Analytical Modeling of Crack Widths and Cracking Loads in Structural RC Members

Abstract

Crack width is a major performance criterion in reinforced-concrete structures, in general, and is of utmost importance in ensuring bridge performance, in particular. A reliable theory-based method is required to assess crack widths and gain insight into their dependence on material, geometry, and loading parameters. A new, exact analytical method is proposed for a one-dimensional reinforced concrete element based on equilibrium, constitutive, and kinematic relationships, accounting for the geometrical and material behavior of the concrete and reinforcement. A linear interfacial bond stress slip is assumed to represents the small slips associated with the limited allowed crack width. Closed-form expressions have been developed and a wealth of information can be calculated immediately, such as the cracking load levels, the crack width dependence on the load level, the expected number of cracks, and the cracks spacing. The entire nonlinear force-displacement relationship of a cracked reinforced-concrete element may be depicted, demonstrating the tension-stiffening behavior that depends on the variations in the crack width throughout the loading history. Comparisons of the model with experimental data demonstrate very good agreement.