Keywords: composite beam, steel-concrete composite beam, shear connection, non-linear analysis, finite element method, mixed finite elements, limitation principles, Hu-Washizu functional, locking.

A composite beam model that accounts for the non-linear behaviour of materials and deformable shear connectors is very useful for an accurate and reliable description of the deformability and the ultimate behaviour of structures that are widely used in structural and bridge engineering (e.g. steel-concrete composite decks).

Different displacement beam elements based on the Newmark kinematical model [1] have been proposed [2,3,4] for the non-linear analysis of composite beams. Displacement finite elements have a simple formulation but their behaviour is not always satisfactory. Some elements are affected by locking problems when shear connection stiffness increases [5] and even if locking-free elements are adopted, a high number of DOF may be required for reliable results in non-linear analysis [4].

Models that attempt to overcome the limitations of the displacement-based formulations have been proposed. Salari et al. [6] and Salari and Spacone [7] adopted a finite element based on the force method (flexibility formulation). However in the flexibility formulation a not straightforward iterative procedure is needed to determinate the element state and difficulties arise in the selection of force interpolation functions. In view of the limits of the displacement formulation and the difficulties of the flexibility formulation, Ayoub and Filippou [8] and Ayoub [9] introduced a displacement-stress mixed element.

In this paper the authors propose a three fields mixed element, based on the Hu-Washizu variational principle, in order to evaluate its efficiency in comparison with locking free displacement elements with internal nodes. The mixed approach is adopted to obtain more accurate solutions in the non-linear range since the Hu-Washizu mixed formulation can be viewed as a stress recovery method [10].

Numerical applications are performed using as working example a steel-concrete two span continuous beam, a problem of practical interest representing a difficult test for composite beam elements, due to high slip gradient, strain localizations, slab cracking in the hogging region and concrete softening in the sagging regions. The comparisons between the established mixed element and the locking-free displacement element from which it is derived evidenced that the two elements perform in very similar way for what concerns the global behaviour and the local description of displacement and strain fields. Regarding the local description of the stress field, the mixed element permits a smoother representation of the axial force and bending moment with respect to the related displacement element, while discontinuities arise in the interface shear force trends. In addition the mixed element has a cumbersome formulation and requires longer computation times. If the locking-free displacement based element with richer shape functions [4] is used, more accurate descriptions of the global behaviour and of the interface shear force are obtained, while only slight irregularities occur in the axial force and bending moment under high load levels.

1

Newmark N.M., Siess C.P. and Viest I.M. Tests and analysis of composite beams with incomplete interaction. Proc. Soc. Exp. Stress Anal.; 9:1, 75-92, 1951.

2

Arizumi Y., Hamada S. and Kajita T. Elastic-plastic analysis of composite beams with incomplete interaction by finite element method. Comp. Struct. 14:5-6, 453-462, 1981. doi:10.1016/0045-7949(81)90065-1

3

Daniels B.J., Crisinel M. Composite slab behaviour and strength analysis. Part. I: calculation procedure. J. Struct. Engrg. ASCE 119:1, 16-35, 1993. doi:10.1061/(ASCE)0733-9445(1993)119:1(16)

4

Dall'Asta A., Zona A. Non-linear analysis of composite beams by a displacement approach. Proceedings of The Fifth International Conference on Computational Structures Technology, 6-8 September, Leuven, Belgium, vol. "Computational techniques for materials, composites and composite structures", 337-348. 2000. Accepted in a revised and extended form for publications on Computer and Structures. doi:10.4203/ccp.75.136

5

Dall'Asta A., Zona A. Locking in composite beams with weak shear connection. Technical Note n.264. Istituto di Scienza e Tecnica delle Costruzioni, University of Ancona, Italy, 2001.

6

Salari M.R., Spacone E., Shing P.B. and Frangopol D.M. Non-linear analysis of composite beams with deformable shear connectors. J. Struct. Engrg. ASCE 124:10, 1148-1158, 1998. doi:10.1061/(ASCE)0733-9445(1998)124:10(1148)

7

Salari M.R., Spacone E. Finite element formulations of one-dimensional elements with bond-slip. Engineering Structures, 23(7), 815-826, 2001. doi:10.1016/S0141-0296(00)00094-8

8

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

9

Ayoub A. A two-field mixed variational principle for partially connected composite beams. Finite Elements in Analysis and Design. 37, 929-959. 2001. doi:10.1016/S0168-874X(01)00076-2

10

Mota A., Abel J.F. On mixed finite element formulation and stress recovery techniques. International Journal for Numerical Methods in Engineering 47:1-3, 191-204, 2000. doi:10.1002/(SICI)1097-0207(20000110/30)47:1/3<191::AID-NME767>3.0.CO;2-S

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