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When we think of membrane shapes, we often think of saddle shapes – sometimes referred to as synclastic or anti-synclastic shapes. The basis of these shapes is a simple square. When two opposite corners are moved up and the other two corners are moved down, a saddle is created, like a saddle on a horse. Shapes like these are often used in jewelry, especially earrings.
Triangles are always flat because any three points define a planar surface. I have always been interested in triangular membranes for a number of reasons, and have used triangles in a number of projects including a project in Los Angeles in 2012 with twenty triangles over outdoor retail mall spaces for Westfield, and three triangles over an outdoor retail terrace in Grand Cayman in 2014 for Dart Realty. I even created a structure product that I somewhat jokingly call a 'four-pointed triangle', which has a fourth point in the middle of one side of the triangle, allowing the membrane to deform, but maintaining the overall shape of a triangle.
Our latest project, for Google Tech Corners, is an installation in the central plaza of the new campus expansion in Sunnyvale. The project was designed by Valerio Dewalt Train Associates, and engineered by Thornton Tomasetti. Originally, the architect designed a large curved steel trellis to shade the plaza. At some point, Google expressed a desire to have the trellis create a shade pattern like the sun passing through leaves on a tree, and a pattern of several hundred triangles was introduced to the steel. Since the steel structure had already been fabricated without the sails, the challenge was to design the triangles to tension with less than 350 pounds per point.
When discussing fabric options, TENARA Fabric immediately came to mind because of its ability to diffuse sunlight. I had worked with the fabric extensively in the tropics, where we designed structures over retail and restaurant spaces. The self-cleaning quality of TENARA Fabric distinguishes the fabric from other options, as it always looks new, even after many years. I drive by our installation on the entry to the Farnsworth Art Museum in downtown Rockland, Maine daily, so I can confidently stand behind the self-cleaning characteristic of TENARA Fabric after five years.
We started the Google project by producing several mock-up triangles, which we tensioned on steel frames and shipped to the job site. I knew from experiments conducted the previous summer that our new 3,400-pound-test high-strength edge webbing tensioned nicely between 300 and 400 pounds, as we had been measuring the tension in the wind of some new outdoor shade structures attached to our building.
One request from the architect was to provide as much shade as possible, and to curve the edges, but only slightly. After many experiments, we found an unusual curved shape, which was shallow in depth yet allowed the membrane to tension evenly. This curve is somewhat flat across center and pointed at the corners of the triangle.
The project required nine distinct triangle shapes to fit within the steel geometry. Each triangle had to be within 1.5 inches of the connector hubs when fully tensioned. We designed a series of fourteen laser-cut and formed hubs out of stainless steel plate, which simply bolted onto threaded studs that we retrofitted onto the existing steel.
One beauty of TENARA Fabric is the protective layer laminated to both of its sides. We cut away the edge by one-inch to bind the triangle, and only removed the layers after it was installed, so no one ever touched the surface of the fabric.
Typically, when working with fabric membranes, the edges curve inward. There are several reasons why edges need to curve inward instead of being straight. The edge of a membrane is a structural component, which acts to evenly tension the membrane. It is impossible to tension the edge into a straight line. This concept is obvious in the case of a wire. No matter how much tension is placed on a wire, the wire is still very deformable at mid-span. It is the nature of a wire.
Once curvature is introduced into the edge, the edge requires less tension to maintain tension in the membrane. The deeper the curve, the less tension that is required up to a certain point.
The interesting thing about triangles is that if you curve the edges inwardly, the surface area of the triangle is greatly reduced and the points become very sharp. The sharpness is an interesting sensual quality. Yet triangles tend to disappear. There is nothing left. So in this respect, triangles are difficult to tension and pattern depending on the shape of the triangle. For a membrane structure, different materials also respond in different ways.
Fabrics have a grain structure, a warp, and weft. The bias is the diagonal. Clothing patterns utilize the bias for the best fit. Yet, we frequently see seams and edge bindings on clothing to control the bias. Triangles always cut across the bias, and along these cuts, the fabric has more stretch, even with a more rigid material. The way the curve is cut across the bias is critical to the tension in the membrane. Curves can be made in different ways: more elliptical, more flat, or more like a radius. Shape matters.