Time-Dependent Differential Equation of PSC Flexural Member with Constant Eccentricity

직선배치 긴장재를 갖는 PSC 휨 부재의 시간종속적 지배미분방정식

A governing differential equation (GDE) of PSC flexural member with constant eccentricity considering the long-term losses including concrete creep, shrinkage, and PS steel relaxation is derived based on the two approaches. The first approach utilizes the force and moment equilibrium equations derived based on the geometry of strains of the uniform and curvature strains while the second one utilizes the principle of minimum total potential energy formulation. The identity of the two GDE's is verified by comparing the coefficients consisting of the GDE's. The boundary conditions resulting from the functional analysis of the variational calculus are investigated. Rayleigh-Ritz method provides a way to get the explicit form of the continuous deflection function in which the total potential energy is minimized with respect to the unknown coefficients consisting of the trial functions. As a closure, the analytically calculated results are compared with the experiments and show good agreements.