Theoretical Method for Calculating the Second-Order Effect and Reinforcement of Reinforced Concrete Box Section Columns

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.