Optimal CFRP strengthening of RC frames based on reliability analysis

One of the methods for the seismic strengthening in structural engineering is using FRP composites. These composite has some advantages such as increase in ductility, stiffness and lateral strength, the ability to adapt with the architecture, and also the minimum weight added to the structure. Uncertainty in the structure is due to reasons such as the lack of prediction of additional loads over the lifetime of the structure, the inadequate knowledge of the mechanical properties of the materials, the existence of human errors and the simplifications in analytical relations for modeling, and makes reliability analysis of structural inevitable. The First-Order Reliability Method (FORM) and Monte Carlo Simulation (MCS) are the most common and accurate methods of reliability analysis. Structural reliability analysis leads to the construction of an acceptable safety grade structure. In this paper, an optimal pattern for reinforcing RC frame with FRP layers is presented using reliability analysis. Carbon fiber reinforced polymers (CFRP) are used to increase the shear strength of existing RC frame. The beams and columns are wrapped by the CFRP layers at the ends, and in the reinforcing patterns, the reinforced beams are assumed to be constant and the difference is in length of the reinforcement of the column. After verifying and ensuring the results of modeling, the seismic behavior of the 8-story RC frame was assessed by nonlinear time history analysis (NTHA) with finite element program OpenSees under three far-field records earthquake from fault TABAS, Borah Peak and Imperial-Valley. Four random variables represented the variation in compressive strength of concrete, yield strength of steel, live load, and elasticity modulus of CFRP materials are defined and the limit state function defined to perform reliability analysis based on the maximum drift ratio inter-story. The reliability analysis of RC frame under three earthquake records and five reinforcement patterns was first determined using the Importance Sampling Method (ISM), and then the accuracy of the method was measured using MCS. Based on the results of the reliability analysis, the optimal length value corresponding to the maximum value of the reliability index ( ) for each earthquake record is determined. Survey results show that increasing the length of the reinforcement does not lead to an increase in the reliability index and even decreases with the inappropriate reinforcing length. The results of reliability analysis show that the number of layers of CFRP is not considered safe for Borah Peak record and requires more layers to reinforce. The optimum lengths of reinforcement in TABAS and Borah Peak earthquakes are 20% of the length of the column and in the Imperial-Valley record is 30% of the length of the column, while with a change of 5% of the length strengthening, the reliability index is significantly reduced. The most accurate method for analyzing reliability and calculating the probability of structural failure is MCS, but this method requires a large number of simulation samples to perform calculations. Which significantly reduces the number of simulation samples and the time to perform calculations by selecting the ISM method and the appropriate amount of random variables to begin the analysis.