Case Study

Design Check of Post-tensioned Flyover

When CMPS&F were engaged to undertake the structural design of a 4-span curved flyover in Brisbane, Australia they decided to use LUSAS Bridge analysis to check the design.

Dr Nick Stevens was CMPS&F's project manager for the structural design. due to aesthetic requirements, he selected a continuous, post-tensioned, voided slab type of construction. The bridge has a total length of 102m and consists of four spans with a longest span of approximately 31m. The included angle of curve is 79 degrees. The cross-section consists of a central trapezoidal section 6m wide and a deck cantilevering 1.25-1.75m on either side. With an overall depth of just 1100mm the bridge is particularly slender. For this reason it was decided to use finite element analysis to undertake the design check.

To take full advantage of the benefits offered by finite element analysis, a fairly unusual modelling technique was used. All of the post-tensioning tendons were modelled as separate elements. The reinforced concrete was modelled using thick shell elements with the tendons being 3D bar elements, connected by vertical rigid beam elements to the appropriate node in the plane of the thick shells. The profile of the tendons in the model accurately representing the actual profile. The post-tensioning is input by applying initial strains to all the elements representing the tendons. The initial strain varies along each tendon in accordance with the friction losses.

This modelling approach offered several advantages over conventional methods that do not separate out the tendons. Principally it allows the effects of post-tensioning to be accurately modelled including all effects of creep, shrinkage, relaxation, and secondary effects. Also, resulting moments and shears in the thick shell elements are those that need to be resisted by the reinforced concrete alone. This eliminates the need to remove the contribution carried by the tendon at a later date.

The output from the analysis included plots over the bridge deck of resultant forces and moments per unit width (including in plane and out of plane shear). By using theory based upon the truss analogy it was possible to combine the resultants for a particular load case so that contour plots of reinforcing requirements could be produced. This in turn could be enveloped over all relevant ultimate load cases to result in overall contours of reinforcing requirements for the whole deck. In a similar manner contours of concrete compression requirements could also be produced.

To enable the bridge to be constructed with minimum traffic disruption it was necessary for it to be built in two stages. It was important to model this to determine its effect on the overall bridge response. This was easily accommodated in LUSAS. In modelling the first stage the model of the entire bridge was used but with the unconstructed part having its elements 'de-activated'. A unique feature of LUSAS allows the combination of results from different analyses with varying geometrical, support and material properties provided that the mesh is identical or forms a subset of the full model. Using this feature the results for this first stage could then be combined with the results from other runs with loading on the full bridge to accurately model the effect of construction staging.

The results of the analysis generally indicated significantly lower reinforcing requirements than resulted from the conventional analysis. The potential saving of this was largely reduced by satisfying code requirements for minimum reinforcing. However , according to Dr Stevens: "The real benefit of using finite element analysis is a high level of confidence in the results and in the actual service and limit state performance of the bridge itself".