An extract of a lecture to be presented at the Lightweight Structures Association of Australia (LSAA) Conference in Auckland, November 13-15 2013
A parametric model depends upon relationships between parts. A parametric model is defined by rules and constraints, which define aspects of a design and their relationships with each other. Changing a rule or constraint, or modifying a part of the model itself, has implications for the entire model.
With non-parametric models the geometry is explicit but the rules are implicit – the model does not keep track of the rules. By contrast, parametric models have explicit rules and implicit geometry. The relationships and rules between the parts determine the geometric outcome. By establishing rules, or parameters, within a model allows for several important advances.
It provides the ability for real time iteration – rather than rebuilding an entire model, a simple integer can be changed with the software then updating automatically, for example, the diameter of an arc that then drives the entire geometry of a bridge deck and everything that follows downstream; the spacing of cables along an arch, or panelisation of a complex surface.
Several tools have been developed in the past decade for creating parametric architectural models. These include Dasault Systemes Catia and Solidworks, Gehry Technologies Digital Project (which employed the same parametric engine and was derived from Catia), Generative Components by Bentley Systems, Rhinoceros with Grasshopper by McNeel and Revit and Inventor by Autodesk.
Warren and Mahoney employ two pieces of parametric software – Bentley’s Generative Components and McNeel’s Rhinoceros for all complex geometric modeling in conjunction with Grasshopper. Rhinoceros is a powerful but simple to use modeling platform while Grasshopper is an algorithmic editor that provides computational and parametric capability to Rhinoceros.
Warren and Mahoney have recently won several infrastructure design projects and have begun design work on several bridges using Rhinoceros and Grasshopper.
In 2012, Warren and Mahoney were part of the winning alliance for the Waterview highway and tunnel connecting Auckland’s state highway network together. Hendon Bridge was designed as a pedestrian link to re-connect the local community split by the new highway.
As a large and highly visible element, the design, for both motorists and the local community was extremely important. The aim was to create a very simple but beautiful trajectory with the deck curving three dimensionally through space. The deck would in turn be supported by a simple but sculpted arch over the highway.
The alignment of the bridge was predicated on the relatively tight site constraints of Hendon Park at the north and the neighbouring Oakley Creek and its catchment on the southern edge of the highway. The deck plan was generated from three arcs, meeting tangentially and decreasing in diameter as the deck moved south. The simple geometry of the plan was projected up to form a theoretical surface and a constant 7% ramp slope was inscribed onto the surface. This geometrical definition standardized the components required to form the deck while still allowing for a complex and sinuously curved bridge.
As the arch crosses the highway in a near perpendicular relationship and straddles the curving deck underneath obliquely, the non parallel relationship between the deck and the arch resulted in a complex cable configuration – the theoretical surface described by the cables forms a hyperbolic paraboloid.
As a sculptural piece the bridge is treated as a simple white object. The deck is formed with precast concrete sections stained arctic white while the triangular profiled arch is painted a similar colour. The supporting cables and outriggers from the deck that pick these up are painted a silver metallic to highlight their highly mechanical function and differentiate them from the deck and arch elements.
The bridge was designed and modelled in Rhinoceros using Grasshopper to drive the parametric relationships. The model allowed iterative testing and optimisation of the design of the bridge. As the bridge was comprised of different components – arch, cables, posts, outriggers that were all interrelated, rules were established that could give a live and responsive model if these relationships were modified. The location of the arch and the associated cables impacts the vertical clearance requirements of the deck. By optimising the relationship of arch to deck, the intrusions of cables into the pedestrian vertical clearance zone were eliminated and the cables could be symmetrically propagated along the arch and deck.
Dusk view of Hendon Bridge looking south across the proposed State Highway 20.
Screenshot of the Hendon Bridge Rhinoceros model.
The Grasshopper algorhythmic model was used to drive the Rhinoceros model.
In 2010, Warren and Mahoney were part of the winning bid for the proposed Memorial Avenue Bridge outside Christchurch. The bridge, essentially a grade separation of State Highway One, straddles Memorial Avenue which is the primary link between Christchurch International Airport and the city.
The Christchurch City Council, Christchurch International Airport and the New Zealand Transport Agency all recognised the bridge as a moment to create a gateway – both to Christchurch and New Zealand. As such, the aim was to create a very simple but elegant gateway which would speak about the dynamism, excitement and speed of travel and echo the natural beauty of the Southern Alps.
Both arches had their conceptual starting points along opposing edges of the highway. The diamond shaped barrier bifurcated and transformed into two triangular sectioned arches that rose diagonally over the Memorial Avenue and State Highway One. The longer primary arch was arranged to create an alignment perpendicular to Memorial Avenue and provide a symmetrical gateway. The secondary arch finds the shortest span across the intersection and supports the highway road deck underneath.
The elevated deck is cable supported and was given an aerodynamic profile to its outer leading edge to resonate with the language of the arches.
The simple berm was treated in mono-cultural fashion with a native tussock proposed to again echo the Canterbury landscape.
After importing the road geometry from the civil team, the bridge components were modeled in Rhinoceros with the defining parametric limitations placed in Grasshopper. Variations, road geometry and road clearance changes were managed efficiently with the parametric control over the geometry.
View of the proposed Memorial Avenue Bridge looking west with the Southern Alps behind.
Extract from the Rhinoceros model of the arches.
Screenshot of the Rhinoceros model of the proposed Memorial Avenue Bridge.
In 2012, Auckland Council invited Warren and Mahoney to design a new pedestrian footbridge at Pt Resolution to replace the existing structure connecting St Stephens Avenue and Parnell Baths to Tamaki Drive. The Council, recognising the importance of the location both in terms of its prominence along the waterfront and its proximity to the baths, wanted to create something sculptural, elegant and iconic.
It was critical that the design of the new bridge have a resonance with the historic Parnell Baths. The baths, designed in the early 1950s in the International Modern style of lido bathing pools with its fluid and abstracted mural of swimmers, offered a clear language of angular lines meeting sinuous form and became a key motivator of the language and geometry of the bridge. The location of the bridge at the edge of the harbour also provided obvious nautical allusions, both historic and contemporary - the waka and the super yacht.
It was determined that the bridge would be formed using three primary elements. A simple but sculpted and hull-like concrete deck would extend from the headland and protrude out into the harbour. This would in turn be cradled by a highly expressive steel armature or exoskeleton which sinuously referenced the language of the baths beyond. A simple cantilevered glass balustrade, co-planar with the concrete deck would provide barrier protection.
The steel supporting the deck was designed to pay homage to the original bridge by echoing its three arches. The arches begin under the deck as diamond shaped columns which bifurcate to form the arches. The deck is formed with three separate twin-celled post tensioned precast concrete sections joined with in-situ stitches. The deck is supported by the steel armature through discrete pin connections.
Artist Henriata Nicholas developed a pungarungaru (water ripple) pattern over the concrete and glass surfaces. It was important that the patterning was delicately completed in a contemporary manner and seamlessly integrated into the design language of the bridge rather than merely applied art. To ensure consistency of the concrete colour, a pigmented stain was applied.
The bridge was designed and modeled in Rhinoceros with Grasshopper.
The parametric capability allowed for design iterations to be produced quickly and tested against architectural and structural requirements. The final parametric model was then baked (the parametric connections severed and the model rendered static) and given to the fabricators as a master model and formal contract document, making the paper drawings effectively redundant.
The reason for employing parametric software is not just for technical, constructability or cost efficiency, nor is it because of a desire to use parametric software. Parametric modeling in infrastructure design allows us to realise expressive, elegant forms that reflect a structural honesty and create sculptural and timeless pieces of architecture.
View of the completed Point Resolution Bridge showing the complex geometry of the steel exoskeleton.
Rhinoceros model showing the geometric studies of the bridge.
The Grasshopper algorhythmic model was used to drive the Rhinoceros Point Resolution model.
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