Numerical modelling of concrete beams at serviceability conditions with a discrete crack approach and noniterative solution-finding algorithms

Abstract

This paper describes the development and validation of a comprehensive numerical model enabling the simulation of reinforced concrete beams at serviceability conditions using a discrete crack approach. The highly non-linear behaviour introduced by the different material models and the many cracks localising and propagating within the member pose a challenging task to classic iterative solvers, which often fail to converge. This limitation is solved with a non-iterative solution-finding algorithm, in which a total approach was used to overcome critical bifurcation points. The finite element model was validated using experimental data concerning lightweight aggregate concrete beams under flexural loading. The model was shown to properly simulate both overall and localised features of the structural response, including curvature, crack openings and crack patterns. The model was used to carry out a numerical study on the role of the longitudinal reinforcement ratio and crack widths in reinforced concrete beams. It was observed that the total crack openings along the member seem to remain nearly independent of the tensile reinforcement for ratios above 2.5% and the same level of strength.