Keywords: analysis, composite, finite beam element, elasto-plastic, nonlinear, steel-concrete, three-dimensional.

This paper presents a three-dimensional finite beam element for the nonlinear elasto-plastic analysis of composite steel-concrete members. Most finite element models for the nonlinear analysis of composite steel-concrete members have considered nonlinearity of the materials, but have not included geometric nonlinearity as pointed out in references [1,2], and these models can be used with a sufficient number of elements for the small deformation analysis of composite members. However, it may be difficult to use these finite element models to predict the three dimensional nonlinear large deformation behaviour of composite steel-concrete members. In a three-dimensional nonlinear analysis of composite steel-concrete members, in addition to the nonlinearity of the component materials themselves, the partial interaction between the steel and concrete components and the geometric nonlinearity are also important and need to be considered. The total deformation was assumed to result from three successive motions: displacements of the shear centre and a finite rotation of the cross-section, a superimposed warping displacement and a superimposed relative slip displacement between the steel and concrete components in the deformed configuration. The nonlinear strain-displacement relationships including the relative slip between the steel and concrete components for several composite cross-sections were then derived based on the rotation matrix. In this formulation, early approximations were not made for the coupling between the displacements and twist rotations, so that higher order terms for the twist rotations are included in the nonlinear strains, and overstiff solutions resulting from superimposed rigid body motions are therefore eliminated.

The relative slip between the steel and concrete components arising from flexible bond at their interface was considered as an independent displacement in the formulation. Hence, each node of the element has eight degrees-of-freedom. The effects of nonlinearities and slipping on the deformations and strains in the steel and concrete components and so on the stress resultants (i.e. internal forces), stiffness and strength of the composite member are thus combined together in the formulation.

The constitutive model for the concrete component consists of a compressive yield surface to model the concrete response in the predominantly compressive states of stress, together with damaged elasticity modelling to represent cracks that have occurred at an integration point of the cross-section; the occurrence of cracks was defined by a crack detection failure surface and was considered as part of elasticity. On the other hand, the von Mises yield surface was used for the steel component. The associated flow rule and isotropic hardening rule were used for both steel and concrete components. The results showed that these constitutive models lead to an algorithm that is computationally efficient, and results that correlate well with independent experimental results for composite members.

1

Y.-L. Pi, M.A. Bradford, B. Uy, "Second order nonlinear inelastic analysis of composite steel-concrete members. I: theory", Journal of Structural Engineering, ASCE, 132(5), 751-761, 2006. doi:10.1061/(ASCE)0733-9445(2006)132:5(751)

2

Y.-L. Pi, M.A. Bradford, B. Uy, "Second order nonlinear inelastic analysis of composite steel-concrete members. II: applications", Journal of Structural Engineering, ASCE, 132(5), 762-771, 2006. doi:10.1061/(ASCE)0733-9445(2006)132:5(762)

purchase the full-text of this paper (price £20)

go to the previous paper
go to the next paper
return to the table of contents
return to the book description
purchase this book (price £140 +P&P)