Analysis On Reliability And Flexural Capacity Of Concrete Beams Strengthened By CFRP Under Secondary Loading

CFRP have become the major materials for strengthened concrete structures because of their advantage of high strength, high elastic modulus, excellent anticorrosion and simple construction. Based on flexural capacity experiment of reinforced concrete beams under different loading history before and after strengthened by carbon fiber reinforced plastic (CFRP), the variation of hysteretic strain with loading history and the influence on the reinforcement effect are found, a revised formula for hysteretic strain is proposed to accord with engineering practice. From the view of reliability, the practicable formula with material requirement controlled by limit ratio of CFRP is presented for flexural capacity of strengthened concrete beams satisfying ductile and reliable design. The following are the main research results:(1) The hysteretic strain is relevant to loading history, which is higher after unloading with the higher load before unloading. According to the variation of strain of concrete and of steel bars after unloading to varying level under different loading history, cross-sectional strain is still subject to the plane section assumption, the stress-strain relationship of compressed concrete and of tensile steel bars obey the offloading theorem, and then location of the neutral axis remains the same because of cracks closing gradually during unloading.(2) A revised formula for hysteretic strain is presented. In accordance with four elastoplastic states of compressed concrete and of tensile steel bars, the corresponding theoretical formulas are established especially. The reinforcement ratio and the relative amount of unloading are the important influential factors, so the simplified formula for hysteretic strain associated with above-mentioned influential factors and the experiment results are obtained after a series of regression analysis, which considers the load history.(3) The steel yielding is advantageous to the ductile failure for CFRP-strengthened beams. On the basis of the experimental results under different damage degree, the redistribution of stress will occur only after the steel yielding with firm interface bond, and the growing stress is born by CFRP. That is CFRP would play a greater role after steel yielding. Therefore, the steel must be yielded before ductile failure in the design.(4) Material requirement is controlled by limit ratio of CFRP satisfying ductility. Because of hysteretic strain, the critical failure condition, different from ordinary critical failure basis, are reconsidered upon experiments in order to achieve economical design, for the sake of functioning adequately and avoiding brittle failure.(5) Statistical parameters and the probability distribution model with hysteretic strain as a random variable for flexural capacity of CFRP-strengthened concrete beams are obtained. Based on the mechanical property tests of CFRP, statistical characteristics of tensile strength and elastic modulus are acquired by mathematical statistics. Then, the flexural capacity suggested in this paper are simulated for engineering material strength, and cross-sectional dimensions commonly used, using optimized statistical tool-box in Matlab and Monte-Carlo method. So in the case of hysteretic strain as a random variable, statistical characteristics of resistance ratio for compression failure are given.(6) The limit ratios of CFRP are optimized on the basis of reliability. Reliability indexes of flexural capacity suggested in this paper meet the object reliability index for ductile failure of secondary structures, using JC method under different load effect ratios for usual three load combinations respectively. The limit ratios of CFRP are optimized from the point of reliability, which achieve better consistency of reliability index.