Shear Capacity Stochasticity of Simply Supported and Symmetrically Loaded Reinforced Concrete Beams

For shear tests of reinforced concrete (RC) beams, a simply supported and symmetrical loading system is usually applied. In deterministic analysis, shear capacities of the paired shear spans of such beams are the same. However, considering the randomness of concrete strength, geometric dimension, and other factors, shear failure often occurs in the weaker one of the paired shear spans of a beam rather than occurring in the two shear spans simultaneously. Therefore, from the perspective of probability theory, the shear capacities of the paired shear spans of such simply supported and symmetrically loaded beams can be regarded as two random variables with the same distribution. The beam shear capacity, which is the minimum of the two random variables, is also a random variable. Hence, probabilistic differences exist between the shear capacities of shear spans and beams. In this paper, the transformation relationship between the stochasticities of shear span shear capacity and beam shear capacity is theoretically derived. By taking the RC beams without web reinforcement as an example, the shear capacity stochasticities of shear spans and beams, which are valuable for reliability-based design codes, are quantitatively analyzed based on three shear strength models in design codes and a reliable experimental database. Their probabilistic differences are identified and verified to have an impact on the model calibration in the reliability analysis. The results also show that there are obvious differences in the shear capacity stochasticities obtained by different models. It indicates that to obtain the real stochasticity of the shear capacity, it is not enough to consider the model uncertainty merely but to minimize it. Therefore, models based on a solid understanding of the shear mechanisms are urgently needed for practical design.

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