Numerical analysis of the relaxation of a bending moment, aroused over the support due to its settlement in a continuous composite steelconcrete beam, using integral equations of volterra

Abstract

The paper presents numerical analysis of the stress changes due to creep in statically indeterminate composite steel-concrete beam. For determining the relaxation of a bending moment, aroused over the support due to its settlement, in a continuous composite steel- concrete beam, with respect to time “t”, system of two independent Volterra integral equations of the second kind have been derived, on the basis of the theory of the viscoelastic body of Arutyunyan–Trost-Bažant. The mathematical model involves the equation of equilibrium, compatibility and constitutive relationship, i.e. an elastic law for the steel part and an integral-type creep law of Boltzmann – Volterra for the concrete part. Numerical method, which makes use of linear approximation of the singular kernal function in the integral equation. Example with the model proposed is investigated. The creep functions is suggested by the “CEB-FIP” models code 2010. The elastic modulus of concrete Ec(t) is assumed to be constant in time „t‟.