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Form follows logic. Forms based on Euclidean geom-etry can be described precisely and unequivocally by using a few parameters only.² Yet this is only true for forms that can be described, codified, contained. In contrast, forms based on Non-Eucledian geometries, as those found in nature, may also use a mathematical logic but extend generic shapes towards highly complex formations that are the result of a morphogenesis, the transformation of shape in matter over a period of time.

Forms are consequences of processes. Form finding models directly use physical properties to shape the structure of forms, as they contain force flows and material contin-gencies, and thus deliver a certain degree of approximation for the object of design. Analogue models are not just formal approaches but design tools that consider the result of material and structural reactions to forces.³ Impacts on the consistent relationships between structural elements (as opposed to fixed metric quantities) allow us to review changes. Interventions to form thus register systemic rules of a model, as for example by varying the number or length of members or elements, or by adding or removing weight). Changes to a single element propagate corresponding changes throughout the whole system (in position, magnitude, or frequency).

Forms are resistances. Exerted through systems of compression and tension, forces prompt alterations to form that result in transitions; deflections; collapse; or in the best-case scenario, an optimised solution. In design models, these local interventions have an effect on extended fields or even on the entire structure, similar to nature in which protocols of minimum inventory enable systems with maximum diversity.⁴ In this manner, the behaviour of form can be explored as the model acts within boundary conditions, effectively enabling a two-fold generative design: a process of design (boundaries), and process of self-generation (object).

Forms are variables. In continuation, forms in digital processes can afford momentary delays of material in favour of shape protocols and iterations derived through control of geometrical or mathematical rule sets. Parametric protocols enable systems that are defined (through an order of compo-nent rules and based on optimised or confirmed behaviour)⁵ to undergo series of iterations while preserving specified qualities.

Finally, forms are maps. Form can be used to map and distribute internal forces (such as dead-load patterns within an object) and external force flows (of context, such as gravity,

2 David Wendland, Model-Based Formfinding Processes: Free Forms in Structural and Architectural Design (Stuttgart: Universitat Stuttgart, http://Elib.Uni-Stuttgart.De/Opus/Volltexte/2001/761/Pdf/Wendland.pdf).

3 Dagmar Reinhardt and Alexander Jung, “Representation as Research: Design Model And Media Rotation”, RIBA Journal of Architecture, ed. Hilde Heynen (Routledge Taylor Francis, Vol.13, April 2008), 185-201.

4 Peter Pearce, Structure in Nature is a Strategy for Design (Cambridge: MIT Press, 1978), 54.

5 “If the parametric is a technique for the holistic control and manipulation of design objects at all scales from part to whole, the algorithmic is a method of generation, producing complex forms and structures based on simple component rules.” Michael Meredith, From Control to design – Parametric/Algorithmic Architecture (Barcelona: Actar, verb monograph, 2007), 3.

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This essay discusses SmartStructuresLab2014, a postgradu-ate studio that approached the engineering of architecture in process. Relationships between form, force and structure are explored here as a dialogue between analogue design models, computational design series, and engineered structural analysis and optimisations; through digital fabrication of 1:1 plywood prototypes, 1:20 skeleton structures and 3D printed form studies. SmartStructuresLab2014 reviewed engineering precedent of self-formation and rule-based designs, and extended these in a process of design iteration, structural behavior review and material affordances. This involved the full integration and seamless transition between 3D modeling (Rhino/McNeel Rhinoceros), parametric design (Grasshopper) and structural analysis (karamba) environments. Thus, a descriptive language of complex curved surfaces becomes available that combines parameterized geometry, finite element calculations and optimization algorithms in rule based scenarios at the intersection between digital and analogue modelling. As a consequence, the resulting design models develop formative principles for tension, compression, or hybrid systems, to be deployed as grid shell, masonry, concrete or membrane structures. This paper reviews the underlying conceptual framework and protocol of the studio.

FORM Central to any architectural discourse is the discussion of form, and its genesis, design, rules, translations, processes. Forms can be addressed as typologies, as variants, as singu-lar solutions, as dependent on context. This paper is interested in forms that do not merely pose an aesthetic problem, but which are informed by (and inform) material and structural behaviour. We argue that forms are containers of forces as much as they are expressions thereof. We further argue that forms need a foundation that enables continuations into and out of structure and material considerations; a geometric or mathematical logic through all stages of a design and construction process, and continue even after form has been brought into existence. In that sense, forms must be considered non-finite states or ‘conditions’ in space and time, as multiplicities.¹

1 As Lynn argues, “[f]orm can be shaped by the collaboration between an envelope and the active context in which it is situated. While physical form can be defined in terms of static coordinates, the virtual force of the environment in which it is designed contributes to its shape. In this way, topology allows for not just the incorporation of a single moment, but rather a multiplicity of vectors, and therefore, a multiplicity of times, in a single surface.” Greg Lynn, Animate Form (New York: Princeton Architectural Press, 1999), 10.

DAGMAR REINHARDT & ALEXANDER JUNG

FORM AND FORCE

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Self-forming structures have a long history of invention. Hooke’s Law (1675) described the catenary as “the true mathematical and mechanical form for all manner of arches in building” “[A]s hangs the flexible line, so but inverted will stand the rigid arch.”⁸ These hanging chains are the first self-forming structures: the catenary forms a curve in tension under its own weight, and responds through shape formation to changes in location and magnitude when forces act upon it. Moreover, when such a self-formed curve is turned upside down, the arch stands equally in compression. Both are forms in equilibrium with the forces running through their geometrical and material system. This structural, formative principle can be used as a design model in different material systems spanning from masonry to grid shells, or membrane structures that then act as tension, compression, or hybrid systems.

In Experiments: Form, Force, Mass (1960), Frei Otto strategically extended Hooke’s mandate to strategic structural form-finding, and developed a matrix for the structural design of membranes, minimal surfaces, tensile and pneumatic structures, and shells. Here, the form of a structure as constituted in a self-forming process is of primary importance.⁹ Defined by boundary conditions, Otto’s models give visual evidence of force flows within. Rather then providing analytical descriptions of form, they effectively store forces within form.¹⁰ In ‘unforced’ or un-deformed condition, the surface rests in a formation of regular elements. Surfaces are deformed according to forces applied to control points; vertically by pulling one point upwards, or horizontally from several sides. For example when exposed to force, a mesh surfaces self-forms as it interpolates between two points (interval expansion), and organises itself in a pattern of densities and voids. Self-forming structural tests thus become design models that economise the design effort through the simulation of the material and structural behaviour of spline curves in systems which draw on the equilibrium figures of the architectural object. Form is then neither architectural language nor typology, but a prototype that is governed by universal principles, and which constitutes a rule system of spatial and structural complexity.

Generic rules of geometry can, on the other hand, equally become project definitions, as is the case with Felix Candela’s shells structures, and his rule-based system of doubly curved surfaces applied to hyperbolic paraboloids (hypars), tympans and umbrellas.¹¹ Specifically, compression

8 Edward Allen, Waclaw Zaleski and Boston Structures Group, Form and Forces: Designing Efficient and Expressive Structures (New York: Hoboken, John Wiley & Sons, 2010), 219.

9 As Otto notes: “The fundamental interrelation between the form of a structure, the forces which act during its creation, or which it transmits, and the mass required to fulfil this structural task, without primarily aiming to find a direct application in the field of architecture… result in greater knowledge of forms, structures and the processes, which lead to their development.” Frei Otto, ed., IL 25: Experiments - Form, Force, Mass (Stuttgart: University of Stuttgart, Information of the Institute for Lightweight Structures IL, 1990), 0.14.

10 Lynn argues that ‘the context for design becomes an abstract space that directs form within a current of forces that can be stored as information in the shape of form.’ Greg Lynn, Animate Form (New York: Princeton Architectural Press, 1999).

11 Maria E. Moreyra Garlock and David P. Billington, Felix Candela: Engineer, Builder, Structural Artist (Princeton, N.J.: New Haven: Yale University Press, 2008).

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and wind or snow loads). In repeated conversions between analogue and digital mediations of form, a computation of form and force relationships becomes key to effective structural behaviour. In what has been termed ‘reverse engineering’, models that exist as equilibrium figures (where forces and form have found a balance) are used as base data sets of: shape, node coordinates, or spline curvatures. These approximate forms are stability figures with homogeneous force distributions, which give definitions to structure. A combination of material interaction with a physical model and geometric‚ ‘reverse engineering’ thus enables the control, variation, and realisation of form, free-form and form mul-tiplicity. As a consequence, formers top-down processes of form-making can be replaced with a bottom-up logic of form finding.⁶ This is significant because it allows the designer to include intuitions of structural behaviour, of structural action, and of structural adequacy.⁷ It allows forms to be expressions of force.

FORCE In the development of forms, one might argue that two major models, two schools of thought, exist: that of self-forming systems, and that of rule-based designs. Both are expressions of force flows within, and share similar resulting structural capacities and characteristics, but depart from different structural viewpoints. While the first establishes form through material computation—the possibility of material to self-form under the impact of external forces—the second establishes form through rule-base, optimised geometries that govern complex shapes.

This is significant because systems vary between reg-ular and irregular organisations as result of self-forming pro-cesses that build according to a logic of material formation. And without the logic of rule-based paradigms, form becomes arbitrary and meaningless. At the intersection between digital and analogue, the investigation of structural forms–strate-gized tectonics that take architectural design from concept to fabrication and construction–enhance the core competence of an architect; and enables firstly, an understanding, and secondly, the collaboration between engineers and architects. In fact, the legacy of structural complexity we inherit in works by Otto, Fuller, Candela, Dieste, has been set by these

engineer-architects variably as self-forming structures, and rule-based geometries.

6 Neil Leach, Digital Morphogenesis (London: Wiley Academy, AD 79, 2009), 34.

7 Pedreschi quotes Mainstone on three forms of intuition that have guided structural innovation: “1. Intuitions of structural behaviour: a spatial or muscular sense of the actions of force and stability, that an arch may spread if the abutments are not sufficient to push against the thrust or that a tall slender column is less stable than a short broad column. 2. Intuitions of structural action: a deeper understanding of structural behaviour, supported by careful observation that led to more precise ideas of force, moment and equilibrium; the start of a quantitative understanding of structure. 3. Intuitions of structural adequacy: a perception of the adequacy of a generic structural form for a particular application, conditioned perhaps by the significance of changes in scale and proportion.” Remo Pedreschi, “Form, Force and Structure: A Brief History” in Achim Menges and Michael Weinstock (eds.), Versatility and Vicissitude: Performance in Morpho-Ecological Design (London: Wiley Academy, AD 78, March 2008), 12-19.

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principles. In continued applications and physical tests in 1:1 prototypes, this allowed us to think through structural logic and rule-based scenarios for a variety of architectural paradigms by manipulation, adaptation, and evolution of form, force and structure.

In the design of form and force, SmartStructures-Lab2014 was segmented into the following distinct phases; a. the physical form finding through a spacebox after a structural precedent, b. the transfer modeling of form and system into 3D-modelling software (McNeel Rhinoceros); c. the continued variation through rule-based descriptions (GH Grasshopper); d. the testing and revision for structural fitness (karamba); and e. the organization into segmented elements for digital fabrication. The initial production of the design framework was then followed by a prescribed path for the testing of complex hypar or other rule-based geometries. Each of these phases reviewed criteria that impacted on the design decisions for form / architectural object: a. Students were asked to select a design strategy or exploratory model by an engineer-architect, research its context and variations, and remodel the precedent as a tension, compression or hybrid model. The physical form-finding started with a spacebox (a wooden frame with base, a support boundary condition able to withstand tension/compression), in which students set up a series of material form studies (membranes with anchor points and cables/threads). Students reviewed the resulting model through stress testing and defor-mations (subjecting the shape to additive impact in tension or compression. For example, the curvature of a surface can be formed by pulling anchor points in three or more directions (x-,y-, and z- axes). This allowed us to demonstrate the force flows within, and enabled students to experience form and force relationships as the formative behavior of structures. b. The studio then transferred the analogue form studies into advanced computational software. The translation of self-forming behavior into digital modeling (McNeel Rhino) provided the potential to establish, rethink and revise rules for forms. For example, models could be described by setting a series of defined curvatures and sweeping along set line, effectively expressing design as a ruled-based and self-form-ing system. As a consequence, the force flow set a parametric definition for the geometry of digital form (in contrast to non-geometrical form finding). Design variations could initially

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structures (shells, vaults, conoids) and tension-compression combinations (space grids or geodesic domes) are complex but structurally very efficient geometries. Shells can be singly curved (cylinders, vaults, cones), or doubly curved (domes, hyperbolic paraboloids). Similar to form-found or self-forming structures such as the tension membranes discussed earlier, shells are form-resistant: they resist loads by virtue of shape¹² and are inherently geometrical, therefore rule-base, because

“all constructed shells are fragments of a more complete geometrical shape, and all geometric surfaces either continue to infinity or intersect with themselves.”¹³ Hyperbolic paraboloids can be described as doubly curved surfaces with a negative curvature, formed as a saddle. Moreover, of all complex doubly curved geometries, hypars are specifically smart because their shape can be defined with straight lines. We can argue that these hypars are conceptual extensions of the self-forming membranes or catenary arches, and have simple equations describing their warped surfaces that

“permit stress calculations through simple mathematics.”¹⁴ More importantly for architectural design, they are generic geometrical forms that offer a multitude of applications through simple manipulations—via curved boundaries or straight cuts, through rotations, or intersections of the hypar surfaces. These doubly curved surfaces thus become rule-based design systems—design models that expand the structural and material arsenal of architecture.

STUDIO The SmartStructuresLab2014 (Self-Forming Systems and Rule Based Geometries for Catenary Structures, Membranes and Shells)¹⁵ reviewed the means by which architectural systems respond, adapt and achieve form through interaction with external and internal forces. We used engineering precedents as a springboard for design; to reflect upon structure and skin, force behavior and spatial performance, and to use these precedents for innovation and invention in architecture, referencing and researching the work of engineer-architects Frei Otto, Eladio Dieste, Buckminster Fuller, and Felix Candela.

The studio pathway proceeded through the two-fold agenda from self-formation to rule-based design in a continuous process. The students designed, simulated forces, analysed, systematized and re-articulated structural systems

of hypars (in catenary, shell, or membrane systems), which acted as design drivers that apply mathematical

12 An excellent discussion of structures can be found here. Richard Bradshaw, David Campbell, Mousa Gargai, Amir Mirmiran, Patrick Tripeny, Special Structures: Present, Past and Future (American Society of Civil Engineering. Journal of Structural Engineering, June 2002), 691-708.

13 Ibid., 695.

14 Maria Moreyra Garlock and David P Billington, Felix Candela: Engineer, Builder, Structural Artist, 76.

15 This postgraduate Master of Digital Architecture Research studio at the Faculty of Architecture, Design and Planning, The University of Sydney, was led by Dr Dagmar Reinhardt with Eduardo De Oliviera Barata, UFOSydney, Rob Beson, AR_MA, and Alexander Jung, reinhardt_jung|architecture.

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CONCLUSION Relationships between form, force and structure remain a core question in architectural discourse. Critical to under-standing this is the dialogue between the parallel realms of architecture and structural engineering, which can produce forms that go beyond aesthetic criteria, and which can be smart—in their design, their structure, and their construc-tion. In this context, advanced computational software offers not so much an effective medium but a collaboration tool for the exchange of work within a multi-disciplinary team. 3D modeling, scripting and analysis software can be considered a platform that interfaces between architect, engineer, and fabrication.

As has been discussed, SmartStructuresLab2014 deeply engages with the conceptual and practice sides of architectural design. On the practice side and aiming at the architectural profession, the course prepares students for multiple exchanges of form in a design process that—beyond form variations available through scripting software—includes structural performance as a key design criterion.

On the academic side, the SmartStructuresLab stu-dio series continues to engage design as design research. Through a discourse of form and force, design is a systemic process of collaborations and shared design intelligence that advances knowledge in the field of architecture. By developing potential methodologies for interdisciplinary practice, a horizontal learning structure empowered paradigms of the digital–through advanced geometries, structural engineering, and digital fabrication—that can act as pilot projects and prototypes for new architectural and engineering approaches.

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be formed intuitively, and then described as rule-based protocol. c. In continuation, the ruled-based iteration of form was translated into rules in the parametric environment Grasshopper (GH, McNeel Rhino plug-in), whereby form was solved in precise descriptions of geometry, relations, and mathematical prompts in code (if-then scenarios). In this design environment, form similar to its analogue parallel corresponds to threshold conditions set by predefined criteria. For example, spline curves can be set as tangents between three defined points, and closed with a minimal surface that is

‘released’ between all curve boundaries (through gravity sim-ulations in kangaroo, a Live Physics plug-in for Grasshopper that provides interactive optimization and form-finding). d. Interlocking with physical and digital modeling, the studio then continued iterations of complex hypar forms into the simulation and analysis of forces, and into optimisations of spatial and structural performance. For the gravity and load testing exercises, students were trained in a custom-de-signed engineering workshop in karamba (a structural engineering software plug-in for Grasshopper). This software provides accurate analysis of spatial trusses and frames, and thus allows the further definition of form and force by combining parameterized geometric models, finite element calculations and optimization algorithms. e. Finally, the design continued the process into a series of digitally fabricated models, from representational 3D-printed form studies, to precise and detailed fabrication for construction. Students organized form into segmented elements for digital fabrication and construction, as 1:20 skeleton structures, and finally into 1:1 scaled plywood proto-types. Based upon the structural engineering analysis, design principles were revised so as to account for and integrate material properties and fabrication requirements. This stands for an applied architectural solution derived from previous analogue and digital exercises. Students thus applied their previously acquired understanding of force flows within forms to a detailed, efficient prototype of an architectural object in a context. The resulting structures are smart, structurally informed, and represent a design that has come full-circle

back to an analogue model.

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ARCHITECTURE ANNUAL 2014: PROPOSITIONS First published in 2014 by Freerange Press in conjunction with the Graduate Architecture Exhibition 4th-12th December, 2014

Freerange Press is an online and print publishing co-operative based in Australia and New Zealand. Freerange's focus is on global issues of design, politics and life for an urbanised humanity.

www.projectfreerange.com

Tin Sheds Gallery, 148 City Road University of Sydney, NSW 2006, Australia

ISBN: 978-0-9808689-6-8

Editor: Ross Anderson

Associate Editors: Sean Bryen Kevin Liu

Designer: Ryan Phung

Printer: Peachy Print Australia Pty Ltd

© 2014 PROPOSITIONS This book, PROPOSITIONS, and all works depicted in it are © editors and contributors, 2014. All rights reserved.

004

Proposition

“The setting forth of something as a subject of discourse; something proposed for discussion, or as a basis of argument.

A question proposed for solution; a problem, a riddle.

The action of setting forth or presenting to view or perception.”

Oxford English Dictionary, Vol. 9, 2nd ed., s.v. “Proposition.”

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NT

EN

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FOREWORD LEE STICKELLS

ARCHITECTURE STUDIO INDEX

STUDENT INDEX

SETTINGS FORTH ROSS ANDERSON

CUBES, SPHERES, PYRAMIDS: ORTHOPAEDICS AS ARCHITECTURAL PEDAGOGY FRANÇOIS BLANCIAK

FROM THE VERY BIG BOOK OF ARCHITECTURAL PATHOLOGIES: MALADY NO. 1—ATTENTION SEEKING BEHAVIOUR GLEN HILL

FORM AND FORCE DAGMAR REINHARDT & ALEXANDER JUNG

NOT NOW SEAN ANDERSON

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