Proquest Dissertations

Rice University

Architecture in 2Y2 Dimensions by

John Carr

A thesis submitted in partial fulfillment of the requirements for the degree of

Master of Architecture

Approved, Thesis Committee:

Gordon Wittenberg Professor of Architecture, Director

SL Albert Pope Gus Sessions Wortham Professor of Architecture

John J. Casbarian Associate Dean, Professor of Architecture

Houston, Texas May 2008 UMI Number: 1455222

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Architecture in 2V2 Dimensions byJohnCarr

Complex forms call for complex formwork—flat material is often laminated together or stretched over an underlying structure to produce a curvilinear surface. Or perhaps there is another way? As templates for production, patterns possess an under-utilized potential for generating forms with complexity beyond that of simple pasteboard box construction. This thesis is an investigation of that potential, pursuing pattern-based techniques for constructing stressed-skin structural panels from plywood. Contents

Introduction 1

Morphological Vocabulary 10

Structural Panels 45

Bibliography 61 Introduction

The push for unprecedented forms in architecture is nothing new—even the dome was exotic once—and advancements in digital modeling and rapid-prototyping techniques have spurred architects to realize increasingly complex forms. These pursuits have mirrored similar developments in the field of industrial design, where complexity has arisen from aesthetic and ergonomic concerns. Industrial designers have at their disposal techniques such as injection molding that, combined with the economic advantage of mass production, have allowed these complex forms to be achieved with relative ease.

Architecture, on the other hand, is typically a one-off affair—even "cookie-cutter" houses are custom-built—and beyond the scope of most manufacturing methods associated with industrial design. Consequently, architects have relied on traditional construction methods, even as they have begun to employ advanced materials and rapid prototyping techniques. Curvilinear surfaces have be achieved, for example, by affixing flat panels to an undulating structural grid. Even concrete, which offers near limitless formal possibilities due to its plasticity, requires temporary formwork produced in a similarly traditional manner. The disconnect between advanced forms and traditional methods exposes a lost opportunity. Is there another way to pursue these forms, in a manner that more efficiently employs rapid-prototyping methods?

This thesis offers pattern-based solutions as one such possibility. As templates for production, patterns possess an under-utilized potential for generating forms with more sophistication than a simple pasteboard box. The work presented here is an investigation into that potential, exploring techniques for constructing stressed-skin structural panels at an architectural scale.

1 2D to 3D

A pattern is perhaps most obviously thought of as a template — a definition embodied in this pattern for a cardboard box. While not particularly useful as an end product, templates provide a means to an end — a functional container, in this example. But why is a pattern needed at all? Why not just make the desired form outright? Patterns facilitate production by providing an efficient means of dealing with raw materials, which are often produced in sheet form in order to simplify manufacturing and transportation. It is generally easier to work with material in two dimensions rather than three, but with this advantage comes a limited range of formal possibilities.

Pattern and assembled box, redrawn from Structural Package Designs, p. 84-85.

t J 3D to 2D

A pattern need not be a template. This toad example demonstrates how a pattern can be a resultant. As Edward Tufte describes it, the toad's molted skin "collapses into flatland," where it is more easily analyzed. The flattened skin would make a poor template for producing a three-dimensional toad — in fact this is an ideal example of the limitations of templates in producing complex forms — but it does make the cumbersome toad easier to examine.

Toad and molted skin, reproduced from Mary C. Dickerson, The Frog Book: North American Toads and Frogs, with a Study of the Northeastern States, in Edward R. Tufte, Envisioning Information, p. 14.

3 2V2D

This handbag, designed by Josh Jakus, represents a confluence of both of the previously described pattern types. Its flattened state is both a template, providing an easy means of production, as well as a resultant, allowing for an easy means of storage. The richness of this bag's design lies in its novel accommodation of competing 2D and 3D limitations.

Handbag, in flattened and unflattened states, .

4 Developable Surfaces

Surfaces that can be flattened without distortion are known as developable surfaces. The plane, cone, and cylinder belong to this set, forming a limited yet powerful design palette. Slivers of planes, cones, and cylinders can be pieced together to create seemingly complex surfaces which remain unroll able. Geometrically speaking, if a surface can be modeled out of paper, then it is developable. This fact makes paper an ideal material exploring the possibilities and limitations of developable surfaces.

Three developable surface types — plane, cone, and cylinder— in relation to the sphere, Peter Richardus and Ron K. Adler, Map Projections for Geodesists, Cartographers, and Geographers, p. 4.

(a) (b) (c) Inverse Cartography

Map makers have long dealt with the problem of representing the round Earth as a flat surface. There are countless solutions to this problem, some better than others, but none of them perfect. Instead, each map projection is a compromise that distorts some aspect of the Earth's surface for the sake of another.

The maps shown here serve to illustrate the range of possibilities for transforming a single form — the sphere—into a planar pattern. The body of work that cartographers have produced contains many points of inspiration for producing pattern- derived forms. Of course, cartographers are concerned with accuracy and legibility rather than issues of fabrication, so it is also helpful to look at material applications of patterns.

Map projections, clockwise from upper left: Werner projection, Schjerning VI t equal-area projection, Goode homolosine -tr-t projection with interruptions for T J1 SO 1 landmasses, Sylvano's modified Bonne 4jr 4^ projection, Fisher's gnomic projection onto an icosahedron, Mercator's double cordiform projection, Waldseemuller's twelve gore projection, Ruysch's equidistant conic projection, John P. Snyder, Flattening the Earth: Two Thousand Years of Map Projections, pp. 36,255,197,34, ' *• 270,37,42,31.

6 Folding

Ammar Eloueini's work shown here makes use of folded patterns to create free-form surfaces. As opposed to the box pattern shown earlier, which consists mainly of rectangles, Eloueini's patterns are made up entirely of irregular triangles. The example shown is part of a stage set — a custom piece made feasible with CNC machining. This piece is supported by cables and intended as a dynamic part of the dance production it is associated with. Is constructed entirely of planar elements and bears no structural responsibility.

Stage set, Ammar Eloueini, CoReFab, p. 8.

7 Bending

In contrast, the plywood leg splint designed by Charles and Ray Eames is a quintessential example of pattern-based strength. The molded form incorporates planar as well as conical and cylindrical forms, taking cues from both the natural shape of the leg and the material limitations of plywood. Layers of veneer, shown here prior to molding, consist of varying patterns overlaid and adhered to one another to produce a richly formed yet rigid shell.

Veneers cut to shape for Charles and Ray Eames's plywood leg splint, Dung Ngo and Eric Pfeiffer, Bent Ply: The Art of Plywood Furniture, p. 55- Dry Bending

The greatest limitation of molded plywood is its reliance on complex and expensive production methods. The veneers must be glued together and clamped in place with sufficient heat in order to retain their shape. The work shown here, produced by students at Harvard, has sidestepped that limitation through the use of a dry bending technique: thin wood veneers are lasercut and fastened together with hardware rather than adhesives. Since there is no required formwork, variations within the pattern can be easily produced to create modulated surfaces.

Student work from a material investigation conducted at Harvard, Toshiko Mori, ed, Immaterial/Ultramaterial: Architecture, Design, and Materials, p. xii.

9 Morphological Vocabulary

As already noted, there exist forms that lay beyond the scope of pattern-based methods of production. It would be ineffective, then, to pursue a general method for distilling any given form to its underlying pattern. Indeed, such a pattern may not exist. What is needed is an understanding of the formal possibilities of pattern-based design. In order to establish a morphological vocabulary, studies were produced in several groupings. These groups correspond to the requisite properties of a structurally sufficient architectural system — rigidity, propagation, and so on. By no means exhaustive, this work nevertheless offers a framework for further development. Rigidity (1.1-1.4)

The first problem investigated was the question of how to stiffen an otherwise flexible sheet. Developable surfaces are useful, after all, because they are easily unrolled. The goal of this first series of studies was to counteract that natural tendency with forms that could maintain their shape without external reinforcement. Four studies are presented here, each consisting of a rigid surface deriving from a contiguous pattern. A simple shifted plane was chosen as the starting point — it measures 12" wide by 9" tall with a 3" horizontal offset — to which ridges were introduced. These corrugations progress from slight (1.1) to severe (1.4), with deeper corrugations producing a stiffer surface but also requiring a tighter bending radius. Study 1.1, form, 2" = i'-o".

Study 1.1, pattern, 2" = i'-o".

12 Study 1.1, constructed out of paper.

13 Study i.2, form, 2" = i'-o".

Study 1.2, pattern, 2" = i'-o".

14 Study 1.2, constructed out of paper.

15 Study 1.3, form, 2" = i'-o".

Study 1.3, pattern, 2" = i'-o".

16 Study 1.3, constructed out of paper.

17 Study 1.4, form, 2" = i'-o".

Study 1.4, pattern, 2" = i'-o".

18 Study 1.4, constructed out of paper.

19 Material, Scale, and Joinery (2.1-2.2)

With developable yet rigid surfaces shown to be feasible, attention turned next to alternate means of joinery. The previous studies rely on a paper seam formed by scalloped edges on either side of a scored centerline.This method works quite well, as it allows for a strong surface-to-surface adhesive bond while accommodating the variable joint angle inherent to the corrugations. However, this method does not translate well to other materials. As an analog to zippers, seals from Ziploc storage bags were examined. These seals allow for a variable joint angle, just as the paper seam does, while remaining reversible. Study 2.1 shares the same pattern as study 1.2, albeit with material removed around the seams to allow sufficient space for the Ziploc Seals. Plastic was substituted for paper, and the seals are held in place with double-sided cellophane tape.

With an eye toward architectural usefulness, study 2.2 incorporates material and joinery changes as well as a shift in scale. The pattern from study 1.2 was again used, though it was scaled up by a factor of four and produced from W thick plywood rather than paper. To allow the plywood to bend, 1/s" wide grooves were cut into the face of the material. Each groove is aligned perpendicular to the direction of bending and accommodates 1.5 degrees of bending. These grooves, as well as the contour of the pattern, were cut with the aid of a CNC router. The seams of the surface are held together with zip-ties — 90 in total — which are laced through evenly spaced pairs of holes. Taking a cue from Ammar Eloueini's stage sets, zip-ties provide a cheap, reversible, and secure method suitable for this scale of work.

20 Study 2.1, form, 2" = i'-o".

Study 2.1, pattern, 2" = i'-o". MM

21 Study 2.1, constructed out of plastic and Ziploc seals. J '-.If v ' ••

L •' -AS! Detail of the paper seam used in studies 1.1-1.4.

23 Detail of the seam used in study 2.1, consisting of a Ziploc seal adhered with double-sided cellophane tape.

24 Study 2.2, form, V2" = i'-o".

Study 2.2, pattern, 1/2" = i'-o".

25 Study 2.2, constructed out of plywood and zip-ties.

26 The CNC machining process, used for study 2.2.

27 Detail of the seam used in study 2.2, consisting of zip-ties laced through evenly spaced pairs of holes.

28 Propagation (3.1-3.2)

The investigations presented so far were constrained by certain technical limitations. The laser cutter used has a cutting area measuring 12" x 24", so the paper patterns produced were limited accordingly.The CNC router has a cutting area measuring 48" x 96", and the plywood used measures 60" x 60", which limits the plywood patterns to an area measuring 48" x 60". Studies 3.1-3.2 investigate how effective pattern size could be increased by splicing together two or more smaller patterns. Both of these studies are based on study 1.2.

29 Study 3.1, form, 2" = V-o".

30 Study 3-i, pattern, 2" = i'-o".

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31 Study 3.1, constructed out of paper.

32 Study 3.2, form, 2" = i'-o".

33 Study 3.2, pattern, 2" = 1 '-o".

34 Study 3.2, constructed out of paper.

35 Variation (4.1)

Disregarding the corrugations, the investigations up to this point have essentially been horizontal extrusions. Study 4.1 introduces cross-sectional variation, tapering outward from 3" wide to 6" wide. This in itself may not seem like a significant achievement, but the underlying techniques used are important and worth commenting on. Previous investigations have used only cylindrical surfaces to obtain rigidity. The corrugations in study 4.1, however, are constructed from conical surfaces. Conical surfaces figure heavily in the remaining investigations.

36 Study 4.1, form, 2" = i'-o".

37 Study 4-1, pattern, 2" = i'-o".

38 Study 4.1, constructed out of paper.

39 Enclosure (5.1-5.4)

Studies 5-1-5-4 present a slight deviation in trajectory. Based on the understanding of conical surfaces gained from study 4.1, these investigations derive from a barrel vault rather than the offset plane used previously. Study 5.1 is an analog to study 1.2 — an extrusion stiffened with corrugations. Likewise, study 5.2 is based upon study 4.1, with sides tapering from 6" to 9" wide. The remaining studies, 5-3-5-4, extend the tapering technique further. The lower edges of the forms are curved, bulging inward (5.3) or outward (5.4)- This results in saddle-like and dome-like forms, respectively.

40 Study 5.1, form, 2" = i'-o".

Study 5.1, pattern, 2" = i'-o".

41 Study 5-2, form, 2" = i'-o".

Study 5.2, pattern, 2" = i'-o".

42 Study 53, form, 2" = i'-o".

Study 53, pattern, 2" = 1 -o".

43 Study 5.4, form, 2" = I'-O".

Study 5.4, pattern, 2" = i'-o".

44 Structural Panels

The previous chapter detailed investigations into developable surfaces and the morphological applications thereof. The work presented here is a condensation and continuation of that research. This chapter documents the production of a series of stressed-skin structural panels, constructed out of plywood in a manner similar to study 2.2. These panels were conceived of as a formal whole — exhibiting and extending the findings of the previous chapter. However, they were not intended as mere display pieces, but as investigative pieces as well. To that end, each panel was produced separately with the production of panel A influencing the joinery and production of panel B. Each panel measures 36" wide by 72" tall, with a maximum depth of 18". This size, coupled with the limitations of the CNC router, required that the patterns to be subdivided. Many of the results obtained in study 2.2 were applied here.

45 Panels A and B, mounted vertically to a rollable wall.

Following page: Each panel is supported at its four corners. At the point closest to the viewer, panel B extends 24" from the wall.

46 47 Side elevation of the mounted panels, with panel B in the foreground.

Following page: Detail elevation, which shows the unscored back sides of panels A and B.

48 ».>'..

49 Panel A, elevations, %" = i'-o".

50 Panel A, pattern, i" = i'-o".

51 Time-lapse sequence showing the assembly of panel A.

52 Detail of panel A. Note the splice which holds separate pieces of the panel together. Note also the varying density of score lines, indicating areas of differing curvature.

53 Detail of panel A. The seaming method used is the same as study 2.2.

54 Panel B, elevations, %" = i'-o".

55 Panel B, pattern, i" = i'-o".

56 Time-lapse sequence showing the assembly of panel B.

57 Detail of panel B.The seams of this panel were joined at specific points, rather than the entire length of the panel. A spacer, held secure by a zip-tie on either side, keeps the connection at the proper angle.

58 \\1\ -v\ 1

Detail of panel B. Note that the spacers used have angles indicated on their surfaces, since they are specific to their respective joints.

59 "V

<#**'»*'

Detail of the spoilboard used in the machining process.The spoilboard was used to protect the bed of the CNC router, and so bears markings of all of the work produced.

60 Bibliography

Eloueini, Ammar. CoReFab. San Rafael, CA: ORO Editions, 2005.

Hensel, Michael, and Achim Menges, eds. Morpho-Ecologies. London, Architectural Association, 2006.

Jakus, Josh, .

Krausse, Joachim, and Claude Lichtenstein, eds. Your Private Sky: R. Buckminster Fuller. Baden, Switzerland: Lars Muller, 1999-

Mori,Toshiko, ed. Immaterial/Ultromaterial: Architecture, Design, and Materials. New York: George Braziller, 2002.

Ngo, Dung, and Eric Pfeiffer. Bent Ply: The Art of Plywood Furniture. New York: Princeton Architectural Press, 2003.

Reiser, Jesse, and Nanako Umemoto. Atlas of Novel Tectonics. New York: Princeton Architectural Press, 2006.

Richard us, Peter, and Ron K. Adler. Map Projections for Geodesists, Cartographers, and Geographers. Amsterdam: North-Holland Publishing Company, 1972.

Snyder, John P. Flattening the Earth: Two Thousand Years of Map Projections. Chicago: University of Chicago Press, 1993-

Structural Package Designs. Amsterdam: Pepin Press, 2003.

Tufte, Edward R. Envisioning Information. Cheshire, CT: Graphics Press, 1990.

Weisstein, Eric W. Math World, .