Reinforced concrete is the most widely used composite material in civil engineering. It combines the advantageous mechanical properties of concrete in compression and steel in tension to provide the staple ingredient for a variety of structures including the widely used framework-type structures designed to carry the loading primarily by resisting the effects of bending. In the process, the reinforcement bars normally become stretched while the adjoining concrete experiences fully developed cracking or sizeable micro-cracked regions with limited resistance to tension (see e.g. Bažant and Cedolin, 2003). The so-called tension-stiffening effect is the principal load-bearing mechanism in reinforced-concrete structures once cracking of concrete in tension and subsequent slippage of the reinforcement bars with respect to the surrounding concrete take place (see e.g. Stramandinoli and La Rovere, 2008). In this way the tensile stresses in the reinforcement at the crack positions gradually become transfered to the concrete between the cracks. The tension-stiffening effect may be mathematically modelled in many different ways, from highly complex models involving fully spatial concrete behaviour (see e.g. Ožbolt and Bažant, 1992), non-linear damage properties of concrete (see e.g. Marfia et al., 2004), isotropic and kinematic hardening of reinforcement steel (see e.g. Marfia et al., 2004) and non-linear bond-slip relationship (see e.g. Ožbolt et al., 2002) including the detailed effects of the reinforcing bar rib resistance (see e.g. Wang and Liu, 2006) to fairly simple yet sufficiently accurate models in which these effects are lumped together (see e.g. Stramandinoli and La Rovere, 2008). In this work the tension-stiffening effect is modelled on the basis of the experimental results reported in literature, which provide the force-extension relationships for a uniaxially loaded reinforced-concrete specimen. From these results, an average strain of the specimen may be easily deduced and used to define the constitutive relationship needed for the numerical analysis. In this way, the complex issues of crack initiation and growth as well as the stress transfer from the reinforcement to the surrounding concrete are effectively by-passed. This model is applied to beam-like structures in which, owing to the standard kinematic hypothesis of cross sections remaining planar, a relatively fast computational procedure is expected. The strain measures in the beam element are related to the displacement and rotation functions using the geometrically exact Reissner’s beam model (Reissner, 1972), which in the case of geometrically linear analysis reduces to the standard Timoshenko beam model. These strain measures are then considered as the average strains along the beam element for which the resulting axial force is deduced from the known experimental results for a suitably chosen effective area of the reinforced-concrete beam in bending. The approach proposed here results in a very simple model for the analysis of reinforced-concrete beams in which the analysis of the complex issues of crack initiation and growth as well as the stress transfer from the reinfocement to the surrounding concrete is effectively avoided. As the next step, a more refined model will be proposed in which a suitable non-linear bond-slip relationship will be taken to govern the stress transfer upon crack occurrence as predicted by the model codes. |