Research On Shear Capacity And Its Reliability Of Reinforced Concrete Beams

The mechanism of diagonal shear failure of reinforced concrete beams is very complicated,and it is influenced by many factors.The semi-empirical and semi-theoretical calculation models proposed by researchers are normally based on test results,and there are great differences in the shear design provisions in some of the most important national codes of practice.Although a test database has been created in 1985 and plays an important role in the revision process of the Code for design of concrete structures in China,the number of members and the range of test parameters have certain limitations.Thus,based on updating test data,the analyses of influencing factors of shear capacity for reinforced concrete beams were conducted.Meanwhile,the accuracy and reliability of GB 50010-2010 in China were evaluated by comparing those shear design provisions in some of the most important national codes.Based on collecting the shear test data of 987 beams without web reinforcement and 531 beams with stirrups subjected to one or two concentrated loads,and 136 beams without web reinforcement and 42 beams with stirrups under uniformly distributed loads from home and abroad,the effects of shear span-depth ratio,concrete strength,longitudinal tensile reinforcement ratio,maximum coarse aggregate size,effective depth and shear reinforcement on shear strength of beams were discussed,and impact assessments of major design parameters were conducted on the calculation methods such as the compressive force path theory,the splitting failure theory,the strain based shear strength model,the modified compression field theory,the critical shear crack theory and Zsutty's formula.Experimental studies on shear behavior of 6 beams without web reinforcement and 12 beams with stirrups under different loading rates were carried out within the strain rate that might be experienced during earthquakes.The test results indicate: With the increase of loading rate,the failure patterns of beams transforming from the shear failure before the yielding of longitudinal tensile reinforcement to bending-shear failure,and the distribution of cracks changed too.Stirrups play a more significant role in increasing the energy-absorbed capacity of beams with relatively larger shear span-depth ratios,and it presents a rising tendency as the loading rate increases.The analyses in combination with the test results of existing 54 beams show that when the loading rate remains the same,the dynamic increase factor(DIF)of the shear capacity of beams with relatively smaller shear span-depth ratios is significantly higher than beams with larger shear span-depth ratios,and the DIF generally decreases when the stirrup ratio increases.Based on these updating test data,modeling error analyses associated with several shear design provisions in GB 50010-2010,JTG D62-2004,ACI 318-14,EN 1992-1-1:2004,CSA A23.3-04 and fib Model Code 2010 for predicting shear capacity of reinforced concrete beams were carried out.The results show that the shear design provision of GB 50010-2010 overestimates the shear capacity of these beams,which can't meet the requirement of partial lower bound.In addition,the comparisons between the experimental values of ultimate shear capacity and critical cracking shear capacity of beams with stirrups demonstrate that the minimum values of stirrup ratio in such codes are relatively rational.The first-order second-moment method considering the probability distribution of basic variables was adopted for reliability analysis of the shear design provisions in GB 50010-2010,ACI 318-14 and EN 1992-1-1:2004,and the safety level between the shear capacity and flexural strength of normal section of reinforced concrete beams designed by GB 50010-2010 was compared.The results indicate: For specimens with stirrups under uniformly distributed loads,the reliability index of calculation formula in GB 50010-2010 can meet the requirements of GB 50068—2001 well.For specimens with stirrups subjected to one or two concentrated loads,the reliability index of the shear design provision in GB 50010-2010 is larger than that of ACI 318-14 and EN 1992-1-1:2004 when the shear span-depth ratios of beams are not less than 2.0,which can meet the basic requirement of the GB 50068—2001,but it is also significantly lower than the reliability index of bending capacity of normal section.When the span-to-height ratios of beams are not less than 5.0,the reliability index of calculation formula in GB 50010-2010 is lower than target value.In addition,the sensitivity analysis based on the “Tornado Diagram” method discovers that the influence of random variable of calculation model uncertainty on the reliability index of shear capacity of reinforced concrete beams is the greatest,indicating that the larger the samples of test data are,the better results will be.A calculation formula of concrete contribution was presented by using the test data of 987 beams without web reinforcement to conduct nonlinear fitting,and the rationality of 45 degree truss model was taken for calculating stirrup contribution,which was verified by comparing 103 beams with stirrups and those beams without web reinforcement under the same condition accordingly,and then a revised formula was put forward.The revised formula takes longitudinal tensile reinforcement ratio and size effect into account,and the reliability indexes under two kinds of load conditions are relatively closer.It makes the probability of shear failure of reinforced concrete beams can be less than the probability of flexural failure by introducing the reduction coefficient of shear capacity.