Normal Sections Calculation of Bending Reinforced Concrete and Fiber Concrete Elements

Abstract

The basic principles of the normal sections calculation of reinforced concrete and fiber reinforced concrete bending elements are considered. In the article the power and deformation methods of calculation of reinforced concrete and fiber concrete elements of rectangular cross-section are presented. The deformation model of the calculation of reinforced concrete and fiber concrete elements is presented in the framework of the method of calculation resistance of the section. This method makes possible from the common methodological positions to perform calculations of reinforced concrete and fiber concrete elements. Namely, to select reinforcement and to determine the carring capacity. The proposed deformation model for calculating fiber concrete elements is based on generally accepted preconditions. A hypothesis of plane cross sections is accepted as fair. The deformation diagram of compressed concrete is described by a nonlinear function with established parametric points. Distribution of stresses in stretched concrete is taken rectangular with corresponding coefficients which are taken depending on the type of deformation diagram. Determination of the carring capacity of fiber concrete elements occurs under extreme deformation criteria. Two cases of destruction of the investigated elements are considered. The first case is the destruction due to the achievement of limiting deformations in the concrete of the compressed zone with the simultaneous achievement of the fluidity limit in the working reinforcement. The second case is the destruction due to the achievement of limiting deformations in the concrete of the compressed zone without reaching the fluidity limit in the working reinforcement. Both cases of calculation are reduced to one functional dependence. This avoids the delimitation of different calculation cases. The main no dimensional modifier is the mechanical coefficient of reinforcement. According to the developed method, examples of calculations of reinforced concrete, fiber reinforced concrete elements and fiber concrete elements with longitudinal reinforcement are executed. The possibility of a spread variant design of reinforced concrete and fiber concrete elements is shown.

Bending deflection reinforced concrete elements determination

“…The calculation results are given in Table 4. It displays that the deflections, calculated by formula (9), are not significantly deviating from the most accurate result, even at a load level of 1.0. It allows recommending such a method for calculating deflections for practical applications.…”

“…Consider the methods for calculating bending deflection reinforced concrete elements, which are based on the method of calculation resistance of reinforced concrete [9] and on the use of cross-section curvature. In this case, deflections are determined by the known expression Mora…”

“…Let us compare the beam deflections on two supports with a uniformly distributed load in two methods: the Simpson formula, as the most accurate, and formula (9). We will accept reinforcement class A400С, concrete С16/20 and reinforcement proportion: 0.05; 0.25; 0.5; 1.0; 2.0; 3.0 for load levels 0.6; 0.8; 1.0.…”

“…More precise calculation methods are in curvature usage to determine deflections. Reinforced concrete elements cross sections curvature is determined directly from the equilibrium equations, which are written taking into account nonlinear materials deformation diagrams or piecewise linear diagrams [8,9]. There are methods where a reinforced concrete beam is considered as a composite rod [10].…”