APPROXIMATION OF DEFLECTIONS OF FLEXIBLE REINFORCED CONCRETE ELEMENTS IN CONDITIONS OF PURE BENDING

Abstract

At the current stage, scientists agree that the hysteresis curves of deflection in reinforced concrete beams, at critical points, occur as shown in Figure 1 [1]. The figure shows that beam elements are usually subjected to two deformations: bending and shear (Fig. 1). In the zone of pure bending, only bending deformation occurs, whereas in region 2, where both bending and shear exist, both bending and shear deformations occur. After cracking under the action of an external load, reinforced concrete elements demonstrate a behavior different from that described in the classical theory of elasticity.Setting the goal and tasks of research. The task is:  1) to demonstrate with the help of standardized methods [6] the possibility of describing the "load – deflection" dependences using linear approximations, in the conditions of pure bending, in the areas preceding the critical loads , Pcr , Py , Pmax ;Based on the given methodology and experimental results obtained by the researchers [3] (Table 2), we will establish deflections for linear approximation and make sure of the validity of the simplified (linear) approach for describing these processes.The given numerical values show that, with sufficient probability, the change in deflections of a flexural reinforced concrete element from the load level P, in different areas, can be described by a linear dependence.1. The presented results show that when applying a simplified model based on the mathematical apparatus provided in [6], it ispossible to describe the development of deflections by rectilinear sections, dividing them into certain stages (sections) that take into account the change in the stiffness of reinforced concrete elements during the formation and development of cracks in reinforced concrete elements2. This approach allows researchers to significantly simplify practical deformation calculations, and using a mathematicallyreliable tool. 3. The model is simple and logical, allows experimenters to analytically obtain critical values of the applied load.4. Indirectly, the presented linearized load-deflection model makes it possible to verify the correctness of the experimental dataand the obtained results.5. Based on the dependencies obtained under experimental conditions, it is easy to find the forces that affect similar structuresunder real operating conditions.