Keywords: composite beams, partial interaction, curved beams, geometric non-linearity, moving loads, dynamic analysis.

Composite steel and concrete beams which are curved in-plan are used very widely in highway bridges. In deference to curved steel bridges (e.g. Nevling et al. [1]), comparatively few studies have been reported on curved composite beams, and in particular on their dynamic analysis which is required in order to accurately compute the effects of moving loads. The behaviour of composite beams is influenced significantly by the flexibility of the shear connection. Several studies have been reported in the literature that take the longitudinal partial interaction into account in composite straight beams. However, it has been shown (Erkmen and Bradford [2]) that adequate modelling of composite curved beams needs to account for the partial interaction in horizontal direction as well as in longitudinal direction. It is also important to consider geometric non-linearity in order to accurately predict the response of curved beams, even under service loads, as noted by Pi and Trahair [3] and Erkmen and Bradford [4].

In this paper, a total Lagrangian finite element formulation for the elastic dynamic analysis of steel-concrete composite members that are curved in-plan is developed. The kinematic assumptions as well as the derivation of the weak form of the equilibrium equations are explained in the paper. The step-by-step solution procedure of the non-linear equilibrium equations is also explained. The formulation includes the effects of geometric non-linearity as well as partial interaction in the longitudinal and horizontal direction between the steel and concrete components. A linear finite element is also derived by omitting the second order effects due to geometric non-linearity for comparison purposes.

Examples are provided to illustrate the significant effects of partial interaction as well as geometric non-linearity and initial curvature on the behaviour of curved composite beams subjected to moving loads. Some special cases are compared with the analytical solutions of Tan and Shore [5].

[1]

D. Nevling, D. Linzell, J. Laman, "Examination of level of analysis accuracy for curved I-girder bridges through comparisons to field data", Journal of Bridge Engineering ASCE, 11(2), 160-168, 2006. doi:10.1061/(ASCE)1084-0702(2006)11:2(160)

[2]

R.E. Erkmen, M.A. Bradford, "Non-linear elastic analysis of composite beams curved in-plan", submitted for publication.

[3]

Y-L. Pi, N.S. Trahair, "Non-linear elastic behavior of I-beams curved in plan", Journal of Structural Engineering ASCE, 123(9), 1201-1209, 1997. doi:10.1061/(ASCE)0733-9445(1997)123:9(1201)

[4]

R.E. Erkmen, M.A. Bradford, "Non-linear elasto-dynamic analysis of I-beams curved in-plan", International Journal of Structural Stability and Dynamics (in press).

[5]

C.P. Tan, S. Shore, "Dynamic response of a horizontally curved bridge", Journal of Structural Division ASCE, 94(3), 760-781, 1968.

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