Mathematical Models for Tensile Resistance Capacities of Concrete

Although the uniaxial tensile strength ($f_t$) of concrete is one of the most essential properties in designing and analyzing the tensile performance of a concrete member, a rational consensus to assess it is still lacking because of experimental difficulties. The objective of the present study is to generalize $f_t$ through mathematical analysis based on the plasticity of concrete. The principle of equivalent resultant tensile forces at failure planes is introduced to straightforwardly determine the splitting tensile strength ($f_{sp}$) and modulus of rupture ($f_r$) from $f_t$. The accuracy and reliability of the proposed equations are confirmed at different ranges of the compressive strength and unit weight of concrete by comparing with test data, including 219, 674, and 242 data sets for uniaxial tension tests, splitting tension tests, and flexural tests, respectively. Thus, the present mathematical approaches proved the significance of considering the concrete unit weight and maximum aggregate size in predicting the tensile resistance capacities of the concrete. However, with the variations of the compressive strength and unit weight of concrete, the empirical equations recommended in previous studies and code provisions are insufficient.