The analytical curvature distribution model of columns and mathematical solution for pushover analysis

Abstract

The acquisition of a flexural backbone curve for columns primarily relies on finite element analysis and experiments, of which the complexity and high cost are significant challenges. Hence, this study proposes an analytical curvature distribution model (CDM) along the full height of the column, which is the key point of formula derivation and theoretical solution of the column backbone curve. The proposed CDM is a piecewise function model composed of linear and quadratic functions, with the characteristics of continuity and differentiability at the intersection point. The deformation compatibility equations, equilibrium equations, and material constitutive equations based on the variables of CDM are constructed to form an equation system, the solution of which can be theoretically determined by an iterative algorithm. Furthermore, 155 test specimen columns of different materials, for example, reinforced concrete, high-strength reinforced concrete, and shape memory alloy are used to validate the proposed CDM and mathematical solutions of pushover analysis through three crucial indicators, that is, goodness of fit of backbone curve, ultimate displacement, and peak force, indicating strong practicability, high accuracy, and wider applicability. This theoretical method can be applied to deal with the key issues of interest during pushover analysis, that is, predicting the flexural backbone curves with different materials, determining the curvature distribution throughout the entire process of pushover analysis, and characterizing the evolution process of the plastic region.