Load Deflection Analysis of Beam-Column using Total Potential Energy (TPE) Principle

A modified TPE approach to perform finite deflection analysis of slender beam-column elements has been developed. The proposed approach utilizes the energy principal method and takes into account the geometric nonlinearity including the effects of axial force on bending stiffness, the end moments on axial stiffness (bowing), and the initial imperfection. A new equation of the deformation curve that approaches to the exact solution is used in the strain-displacement relation to obtain a more accurate beam-column response. The derived formulation of displacement of the beam-column under axial compressive load with single curvature bowing is presented with initial imperfection and different end eccentricities. The Green strain tensor equation is developed to consider higher-order bowing term. Nonlinear analysis of central finite deflection is carried out using Newton-Raphson iteration that includes high order terms of total potential energy (TPE). The beam-column stability is verified by computing the hessian determinant of the total potential energy. The validity of the new approach is established by comparing the numerical results obtained using the proposed equations against data previously published in the literature. Outputs from the analysis indicate that the proposed approach is capable of capturing the deflection of the beam-column with enhanced accuracy, ranging from 8.5% for e = 0.025 and up to 23.5% when e = 0.125.