Design Aids for Calculating Idealized Moment-Curvature Relationships of Circular Reinforced Concrete Bridge Columns

This manuscript first presents the development and then the implementation of simple design aids that allow bridge engineers to quickly estimate idealized moment–curvature relationships for circular concrete columns in compliance with current specifications by using a pocket calculator or a spreadsheet. The design aids were developed in a normalized domain so they are particularly convenient for preliminary stages of design when the engineer may want to know the nonlinear static (pushover) response of circular columns for selected reinforcement ratios (longitudinal and transverse) and axial load levels. The formulation is applicable to column diameters up to 2.44 m (8 ft), longitudinal reinforcement ratios ($\rho$) from 1% to 3%, spiral reinforcement ratios (${\rho }_s$) from 0.5% to 2.5%, nominal concrete compressive strengths ($f_c^{\prime }$) from 28 MPa (4 ksi) to 56 MPa (8 ksi), axial loads from $–0.5f_y\rho A_g$ (tension) to $0.5f_c^{\prime }{A}_g$ (compression), and grade 420 MPa (60 ksi) reinforcement. Application examples are presented to illustrate the use of the design aids and to validate the obtained results with commercially available software.