Background to the analysis

The first of the earlier analyses ‘failed’ the structure and concluded that the bridge was inadequate for pedestrian loading due to permissible tension in the masonry being exceeded. Next, Lincolnshire County Council carried out an in-house assessment using a serviceability limit state check under nominal loads with a ‘line of thrust’ method. Unlike the first analysis, this took the formation of a hinge as the failure criterion, implying an acceptance of tension up to the formation of the first hinge. This assessment deemed the structure to have ‘passed’. Lincolnshire’s approach was felt to be a more rational basis for determining ‘failure’ than the onset of tension since many masonry arches regularly experience tension and remain perfectly viable structures. Because of this, Sheffield City Council used the plane stress ‘concrete model’ in LUSAS to mimic the behaviour of the masonry. An ultimate limit state, rather than serviceability state, analysis was applied, because the issue was considered to be primarily one of structural safety.

Modelling in LUSAS

The technique used was to trace crack formation as nominal loads, i.e. without partial load factors, were applied incrementally with manual amendment of the model between each analysis. Repeated re-appraisal of the structure’s stiffness between runs was necessary since the model allows cracks to develop and propagate as the load increases and the structure degrades. As the model developed, the load factor achieved increased. This procedure continued with the aim of reaching an acceptable value. To reduce processing time, a series of linear analyses were done prior to a full nonlinear analysis.

The initial linear analyses determined that ‘out of balance’ effects from applying pedestrian loading to quarters of the plan area were minimal. The worst load case was shown to be pedestrian loading of 5kN/m2 over the entire plan of the structure. This allowed a simpler 3D quarter model to be employed thereafter, giving faster results.

Additional linear analyses found that support conditions were critical to the mode of failure. With the supports rigid in respect of vertical settlement, as initially modelled, failure in the structure’s ‘legs’ occurred very early in the loading regime. Truly rigid supports were felt to be unrealistic, so springs were introduced, resolving the premature leg failure. A final refinement was to introduce spring lateral restraints. These replaced the earlier rigid ones (which modelled lateral soil pressures) since it was felt that complete rigidity was unrealistic and furthermore had caused problems for the legs.

The cumulative effect of all the modelling changes was to raise the structure’s load factor to 3.43, an acceptable figure, and proving the safety of High Bridge for pedestrian loading. Achieving this outcome depended upon certain assumptions, as well as lateral support derived from the surrounding soil and adjacent buildings. This point was made clear to the Client in case future construction or demolition work nearby affected this beneficial soil pressure.