Bridge analysis, design + assessment

Case Study

Watergate Bridge

  • Arch profile investigations

  • Linear and nonlinear buckling analysis

  • Global modelling of structure and local modelling of connections

The new Watergate Bridge across the River Boyne in Trim, County Meath, in the Republic of Ireland is a low rise, parabolic arch road bridge with cantilevered pedestrian walkways. The designers, Roughan & O’Donovan, used LUSAS Bridge to assist with all aspects of its analysis including the preliminary design and selection of the structural form, linear and geometric nonlinear buckling analysis of the superstructure, and also for local analysis of selected complex fabricated connections.


The new bridge spans 35m and comprises tapering pentagonal arch chord sections with pairs of Macalloy hanger bars connecting to Universal Beam tie members. Universal Column transverse members and end diaphragms support a 225mm reinforced concrete deck which acts compositely with superstructure steelwork. It replaces a previous composite multi-span structure that had a weight restriction and was in a bad state of repair. A clear-span replacement structure was required in order to eliminate the regular upstream flooding problems caused by the three wide piers and deck superstructure of the existing structure. The result for the client Meath County Council is a landmark modern structure that complements the heritage of the town and its surroundings.

Watergate Bridge

2D preliminary design

Preliminary design with LUSAS involved the creation of 2D line beam models to investigate alternative arch profiles, hanger configurations and relative section sizes. These models quickly showed the advantages and disadvantages of each arrangement. A low rise arch with vertical hanger rods was chosen in preference to a higher rise arch for aesthetic reasons. However, this meant that greater bending effects would occur in the arch chord and longitudinal members, and also the arches could not be braced horizontally, so careful consideration of their buckling capacity would be required.

Having chosen the arch type the next step was to carry out a comparative analysis of the relative section sizes of the arch chord member against the longitudinal tie member because a stiff arch would reduce the effects in the deck and vice versa. This process was very much simplified by using the section library built into LUSAS. This led to an influence line analysis which showed that the worst effects in the arch are caused by quarter span loading and by high intensity, short loaded lengths.

The final and possibly most important stage of the preliminary design was the buckling analysis. UK design code BS5400 Part 3 gives a table of effective lengths for compression members, all of which are rather conservative, but allows the designer to determine the effective length by an elastic critical buckling analysis. LUSAS calculated the first few mode shapes and the effective length and critical buckling load was found.

3D detailed analysis

A complete elastic analysis was carried out on a 3D line beam model with the deck modelled with thick shell elements. Live loading, temperature loading, and the effect of a collision on the arch rib were all analysed. From this, it was found that the tensile forces in the tie beam were shed to the composite concrete deck and as a result the girder size was reduced and additional reinforcing steel was added to the deck to take the tensile stresses. This made the deck monolithic with the tie beam, and torsionally stiffened the girder as a result.

It was considered that the linear buckling analysis from the two dimensional model had over-estimated the critical buckling load so this was recalculated for the 3D model with more accurate modelling of the end fixity. A full geometric nonlinear buckling analysis investigated 2nd order effects of loading the deck and from the load cases considered it was seen that loading the full span with a Uniformly Distributed Load caused the greatest lateral deflections of the arches. A comparison of the effective lengths from the 3D linear and nonlinear analyses gave very similar results of 12.7m and 12.5m respectively. Based on these values a maximum allowable compressive stress of 212N/mm2 was obtained for the steel type used.

Geometric nonlinear buckling analysis

Local modelling

While the 3D line beam model was satisfactory for the design of individual members, more detailed local models were required for complex fabricated connections such as the arch/girder connection above the bearing and for the arch/tie rod connection. Forces and moments derived from the 3D global model were applied to the local model allowing stresses and shear distribution in these connections to be easily seen and economical weld sizes obtained.

Stresses in arch to girder connection

"LUSAS was used throughout the design, from preliminary sizing of members right through to the detailed design of the more complex fabricated elements. It helped us to provide the client with an efficient, aesthetically pleasing structure."

David Doyle, Structural Engineer, Roughan & O’Donovan

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