Biomimicry at the Leaf

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The Leaf at Canada’s Diversity Gardens in Assiniboine Park in Winnipeg, Manitoba, has been described as a “horticultural sanctuary for the 21st century.” Interior biomes celebrate the flora of Mediterranean and tropical climate zones, and a butterfly garden allows guests to interact with a wide range of butterflies. The principals of biophilia, which is the human tendency to interact or be closely associated with other forms of life in nature, inform every aspect of the design of the building.

The structure of the building, which must be non-combustible due to its public program and scale, takes advantage of biomimicry—the emulation of elements of nature in design. Biomimicry can take two forms. Formal biomimicry emulates natural forms, while functional biomimicry emulates natural systems to solve functional problems. The Leaf employs functional biomimicry with resulting biomimetic forms using state-of-the-art technologies.

The most striking formal element of the Leaf is the sweeping spiral cable net of the roof. The roof supports inflated pillows of ethylene tetrafluoroethylene (ETFE), a fluorine-based plastic with high corrosion resistance and strength over a wide temperature range. Technologically, the pillows follow directly from Frei Otto’s soap bubble experiments in the early 1960s.

ETFE was chosen for the project for its high light transmissibility, particularly the plant-critical UV light, and economy, particularly when compared to glass. While ETFE is not “vision clear,” it diffuses light slightly in its passage through the membrane, so shapes and forms are easily distinguishable, and it reflects or absorbs only around 5% of the light. This is a critical factor when designing an indoor botanical garden at a latitude of 50° where the shortest day is barely more than 8 hours.

The functional objective of the roof was to minimize shading. A cable net was considered ideal because, with a light transmissibility of 95% in the membrane, most of the shading is structural shading. Cables, by virtue of their high strength (fully locked strand cable has a breaking strength in excess of 180 ksi) can be dimensionally small when the form allows. ETFE as a system can accommodate large movements without a reduction in performance. A large deformation structural system allows each element to be fully utilized for strength (demand/capacity ratio close to 1) minimizing its size.

ETFE, the foil, is extremely economical and the surface area of the foil is a minor contributor to the cost of the system. Working with Vector Foiltec in the early stages of the project, the design team learned that the cost of the system is largely in the extrusions, which form the boundaries, and in the labor to install them. The key to an economical system, as well as the key to minimizing shading, is to minimize the boundary to surface ratio. This constraint suggested two possibilities: long parallel pillows and large discrete rhomboid or hexagonal “tiles” (similar to Grimshaw’s Eden Project in the UK).

ETFE pillows are leaky and require a constant supply of air to remain inflated. A tiling of discrete pillows would require a system of ducts to bring air to the pillows, adding cost and shading to the system.

The planning of this building placed the mechanical equipment, including the inflation fans, in the central core. To avoid air distribution ducts, each pillow must terminate at the core. Conventional planning would orient the pillows radially, requiring over 100 pillows, tapering from a minimum width of around 1 foot to a maximum around 10 feet at the perimeter (the approximate maximum span of the ETFE cushion in a one-way system). This would result in almost 50% shading near the core. Reducing the number of pillows to limit shading would require two or more subdivisions of the pillows over their length—the strategy employed at Foster’s Khan Shatyr Entertainment Center in Kazakhstan. This solution would require air distribution ducts to bring air from the core to the subdivided pillows.

The solution chosen for this structure borrows from the mollusc. The mollusc builds its shell by laying down a single continuous strip of calcium carbonate in a spiral form to create an ever-expanding cone of constant proportion. These cones might be acute and wound like a snail or flat like a clam. In this project, rather than one, the design team chose 36 pillows, one for each 10 degrees of cardinal direction, each pillow following a continuous spiral path from the core to the perimeter. The choice of 36 pillows allows each pillow to intersect the boundary at an angle that is not so acute that it is essentially flat, maintaining a minimum slope for drainage.

The spiral form of the roof also borrows from phyllotaxis, the arrangement of leaves on a plant stem. When the angle between the spawning of sunflower seeds from the central meristem is equal to Fibonacci’s “golden angle” (the smaller of the two angles created by sectioning the circumference of a circle according to the golden ratio) the result is an optimal packing of seeds and a pattern closely resembling the roof of the Leaf, which was optimized to a near constant 10 feet pillow width.

As an aside, the hairy ball theorem of algebraic topology states that “there is no nonvanishing continuous tangent vector field on even-dimensional n-spheres.” In other words, you can’t comb a coconut. Any parallel-sided pillow solution on a compound curved surface was likely to lead to spirals.

ETFE foil is very thin—less than 0.5mm—but strong. As a membrane, it has no flexural stiffness and relies on prestress and curvature to span. Prestress is maintained by the inflation pressure of the pillows, similar to a soap bubble. Two pressure equalized chambers make up the assembly to provide good thermal performance with an R-value in the range of 2.0. Internal pressure is maintained at about 5 psf in the summer and 10 psf in the winter to resist modest snow loads. Heavy snow fall (up to 30 psf in this case) will cause the pillow to deflate with the snow load to be shared by all three layers of foil. With the three layers in contact, the R-value drops to something around 0.1 and the heat from the biomes quickly melts the bottom of the snow forming a slick boundary layer of water. This precipitates sliding of the snow to the perimeter, after which the pillow reinflates.

The cable net for the roof is a triple layer spiral cable net supporting the spiralling pillows. The spirals were derived from the complementary diagonals associated with a radial/annular grid of 36 radials and annular parallels at 10’ c/c.

Like membranes, cables have no flexural stiffness, yet in this case the system must span as much as 150 feet. Cables rely on curvature and prestress to span. The job of the compression chord in a bending system is done by the boundaries in a cable net. If a cable experiences compressive forces, it will instantly buckle, losing all stiffness. Prestress is applied to ensure that all cables remain in tension during all loading conditions.

The form of the roof is anticlastic, derived from a rotational hyperboloid, meaning at any given point, the surface curvature is convex in one direction and concave in the other. An anticlastic curve has the benefit that the prestress in the convex layer is balanced by the prestress in the concave layer and can be maintained in the absence of external forces such as inflation pressure.

In order to provide the large east-facing, overlooking window at the butterfly garden, the rotational form was split and, rather than revolving around a continuous ring, the curve was revolved around a helix. While the net remains anticlastic, the break from the pure form complicated the loads in the boundaries.

The plan of the building, resembling a pair of overlapping beech leaves, was derived by trimming the rotated form along selected spirals, chosen to optimize the interior spaces to their respective programs.

Introducing three layers to the grid (as opposed to simple radial-annular or two complementary diagonal spirals) adds indeterminacy and complication to the behavior. While the spiral net was crucial for supporting the spiral pillows, any tailor knows that fabric cut on the bias is stretchier. Radial cables were required in addition to the spiral net to provide stiffness.

The three layers of the net were described as the Radials, the Positive Spirals, and the Negative Spirals, positive and negative determined based on the “right hand rule.” Negative spiral cables by Redaelli are single 24mmØ Locked Strand cables and were designed to have constant prestress over their length of around 15 kips. Positive spirals are pairs of 16mm locked strand cables, prestressed at roughly 7.5 kips to balance the negative spirals. Radial cables, locked strand cables ranging from 52mmØ to 64Ø, accumulate load at each “node” (the points where the spirals intersect the radials) at roughly 40 kips per node to a maximum tension of about 250 kips in the longest radial.

Under balanced load conditions the pillows pull equally horizontally on their extrusions and little lateral force is resolved into the net. But in a snowfall event, the snow can’t be relied on to be uniformly distributed nor to slide at the same time in adjacent pillows. A condition with full snow on one pillow and none on the adjacent pillow is a very real possibility. Additionally, the pillows must be lifted roughly 18 inches above the negative cables to ensure that they don’t bear on the crossing cables which would result in premature wear. The result is that unbalanced loads place large torsional forces on the extrusions and the paired positive cables. Anti-rotation cables complete the net, installed below the negative cables.

The node elements, resembling huge prehistoric bugs, consist of a top and bottom clamp plate with a machined cable groove affixed to the radial cables with torqued high strength bolts. A third clamp plate clamps the negative cables in place in a curved groove. Positive cables, lifted roughly 10 inches above the negative cables, are clamped in place atop a steel post. The final piece, an S-post, is bolted to the bottom to connect the anti-rotation cables. The geometry of each of the 333 nodes is unique, accommodating the subtle differences in cable incidence angle and forces. Geometries were precisely determined to attempt to limit the “kink” as the cable passes in and out of the clamp to less than 1.5°.

Like the roof, the interior partitions separating the biomes consisted of ETFE foil supported by cables. Rather than pillows and spirals, however, the structure of the partitions resemble a bat’s wing, consisting of a single layer of tensioned foil membrane spanning between vertical cable stiffening elements. The vertical cables themselves are supported from catenary cables below the roof.

The cable wall was designed to limit the lateral movement under an interior wind pressure of 5 psf to H/36, requiring significant prestress. Those vertical cable forces would result in enormous catenary cable forces should the catenaries follow the roof profile—a requirement to achieve environmental separation of the biomes. To address this, the vertical cables were supported by a very deep catenary cable, and a second set of vertical cables span between that and a shallow catenary cable that follows the roof profile. The upper set of cables span a much shorter distance and, as a result, require less prestress. The prestress on the 16mmØ lower and upper wall segments are roughly 10 kips and 2.5 kips, with the large catenaries carrying up to 150 kips of prestress.

While the ETFE system is strong with excellent light transmission characteristics, it is vulnerable to contact damage and is not “vision clear.” Glass was chosen for the bottom 3m of the partitions to allow views into the biomes.

The partition enclosing the Butterfly Garden presented a separate challenge. While the height of the partition is much shorter, the partition curves in plan to follow the edge of the leaf-shaped platform. Lateral stay cables were installed following the radial lines of the roof to pull partition into its correct alignment.

The diagrid core is the spine of the building. It contains the vertical circulation to access the event spaces and the Butterfly Garden, as well as housing the mechanical equipment for the inflation of the pillows and environmental controls for the building and biomes.

The structure of the diagrid does the heavy lifting for the building, resisting the gravity and lateral loads for the roof and providing the tension ring function to anchor the cables of the cable net.
The diagrid form was developed for its structural rigidity as much as its aesthetic impact. The horizontal elements within the diagrid form a pair of parallel helixes, each rising 30 feet per revolution. The formal reference to the DNA molecule is evident.

Less evident is the functional precedent in the grain of trees. According to The Gymnosperm Database, It (spiral grain) has also been noted that spiral grain may make the tree stronger and better able to withstand stresses caused by wind, particularly if the direction of the spiral is periodically reversed.” (https://www.conifers.org/topics/spiral_grain.php)

A further functional solution borrowed from dendrology is the soft flaring of the branches at intersections. The diagrid incorporates 81 six-limbed ductile cast steel nodes weighing between 1,500 lbs. and 2,500 lbs. each. The branch intersections of the cast node geometries mimic this natural aesthetic with softened fillet transitions. These fillets reduce stress risers and improve the performance and reliability of the joints.

The freeform capabilities of cast steel geometry further enabled the diagrid form by facilitating the helical revolutions along the height while allowing the intermediate elements to remain straight-cut pieces. The castings, designed and supplied by Cast Connex, included precision-machined branch-ends to minimize tolerances and support fabrication. Each branch-end included a bevelled nose to create grooves for the circumferential welds to the incoming HSS members. The diagrid was shop fabricated in large assemblies, carefully planned based on shipping constraints, to minimize field welding.

A unique feature of the cast nodes, proposed by Cast Connex, is the centerline eccentricity. Rather than a single concentric work point, the node has two works points, eccentric from one another by slightly less than one pipe diameter. This eccentricity results in bending (which every good engineer tries to avoid), but as a fully welded frame, some bending is inevitable. Casting use precludes local HSS connection limit states enabling smaller member sizes than otherwise needed, which in turn helped reduce overall tonnage. Introducing this eccentricity also dramatically shortened and lightened the casting, making the whole system more economical.

Rather than attempting to conceal this eccentricity, the design team elected to celebrate it with a continuous soft vertical groove. The unique geometry of the nodes earned them the nickname “hockey pants,” an appropriate metaphor for a Canadian winter city.

Where the transparent partitions provide visual access to the biomes, the skywalk provides a physical connection to the tree canopy, Cantilevering out of the elevator lobby, it loops back to terminate at the Butterfly Pavilion passing the top of the waterfall. The load is primarily carried by the shorter inner girder, a torsionally rigid square hollow steel section, connected for both moment at torsion at each end. Purlins cantilever from this inner girder to pick up the floor and are connected at the outer end by a continuous curved channel.

Roughly halfway along the length of the bridge it is propped by a pair of round hollow steel struts terminated with CastConnex Universal Pin connectors. These struts significantly increase the stiffness of the bridge in normal service conditions. In order to keep them visually light and maintain a high-quality finish, these elements received no fire protection. In the event of a fire, these elements are considered to have failed. The bridge has been designed to maintain its integrity in the absence of these elements to allow safe exit for the occupants.

Approaching The Leaf, one is first struck by the gentle sweep of the spiral roof. Moving closer, the angled cable stays radiating from the perimeter of the building come into view.

In a cable net, the job of the compression chord is done by the boundary. Often this consists of a compression ring around the perimeter. Sometimes these boundary forces are taken into the earth, a strategy employed by the Banyan tree.

A compression ring at the eave was not possible on this project because of the desired visual lightness of the eave and the complications created by the split. The soil conditions in Winnipeg are challenging and not suitable for resisting large tension loads. The solution was to create a closed system, with all forces resisted internal to the structure, below the ground, so that the foundations carry only the weight of the building. Transferring the horizontal loads through a raft diaphragm wasn’t feasible because the raft would interfere with the interior landscaping. A pile supported raft compression ring was buried below the ground, outside the footprint of the building, with the forces transferred to the ring with diagonal stay cables. The raft acts as ballast, balancing the vertical components of the stay forces, as well as transferring the horizontal components around the building.

At the rear of the project, the supporting “bar” building fulfils the function of the raft slab, transferring the loads through the building structure to the foundations.

The conception and design of this project was a tremendous technical challenge. Equal to that was the erection planning. Design is done as though the structure materializes instantly and perfectly. In reality, the structure is erected piece by piece, and cables are installed one at a time. Each element is imperfect, and each dimensional variance has an impact on the distribution of forces in the structure.

The key to success is tolerance. Providing broad guard rails ensures the car stays on the road. Each cable was terminated with an adjustable pin fitting. The pins allow rotation about their axis; adjustable fittings can correct length tolerance and facilitate tensioning. Nonetheless, the guard rails are not always wide enough. Cables and pillows were fabricated concurrent with the structural steel based on objective perfect geometry. Pins allow rotation only about one axis, and steel tolerances in a project with a complicated geometry are difficult to achieve. Extensive surveying and some amount of field rework was required to ensure that the structural supports were compatible with the fabricated net and pillows. Where rework was impractical, the net was recalibrated to suit the existing boundary conditions.

Each step in the erection redistributes forces in the structure, and each element must be confirmed, which the design team did, working on behalf of the contractor.

Cable contractors, Redaelli and Tensile Integrity, would propose a sequence of installing and tensioning cables. The design team then would analyze each step to verify strengths and calculate movements in the structure. If a step created an unacceptable condition—such as overstress—the plan would be adjusted.

The goal was to develop a sequence of installing and tensioning cables that would result in an acceptable final prestress condition in the net that is safe and rigid, and as close as possible to the target model.

The net was tensioned in roughly 39 steps, each cable being adjusted up to three times and each step tensioning six cables until the predicted tensions and set-outs (the predicted position on the adjuster associated with the desired prestress) were reached. The erection proceeds in a forward direction, adding tension and taking up adjustment in order to reach the correct target; the analysis steps were completed backwards, starting with the target model and relaxing each stage. For each stage of the erection, the strength of each member was verified, as was the slip of each node clamp and the kink angle of the cable at the clamps. Movements of the supporting columns and stays were calculated and reported. These values, along with the measured tension from the tensioning jacks, were used to validate each stage. This information was reported to the contractor in a single spreadsheet exceeding 100 MB in size. They distilled this into a series of field work sheets to inform each day’s work.

Two approaches were taken in the design and representation of this project.

The cable net, diagrid, and supporting elements were modelled and designed using NDN, a large deformation non-linear finite element package specifically created for the engineering of membrane structures. The ETFE pillows themselves were a delegated design, with engineering completed by the contractor, Vector Foiltec. The design team worked closely with Vector Foiltec to ensure that the cable net provided adequate torsional rigidity to maintain stability of the pillows and extrusions under unbalanced load conditions.

These components were modelled and drawn for the construction documents using Solidworks, which is effective for complex, non-orthogonal geometries and multi-level assemblies.

olidworks models can be exported to .ifc and other formats to integrate with Revit, Tekla and other software used by coordinating disciplines and trades.

The bar building was analysed and designed using Etabs with input loads at the interface coming from NDN. The bar building was also incorporated into the NDN model for validation of the Etabs results. This portion of the project was modelled for representation using Revit which allowed close coordination with the architects and was also used by the steel fabricator to assist in preparation of shop drawings. ■

David Bowick, P.Eng., is a principal at Blackwell Structural Engineers in Toronto, an innovative structural design practice with expertise in tension and fabric structures, in addition to timber, concrete and steel. Bowick is a frequent lecturer and writer and an adjunct professor at the Daniels School of Architecture at the University of Toronto.