Stochastic analysis on flexural behavior of reinforced concrete beams based on piecewise response surface scheme

•Random analysis method of RC beam is developed by combining MCS with piecewise RSM.•Bimodality probability density of deflections for cracked RC beam is simulated.•The mechanisms of the phenomenon of probability density were analyzed.•The evaluation from bimodal distribution to unimodal distribution was discussed.

To save the computational efforts of Monte Carlo simulation together with nonlinear finite element method, the analysis framework combining the response surface method and Monte Carlo simulation is usually adopted to investigate the stochastic nonlinear behavior of structures. It is found that the traditional response surface method could not describe stochastic behavior of cracked concrete beams. In order to overcome the discontinuity caused by cracking nonlinearity, a scheme by introducing a piecewise response surface is proposed in this paper. This scheme is evaluated by the stochastic analysis of several concrete beams. The comparison between the proposed method and some traditional methods, including Monte Carlo simulation and Monte Carlo simulation with traditional response surface, shows that the proposed method could well depict the stochastic behavior of concrete beams. Finally, the probability density evolution of concrete beams from short-term deflection to a long-term deflection is analyzed.