SELECTION OF LONGITUDINAL TENSILE REINFORCEMENT OF REINFORCED CONCRETE BEAMS, TAKING INTO ACCOUNT THE ACTUAL WORK OF CONCRETE AND REINFORCEMENT

Abstract

The article presents the results of theoretical studies of the possibility of selecting a longitudinal tensioned reinforcement of a reinforced concrete beam without using the method of successive approximations. The method of selection with the help of the computer environment MathCAD is offered.

In connection with the adoption of new design standards for reinforced concrete structures [1], [2], there is a need to develop a methodology for calculating them, taking into account the actual work of concrete and reinforcement. This will allow more adequately reflect in the calculated models the actual processes of work under load, occurring in buildings and structures.

The method is based on the use of a system of equilibrium equations for an infinitely small element of a reinforced concrete beam.

Based on the maximum completeness of the stress diagram in the concrete of the compressed zone, it is possible to solve algebraically such a system of equations, and on this basis, find the desired value of the cross-sectional area of the longitudinal working tensioned reinforcement. Such a problem leads to solving a second-degree algebraic equation with respect to the unknown height of the compressed zone of concrete.

In the case when the possibility of any completeness of the stress diagram in the concrete of the compressed zone is assumed, the above-described method cannot be used, since the relative deformation in the extreme compressed concrete fiber will be unknown. Due to the fact that the calculated parameters are expressed through these deformations in the form of a fifth degree polynomial [3], an algebraic solution of the system of equilibrium equations is almost impossible.

In this case, it becomes expedient to use the computer environment MathCAD, where using the operators Given and Find, one can solve systems of equations numerically.

The proposed approach can be used by design engineers in the calculation of reinforced concrete beams of buildings and structures.