P - δ Effects on the Plastic Region of RC Bridge Columns: Closed-Form Solution

A closed-form solution to the effect of member deformations (δ) on the inelastic response of RC bridge columns is presented. The formulation is based on an equivalent elastic structure with a constant flexural stiffness for the cracked RC section that enables the solution to be independent of the structural global displacements (Δ). The ability of the proposed solution for predicting moment, curvature, and displacement profiles in RC columns is demonstrated and verified against experimental data from four half-scale test columns. The closed-form solution led to the identification of a dimensionless slenderness parameter that measures the susceptibility of RC columns to second-order effects. Simplified formulas for the spread of the plastic region (Lpr) and the magnitude of P-δ moment are proposed for use in seismic design. The design formulas, derived from the mechanics-based solution, are shown to be able to predict experimental data on the P-δ effects with satisfactory accuracy.