This study investigates the elastic response and stability of axially functionally graded (AFG) tapered pinned columns under centroidal and eccentric axial loading. The columns are modeled with a linearly varying Young’s modulus to capture AFG properties and a linearly tapered cross-section. Using Bernoulli–Euler beam theory, governing differential equations for elastic deflections and buckled mode shapes are derived, with numerical solutions obtained via the Runge–Kutta and shooting methods. The effects of key parameters—including modular ratio, taper ratio, eccentricity, and axial load—on elastic behavior and critical buckling loads are evaluated. For eccentric loading, initial rotation, maximum lateral deflection, and maximum bending moment are numerically examined. Results indicate that higher modular and taper ratios enhance stiffness and reduce deformations, while larger axial loads and end moments amplify responses. Slenderness and aspect ratio significantly influence maximum stress. For centroidal loading, critical buckling loads and stress distributions are assessed under varying material and cross-sectional properties. The findings provide a comprehensive framework for designing AFG tapered columns, ensuring structural stability and safe performance under diverse loading conditions.
Lee et al. (Sun,) studied this question.