The Stiffness Matrix of the Fixed-End Composite Frame Element
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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 o...f a
composite section is developed. The results of the two approaches are compared in the
numerical example.