The analysis phase involved the development of a mathematical model, where the LR55 track system was treated as multilayer beams on elastic foundations. This model was solved following both analytical and numerical techniques. In the analytical approach, the governing set of fourth order differential equations for the system of infinite length subject to wheel load was solved using a classical calculus method. Accordingly, well defined mathematical expressions for the deflection, shear, bending moment and pressure distribution at any point along the track were obtained.

In the numerical approach, a one dimensional finite element method was adopted where the rail and concrete trough were represented by conventional beam elements with three degrees of freedom per node, whereas the pad and track base were characterised by linear elastic springs. The computer program developed for this purpose was incorporated with special features namely: nonlinearity due to track base separation (uplift), beams with internal hinges to simulate the construction joints at the ends of the concrete trough units, existence of a soft patch or cavity underneath the track system to simulate track base weakness or collapse, combined effect of vertical wheel load, horizontal traction load, track self weight and temperature variation.

At the design phase, a nonlinear optimisation technique based on the complex method [3,4] was employed to find the minimum area of a pre-tensioned prestressed concrete trough section satisfying the serviceability and ultimate states as per BS 8110 for the most critical loading and boundary conditions.

The mathematical model was then validated experimentally through a series of static non-destructive tests on a full-scale 6m long LR55 tram track model including the case of 1m collapsed foundation simulation. The results obtained from these experiments compared well with the theoretical solution. The experimental work also ensured the safety of the theoretical design of the LR55 track system as no sign of failure occurred to any of the track components when the track model was subjected to a maximum service load around 100kN [5].

1

L. Lesley, "A New LRT Track System", Proceedings of Light Rail 89 Conference, Bristol, UK, Nov, 205-212, 1989.

2

L. Lesley, "Light Rail Transit Development in the UK", Rail Engineering International, 22(3), 2-4, 1993.

3

M.J. Box, "A New Method of Constrained Optimisation and a Comparison with Other Methods", Computer Journal, 8, 42-52, 1965.

4

M.I. Haque, "Optimal Design of Plane Frames by the Complex Method", Computers & Structures, 20(1-3), 451-456, 1985. doi:10.1016/0045-7949(85)90093-8

5

F.A. Mohammad, "Analysis and Design of the LR55 Track System", Ph D Thesis, Liverpool John Moores University, UK, 1998.

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