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.

Empirical Modeling of Transverse Displacements of Single-Sided Transversely Cracked Prismatic Tension Beams

“…Simultaneously with other studies, the development of appropriate computational models of cracked elements that support effective detection and identification was carried out. Although there are some analytical approaches [25,26], research has mainly focused on numerical models, where the finite element method has taken precedence. Different approaches to the derivation of the stiffness matrix and the corresponding load vector due to transverse loads can be found in many references, both for non-cracked uniform straight beams ( [27,28]) as well as for cracked multi-stepped beams and beams with linearly-varying heights [29,30].…”

A Modified Approach to the Mathematical Model of Crack with Pre-destruction Zones

“…At the same time, in contrast to Griffith's theory, this assumption leads to a differential equation, the solution of which generalizes relations obtained through the application of this theory. propagation via an ordinary second-order differential equation [9]. There are estimated parameters of crack width which are the main effectiveness criterion in ferroconcrete constructions and also are essential for bridge safety exploitation.…”