A Short-term Deformation Analysis Method of Flexural Reinforced Concrete Members

The deformation analysis of cracked reinforced concrete (RC) members is not straightforward and often controversial. The main difficulties arise from the complex structure of concrete matrix, different mechanical properties of concrete and reinforcement, the creep and shrinkage of concrete and tension stiffening. The latter effect is related to intact concrete and reinforcement interaction between cracks. Tension stiffening effect has a significant influence on the results of a shortterm deformation analysis of RC members. The present research is aimed at deriving tension-stiffening relationship in accordance with the provisions of the Eurocode 2 technique. Using the inverse technique proposed by the second author, tension-stiffening constitutive laws were derived from the moment-curvature diagrams of RC beams calculated by Eurocode 2. The diagrams were calculated for a number of RC sections having a different amount of tensile reinforcement, the grade of concrete, effective depth and a modulus of steel elasticity. For the above model parameters, 450 moment-curvature diagrams were generated. For each of them, tension-stiffening relationships were obtained. The performed regression analysis led to analytical tension – stiffening relationship, which takes into account the reinforcement ratio, modulus ratio and concrete grade. A simplified short-term deformation analysis method of flexural RC members has been also proposed. This method is based on a bi-linear moment-curvature diagram: elastic and cracked parts. For the cracked part of the moment-curvature diagram, coefficient γ was introduced, which deals with the degradation of stiffness after cracking. An analytical expression was proposed for calculating coefficient γ, which takes into account the effective depth of the beam, reinforcement ratio and modulus ratio. A statistical verification of the proposed models has shown that a good agreement between calculated and experimental results was obtained at service loadings.