Graph Algorithm for considering Second-Order Effects of Rc Ring-Section Columns

• Published in: Wireless communications and mobile computing Vol. 2022; pp. 1 - 11
• Main Authors: Yao, Kaicheng, He, Yingcheng, Wu, Shilong, Zhou, Donghua
• Format: Journal Article
• Language: English
• Published: Oxford Hindawi 10.06.2022; Hindawi Limited
• Subjects: Algorithms; Columns (structural); Concrete; Equilibrium equations; Iterative methods; Iterative solution; Mathematical analysis; Nomograms; Nonlinearity; Reinforcement; Tensile strength
• ISSN: 1530-8669; 1530-8677
• DOI: 10.1155/2022/3409368

The calculation of ring-section reinforcement considering the second-order effect has triple nonlinearity, that is, the nonlinearity of material, geometry and section-width variation, it’s very difficult to calculate. In order to provide a fast calculation tool for the design work, a simplified model of the ultimate curvature of the ring-section column is proposed through calculation and analysis, then calculated the second-order eccentricity by the quadratic parabola hypothesis of the second-order deflection shape of the member, and finally the simplified n-mu second-order equilibrium equation has been obtained. The three-coordinate nomogram for calculation was drawn to further facilitate the design in the paper. The hand-calculated reinforcement of the ring-section column could be done only by making 4 auxiliary lines in the diagram, avoiding iterative solution of the transcendental equation. Because of the dimensionless derivation, this nomogram is multipurpose, it could solve the calculation problems of second-order reinforcement in the case of arbitrary section size and concrete grade of C15 ~ C50.