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.
Highlights
When a slender concrete element with central longitudinal rebar is subjected to tensile loads at the rebar ends, the load is carried by both the concrete element and the rebar
Tension-stiffening is commonly related to the one-dimensional (1D) tensile behavior of a Reinforced Concrete CrackingReinforced concrete (RC) element that is composed of a concrete slender rod having a constant cross-section and central steel rebar along its longitudinal axis, where the rebar is subjected to equal tensile forces acting at its ends
The variable term is larger than unity and may be interpreted as an amplification factor with larger effect at shorter values of α (Figure 5). This means that for a slender Uniaxial Reinforced Concrete Element (URCE) of length 2L, the second cracking load calculated for half-length L/2 will not differ much from the first cracking load that is calculated for halflength L, and at shorter sub-elements the amplification parameter will determine a higher cracking load
Summary
Reinforced concrete (RC) is commonly used in civil engineering structures. As hardened concrete is relatively weak and brittle, it cracks under the action of a significant tensile stress. The rebars provide ductility to the structural element under tension and control cracking. Increasing tensile load produces higher tensile stresses in concrete and causes it to crack. Variations in tensile stress along the element determine the location of new cracks and the corresponding cracking loads. This affects the crack width and the structural member’s axial stiffness, which decreases with an increasing number of cracks. At each cracking load level, stress redistribution occurs, and a new stress profile is formed along the concrete element and the rebar. The maximum allowable crack width depends on the environmental conditions and the risk of corrosion attack [2]. Infrastructures 2022, 7, 40 attacks lead to smaller maximum allowable crack width. As a rule of thumb, this should not exceed 0.2–0.3 mm
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