Calculation of the Effective Section of Cracked Concrete Beams Based on Gradual Strain Distributions

Concrete loses its tensile resistance at crack interfaces in reinforced concrete beams but still can carry tension between two cracks, which is defined as tension stiffening. To model the stiffening effects on structural serviceability, an effective tension section was introduced based on homogenized average strain distributions in existing methods. However, the strain distribution of concrete gradually changes near the cracks. To calculate the effective section exactly, an alternative method is proposed by considering the gradual distribution. First, the gradual change in the tensile strains is modeled based on the crack location and depth and the internal force equilibrium is adopted to find a solution to the strain distribution along the height of cross sections. Then, based on the neutral axis and tensile force of the distribution, the area of the effective tension section is calculated. The effectiveness of the proposed method was validated using experimental data from reinforced concrete beams. The results show that the concrete strains of the cross sections changed from the obviously nonlinear distribution to approximately linear distribution according to the distance to cracks, which caused the neutral axes and effective tension section to change with the cracking pattern. The effective section reached its local minimum at every crack and the minimum would become smaller the deeper the crack. The proposed method could predict these changeable distributions and effective sections without introducing any additional simplification. The effective section could be used to assess the instantaneous deflection of the beams, whose calculated results were in good agreement with the experimental data but its application to the prediction of long-term responses should be further studied. Keywords: cracks; deflection; effective tension section; reinforced concrete beams; strain distribution.