Purpose: To calculate the bearing capacity of annular reinforced concrete (RC) columns, if the second-order effects of members under bending and axial forces are further considered, both the nominal curvature method and the nominal stiffness method in EC2 require iterative calculations. To obtain a non-iterative calculation method.Design/methodology/approach: The constitutive relationship of RC in EC2 is adopted, the known cross-sectional strain is used to determine the bearing capacity of the section, and the model column method is adopted to calculate the component’s second-order effect. The curvature distribution law of the equilibrium point of sectional resistance and external action is analysed, and the simplified formula for calculating the equilibrium curvature is proposed.Findings: Based on the above work, a nomogram is drawn to determine the bearing capacity of columns. Finally, the nomogram and numerical calculation results are compared through specific examples. The results show that the nomogram is very close to the numerical calculation and always leans towards safety. It can serve as a supplement to the code and provide a method for the design and verification of annular columns.Originality/value: A method for calculating the reinforcement of RC annular columns by hand.

Purpose: This paper aims to obtain a calculation method by hand without iteration.Design/methodology/approach: This paper adopts strains as known quantities to solve the internal forces and deformations of the section, simplifies the deflection curve of the column and obtains nomograms that can calculate the bearing capacity and reinforcement of circular reinforced concrete (RC) columns by hand.Findings: Nomograms include five variables: mechanical reinforcement ratio, relative normal force, dimensionless bending moment, slenderness ratio and ultimate dimensionless curvature. Nomograms corresponding to all classes of concrete have been drawn, and their dimensionless form makes them widely applicable. The calculation results of nomograms are compared and analysed with numerical calculation results, and the difference is within 5%, meeting the engineering requirements.Originality/value: Calculating the bearing capacity of compression bending components requires considering second-order effects. Therefore, the calculation of the bearing capacity of circular RC columns requires iterative calculation, as it includes dual nonlinearity of material and geometry, and the two are coupled with each other. To calculate the bearing capacity of the section adopting ordinary concrete, it is necessary to solve the transcendental equation iteratively. For high-strength concrete, it can only be solved by numerical integration. A fast calculation method by hand is proposed in this paper.

Calculating the second-order effect and reinforcement of reinforced concrete box section columns has geometric nonlinearity and material nonlinearity. It requires integration and iterative solutions and is inconvenient in practical applications; moreover, China’s “Code for Design of Concrete Structures” (GB 50010-2010) uses the same formula as that for rectangular sections when calculating geometric nonlinearity. To find out a calculation method by hand that is specific to box-shaped sections and does not require iterative procedures, the theoretical derivation is adopted and divided into two gradations: (1) in terms of cross-section: using strain as the known variable to solve the internal force, thus solving the calculation problem of the bearing capacity of the cross-section; (2) in terms of members, the model column method can be used to solve the calculation problem of second-order effects of members. Finally, nomograms that can calculate the second-order effect and reinforcement of columns without iterative calculation are drawn, which contain five parameters, namely first-order bending moment, axial force, curvature, slenderness ratio, and the mechanical ratio of reinforcement. One of the nomograms corresponds to the cross-section resistance, and the other corresponds to the balance of internal resistance and external effect. Compared with the GB 50010-2010, the differences in the total bending moment and reinforcement ratio are within 10% and 20%, respectively. Compared with the numerical calculation results, the remaining examples are within 10% under normal load conditions.