Analytical Solutions for Elevated-Temperature Behavior of Composite Beams with Partial Interaction

Abstract

This paper presents novel analytical solutions to describe the behavior of composite steel–concrete beams with partial interaction at elevated temperatures. The analytical model is derived by means of the principle of virtual work and, based on its strong form, solutions are derived in closed form for the cases of a simply supported beam and of a propped cantilever subjected to a generic regime of temperature. The materials are assumed to behave in a linear fashion, but their elastic moduli are modified to account for the degradation which the materials exhibit at elevated temperatures. The accuracy of the proposed solutions is tested against the results obtained by means of a finite-element method, as no directly applicable solutions appear to be available in the literature with which to validate the formulation. A refined 16 degrees of freedom finite-element is selected for this purpose, and its derivation and modification are outlined briefly. Applications are proposed to illustrate the ease of use of the analytical solutions to gain a better insight into the fundamental structural response, and to provide a convenient design tool. For structural design, the use of a simplified integration method to account for the thermal effects and for the material degradation has been considered in order to circumvent the complex calculation of section properties that can arise when the degraded elastic moduli and induced thermal gradients vary across the cross section. This simplification is valid in general, but it leads to slight underestimations of the structural deformation state at elevated temperatures for high levels of shear connection. A second application of the theory is given, in which the stress state due to thermal effects is superimposed with that due to external sustained loading. The load level to attain first yield of the member is shown to depend significantly on the stiffness of the shear connection.