Analysis of equivalent substitution of rectangular stress block for nonlinear stress diagram

Abstract

This article deals with the analysis of equivalency of the substitution of rectangular stress block for nonlinear stress diagram with descending branch for the calculation of flexural, eccentrically compressed and eccentrically tensioned reinforced concrete members of rectangular cross-section. The method for equivalent substitution of these diagrams is proposed. Analytical relationships of area and its centre for the nonlinear diagram with descending branch are presented. Coefficients for equivalent  substitution of the said diagrams for the standard concrete strength classes are determined and given. It gives the opportunity to design reinforced concrete members  using rectangular stress block model. Substitution of the diagrams applied in EC2 and in STR 2.05.05:2005 is compared with the equivalent substitution of rectangular stress diagram for nonlinear stress diagram with descending branch. It is shown that in STR 2.05.05:2005 description of the ratio between the depth of the rectangular diagram and that of the equivalent nonlinear one with descending branch is very poor. An explicit analytical relationship for this ratio and its linear approximation in respect to the concrete characteristic and design strengths are presented in this article as well.