Assessing the Instantaneous Stiffness of Cracked Reinforced Concrete Beams Based on a Gradual Change in Strain Distributions

Abstract

Concrete cracking causes a gradual change in strain distributions along the cross section height of reinforced concrete beams, which will finally affect their instantaneous stiffness. A method for assessing the stiffness is proposed based on the gradual change, which is considered through modeling different strain distributions for key sections in cracked regions. Internal force equilibria are adopted to find a solution to top strains and neutral axes in the models, and then the inertias of the key sections are calculated to assess the beam stiffness. The proposed method has been validated using experimental results obtained from tests on five reinforced concrete beams. The predicted stiffness and displacements are shown to provide a good agreement with experimental data. The instantaneous stiffness is proven to greatly depend on the crack number and depth. This dependence can be exactly reflected by the proposed method through simulating the gradual change in concrete strain distributions.