The Stiffness Matrix of the Fixed-End Composite Frame Element

Abstract

The displacement method of frame analysis involves determination of the element stiffness matrix. In the paper, the stiffness matrix of the fixed-end composite frame element (type “k”) is derived. In general, the composite section consists of concrete part, steel section, reinforcing and prestressing steel. Concrete is considered as an aging, linear viscoelastic material. The relaxation of the prestressing steel is taken into account. The derived expressions can be used with any creep function and, also, for elements with variable cross-sections. The derivation of the element stiffness matrix follows two different approaches. The first approach is based on the integral stress-strain relation for concrete. The linear integral operators are used. In the second approach, the element flexibility matrix and the resisting force vector are determined through the numerical integration of the cross- section deformations. The class of cross-sections which accounts for viscous effects of a composite section is developed. The results of the two approaches are compared in the numerical example.