DETERMINATION OF CRACK RESISTANCE OF PRESTRESSED REINFORCED CONCRETE BEAMS OF TRAPEZOIDAL CROSS-SECTION

Abstract

Beams of a trapezoidal cross-section with a wide upper edge with prestressed reinforcement combine positive qualities in terms of strength, crack resistance, deformability and resource saving, which allows them to cover significant spans of multi-storey buildings. To develop a method for calculating the moment of cracking in these structures, a nonlinear deformation model was adopted, which includes equilibrium equations, conditions for the linear distribution of relative deformations along the height of the element section, and refined deformation diagrams of concrete and reinforcement. Concrete state diagrams are assumed to be nonlinear without a falling branch. To describe the deformation diagrams of high-strength and conventional reinforcement, a universal dependence is adopted, consisting of one linear and two nonlinear equations, in which the calculation of individual parameters is performed using different formulas. For the initial stage of the crack formation process, a design scheme is presented, in accordance with which the necessary equations and ratios are drawn up in relation to the considered prestressed reinforced concrete beam of a trapezoidal cross-section. The purpose of the study, in addition to developing a calculation methodology, was also the development of an algorithm and a computer calculation program. To obtain and analyze the results, a numerical experiment was carried out, the results of which are presented in tabular form. Due to the fact that the calculation method was built without involving empirical dependencies, the possibility of its application to determine the crack resistance of prestressed reinforced concrete beams of trapezoidal cross-section for any class of concrete and reinforcement was confirmed.