB-CFRPs and steel-stirrups. Afterward, a validation of the proposed model with experimental data is done by conducting a parametric study of the increasing trends with respect to the ratio of EB-CFRP-to-steel-stirrups. A numerical finite-element model for the reduction factor and the corresponding effective strain based on the inverse interactions between EB-CFRPs and steel-stirrups is also proposed, and the results are compared with various current guidelines. The results are presented in terms of shear crack patterns, load-midspan deflections, shear stresses, strain responses along the fibers, maximum strain profiles for all the CFRPs and specimens, applied shear forces and strains for all the steel-stirrups and EB-CFRPs, and interactions between steel-stirrups and EB-CFRPs based on their maximum strain contributions at the maximum shear forces and the maximum strain they experience after shear failure.