How Oasys proved invaluable

A key aspect of bridges that span over major river and road corridors is the need for the structure to support itself at all stages of the erection without temporary falsework. Working closely with the contractor the Arup team designed the bridge to be cantilevered out from each of the two major river piers, effectively using the permanent structure to construct itself.

The superstructure erection had to be planned with the utmost precision to ensure that the bridge would assume its theoretically correct geometry when the thousands of prefabricated pieces were bolted together. The deflections of cables are notoriously difficult to predict accurately, particularly initially when the cable tensions are small – the effective extensions of a cable with low tension are large, whereas in a highly stressed cable they are small. The non-linear axial stiffness can be visualised by thinking about how it is easy to move the end of a sagging rope by pulling, whereas pulling a taut rope produces little movement.

When erecting large complex structures. Two basic approaches can be taken to ensure that the completed project has the correct geometry. The first is to constantly monitor the position of the structure during construction, making adjustments along the way. The second is to accurately prefabricate all the components, and then by scenario planning and sophisticated analysis that connecting the together without adjustment will result in an acceptable final geometry. For the Kurilpa Bridge the complexity of the structure and the time constraints necessitated the second option, with the contractors forced to rely on the accuracy of the designers’ predictions. Arup achieved this using purpose-written software that linked into GSA via the COM interface, allowing thousands of construction stage analyses to be run and checked.

The accuracy of the modelling was demonstrated when the two bridge halves met precisely at mid-span as predicted by the GSA analysis.

Additional information

Initial analyses of the construction sequencing for Kurilpa Bridge were completed using the staging module in GSA. This allowed the design team to easily modify and adjust the model parameters for the final structure, without manually updating the construction models. The module allowed the team to superimpose results from successive stages providing a good indication of stress development and deflection in the structure.

Towards the later stages of the project, when more accurate analysis was required and the final structure was finalised, Arup moved to using separate GSA analysis models for each construction stage. The analysis models were de-constructed from the final model and non-linear analysis run using GSA’s dynamic relaxation solver. This allowed for extensive lack of fit analyses to be undertaken using the construction length tolerances for bridge elements and determine the envelope of bridge position during construction. This facilitated the real time monitoring of construction progress and identification of potential issues before unacceptable stresses were built into the indeterminate structure.

The lack-of-fit analyses were generated using the GSA COM interface, which allows the modification of the GSA model through a Microsoft excel interface. Dead load analysis identified critical compression and tension elements, which allowed us to create positive and negative lack-of-fit load cases in the construction analysis model. Influence of lack-of-fit analysis on member load distribution in construction was checked using load combinations, subtracting the ideal structure results from lack-of-fit results. Arup assessed changes in stress distribution and determined a reasonable envelope for bridge position during construction.

Member checking for construction phase were driven by a Microsoft Excel spreadsheet which using a macro directly output member force and moment results from each GSA model. These allowed automatic calculation of element utilisations and identification of critical stages during construction.

The lack-of-fit study for the full completed structure was completed using the GSA Com interface driven from an excel sheet.

Structural Dynamics

The bridge is relatively light, but has a comparatively long main span and a complex array of masts and cables. All this plus its unique design meant that it could be subject to unusual dynamic or aerodynamic effects with no precedents or “rules-of-thumb” upon which to draw. As a result, extensive wind tunnel, dynamic and fatigue analyses were required to comprehensively investigate and resolve all potential dynamic phenomena.

Dynamic Properties

A linear modal analysis was carried out, and the finite element model included detailed modelling of the concrete deck, piers and abutments, and small amplitude displacement foundation stiffnesses. Due to the geometry, several cables in the support structure are fairly low stressed and careful consideration was given to the effective cable stiffnesses to account for cable sag.

The dynamic behaviour was found to be complex due to the proportion of structure self-weight above the deck (masts, cables, spars and canopy). This led to many lateral torsional modes and significant coupling between mast and deck motions.

The lateral modes were found to be sensitive to the lateral stiffness of the piers supporting the major masts, so a sensitivity study was carried out to bound the lateral stiffness, including consideration of variation in soil stiffness and the potential for future scour around the foundations. Following the completion of the bridge structure, modal identification tests using ambient vibrations were carried out to identify the frequencies of key modes and found to have good correlation with the GSA analysis.

Aeroelastic stability of deck

Aeroelasticity covers a range of effects in bluff body aerodynamics whereby structural motion interacts with the fluid flow causing the motion. Classical flutter, galloping, and vortex shedding, for example, need to be considered in designing long-span bridge decks. Kurilpa Bridge has a very shallow deck and closely spaced, low-frequency vertical and torsional modes. This led to concerns that the deck could become unstable aerodynamically at wind speeds lower than the ultimate design wind speed, so this aspect of the design was investigated. While normal for major long-span road bridges, this is not commonly required for shorter-span bridges.

Wind tunnel studies were commissioned specifically to look at the aeroelastic stability of the proposed cross-section, while sectional wind tunnel tests were carried out using a spring-supported model of the bridge with mass and stiffness adjusted to represent the critical modes of vibration derived from the GSA analysis. These tests lead to the adoption of bull-nose fairings, which gave both an acceptable aerodynamic performance and improved aesthetics.

Vortex shedding excitation of masts and spars

As vortices are shed from alternate sides of bluff bodies in fluid flow, an oscillating force is induced. If the natural frequency of the structure is close to the frequency of this force, resonance may occur and, if unchecked, vortex shedding can lead to noticeable responses and/or fatigue problems. Excitation may occur on different elements at different times depending on the local wind speeds, natural frequencies and element diameters.

Assessment of susceptibility

The Kurilpa Bridge masts were assessed for aeroelastic stability under vortex shedding. The masts are partially fixed at their bases and the connections have geometries that are potentially sensitive to fatigue damage.

The Vickery-Basu method, as incorporated in several codes and standards (most clearly in the new Eurocode 1), was used for assessing vortex shedding response. It compares a predicted “negative aerodynamic damping” with the inherent structural damping of the structure; when the latter exceeds the former, the member is considered stable. Since the masts are mostly welded (and the bolted joints are under compression), the inherent damping will be low and may start to approach levels of material damping of perhaps only 0.10-0.15% of critical.

The vortex shedding susceptibility calculations carried out were based on structural damping of 0.24% critical (as specified in Eurocode 1) in addition to any positive aerodynamic damping arising from movements of the rest of the structure, but included a safety factor of two against instability to account for the possibility of lower damping levels.

The modal properties were taken from the bridge GSA model, and 250 structural modes were considered – taking in all that were potentially at risk from vortex shedding excitation. The major masts were found to be stable, but the minor masts potentially unstable.

Design solution

Measures were taken to reduce the risk of excessive vortex shedding response and potential structural damage of the minor masts. Helical strakes, adding additional mass to the masts, or adding damping, were all considered as ways to control vortex shedding response. Additional damping was the preferred solution as it had the least impact on the aesthetics and proposed structure.

Hanging chain dampers were not possible due to the inclination of the masts, so external ring impact dampers were used. TMDs were considered, but the difficulty of tuning to each mast frequency made them impractical. The ring dampers were designed in close consultation with the architect for minimal impact on aesthetics and lighting, and ability to be maintained or replaced at a future date. Each has a steel annulus weighing between 100kg and 250kg (depending upon mast size and frequency), supported by three steel cables just over half-way up the mast, and able to move relative to it. Impacts between the mast and the ring dissipate the energy that any vortex shedding excitation puts into the masts, and are softened by visco-elastic pads that absorb energy and reduce sound.

Pedestrian-induced vibration

The vertical and lateral response of the bridge under dynamic pedestrian loads was checked in GSA in accordance with current international best practice in addition to meeting the requirements of AS5100.2 2004. The following design scenarios were considered to ensure the bridge’s serviceability for normal use:

• single pedestrian walking at footfall rates of 1.0-2.6Hz
• continuous pedestrian streams and dense walking crowds up to 1.7 people/m²
• a small jogging group of up to 10 people.

The responses of the bridge were predicted to be acceptable with the exception of potential synchronous lateral excitation (SLE) due to crowd loading.

Background to synchronous lateral excitation

Synchronous lateral excitation is the phenomenon whereby pedestrians may “lock in” to the lateral sway of bridge decks, causing significant lateral motions. SLE will tend to happen on bridges with low frequency lateral modes that directly coincide with the frequency of lateral forces due to walking.

Pedestrian lateral force input has been measured experimentally and found to increase linearly with deck velocity, effectively introducing a negative damping term to the equation of motion. The bridge thus becomes laterally unstable if the energy input by the crowd during each vibration cycle exceeds the energy that may be dissipated through damping in the structure. This occurs when the crowd walking across reaches a critical number.

There is ongoing research into the exact mechanism of “lock-in” and lateral pedestrian load modelling, but the design methodology proposed following the remedial works on the London Millennium Bridge has proved robust in assessing the susceptibility of bridges to SLE and designing mitigation solutions.

Assessment of susceptibility

As Kurilpa Bridge is a major urban footbridge that may experience dense crowds during a public event, a design crowd density of 1.7 people/m² (5000+ pedestrians) was chosen (above this, walking becomes difficult).

All lateral modes with frequencies below 1.5Hz predicted for Kurilpa Bridge were checked for susceptibility to SLE, and the critical crowd density that would cause the bridge to become laterally unstable was calculated in each case. If the density predicted was >1.7 people/m², SLE would not occur, but if the density was above 1.7 people/m², SLE was considered possible.

Remedial measures were then investigated that would either stiffen the mode out of the range of concern or increase the critical crowd density to >1.7 people/m². The calculations assumed a structural damping level of 0.7% critical. This is higher than the typical 0.5% critical damping assumed for steel-framed bridges due to the nature of the supporting structure, but was confirmed following measurements on the completed structure.

Design solution

To reduce susceptibility to SLE, ways to increase the lateral stiffness of the river piers and the structural damping of the lateral modes were considered. Lateral tuned mass dampers (TMDs) were selected as the most economical and least visually intrusive solution. Three 3.2 tonne lateral TMDs under the bridge deck at the centre of the main span were designed to provide sufficient additional damping for all modes in the full range of pier lateral stiffnesses predicted during design when tuned with respect to the measured frequencies of the lateral modes. The design takes account of the fact that TMDs add less damping to modes with higher modal masses, but less damping is required in these modes as more people are required to cause instability.

Conclusion

Kurilpa Bridge is a landmark project that is architecturally striking yet sympathetic to its prominent location. Not only has the bridge achieved the client’s requirement that it not detract from the GoMA, but it is acclaimed as a fine piece of civic sculpture in its own right.

Opened on time and on budget, it breaks new ground through the incorporation of tensegrity structure for the first time in a major bridge. Importantly, the design does not obscure the view of the river but enhances its beauty and accessibility, and its connections. Pedestrians and cyclists enjoy a dynamic experience, with the projecting decks affording spectacular views and creating intriguing urban spaces.

In January 2011, southern and central Queensland suffered from disastrous flooding, including a major flood in Brisbane. An extraordinary combination of torrential rain over the river catchment and high tides resulted in the Brisbane River reaching levels approximately 1m above the 100-year flood level. The floods caused an unprecedented amount of damage to buildings and infrastructure, and tragically resulted in a number of deaths. Kurilpa Bridge, however, was not damaged by the flood, and reopened to the public as soon as water levels receded.