General Mathematical Model for Analysing the Bending Behaviour of Rectangular Concrete Beams with Steel, Fibre-Reinforced Polymers (FRP) and Hybrid FRP–Steel Reinforcements

The design guidelines available in building codes for steel and fibre reinforced polymer (FRP) reinforced concrete (RC) beams have been developed on the basis of empirical models. While these models are successfully used for practical purposes, they require continuous improvements with more experimental data. This paper aims to develop a general mathematical model derived from the intrinsic material properties of concrete and certain reinforcements to analyse the bending behaviour of reinforced concrete beams. The proposed model takes into account the effects of non-linearity and ductility on the real behaviour of concrete under compression as well as the concrete tension stiffening. The model focused on analysing the flexural behaviour of rectangular steel, FRP and hybrid FRP–steel RC beams, using the moment–curvature relationship. A general static equilibrium equation was developed and mathematically solved with precise methods to establish a moment–curvature relationship. The effective flexural stiffness (EFS) is therefore calculated by the slope of the moment–curvature diagram, and then the load–deflection response is immediately deduced according to the loading conditions. The present model results were compared with numerous test data reported by various researchers. The comparisons reveal a good accuracy for predicting the EFS and load–deflection response for either steel, FRP, and hybrid reinforced concrete beams, with an error average less than 10%.

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