Simulation of cracks propagation of reinforced concrete beam-to-column joint with FRP strengthening in flexural and shear region

Nowadays, rehabilitation of structural members is a challenging issue for structural engineers, and much effort has been made to predict crack propagation in structural members. In the present study, a stiffness matrix is formulated for the Fracture Process Zone (FPZ). Based on the derived formulation, a new element was developed in order to model crack propagation using finite element analysis. Size effects such as depth, thickness of the beam and effective crack length were considered in the calculation of FPZ length and crack extension. Based on the new element, the Griffith differential energy method was developed to predict the crack propagation criterion with high accuracy. Therefore, in the present investigation a numerical model was developed to model crack propagation in concrete beams flexural or shear strengthened with FRP. To validate the present model, experimental testing on reinforced concrete beams and beam-column joints with and without Fiber Reinforced Polymers (FRPs) strengthening were carried out. Three beam specimens with rectangular cross-section were tested. Two beams were strengthened with externally bonded FRP sheets for flexure or shear strengthening and one control beam were considered. One beam was externally bonded with FRP sheet at the bottom of the beam and another one was bonded with FRP sheet in the shear span i.e. the two sides of the beam. The beams were subjected to two point loads and tested to failure. The experimental results were compared to the present model predictions based on conventional fracture models carried out using commercial finite element software (ABAQUS). The results indicated that the use of FRP composites for flexural and shear–strengthened beams decreased crack propagation for approximately 55% and 37%, respectively, in comparison to the control beam. It was observed that the length of FPZ increased by using of FRP for shear–strengthening. The present model showed that the main diagonal crack formed at the support in the control beam whereas it appeared through the shear span in the shear–strengthened beam.The developed fracture mechanics modeling was also applicable for identifying crack propagation in FRP-strengthened beam column joints. For this purpose, two beam column joints were made and tested to validate the present model. The results of the FRP-strengthened beam column joints by using present study showed good agreement with the experimental results (7 to 11%), whereas the results from numerical analysis using finite element software were considerably greater than experimental results (16 to 20 %). The results revealed that cracks formed in the joint area in the control specimen, while extensive cracks appeared in the beam in the specimen strengthened by FRP