Keywords: slip, steel and concrete composite beams, flexible shear stud, partial shear connection, linear partial interaction theory.

In this paper, a numerical model that can consider the slip effect between the steel beam and concrete slab in a steel-concrete composite beam is proposed. A composite steel and concrete structural member consists of a concrete slab connected by means of shear connectors to a steel beam, and the two components act as an integrated unit in spite of very different physical and mechanical behaviours. In the design of the composite beams, the usual practice was to provide sufficient shear connection between the steel beam and the concrete slab for the effects of longitudinal slip and of uplift to be negligible. But in the partially composite beams that have flexible shear studs, the connection deformability and the consequent loss of planarity of the composite sections cannot be neglected in the analysis and design of the structures.

To develop the calculation method for the behaviours described above, extensive studies based on experimental and analytical approaches have been carried out concerning the strength and deflection of composite beams with partial shear connection. Many the previous methods give an exact solution and are very useful for analysing partially composite beams, but they have some restrictions in application[1,2,3,4]. Since these methods are greatly affected by the boundary conditions, only the symmetric structures with zero slip at midspan can be analysed. To overcome those limitations and to account for the slip effect in the partially composite beams, a few numerical models have been proposed. Gattesco[5] used a double node to represent the relative slip between the steel beam and concrete slab. This requirement leads not only to a considerable increase in the number of degrees of freedom, but also to a complexity in mesh definition.

In this paper, a numerical model that can consider the slip effect between the steel beam and concrete slab without taking the double nodes in one composite beam element is proposed. A linear partial interaction theory is adopted in formulation, and the governing equations at an element are derived on the basis of continuous analytical solutions. In order to construct the governing equation, the following simplified basic assumptions have been made: (1) the horizontal force at both far ends of structure is zero; (2) the distribution of the horizontal force and corresponding relative slip is continuous along the span length; (3) the structure is subdivided into some elements and the moment at each element is linearly distributed; (4) the moment distribution is same for the partial connection and full connection[4]. After constructing the transfer matrix relation for a total structure with the compatibility conditions and equilibrium equations at each node, the nodal forces and displacements related to the slip behaviour are calculated by the successive application of the governing equations for each element.

The favourable comparisons between the numerical and the analytical results available in the literature allow the statement that the proposed model is capable of tracing the detailed response of partially composite beam. Many other numerical procedures[2,6,7] have restrictions in the numerical modelling of multi-span continuous composite beams. However, the proposed model which uses the transfer matrix relation can yield significant savings in the number of nodes needed to account for the effect of slip and gives good applicability to a multi-span continuous beam subjected to many kinds of lateral loads. Accordingly, when a structural behaviour for the shear connectors is well defined through many experimental studies, the slip behaviour of partially composite beams can be simulated more effectively, and an improved horizontal shear design can be achieved by using the model proposed in this study.

1

Bradford, M.A., Gilbert, R.I., "Composite beams with partial interaction under service loads", Journal of Structural Engineering, ASCE, 118(10), 1871-1883,1992. doi:10.1061/(ASCE)0733-9445(1992)118:7(1871)

2

Dezi, L., Ianni, C., Tarantino, A.M., "Simplified creep analysis of composite beams with flexible connectors", Journal of Structural Engineering, ASCE, 119(5), 1484-1497, 1993. doi:10.1061/(ASCE)0733-9445(1993)119:5(1484)

3

Jasim, N.A., "Deflections of partially composite beams with linear connector density", Journal of Constructional Steel Research, 49, 241-254, 1999. doi:10.1016/S0143-974X(98)00206-5

4

Jasim, N.A., Atalla, A., "Deflections of partially composite continuous beams: A simple approach", Journal of Constructional Steel Research, 49, 291-301, 1999. doi:10.1016/S0143-974X(98)00001-7

5

Gattesco, N., "Analytical modelling of non-linear behaviour of composite beams with deformable connection", Journal of Constructional Steel Research, 52, 195-218, 1999. doi:10.1016/S0143-974X(99)00026-7

6

Oehlers, D.J., Bradford, M., "Composite steel and concrete structural members", Pergamon, New York, 1995.

7

Johnson, R.P., Molenstra, IR.N., "Partial shear connection in composite beams for buildings", Proc. Instn Civ. Engrs Part 2, 91, Dec., 679-704, 1991. doi:10.1680/iicep.1991.17485

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