THE PROBABILITY DENSITY EVOLUTION OF TIME-VARIANT DEFLECTION ABOUT REINFORCE CONCRETE BEAM

A piecewise response surface is suggested to reduce the error from the unsmooth response surface caused by the cracking of a reinforced concrete beam, by replacing the traditional single smooth response surface. The stochastic analysis model for the time-variant deflection of a reinforced concrete beam is performed with GL2000 model and nonlinear finite element method of reinforce concrete, by combing piecewise response surface with the Monte Carlo sampling. The probability density evolution of test reinforce concrete beams is analyzed by the present model. The bimodality of probability density curves is observed in results, when the applied loading is close to the cracking loading. Meanwhile, due to the effect of creep and shrinkage of concrete, the bimodal distribution transforms into unimodal distribution gradually, as the loading time goes on.