A new approach to quantification of residual flexural stiffness of reinforced concrete

Abstract

Residual stiffness of reinforced concrete elements is closely related with structural integrity of cracked sections. A plenty of various evaluation procedures, however, does not enable the comparative analysis of different reinforcement schemes, since they are tested in different manner. To solve this problem, a new quantification procedure of the tension stiffening effect is introduced. It employs a new testing layout designed with the purpose to form multiple cracks in a small laboratory specimen. This enables to reduce scatter of the results due to the crack formation peculiarities. The corresponding analytical model, representing the average equivalent stress-strain behaviour of the tensile concrete, is proposed. The model is based on the following simplifications: smeared crack approach; linear strain distribution within the section depth; elastic behaviour of reinforcement and compressive concrete; and rectangular distribution of stresses in the tensile concrete. The latter assumption enables obtaining a closed-form analytical solution of the constitutive modelling problem. That makes the analysis results independent on the loading history: the analysis is performed in a uniform manner for the cases of short-term, sustained, or cyclic load applications. Furthermore, the proposed methodology could be acceptable for estimating residual stiffness of elements with various reinforcement combinations. The application of the proposed technique is illustrated experimentally. Several specimens with composite reinforcement are subjected to monotonic and cyclic load patterns.