PROTOTYPE 01 

PROTOTYPE 02

PROTOTYPE 03

PROTOTYPE 04

PROTOTYPE 05

PROTOTYPE 06 
PROTOTYPE 07
 
PROTOTYPE 08

MATERIAL TESTS
Tensioned Textile Composites *° 

DCS ° Taut & Arcade

DATE2017

LOCATION
Houston, TX

TYPE
Material & Fabrication Research

PRIMARY INVESTIGATORDavid Costanza

RESEARCH TEAMPhilip Niekamp
Ekin Erar
Samantha Schuermann

OVERVIEWTensioned Textile Composites is the culmination of extensive research exploring the potential of tensile surface morphologies to define the geometry of a vacuum-assisted, resin-infused, textile-composite structure. Tensile membrane structures have evolved dramatically since their initial conception, but have consistently relied on elaborate systems of cables, tie-downs, and masts to maintain their structural integrity. Tensile structures are unparalleled in enclosing vast spaces with minimal material. This is possible through the close alignment of geometry, material, and structure. Double curvature in opposing directions, at any point on the surface, guarantees the stability of the membrane. Through the geometric and structural constraint of an anticlastic membrane, formal surface typologies emerge that are both complex and efficient. A demonstration prototype titled TAUT seeks to combine the research on tensile membrane structures with composite structures. Its geometry is defined by tensioning a single surface within a scaffolding frame, and it is made rigid by vacuum-assisted resin infusion.

KEYWORDSTextile Composites, Formwork, Molds, Vacuum Assisted Resin Transfer Molding, Form Finding, Structural Optimization

INTRODUCTIONShells are structures whose shape is directly derived from their flow of forces. Simply put, a shell is a structure that acquires strength from its shape rather than its thickness. Shells include single-curvature geometries such as cylinders and conoids, historically meaning barrel vaults, and double-curvature structures like domes. Shells, particularly thin-shell concrete structures, allow for the enclosure of vast, open interior spans with few supports and minimal use of material. 
        Discrete units of material (bricks) can operate in compression to form walls and columns, but require a closer geometric and material alignment to bridge between walls to create an enclosure. Initially, this was done by switching material, from stone to wood, a material capable of operating in both tension and compression. Historically, large, column-free interiors were created by aligning material properties to form. Masonry was used to construct a spanning enclosure through vaults and domes operating in pure compression. An arch, derived from a circle or a parabola, can produce an opening in a plane or a wall constructed of masonry. The extrusion or revolution of the same arch or parabola can then be used to construct vaults and domes, translating from a 2D curve (in the opening case) to a 3D surface or shell.
        Doubly curved shell structures distribute loads in a plane, meaning the whole cross section is used in tension or compression. Singly curved or developable surfaces rely on material thickness to resist flexural stress in the cross-section, putting the top into tension and the bottom into compression. This includes barrel vaults and conic surfaces. That said, the formwork for surfaces with single curvature is much easier to construct. Forces in a doubly curved shell are distributed equally in the material thickness, activating the complete cross-section structurally, producing a stronger, thinner shell. An egg is a thin shell that demonstrates this well. 
        When discussing a liquid material like concrete, the formwork to produce the double curvature is where the complexity lies. The shape is more efficient structurally, but the construction of the shape is significantly less efficient. 
        Thin-shell geometries can be constructed either as a synclastic surface (curvature in the same direction) or an anticlastic surface (curvature in opposing directions), also known as a saddle. Again, the formwork is quite expensive for both surfaces due to the double curvature. For this reason, double curvature that can be constructed from straight line generators, like ruled surfaces, is preferable because they allow for relatively simple formwork construction but can produce synclastic and anticlastic, doubly curved, efficient forms.
        Conoids are surfaces made from sweeping a line between a line and a curve. Hyperboloids are created from revolving an oblique line around an axis or a paraboloid around an axis. Hyperbolic paraboloids (Hypars) are constructed by sweeping a parabola with positive curvature and a parabola with negative curvature. These geometries are ruled and can be produced from straight lines or generators. A hypar is a doubly curved surface, meaning it cannot be unrolled and therefore is non-developable. That said, the surface can be physically constructed using simple, straight sections, allowing for a feasible formwork in terms of cost. 
        The work of early thin shell engineers and architects like Candela and Torroja relied heavily on these mathematically defined geometries as both a means of constructing, but also at the time, a means of analyzing the structures. 

FORM FINDINGHooke’s hanging chain model, originally simply described through text in 1675, was later interpreted and represented with a drawing. The text and subsequent drawing depict a catenary hanging chain and the inverted, resulting arch. A catenary curve is formed under evenly distributed weight (self-weight), and a funicular curve is formed under a specific loading condition. There is no singular, unique solution to a funicular form; it is based on the length (of the chain) and the loading conditions. Uniform loading produces a catenary, and non-uniform loading produces a funicular curve. Midcentury thin-shell concrete relied heavily on catenary and funicular logics. When using reinforced concrete, a composite material capable of operating in tension and compression, we can assume the shape of the hanging chain (downward) in tension and the inverted chain (upward) in full compression. Because it is either parabolic or catenary, in either tension or compression, it can take on the pure flow of structural forces through space, in positive and negative curvature. 
        In September 1959, Heinz Isler presented his work at the first congress of the International Association for Shell Structures (IASS), an organization founded by Eduardo Torroja. Until then, most thin, reinforced concrete shells had taken the form of surfaces that could be easily described mathematically – spheres, conoids, and hyperbolic paraboloids – to enable the forces and stresses within to be more easily calculated. At this meeting in Madrid, Isler challenged this established technique of mathematically defined geometries. Through the use of models, he introduced several innovative methods for form-finding. Isler demonstrated three methods that he claimed allowed the design of an endless range of new forms, of which he presented thirty-nine. The second and third methods generate forms in pure tension and can operate as either shells or tensile structures. 
        Isler argued that almost any shape could be constructed as a shell. His three proposed methods were: 1. freely shaped hill, essentially building the form from earthwork, 2. pressure membrane (not a funicular) but similar geometries when the shell produced is fairly shallow. This is because internal pressure is perpendicular to the surface, whereas gravity works vertically. The most famous method Isler suggested was that of 3. reversing a hanging cloth.  This was the surface equivalent to Hooke’s Hanging Chain model from 1675. The three methods Isler put forth were constructing new forms by directly addressing the formwork's complexity and a new means of modeling complex forms in a pre-digital context. 
        Isler tested many of the structures in his backyard using fabric and water. By wetting the fabric with water and allowing it to freeze, Isler made the textile rigid and easily tested his shell structures. The formal language that emerged from Isler’s research was ahead of its time; it was no longer limited to mathematically defined geometries but explored new forms and manufacturing techniques. Each of these methods was both a way to physically simulate the forms in a pre-digital context, as well as a way of manufacturing the shells.
        At the same time that Isler was developing his form-finding technique for compression shells, Frei Otto was developing a similar form-finding technique for tensile structures. Frei Otto invented a method using soap films to derive the shape and structure of tensile membranes. Otto produced an isotropic membrane by tying one end of a string into a loop and submerging it in a dish containing soap and water. As Otto pulled the other end of the string from the dish, he formed a “cable loop,” also known as an “eye” due to its shape. The forms derived from the soap films were highly efficient and lightweight, capitalizing on the potential of structural form finding. Due to the surface tension of the soap solution, the formed surface minimized its area with respect to its given boundary conditions, forming a minimal surface operating in pure tension. Like Isler’s hanging cloth, which produced a shell when made rigid and inverted, Otto’s soap film studies produce an optimized tensile structure, which also operates as a shell when made rigid and inverted. 

COMPOSITESHigh-performance textile composites are made structurally by coupling a material that is strong in tension (fabric) with a material that is strong in compression (epoxy resin). This combination of fiber and resin produces an incredibly rigid and light structure. Like reinforced concrete, which carries tension through steel rebar and compression through the concrete, the material can be used in various architectural structures. In addition, like concrete (a liquid), high-performance textile composites have no inherent form. Textile composites are typically manufactured using a rigid, machined aluminum formwork or mold. 
        The most challenging aspect of composite manufacturing, as it relates to architecture, is the production of these molds. Large, custom molds are extremely expensive to construct and are only viable in an economy of scale, such as in automotive or aerospace applications, where the production of one large mold results in the manufacturing of thousands of identical parts. 
        The research seeks to address the role of formwork in freeform (non-ruled or developable) shell structures by using tensioned surfaces, which can be constructed using a simple frame with cables, to replace the role of the mold in producing a composite structure. The tensioned surface is made rigid through vacuum-assisted resin transfer molding (VARTM) and, once cured, can be inverted and operate as a shell.

PROCESSTaut was designed and simulated using Grasshopper and Rhino's Kangaroo physics engine plugin. The ability to simulate the soap film studies in a digital environment with high accuracy made the table design possible. Rather than a single cable loop being pulled along a single vector, as with the physical soap films, the table is designed as three radial cable loops, each with a unique trajectory. The resulting mesh is an anticlastic, purely tensioned surface.
        The scaffolding frame supports the edges of the textile surface while it is stretched taut and infused with epoxy resin. Early prototypes were constructed using multiple layers of burlap fabric on either side of a foam infusion core, facilitating the infusion of the textile through a vacuum pump. The vacuum pulls the resin through the textile, wetting out the fibers while also compressing the composite assembly. After the infusion of the textile membrane, the scaffolding frame is disassembled and removed, leaving behind a permanent, rigid, composite structure.

PRODUCTIONThe discretization of the simulated mesh into flat cut patterns resulted from both the textile's drapability and the resin infusion strategy. The five-ply laminate was laser cut and stitched together along the centerline curves into the textile preform. Though inherently flexible, when stretched taut, the preform takes the shape of the simulated mesh. 
        The stitched preform is then bagged with a nylon film. This entire assembly is still flexible. The bagging of the preform became a moment for invention. Traditional composite vacuum bagging relies on an oversized, non-specific bag. Through the project's development, it became clear that the bag's design and construction had to be as precise as the textile preform. Ultimately, the two-layer vacuum bag was digitally offset from the simulated surface, discretized, and laser cut to ensure compliance with the preform.
        The plywood frame used for stretching the textile is temporary and, therefore, as simple as possible. The cross-section of the top ring has a routed channel that holds the boundary condition at the top as the three connection points are then tensioned. The preform is vacuum bagged on both sides before being inserted into the frame to be tensioned. The plywood frame can easily be scaled up using the logics and fasteners of tensile membrane structures. 
        The vacuum pulls the resin through the textile, wetting out the fibers while also compressing the composite assembly. On one side is the bucket of epoxy resin, and on the opposite side is the vacuum pump. The resin is pulled across the fibers and then through a resin trap. The infusion strategy evolved over the many iterations. Initially, the resin infusion came through the legs, and the vacuum was through the tension ring. This was inverted to accelerate the infusion. Discovering in the process that whichever edge was greater in length should be the resin line and the vacuum line's shorter edge. 
        The nylon bag was marked with the resin infusion pattern every few minutes during the infusion process. This allowed for documentation and adjustments of the pattern and infusion strategy between iterations. The final discretization follows a contour logic along the axes of each leg. This allowed for a close translation, using conic extrusions, from the doubly curved surfaces in the simulation to flat cut patterns for the textile. 

CONCLUSIONDuring the workflow's development, many prototypes were produced. The discretization pattern, infusion strategy, and bagging evolved through the various iterations. We used 3D scans between prototypes to compare the surface's 3D discretization with the stretched membrane, leading to multiple shifts in the way we patterned the surface. 
        The prototype is sized to act as a table, but conceptually is meant to act as a ¼ scale prototype for an occupiable architectural structure. The research's promise is the possibility of using tensile membrane logics as the formwork for large-scale composite structures. This dramatically reduces the cost of the formwork in the production of the architectural-scale composites and also allows for the flexibility of one-off composite production, which is necessary for architectural applications.

REFERENCES
[1]    Otto, Frei. 2005. Frei Otto: Complete Works: Lightweight Construction, Natural Design. Basel, Switzerland: Birkhäuser.

[2]    Otto, Frei, Rudolf Trostel, and Friedrich K. Schleyer. Tensile structures: design, structure, and calculation of buildings of cables, nets, and membranes. Cambridge, Mass: The MIT Press, 1973. Print.

[3]    Adriaenssens, Sigrid, et al. Shell structures for architecture: form finding and optimization. London New York: Routledge/ Taylor & Francis Group, 2014. Print.

[4]    Garlock, Maria E., David P. Billington, and Noah Burger. Félix Candela: engineer, builder, structural artist. New Haven, Conn. London: Yale University Press, 2008. Print.

[5]    Billington, David P., and Jameson W. Doig. The art of structural design: a Swiss legacy. Princeton, N.J. New Haven, Conn: Princeton University Art Museum Distributed by Yale University Press, 2003. Print.

[6]    Garlock, Maria E., David P. Billington, and Noah Burger. Félix Candela: engineer, builder, structural artist. New Haven, Conn. London: Yale University Press, 2008. Print.

[7]    Bechthold, Martin. Innovative surface structures: technology and applications. Abingdon, England New York: Taylor & Francis, 2008. Print.




Illustration 9 from Isler’s paper “New Shapes for Shells” [IASS Archive]



Frei Otto's soap film minimal surfaces. [Photograms: IL-Bach/Klenk 1987]

DCS