Strain Energy-Based Calculation of Cracking Loads in Reinforced Concrete Members

The traditional methods for calculating the cracking loads of concrete members require the introduction of a semi-empirical inelastic influence coefficient of the section resistance moment to reflect the influence of sectional inelastic deformation development, and its value needs to be corrected according to the sectional characteristics and material properties. In contrast, emerging machine learning models for predicting the cracking loads of concrete members lack clear mechanical mechanisms, making their predictions difficult to interpret. Based on this, member cracking is reinterpreted as a change in the macroscopic performance of the member, and the strain energy variation before and after the fracture of plain concrete axially tensioned members is analyzed. A viewpoint is proposed that employs the incremental change in strain energy to characterize member cracking. With the internal tensile deformation representing the total strain energy of the member, a calculation method for the member cracking loads is established based on the critical condition that the second-order differential of this strain energy with respect to the member deformation equals zero. This method is applicable to both axially tensioned and flexural members of steel- and FRP-reinforced concrete that primarily undergo axial tensile deformation. The method is applied to analyze the cracking of axially tensioned and flexural members under different concrete strength grades, reinforcement types, and reinforcement ratios. It successfully explains the mechanism whereby the strain in the tension zone at member cracking exceeds the material ultimate tensile strain. Calculations verified against experimental data from four sets of tests on steel- or FRP-reinforced concrete beams demonstrate that the proposed method can be accurately applied to both normal- and high-strength concrete, as well as to both steel and FRP reinforcement, with a relative error of only 1% and a coefficient of variation of 0.12.