DETERMINATION OF DEFLECTIONS OF U-SHAPED REINFORCED CONCRETE FRAMES

Abstract

This paper presents a methodology for calculating the deflections of reinforced concrete u-shaped frames designed according to the second group of limit states, based on the consideration of deformation characteristics of the material and external loading conditions. The deflections in u-shaped frames primarily depend on bending deformations, which can be determined by calculating the curvature. The curvature of the element is expressed through a formula that accounts for the impact of cracks on the stiffness of the material. The proposed algorithm includes several stages for determining the curvature in the "crack-free" and "cracked" states. These stages involve the calculation of the cracking moment, the internal stresses in the reinforcement, and the deformations in the concrete under tension and compression.

The methodology focuses on calculating the height of the compressed concrete zone, which is essential for ensuring the internal force equilibrium in the cross-section. The algorithm also involves an iterative process for refining the values of internal stresses and bending moments, ensuring accurate prediction of u-shaped frames deflections. The importance of determining the stiffness reduction factor, which accounts for the loss of stiffness due to cracks and material deformations, is emphasized in the paper. Additionally, the paper explores the effect of loading duration and repeated loads on the average deformation behavior of the u-shaped frame.

The methodology is based on the assumption of plane cross-sections and incorporates the use of polynomials to represent the stress-strain relationships for concrete in both tension and compression. The calculation procedure involves determining the initial deformation in the concrete, calculating the stresses in the reinforcement, and then calculating the cracking moment, followed by the deflection calculation using the generalized curvature.

The method also accounts for external loading conditions, including both short-term and long-term loads, by considering the influence of repeated load cycles and the duration of loading on the material’s behavior. The paper provides a detailed explanation of how to use these methods in practical applications, including the necessary formulas and steps for accurate deflection predictions. The proposed methodology ensures the reliable design of reinforced concrete structures, taking into account all relevant factors such as material properties, structural dimensions, and loading conditions. The calculations are consistent with modern standards, such as Eurocode, and can be applied to various types of reinforced concrete structures.