Approximation Model of the Method of Design Resistance of Reinforced Concrete for Bending Elements

Abstract

The paper considers approximation models of the method of design resistance of reinforced concrete for calculation of normal sections of bending reinforced concrete elements. It is proposed to use approximation dependences of two types—polynomial and linear. Both methods are based on the method of design resistance of reinforced concrete, which relies on universally accepted theory-based prerequisites and hypotheses. This method is based on the use of nonlinear deformation curves of concrete, Bernoulli hypothesis (the plane-sections hypothesis) is accepted as the correct one, and the extremum criterion for determining the bearing capacity (carrying force) based on a nonlinear deformation calculation model is used. The proposed techniques can massively simplify the calculation of bending reinforced concrete elements. They relieve from the necessity to use tables and perform complicated calculations with iteration methods, as it is intrinsic to the majority of existing methods. The possibility of determining on their basis both the bearing capacity (carrying force) and the relative height of the compressive zone of the concrete is shown in this article. The authors have conducted a check of the obtained approximation models of calculation on experimental samples of well-known researchers. The computational results indicate the computational accuracy, sufficient for practical calculations of the proposed methods. This paper presents the examples of determination of the carrying force and area of the effective reinforcement of normal sections of bending reinforced concrete elements by both offered methods. The proposed methods of calculating bending reinforced concrete elements can be widely used in design practice.