The hybrid approach in constitutive modelling of tension stiffening accounting for the shrinkage effect

Abstract

Shrinkage, restrained by reinforcement or structural supports, induces tensile stresses in the concrete that might significantly affect the cracking resistance and short-term deformations of reinforced concrete (RC) elements. Incorrect assessment of this effect might result in noticeable errors of constitutive modeling. Recently the authors proposed a methodology for eliminating the shrinkage effect from short-term moment-curvature and tension stiffening relationships. However, due to rather complex issues of convergence and numerical integration, this approach was difficult to apply in practice. To simplify the methodology, the authors introduce a new concept of tension stiffening, the hybrid approach. Similar to the reinforcement-attributed approach, it assumes that tension stiffening stresses act in the area equivalent to the area of reinforcement. As in the concrete-related concept, tension stiffening is attributed to the material having the ability to shrink. The constitutive modeling based on the hybrid concept has become straightforward and easily performed by hand that is illustrated using experimental data of RC beam tested by the authors.