Numerical stochastic analysis of RC tension bar cracking due to restrained thermal loading

• Cracking of reinforced concrete bars due to restrained thermal loading is analyzed.
• A nonlinear FEM model with spatially scattering material properties is applied.
• Results of the numerical analysis are compared to design codes and experiments.
• Mean crack width is considerably underestimated by current design codes.
• Design mean crack width limits underestimate maximum crack widths significantly.

Cracking of concrete has deteriorating effects on the behavior of reinforced concrete structures, which results for instance in stiffness reduction and increase of permeability. In general, it is assumed that the deterioration increases with increasing crack width and, thus, maximum crack width might be most critical. However, models and recommendations in design codes regarding the serviceability limit state are usually based on mean crack width. In this contribution, a model for tensile members based on the Finite Element Method is presented, which takes spatially scattering material properties into account. As a special loading case restrained thermal loading is considered. The model is validated based on comparison with experimental results and with an analytical model. As an example of application, the model is embedded in a Monte-Carlo simulation to predict the statistics of crack widths due to spatial scatter of concrete tensile strength and bond strength. Results are crack width distributions and characteristic statistical values like mean values, standard deviations and quantile values over the entire loading range. Besides the presentation of the methodology of determining statistical properties of crack widths, it is shown that mean and maximum crack widths might be underestimated by analytical models as recommended in current design codes.