Keywords: composite, partial interaction, flexibility formulation, secant stiffness, material non-linearity.

Formulations of simple one-dimensional steel-concrete composite finite elements appear on face value to be almost trivial, but in reality this is not the case and their analysis is usually fraught with simplifying assumptions. This arises because of the coupling of the material non-linearities of the reinforced concrete slab, the steel joist and the shear connection between these two components. In response to the need for accurate but simple solutions, displacement-based, force-based and mixed finite elements have been developed and reported by many researchers. Although the displacement and force-based formulations have the same degree of approximation, for frame elements which are the focus of this paper, the force-based formulations lead to superior accuracy when compared with displacement-based formulations because of the exact fulfilment of the equilibrium equations [1,2].

Salari et al. [3] proposed a force-based element, where cubic interpolation functions are used to approximate the bond slip shear forces along the element. The formulation of the element, however, is rather complex and it does not satisfy the kinematic condition of shear slip continuity. Ayoub [4] developed a forced-based composite element, which takes advantage of a linear function for shear slip interpolation. The mixed formulation concept was adopted by Ayoub and Filipou [5].

The current paper presents the formulation of a novel force-based one-dimensional steel-concrete composite element that captures material non-linearities and partial shear interaction between the steel profile and the reinforced concrete slab. By decomposing the material total strain into its elastic and inelastic components, a total secant solution strategy based on a direct iterative scheme is introduced and the corresponding solution strategy is outlined. Exact force interpolation functions are employed to derive the element secant stiffness, and a direct iteration scheme consistent with this secant formulation is then presented. A composite Simpson integration scheme, together with piecewise interpolation of the slip strain along the element axis, is employed to calculate the slip forces along the element axis consistently.

The accuracy and efficiency of the formulation are verified by some numerical examples reported elsewhere in the literature, and it is shown that the formulation with just one element can lead to virtually closed form analytical results as long as the integrals in the formulation are calculated accurately. The formulation can underpin efficient analyses of complete composite frames, which hitherto are extremely problematic, with a focus on such issues as progressive collapse scenarios whose investigations are known to be laborious in terms of their computational time

1

I. Carol, J. Murcia, "Nonlinear time-dependent analysis of planar frames using an 'exact' formulation. I. Theory", Computers and Structures, 33, 79-87, 1989. doi:10.1016/0045-7949(89)90131-4

2

M.R. Salari, E. Spacone, "Analysis of steel-concrete composite frames with bond-slip", Journal of Structural Engineering, ASCE, 127, 1243-1250, 2001. doi:10.1061/(ASCE)0733-9445(2001)127:11(1243)

3

M.R. Salari, E. Spacone, P.B. Shing, D.M. Frangopol, "Nonlinear analysis of composite beams with deformable shear connectors", Journal of Structural Engineering, ASCE, 124, 1148-1158, 1998. doi:10.1061/(ASCE)0733-9445(1998)124:10(1148)

4

A. Ayoub, "A force-based model for composite steel-concrete beams with partial interaction", Journal of Constructional Steel Research, 61, 387-414, 2005. doi:10.1016/j.jcsr.2004.08.004

5

A. Ayoub, F.C. Filippou, "Mixed formulation of nonlinear steel-concrete composite beam element", Journal of Structural Engineering, ASCE, 126, 371-381, 2000. doi:10.1061/(ASCE)0733-9445(2000)126:3(371)

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