Atthaphan Sespattanachai Dissertation

Structurally-informed design on Form-Finding methodology: Analogue and Computation

160408311 Atthaphan Sespattanachai Newcastle University School of Planning and Landscape ARC3060

Dissertation: Structally-informed design

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Dissertation: Structally-informed design

Content Part 1

Chapter 1: objectives and conceptual framework

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Chapter 2: Importance of structurally-informed

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Part 2

Chapter 3: Analogue form-finding and Computational form-finding method

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Part 3

Chapter 4 : Presenting the emergence of mycelium and the potential of using mycelium-based material as a building structure through TNA approach by using Rhi noVault as a starting platform.

Part 4

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Conclusion

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Dissertation: Structally-informed design

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Dissertation: Structally-informed design

Abstract This dissertation presents significant impacts a structurally-informed design have toward the overall design geometry of funicular architecture through two major form-finding methods: analogue form-finding method and computational form-finding method.

Additionally, this will look into a potential of using a computational method in combination with regenerative resources to propose an alternative sustainable building material.

In the past century, many famous architects and engineers have developed numerous design techniques in order to realise a design with stable and equilibrium structure: graphic statics, hanging model, Soap bubble. Some of these techniques are still being used today, however, with the emerging of new advanced design technique, computational-based design, the form-finding method in architectural design has become much more efficient and effective, especially when the structural awareness is introduced in the early design stage. One of these new methodologies for structurally-informed design is Thrust Network Analysis (TNA). TNA is a structurally-informed design through the use of geometrical representation utilising reciprocal diagrams of force and form of the design which extends from O’Dwyer’s Force Network Method. This methodology offers an interactive and flexible form-finding design, allowing for a variety of complex equilibrium designs. In the combination of TNA with a new emerging sustainable material, mycelium-based material, this computational form-finding method could offer a potential of using mycelium-based material not only just in a building facade but also in a building structure which could be achieved through stability of the structure geometry. This dissertation will also be focusing on using Thrust Network Analysis as a main form-finding method through a software program, RhinoVault developed by Philippe Block and Matthias Rippmann, which offers structure-informed design approach in the early design stage.

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Dissertation: Structally-informed design

Part 1 Chapter 1: objectives and conceptual framework This dissertation aims to present essential impacts a structurally-informed design have in an early form-finding design stage toward the overall design geometry. This will be focusing on funicular architecture design by comparing two different form-finding methods. First one is analogue form-finding method which architects and engineers have been using for centuries. The other form-finding method which has only been emerged for less than 30 years is a computational form-finding method. These two methods have significant impacts on the building design which is used to determine the overall form of the buildings. One of the main reasons is to deal with building stability. Moreover, taking a structurally-informed design approach allow exploration of using potential regenerative resources to design an alternative sustainable architecture such as Mycelium-based material as a building material.

This dissertation is divided into 4 parts.

Part 1, Chapter 1 is an introduction to this dissertation, presenting the objectives and conceptual framework. Chapter 2 is about the importance of structurally-informed design in the early design stage, and background of funicular architecture and form finding.

Part 2, Chapter 3 presents a comparison between two form-finding methods: analogue form-finding and computational form-finding method, including some outstanding approaches taken by a number of well-known architects such as Antoni Gaudi (18521926), Heinz Isler (1926-2009) and Frei Otto (1925-2015). As the main focus of computational form-finding, the basic principles of Thrust Network Analysis (TNA) approach and its advantages in the early design stage will be described, and how this could be used to design various compression-only form, tension-only form or combined tension and compression form, including case studies of previous research and demonstrations using RhinoVault.

Part 3, Chapter 4 presents the emergence of mycelium and the potential of using mycelium-based material as a building structure through TNA approach by using RhinoVault as a starting platform. Additionally, the limitations of TNA and mycelium-based material, and potential of it being used in the building structure will be discussed.

Part 4, Chapter 5 is the conclusion of the analogue and computational form-finding method, and the application of mycelium-based material in building structure (could this be a foundation for future research?). This is linked back to my objective in Part1.

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Dissertation: Structally-informed design

Chapter 2: Importance of structurally-informed design in an early design stage, and background of funicular architecture and form finding.

2.1 The importance of structurally-informed design in an early design stage In order to determine the structural efficiency of a building, form is a significant factor contributing to the overall building stability. In fact, the form might be as important or even much more important than the building material or element sizing. The distribution and magnitude of the forces the building must resist are determined directly by the geometry of a building’s structure (Macdonald, 2001). This inherent interrelation of form and structure is elegantly expressed by Eladio Dieste, architect and structural engineer: “The resistant virtues of the structure that we seek depend on their form; it is through their form that they are stable, not because of an awkward accumulation of material.

There is nothing more noble and elegant from an intellectual viewpoint than this: to resist through form.�

(Rippmann, 2016) As illustrated in figure 2.1 (a), the interrelation of form and force for the three arches with different rise under uniform vertical loading is shown through three possible catenary geometries for a long-span roof (Rippmann, 2016). The maximum axial force is reduced by a factor of four by increasing the height and thus the curvature of the arch.

Fig. 2.1 (a). Three catenary arches with different rise under uniform vertical loading, resulting in (a) a maximum axial force, which can be reduced by a factor of four (c) by increasing the height and thus the curvature of the arch (Rippmann, 2016).

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Dissertation: Structally-informed design

In most building design today, the overall geometry of a building is first conceived by the architect by approaching the design problem from a very wide angle, then narrowing down the range of design solutions and subsequently structurally analysed, dimensioned and constructed in collaboration with the engineer. As a result, a single design or a limited number of possible alternative solutions is developed in detail, eventually, lead to an adequate solution to the design problem. This is an acceptable approach in standard building form for which the architect can rely on fundamental structural knowledge and experience. However, if the architect tries to design more complicated forms especially funicular architecture, this would require a deeper understanding of sophisticated structural design and a more effective designing approach. This applies especially to structures that, despite their formal complexities, they can be realised with minimal use of materials and resources (Allen and Zalewski, 2010). Moreover, this has a big impact on the overall project’s expenditure, material and time consumption.

Today designing is usually not a linear process, especially in the beginning stages. It is an iterative process of jumping forwards and backward and it is an extremely common procedure. This process would be even more difficult when architects are designing a much more complicated form, resulting in a greater designing time consumption, project’s expenditure, and material usage, especially for funicular architecture. This is the case if the architects are taking the usual designing method, however, this complication can be dramatically reduced by introducing structurally-informed design in the early design stage.

Fig. 2.1 (b). Relationship between design freedom and design knowledge in building design projects based on American Institute of Architects, 2007 (Mueller, 2014).

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Dissertation: Structally-informed design

According to Mueller (2014) and Rippmann (2016), the initial design stage is a significant step with the most design freedom where most of creativity and design impact occur, at the same time it is the period that influences the subsequent stages the most.

This level of influence throughout the design stage between design freedom and design knowledge is explained in Mueller’s relationship graph based on American Institute of Architects, 2007 (Fig. 2.1 b). She describes that design impact and creativity normally occurs during conceptual design, but structural considerations usually enter the process afterward. This creates a limitation for structural engineers to contribute impactful ideas in the early design process. This awareness is reflected in the latest modifications of the Royal Institute of British Architects (RIBA) framework for design and construction (Plan of Work 2013) by emphasising earlier project collaboration and team assembly.

The plan comprises 3 design work stages prior to the construction stage: concept design, developed design and technical design. The ability to influence the design of a project decreases throughout these stags. Despite such efforts to involve specialists in the early design process, the role of architects and engineers has hardly changed in this important initial conceptualisation stage (Rippmann, 2016). Typically in the concept design phase, the overall building concept, massing, and geometry are usually defined and carried out by architects without strong involvement from engineering consultants. Especially, the initial form of a building is usually conceived by the architect based on programmatic and conceptual aspects with small attention to structural considerations (Macdonald, 2001). This traditional, hierarchical process limits structural sophistication mainly to structural material and system selection, member sizing, and the development of structural strategies for an overall design geometry that has already been set. This presents a major problem since form significantly determines the structural efficiency of a building.

At the same time, however, altering the form becomes increasingly more difficult as the design process progresses (Rippmann, 2016). In other words, a structurally efficient form for a building must be developed early in the design process.

Stages

The RIBA Plan of Work 2013 organises the process of briefing, designing, constructing, maintaining, operating and using building projects into a number of key stages. The content of stages may vary or overlap to suit specific project requirements. The RIBA Plan of Work 2013 should be used solely as guidance for the preparation of detailed professional services contracts and building contracts.

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Strategic Definition

Preparation and Brief

Concept Design

Developed Design

Technical Design

Core Objectives

Identify client’s Business Case and Strategic Brief and other core project requirements.

Develop Project Objectives, including Quality Objectives and Project Outcomes, Sustainability Aspirations, Project Budget, other parameters or constraints and develop Initial Project Brief.

Undertake Feasibility Studies and review of Site Information.

Prepare Concept Design, including outline proposals for structural design, building services systems, outline specifications and preliminary Cost Information along with relevant Project Strategies in accordance with Design Programme. Agree alterations to brief and issue Final Project Brief.

Prepare Developed Design, including coordinated and updated proposals for structural design, building services systems, outline specifications, Cost Information and Project Strategies in accordance with Design Programme.

Prepare Technical Design in accordance with Design Responsibility Matrix and Project Strategies to include all architectural, structural and building services information, specialist subcontractor design and specifications, in accordance with Design Programme.

Procurement

Initial considerations for assembling the project team.

Prepare Project Roles Table and Contractual Tree and continue assembling the project team.

Tasks

*Variable task bar

Programme

Establish Project Programme. Review Project Programme.

The procurement strategy does not fundamentally alter the progression of the design or the level of detail prepared at a given stage. However, Information Exchanges will vary depending on the selected procurement route and Building Contract. A bespoke RIBA Plan of Work 2013 will set out the specific tendering and procurement activities that will occur at each stage in relation to the chosen procurement route.

Review Project Programme.

*Variable task bar

(Town) Planning

Pre-application discussions.

Pre-application discussions.

Review Feedback from previous projects.

Prepare Handover Strategy and Risk Assessments.

Agree Schedule of Services, Design Responsibility Matrix and Information Exchanges and prepare Project Execution Plan including Technology and Communication Strategies and consideration of Common Standards to be used.

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Construction

Handover and Close Out

Offsite manufacturing and Handover of building and onsite Construction in conclusion of Building accordance with Construction Contract.

Programme and resolution of Design Queries from site as they arise.

Administration of Building Contract, including regular site inspections and review of progress.

7 In Use Undertake In Use services in accordance with Schedule of Services.

Conclude administration of Building Contract.

The procurement route may dictate the Project Programme and may result in certain stages overlapping or being undertaken concurrently. A bespoke RIBA Plan of Work 2013 will clarify the stage overlaps. The Project Programme will set out the specific stage dates and detailed programme durations.

Planning applications are typically made using the Stage 3 output.

A bespoke RIBA Plan of Work 2013 will identify when the planning application is to be made.

*Variable task bar

Suggested Key Support Tasks

www.ribaplanofwork.com

Prepare Sustainability Strategy, Maintenance and Operational Strategy and review Handover Strategy and Risk Assessments.

Review and update Sustainability, Maintenance and Operational and Handover Strategies and Risk Assessments.

Review and update Sustainability, Maintenance and Operational and Handover Strategies and Risk Assessments.

Undertake third party consultations as required and any Research and Development aspects.

Undertake third party consultations as required and conclude Research and Development aspects.

Prepare and submit Building Regulations submission and any other third party submissions requiring consent.

Review and update Project Execution Plan.

Review and update Project Execution Plan, including Change Control Procedures.

Review and update Project Execution Plan.

Consider Construction Strategy, including offsite Review and update fabrication, and develop Health Construction and Health and and Safety Strategy.

Safety Strategies.

Review Construction Strategy, including sequencing, and update Health and Safety Strategy.

Review and update Sustainability Strategy and implement Handover Strategy, including agreement of information required for commissioning, training, handover, asset management, future monitoring and maintenance and ongoing compilation of ‘Asconstructed’ Information.

Carry out activities listed in Handover Strategy including Feedback for use during the future life of the building or on future projects.

Updating of Project Information as required.

Update Construction and Health and Safety Strategies.

Conclude activities listed in Handover Strategy including Post-occupancy Evaluation, review of Project Performance, Project Outcomes and Research and Development aspects.

Updating of Project Information, as required, in response to ongoing client Feedback until the end of the building’s life.

Sustainability Checkpoints

Sustainability Checkpoint — 0

Sustainability Checkpoint — 1

Sustainability Checkpoint — 2

Sustainability Checkpoint — 3

Sustainability Checkpoint — 4

Sustainability Checkpoint — 5

Sustainability Checkpoint — 6

Sustainability Checkpoint — 7

Information Exchanges

Strategic Brief.

Initial Project Brief.

Concept Design including outline structural and building services design, associated Project Strategies, preliminary Cost Information and Final Project Brief.

Developed Design, including the coordinated architectural, structural and building services design and updated Cost Information.

Completed Technical Design of the project.

‘As-constructed’ Information.

Updated ‘As-constructed’ Information.

‘As-constructed’ Information updated in response to ongoing client Feedback and maintenance or operational developments.

Not required.

Required.

Required.

Required.

Not required.

Not required.

Required.

As required.

(at stage completion)

UK Government Information Exchanges

© RIBA

*Variable task bar – in creating a bespoke project or practice specific RIBA Plan of Work 2013 via www.ribaplanofwork.com a specific bar is selected from a number of options.

Fig. 2.1 (c). Royal Institute of British Architects (RIBA) framework for design and construction (Plan of Work 2013) emphasising design stages: Concept design, Developed design, and Technical design.

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Dissertation: Structally-informed design

Benefits of structurally-informed design 2.1.1 Reduction in environmental impact and project’s expenditure Integrating structurally-informed design in early design stage offers a considerable amount of reduction in structural material and project’s expenditure. As illustrated in figure 2.1 (a), considering the relationship between form and force of the geometry in early design stage could have a significant impact on the distribution and magnitude of forces acting on the building components, allowing for minimisation of the use of material, and improving the overall environmental impact (Rippmann, 2016). This also enables the use of materials that are structurally weak in bending and tension but strong in compression such as unreinforced concrete, stone, adobe and rammed earth or compressed waste materials to cover a large span with minimum material (Block, 2009).

As indicate in Mapungubwe museum in South Africa (Fig. 2.1.1 a). By determining the shape of three-dimensional compression forms, the architects, Peter Rich, Michael Ramage, Henry Fagan, and John Ochsendorf, were able to design masonry vaults with no reinforcing steel. Moreover, the low stresses in structure allow the possibility of using cement-stabilised tiles which made from local soil to be pressed on site, reducing the shipping of materials to the site. This allows the masons to build the museum with minimal formwork, resulting in very little waste. Another similar example is Pines Calyx conference centre in Dover, England (Fig. 2.1.1 b). Embodied energy is significantly reduced through a clear and architecturally integrated structure developed in conceptual design (Mueller, 2014).

On the other hand, when architectural concepts are developed with small structural influence, the outcome can be expensive, material and maintenance-intensive building. In the works of Frank Gehry, Guggenheim Museum in Bilbao, Spain (1997) (Fig. 2.1.1 c), is a unique and remarkable building exploring the limit of architecture and engineering, attracting millions of visitors from all around the world. However, the building is often criticised for its bulky construction and heavy structure, as well as for wasting material and resources that could have been saved through a more structurally-informed and construction-aware design methodology (Block, 2009; Carpo, 2013). The building was conceptualised and designed using sketches and models but planned and realised using Computer-aided design. Without realisation through rationalised planning processes using sophisticated software, this building may not be possible or extremely difficult to realise.

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Dissertation: Structally-informed design

Fig. 2.1.1 (a). Mapungubwe museum (South Africa) (Block, 2009)

Fig. 2.1.1 (b). Pines Calyx conference centre in Dover (England) (Mueller, 2014)

Fig. 2.1.1 (c). Guggenheim Museum in Bilbao (Spain) (Rippmann, 2016)

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Dissertation: Structally-informed design

2.1.2 Architectural richness and elegance Structurally-derived building form could be considered naturally elegant and aesthetically pleasing. Many architects and people from the design community have claimed that “buildings are most remarkable for the clarity of their engineering. The power and grace of these extraordinary shapes and patterns stem directly from their structural logic, and are inseparable from it”, written by Ada Louise Huxtable (Mueller, 2014). Among many others, the works of Pier Luigi Nervi and Frei Otto represent such a structure clarity, for example, Palazzetto Dello Sport (Rome), Turin Exhibition hall (Turin), Palazzo Del Lavoro (Turin), and Multihalle in Mannheim (Germany). This clarity is also demonstrated in other building such as International terminal (San Francisco) designed by Skidmore, Owings & Merrill (SOM) (Fig. 2.1.2). The three-dimensional truss design achieves a long, column-free span while also allowing filtered daylight to enter the space (Rippmann, 2016).

2.1.3 Inherent safety Structurally-informed building geometries are safe by their nature. This is because rather than just employing extreme exertion on the part of structural engineers and the high-strength materials, the stability of the building is also achieved through its overall geometry and efficient load transfer. This design approach offers efficient stability in building structure which could be achieved through the property of building material and geometry (Mueller, 2014). This property is illustrated in many famous architects / engineers’ works, one of them is Heinz Isler’s experiment model comparing the strength of two sheets of thin plastic (Fig. 2.1.3 a). One is a flat sheet with a force applying in the centre, another is made exactly from the same material and thickness but with different geometry. The latter model is formed into a double-curved funicular arch. As a result, the experiment demonstrates the deflection in the first flat sheet but hardly deflected in the other one, even though the weight on the second one is 30 times that of the weight of the first testing model. Isler explains that for the second model, the load bearing capacity and resistance to deformation have been significantly enhanced by the addition of curvature. This leads to the potential of exploring structural forms where the least material is disposed of in the best way to resist the applied forces with a minimum of stress and deformation (Chilton, 2000). Similarly, this principle can also be seen in brick and concrete structure that is weak in tension but strong in compression which could be used to construct buildings with long-span space. This will be discussed further in the next part.

Fig. 2.1.3 (a). Modeldemonstrating the efficiency of a double-curved shell made from then plastic compare to a similar plastic sheet acting as a wide flat beam over the same span. The load on the sheel is 30 times the load on the flat sheet.

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Fig. 2.1.2 (a). Palazzetto Dello Sport (Rome) (Mueller, 2014)

Fig. 2.1.2 (b). Palazzo Del Lavoro (Turin) (Sespattanachai, A.)

Fig. 2.1.2 (d). Multihalle in Mannheim (Germany)

Fig. 2.1.1 (c)Turin Exhibition hall (Turin) (Sespattanachai, A.)

Fig. 2.1.2 (e). International terminal (San Francisco)

Dissertation: Structally-informed design

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Dissertation: Structally-informed design

2.2 Funicular architecture There is a countless number of structurally-driven forms that can be realised in order to achieved building function and programme, and one of them is funicular architecture.

This form is taking advantage of the force transfer in the structure which is behaving like fluid dynamics. The external load acting on the form and the load of the structure itself would transfer down to specific foundation points, allowing for a greater building span, and achieving a structural equilibrium state. Modern funicular architecture’s origin can be traced back to the ancient time when human started to use arches, dome, shell structure to achieve the significant spatial structure of the buildings. The concrete vaults and dome built by Romans, which are the earliest ancestors of modern thin-shell structures, were cylindrical or hemispherical (Addis, 2007). In late medieval cathedrals, pointed arches and vaults, formed with two circular arcs, were widely used because they allowed the height and span of a vault to be valid independently. A large number of design procedures were developed using typical geometrical shape and dimensions of masonry arches and vaults as well as their abutments (Addis, 2014). This is due to the fact that form generation technique was quite limited in the past, hence most designers have to rely on their own experience or typical structural geometry. Nevertheless, they were still able to achieve such an elegant, spacious and longevity building and structure. One of the greatest examples is Pantheon’s dome, it is the world largest unreinforced concrete dome with 43 m in height and diameter. Another example is Since ancient times and still valid today, building designers have used numerous methods to answer these two main questions: • How can a three-dimensional geometric shape be defined, described or communicated from one person to another? In other words, in what way a three-dimensional form can be generated?

• What is the most appropriate three-dimensional forms for a shell / dome structure in order for architects / designers gains sufficient confidence that the structure will work as intended?

(Addis, 2014)

Fig. 2.2. Pantheon (Rome) (Sespattanachai, A.)

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Dissertation: Structally-informed design

2.3 Form Finding For many centuries, architects and engineers have been developing numerous form-finding methods to find the most suitable design geometry which would enable them to achieve design concept and programme structurally and aesthetically. Form is playing a significant role in architecture and engineering, for example, funicular geometry allows building designers to achieve a large spatial structure which could not be easily achieved through typical building beams and columns. As stated by Adriaenssens (2014), form finding can be defined as the “forward process in which parameters are explicitly / directly controlled to find an optimal geometry of a structure which is in state equilibrium with a design loading”.

In another word, the aim for form finding is to define a geometry that only develops membrane stresses for the assumed, dominant load case while also meeting desire architectural, programmatic and aesthetic criteria (Rippmann, 2016). Form finding is a structurally-informed geometry generation process in which parameters can be imposed to control the form-finding process such as boundary conditions, supports, external loads, typology of the model, internal forces, and their relationship to the geometry. One of the earliest examples of structural form finding was published by English engineer and scientist, Robert Hooke (1635-1703) (Block, 2009). He used a hanging chain to find a structure that acts in pure tension with no portion of the structure is subjected to bending moment, and by inverting the hanging chain geometry upside down he was able to find the ideal compression-only geometry for a rigid arch (Fig. 2.3 a). This inverted catenary, Hooke’s law of inversion, was used by Christopher Wren during the design of St Paul’s Cathedral’s inner masonry cone in London to raise architects’ structural awareness of the dome so that it would work satisfactorily as a compression structure (Fig. 2.3 b) (Addis, 2014). This technique would later inspire a number of architects and engineers to find the most efficient form-finding method such as Antoni Gaudi (1852-1926), Heinz Isler (1926-2009) and Frei Otto (1925-2015). Moreover, with the emergence of cutting edge design tool, computer-aided design, Hooke’s law of inversion combining with graphic static, mathematical analysis, and other techniques have been adapted and programmed, enabling architects, designers, and engineers to simulate and explore an infinite number of funicular forms. In chapter 3, two main form-finding methods, analogue form-finding, and computational form-finding methods, will be discussed.

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Dissertation: Structally-informed design

Fig. 2.3 a. (a) Poleni’s drawing of Hooke’s analogy between an arch and a hanging chain. (b) Analysis tool for the dome of St. Peter’s in Rome (Addis, 2014)

Fig. 2.3 b. (a) The inverted hanging chain in front of the section of the dome of the St Paul’s Cathedral in London by Christopher Wren (1720) and (b) the architectural section of the building.

(Rippmann, 2016)

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Dissertation: Structally-informed design

Part 2 Chapter 3: Analogue form-finding and Computational form-finding method Funicular architectural form will always have a role for architecture and engineering. The form has the ability to create eye-catching forms, to provide freedom for design exploration and to resist loads efficiently (Ochsendorf and Block, 2014). For even, the most highly constrained geometry, number of solutions are available to architects and engineers. But each different funicular geometry has its own advantages and disadvantages, and all forms are not equal. In order to determine the most appropriate and efficient form, the design of funicular architecture demands a structurally-informed design process in early design stage connecting architectural intent and structural necessity, an understanding of the relationship between form and force (Rippmann, 2016). This chapter will discuss two main form-finding methods architects and engineers have been using: Analogue form-finding method, and computational form-finding method.

According to Adriaenssens (2014), the geometry of shell architecture can be divided into two major categories based on their generation process: Freeform shell : This type does not take structural consideration into account in the early design phase. They are conceived through a sculptural design process (Fig. 3 a). Typically, the form is derived by an architect and then analysed and dimensioned later by an engineer.

Funicular shell : This is generated from a structurally-derived design process. Such geometries are generated mainly through the use of physical models, suspended models, and mathematical function in the early designing stage. Recently, the use of computational form-finding methods has a significant influence in exploring states of equilibrium (Fig. 3 b).

Fig. 3 a. Freeform shells : Eastman Kosak Pavilion, New York. (Ochsendorf and Block, 2014).

Fig. 3 b. Funicular shells : Sicli SA factory, Switzerland. (Chilton, 2010).

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Dissertation: Structally-informed design

3.1 Analogue form-finding method The challenge of funicular architecture design is to find the appropriate form for the given problem. There is an infinite number of structural forms are waiting to be discovered.

Even highly constrained boundary conditions can still lead to a vastly rich landscape of forms to explore. In order to determine these forms, many approaches can be taken, and one of these approaches is model-making. Combining with other factors/approaches, the model-making technique could help to raise the engineer’s confidence and provide some indication of structural behaviour in the proposed design. This may have been for one of many reasons. For example: • The available calculation methods were too complicated and/or time-consuming.

• Building a full-size prototype would be too costly and time-consuming.

• The standard structural analysis method might be inadequate for advanced fu

nicular form.

• A mathematical equation could not be easily used to defined geometry of the structure.

• The type of structure was unique and unprecedented.

• There is a need for a starting point to define an appropriate form.

(Addis, 2014) In term of model-based approach, there are number of different ways of model making have been taken by architects and engineers such as nature-inspired method, a hanging chain (one of the earliest approach), a hanging set of net or membranes, a soap bubble, inflation of an elastic membrane (a ballon), or even crumpling a sheet of paper. The designers must seek forms that offer multiple load paths for all expected applied loads, and whose formal possibilities are closely linked to the modes of constructions. As this approach can be seen in many famous architects, for instance, Antoni Gaudi, Heinz Isler, and Frei Otto. Furthermore, not only funicular architecture demands structurally-informed design for the most efficient form, but also require a well understanding of the relationship between form and force in the design process (Allen, E. and W. Zalewski, 2010), which could be summarised through two related methods. First, the application of graphic statics as a two-dimensional design and analysis tool. Second, the function of suspended physical models as a three-dimensional design process. These methods, later, are used as essential foundations for development and application of Thrust Network Analysis (TNA) (Block, 2009).

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Dissertation: Structally-informed design

3.1.1 Graphic statics Graphic statics is a powerful and intuitive method in exploring two-dimensional equilibrium funicular architecture for given loads based on graphical representations of form and force diagrams. Form diagram is representing the geometry of the structure, as shown in this funicular polygon. Force diagram is representing the state of equilibrium of internal forces and external loads acting on the structure, and magnitude of forces in the individual elements of form diagram by measuring the length of the corresponding, parallel element in the force diagram, which is drawn to scale (Fig. 3.1.1). This relationship of geometry and topology between form and force diagram is called reciprocal (Block, 2009). By having these topological, geometrical and structural properties:

•Reciprocal diagrams between form and force: both diagrams have the same number of edges, and each node with a valency higher than one in one diagram corresponds to a space, formed by a polygon of edges, in the other diagram.

•Each edge e in the form diagram has a corresponding edge e*, parallel to edge e, in the force diagram.

•The length of edge e* in the force diagram is, to scale, equal to the magnitude of axial force in edge e in the form diagram.

(Rippmann, 2016) Form diagram

Force diagram

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Dissertation: Structally-informed design

Since the relationship between force and form diagrams is reciprocal, the state of equilibrium of the form diagram is guaranteed by forming closed vector polygon in the force diagram (Fig. 3.1.1 b). Closed polygon is constructed from edges coming together at a particular internal node of the form diagram (Fig. 3.1.1 b). The reciprocal property, therefore, leads to a unique force diagram for a given statically determinate structure and loads (Fig. 3.1.1). However, if the structure is statically indeterminate, there are more than 4 edges coming together at a particular node, more than one force diagram is available for the given form diagram ( this will be discuss further in 3.2.1 Thrust Network Analysis). This property provides a number of possibilities in exploring the state of equilibrium in force and form diagrams (Block, 2009). Additionally, a particular quality of graphic statics is its bi-directional nature, in other words, force diagram can be constructed from a form diagram or this can be the inverse process for constructing form diagram (Block, 2009). Hence, if constraints are imposed on the form diagram, such as a maximum depth of the structure or given points for the structure to go through, then the force diagram would be influenced and constrained; if constraints are imposed on the force diagram such as upper bounds on the thrust values, then the form diagram would be constructed according to these limitations. This provides a flexible design framework in which constraints can inform design possibility. Another key benefit is its straight forward comprehensibility and visualisation, represented by simple vector calculus and drafting (Block, Lachauer and Rippmann, 2014). As this can be seen in the works of many famous architects and engineers such as Gustave Eiffel (1832-1923), Rafael Guastavino (1842-1908), Antoni Gaudi (1852-1926) and Pier Luigi Nervi (1891-1979) (Lachauer, 2015).

However, graphic statics is practically limited to two-dimensional problems. In order to solve the three-dimensional structure, the process becomes much more complicated, tedious and time-consuming, requiring much more in-depth calculation, precision. This is due to the fact that three-dimensional problem is analysed and solved on two-dimensional media, flat paper sheets. In contrast, physical models provide a simpler interactive exploration of the equilibrium funicular forms of fully three-dimensional networks, although force information of the resulting networks need to be obtained separately.

Nevertheless, the significance and strength of graphic statics in the design process has been emphasised constantly. For instance, the importance of graphic statics in the education of architects and engineers, providing a basic understanding of structure as stated

by Nervi: “I believe that graphical statics should play an important role in this last educational phase, since its procedures give a direct understanding — much better than that afforded by analytical methods — of force systems and their composition, decomposition, and equilibrium.”

(Rippmann, 2016) Fig. 3.1.1 (on the left). The reciprocal diagrams of force (a) and form (b) for a uniformly loaded funicular polygon in compression. (c) The same funicular polygon but inverted in tension. (d) Additional point load. (e) Constant axial force (Rippmann, 2016).

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Fig. 3.1.1 b. A masonry arch of arbitary geometry with (a) thrust line and (b) corresponding hanging string, (c) the force diagram, showing (d) the equilibrium of one stone block (Block, Lachauer and Rippmann, 2014).

Form diagram

Force diagram option 1

Force diagram option 2

Fig. 3.1.1 c. Indeterminated structure of a form diagram and two possible reciprocal force diagrams with different horizontal force distribution (Block, 2009).

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3.1.2 Physical models Comparing to graphic statics, the use of physical models represents another method in analysing and developing the design of funicular architecture in three-dimensional design approach. The physical model experiment is an essential form-finding tool in the early design stage for structurally-driven funicular forms in which it cannot be easily generated using a standard vocabulary of geometrical forms such as sphere and ellipsoids, or using two-dimensional design approach. One of the significant advantages is its interactive three-dimensional visualisation, providing substantial information for fundamental structural behaviour in different load cases. This is due to the fact that the building stability is not only focusing on the strength of materials but also the overall geometrical static equilibrium has an essential function in this. Moreover, a physical model can serve to emphasise the degree to which its optimal form could deform before collapsing due to different acting forces, in other words, how much bending the funicular form will be required to endure - and the more bending must be resisted, the heavier the structural elements will be (Bletzinger and Ramm, 2014). This could even lead to finding other optimal forms for such a case. The model can also act as a testing prototype, confirming the structural performance, and raising architects and engineers’ structural awareness in case of determining the most suitable funicular form corresponding to many different loading cases (Fig. 3.1.2 a).

Fig. 3.1.2 (a). Plexiglas model of the Kilcher shell, Recherswill, used to determine the force distribution in the shell and its buckling behaviour. Tested by Heinz Isler (Chilton, 2000).

One of the earliest use of the physical model as a structurally-informed design process was established by English engineer and scientist, Robert Hooke (1635-1703), for his work on using inverted, hanging models to explain the equilibrium of funicular arch as discussed in section 2.3. Giovanni Poleni used this theorem, Hooke’s law of inversion, as an analysis tool for the dome of St. Peter’s in Rome (Fig. 2.3 a) (Addis, 2014). Many famous architects and engineers acknowledge the potential of the physical model’s role as one of the most efficient structurally-informed design tool which would later result in numerous fascinated funicular forms. The use of this methodology can be seen in many well-known builders and designers such as Antoni Gaudi, Heinz Isler, and Frei Otto.

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3.1.2.1 Antoni Gaudi One of the well-known architects who had successfully employed structurally-informed design through physical model is Catalan architect, Antoni Gaudi. He mainly focused his design approach on three-dimensional method rather than just designed on two dimensions, resulting in his style development from 2-D plane to spatial geometry and ruled geometry. Gaudi’s utilisation of complex, 3-dimensional hanging models during the design progress had allowed him to further explore variety static equilibrium of funicular forms. This was emphasised during his visualisation of Sagrada Família church design, in Barcelona, by employing high-precision gypsum models as he stated “The necessary geometry for executing surfaces does not complicate, but rather simplifies the construction process; ‘complicate’ is the algebraic expression of geometric things that are not completely possible, which gives occasion to misunderstandings – which, however, disappear when observing such bodies in space.”

(Tomlow, 2011)

Fig. 3.1.2.1 (a): Colònia Güell church. Hanging model developed by Gaudi’s team in 1898– 1908. A paper decoration gives the model an aspect of volume (Block, 2009).

Fig. 3.1.2.1 (b): Colònia Güell church. Reconstruction model in an abstract black and white in inverted position (Tomlow, 2011).

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Fig. 3.1.2.1 (c): Crypt interior with similar view point to that of the model (Tomlow, 2011).

Fig. 3.1.2.1 (d): The reconstruction of Gaudı’s hanging model by Rainer Graefe, Frei Otto, Jos Tomlow, Arnold Walz and team (Tomlow, 2011).

This approach was further emphasised in his unfinished work of Colònia Güell church near Barcelona. The design of the church suspended physical model took about 10 years to finish, began in 1898 and completed in 1908 on a scale of 1:10 and a weight scale of 1:10,000 (Fig. 3.1.2.1 a). According to Hooke’s law of inversion, Gaudi was able to establish equilibrium forms of arches and vaults that are independent and self-supporting, creating perfectly supporting structures without the need of buttresses, as demanded in Gothic architecture (Tomlow, 2011). By constructing suspended models that consisted of strings held in a stable net-like shape by the weight of sandbags led to a parametric, structurally-informed modelling process, in which each change in variable element would result in modification of overall design geometry such as string lengths and sandbag weight distributions (Fig. 3.1.2.1 b) (Rippmann, 2016).

Additionally, he sketched the church exterior design directly on the inverted photographs of the suspended model. In order to complete the design, Gaudi used the model test results with statical calculations and graphical statics to determine the structures and forms of the crypt, tilted columns, and vaults. However, making such a modification was not a straightforward process. In fact, the process was tedious and time-consuming, it took ten years for a highly skilled team to realise the form. The topology of connected string networks had to be constantly adapted and updated with high-precision control toward ideal forms. As a result, the alterations made to individual element could not be easily predicted or controlled in what way it would affect overall geometry, requiring a careful and iterative process (Block, 2009).

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3.1.2.2 Heinz Isler Further utilisation of hanging model as a structurally-informed design tool was refined

by Heinz Isler. In Isler’s paper ‘New shapes for shells’ (1960), three methods for shaping shells were described:

• Freely shaped hill is a form-finding approach where the concrete is formed by the earth that is carved to its desired form, and then remove the soil after con crete hardens (Fig. 3.1.2.2 a).

• Pneumatic form is a form-finding approach through utilisation of inflatable rubber membrane model (Fig. 3.1.2.2 b).

• Hanging reversed membrane in which he explained as ‘the best method for design’ (Fig. 3.1.2.2 c).

(Moreyra Garlock and Billington, 2014)

Fig. 3.1.2.2 (a). Freely shaped hill for form finding. (Chilton, 2000).

Fig. 3.1.2.2 (b). Inflated membrane model with a square grid marked on the surface so that the effect of inflation is easily discernable (Chilton, 2000).

Fig. 3.1.2.2 (c). Hanging membrane model generated by self-setting polyester resin (Chilton, 2000).

Fig. 3.1.2.2 (d). Hanging membrane model upturned stiffened free edges(Chilton, 2000).

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As Isler stated that hanging membrane is ‘the best method for design’ of funicular architecture, he further refined the method by using other suspended materials and techniques such as the used of hanging fabric models soaked in liquid plaster, resin or self-setting polyester. Regarding Hooke’s law of inversion, the models formed perfect funicular tension membrane, once they hardened and were inverted, creating a compression-only form. In another similar experiment, a piece of wet cloth was suspended outdoor during winter night to freeze the form. Using statical/elastic mathematical models combining with physical models, Isler was able to generate forms whose structural behaviour he could analyse in detail to determine the appropriate reinforcement needed to achieve the necessary strength, stiffness, and resistance to buckling (Chilton, 2000).

Not only were these techniques able to generate the form of the main structure, but also the fold that provides stiffening to the free edges of the shells (Fig. 3.2.2.2 d). Such hanging forms had been used for many of his projects, for example, Sicli SA factory, Geneva (1969), the outdoor theatre and dance studio at Stetten (1976), an outdoor theatre at Grötzingen (1977), near Stuttgart and a large number of tennis and sports hall.

Fig. 3.1.2.2 (f).

Sicli SA factory underconstruction (Chilton, 2010).

Fig. 3.1.2.2 (f).

Sicli SA factory underconstruction (Rippmann, 2016).

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3.1.2.3 Frei Otto A new development of physical form-finding method was established by Frei Otto, who was exploring designs based on the structural principles derived from his experimentation with lightweight structures and materials. He propagated this “natural form of architecture” as an expression of a modern, mobile and open-minded attitude. Influenced from second world war, Otto developed his philosophy of adaptable architecture, he believed that nothing should be built ‘for eternity’ (Meissner and Möller, 2015). In the 1950s, Otto and his team began experimenting with models as a way of establishing the structurally-derived form of a three-dimensional membrane and cable-net structures whose final geometry could not be determined using just analytical methods. His structural models were used to construct different structures, one of which is tension structure. Since gravity loads played a minor part in establishing the form of tensile structures, the models themselves were made of membranes or net with different characteristics with minimal surface area: soap bubbles which have a constant surface tension; elastic sheets whose surface tension depends on the strain; and net whose surface tension arises partly from the elastic extension of fibres, and partly from shear deformations of the net. Otto and his team also developed ingenious methods for measuring and surveying their complex forms which could not be defined using mathematical models. Having established the equilibrium geometry of the tensile structure, it was then possible to use analytical methods to determine in-plane stresses and forces at the boundary supports (Addis, 2014). For example, his project for the roof of the Institute for lightweight Structure, the Stuttgart University (1966), the German pavilion at EXPO (1967) in Montreal, Canada, and the roof for the main sports facilities in Munich for Olympic in 1972 (Fig. 3.1.2.3 a). Apart from tension structure, Otto also experimented suspended to determine compression structure as similar approaches had been taken by Antoni Gaudi and Heinz Isler, involving hanging chains and fabrics. These could be seen in many of Otto’s design such as KOCMMAS government centre, Saudi Aribia (1974), and Multihalle in Mannheim, Germany (1975) (Fig. 3.1.2.3 b).

Fig. 3.1.2.2 (a). (Left) The soap bubble film for structural experiment to find minimum tension surface area, Institute for lightweight structure. (Middle) Double exposure of the wire model.

(Right) The roof construction, the skin was suspended 50 cm under the net to test the membrane suspensions (Schanz, 2001).

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Fig. 3.1.2.2 (b). German Pavilion EXPO, 1967. Measurement model to determine individual force in the net membrane (Nerdinger, 2005).

Fig. 3.1.2.2 (c). Multihalle Mannheim, suspension model (Nerdinger, 2005).

Fig. 3.1.2.2 (c). Roofs for Munich Olympic measurement model with photogrammetric apparatus (Nerdinger, 2005)

Fig. 3.1.2.2 (d). KOCOMMAS government centre, suspension model to find compressive branching form (Schanz, 2001).

Although these funicular form-finding models was a great starting point to address structural principle as built by Antoni Gaudi, Heinz Isler and Frei Otto, their use to define and analyse were fairly limited. They depended heavily on further detailed experimenting models to analyse their structural performance and geometry reacted to various forces in scale. This demanded careful, iterative and time-consuming approaches as well as architects and engineer’s decades of experiences and highly skilled teams. As this issue was addressed in German Pavilion (1967) by JÜrg Schlaich, project leader, he questioned the accuracy of such methods and argued for the need to develop a new method, computational method, that was more accurate, fast and flexible (Rippmann, 2016). Consequently, this led to the developments of Force Density Method (FDM), Dynamic Relaxation Method (DR) and Particle-spring (PS) which would later inform the development of Thrust Network Analysis (TNA) (Block, 2009; Rippmann, 2016).

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3.2 Computational form-finding method Nowadays, the utilisation of computational form-finding method has become increasingly popular in architecture and engineering than ever before, especially for funicular architecture, due to the benefits of its significant accuracy, speed, and flexibility. For more complicated forms, using physical suspended models was a slow, tedious and limited process, and recently it has been often replaced by computational method. In the case of Guggenheim Museum, this marks the breakthrough of the use of advanced building technology. However, structural consideration is not presented in the early design phase, it is only rationalised and realised later on. As a result, the building expenditure and resources have been used excessively to realise such a sophisticated geometry (Section 2.1.1). This addresses the necessity of the structurally-informed design in early design process by utilising computational approach (Carpo, 2013). In order to achieve this, digital tool need to provide interactive, comprehensible and flexible control over the design form and its variants:

• • •

The given boundary conditions The preset design loads The define stress state

These parameters are the main focus of Thrust Network Analysis invented and developed by Philipe Block and Matthias Rippmann. TNA is a structurally-informed design tool with geometrical representation utilising reciprocal relationship between force and form diagrams, similar to Graphic statics. This tool offers an interactive and flexible form-finding design, allowing for a variety of complex equilibrium designs. TNA will be discussed further in the next subsection.

3.2.1 Thrust Network Analysis (TNA) Thrust Network Analysis is a three-dimensional representation for analysis and design of funicular structures combining the advantages of graphic statics, interactive and feedback-based computational method. In the early design stage, this is a good starting point for structural-aware design, especially for nonstandard building form. It provides a highly controlled and flexible form-finding process by using discrete equilibrium networks under vertical applied forces to analysis and design for compressive structure.

The visualisation of TNA provides identification and control over numerous degrees of freedom of equilibrium system, and what modifications are allowed to achieve the conditions of static equilibrium funicular. Block and Rippmann have been developed and programmed TNA on RhinoVault, allowing designers to explore structural-aware design and gain structural knowledge and a better understanding of funicular form. The tool offers a potential of exploring the use of materials that are weak in tension but relatively strong in compression to be able to support a variety of loading cases with many different geometries such as brick (Fig. 3.2.1) (Block, Lanchauer and Rippmann, 2014; López López et al., 2014). As a starting platform, this raises the hope of using a new emerging sustainable material such as mycelium-base material as a building structure which could be achieved not only through the material property but also the stability of the structure geometry.

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Fig. 3.2.1 . ‘‘Brick-topia’’, the thin-tile vaulted pavilion, Spain The project was based on a combination of TNA tool with a traditional, cheap and effective construction techniques. (López López et al., 2014))

Key principles TNA allows for the intuitive design of funicular networks with a high level of control due to the following key concepts:

• Reciprocal diagrams

Utilising reciprocal relationship between form and force diagrams allows TNA to define the thrust network (G) of the structure through form diagram (Γ) and force diagram (Γ*) for a given vertical forces as shown in (Fig. 3.2.1 a).

-Form diagram (Γ) : represents in-plane projection of the equilibrium solution, thrust network (G).

-Force diagram (Γ*) : represents horizontal equilibrium, distribution of forces and their magnitude to a given scale factor (ζ).

-Thrust network (G) : represents three-dimensional equilibrium structure under vertical applied loads.

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Form and force diagrams are related by a reciprocal relationship. This means that Γ and Γ* are parallel dual graphs: edges which come together in a node in one of the diagrams, form a closed space in the other, and the corresponding edges in both diagrams are parallel (Fig. 3.2.1.1 b). Structurally, this means that the equilibrium of a node in one diagram is guaranteed by a closed polygon of edges in the other. Force magnitude can be determined by measuring edge lengths for a given scale factor (Block, 2009; Rippmann 2016; Block, Lanchauer and Rippmann, 2014).

• Vertical loads constraint

Since only vertical loads are considered in TNA, the equilibrium of the horizontal and vertical force components in the thrust network can be computed independently. This allows the equilibrium problems to be decomposed into two steps: 1) Solving for a horizontal equilibrium 2) Solving for a vertical equilibrium

Step 2: Vertical equilibrium Step 1: Horizontal equilibrium

Fig. 3.2.1 (a,b). (a) Relationship between the thrust network G, its planar projection, the form diagram Γ and the reciprocal force diagram Γ* and (b) the reciprocal relationship between Γ and Γ* (Block et al., 2014).

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• Statically indeterminate networks

The static indeterminacy of networks with fixed horizontal projection and subjected to vertical loads can be explained with a geometrical analogy: for a given form diagram, there could be several reciprocal force diagrams available (Block, 2009; Rippmann, 2016).

A three-edge form diagram is structurally determinate, which means that there is only one unique internal distribution of forces available (up to a scale factor), only one horizontal equilibrium available. Such networks only have one degree of freedom: the scale of the force diagram, in other words, the designer can only manipulate the height of the vertical equilibrium solution (Fig. 3.2.1. c). However, if the node consists with more than three edges, the network is structurally indeterminate because the internal forces can be redistributed in many different ways, resulting in a variety of thrust networks solution for the given form diagram (Fig. 3.2.1. d). Since TNA allows designers to directly manipulate form and force diagrams, this provides significant flexibility and possibilities for equilibrium form-finding process (Fig. 3.2.1.1 f).

Fig. 3.2.1 (c). Static equilibrium of a single node i, with corresponding: Left - form diagram Γ, Right - force diagram Γ*. (Block et al., 2014).

Fig. 3.2.1 (d). Indeterminacy of a four-bar node: for the same load P: Left - an equal distribution of horizontal forces results in a symmetric network.

Right - attracting more thrust in one direction results in a shallower network in that direction.

(Block et al., 2014).

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Using this two-step approach with these fundamentals enable the control of multiple degrees of freedom in statically indeterminate networks. As shown in figure 3.2.1 (e), these design parameters enable the modification of, for example (these are constructed by author through the use of RhinoVault): Form diagram Γ

(a)

Force diagram Γ*

Thrust network G

A typical form and force diagrams, and thrust network based on rectangular form boundary under vertical uniform distributed loads

(b)

(b)

A modification of re-ditributed horizontal forces, creating a crease

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Form diagram Γ

Force diagram Γ*

Thrust network G

(c)

Modifications of a supporting edge condition, and form diagram boundary, creating an arch on equilibrium solution

(d)

Modifications of a supporting edge condition, and form diagram boundary, creating an arch and opening on the solution These are only small possibilities of using TNA to determine equilibrium forms. There are more possibilities for form-finding; vertical applied can also be altered to an individual point, supporting edge can be re-positioned vertically, more constrained can be imposed and many more. Thus, TNA offer a significant potential for equilibrium form-finding process. More exploration will be illustrated in the next subsection.

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Design workflow In order to determine thrust network equilibrium solution, Thrust Network Analysis form-finding process can be decomposed into two main steps : First step is solving for horizontal equilibrium by utilising reciprocal force and form diagrams. Second step is solving for vertical equilibrium based on the obtained horizontal equilibrium. This subsection summarises the overview of multiple stages and components for typical design workflow on RhinoVault (Fig. 3.2.1 f) (Rippmann, 2016).

Initialisation

1) To initiate the form-finding process, a form diagram (Γ) is set by the user including structure boundary, force paths and meshing technique such as triangulation, quadrilateration or subdivision (a).

2) Based on the form diagram in first step, the first topological reciprocal force diagram (Γ*) is generated (b). This force diagram will, then, be rotated anti-clockwise 90 degrees, providing a starting point for the iteration process of determining horizontal equilibrium (c). i.e. imposing reciprocal relationship constraint. These two steps set the starting point for later form-finding process.

Form-finding process

3) Modification: force (Γ*) and form (Γ) diagrams. Reciprocal diagrams are modified by user to reflect formal or structural design intents (d). This transformation can be done by moving an individual / multiple vertices and / or imposing constraints.

This makes it possible to modify boundary condition, opening, and supporting edge / point condition.

4) Since user has been modified the diagram, they are no longer equilibrium horizontally. Thus, horizontal equilibrium need to be computed again (e). Some changes will be made during the process on either force or form diagram or both depending on user’s preference. This means that one diagram over the other will be adapted less or more depend on user’s design intent, or both diagrams will be adapted slightly if user does not want neither of them to alter dramatically.

5) In some cases, if the modification is too extreme and horizontal equilibrium cannot be computed, the setting during horizontal process need to be changed and / or user have to re-modify the diagrams (f).

6) Based on equilibrated reciprocal diagrams, vertical equilibrium can be computed depending on a user-defined scale factor ζ and applied forces. Then, the form of thrust network (G) and height will be calculated and determined (g,h).

7) If the obtained form does not satisfy user’s design intent, the user can repeat the processes until the final solution meets the design requirements (i).

(Block, 2009; Rippmann, 2016)

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Fig. 3.2.1 (f). Design workflow of a form-finding process (Rippmann, 2016)

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Thrust Network Analysis This next subsection are more examples of equilibrium form under different conditions and modification. There are also force analysis of particular structure under certain loading case (these possibilities are constructed by author).

Form diagram Γ

Force diagram Γ*

Thrust network G

Thrust network G force analysis (mesh)

(a)

A modification on distribution of horizontal forces results in a thrust network with the attraction of higher force in certain regions results in creases in the equilibrium solution. Force analysis mesh shows concentration of forces transfer to supporting points which the structure is compression-only form

(b)

This is similar to the previous example but an extra modification is added: 3 openings are added.

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Form diagram Γ

Force diagram Γ*

Thrust network G

Thrust network G force analysis (Pipe)

(c)

This is similar to previous example (a) but with a difference in form diagram generation through subdivision, resulting in different force diagram and creases.

(d)

A form diagram has been modified so that it creats unsupporting edge, resulting in arches.

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Thrust Network Analysis This is funicular form based on a complicated form boundary with openings and arches on all the sides, resulting in a unique equilibrium solution (constructed by author).

Form diagram Γ

Force diagram Γ*

Thrust network G

(a)

This demonstrates form, force diagrams and equilibruim solution under uniformly distributed vertical loads of 1000 kN. According to TNA principle, under this circumstance the form is a compression-only form.

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Thrust network G force analysis

(b)

This shows a mesh analysis of the force distribution throughout the form, and reaction force around the supporting points.

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Part 3 Chapter 4 : Presenting the emergence of mycelium and the potential of using mycelium-based material as a building structure through TNA approach by using RhinoVault as a starting platform.

As cities around the world are growing rapidly today, the demand for building materials and resources also increase, resulting in a higher amount of material consumption and chemical substances release to the environment. These actions could lead to further global warming and environmental pollution (Stamets, 2005). As a result, this gives rise to the necessity for development and research for new alternative architecture, an environmental-friendly material. In that sense, mycelium-based material has a good potential to achieve such a requirement as it has been used to some extent during 2014 summer in New York city museum for the project called ‘mushroom tower’ (Fig. 4 a).

The tower was constructed from biological bricks which could be decomposed naturally without causing harms to the environments. This potential has been briefly discussed in my proposal. The bricks were made from mycelium-based material, the root network of fungi, a fast-growing matrix that can act as a natural binder. it consists of individual hyphae which grow from mycelium fungal strain spores and consume feedstock containing carbon and nitrogen. Digesting plant-based waste products, such as sawdust, mycelium’s dense network binds the substrate into a structurally adequate material composite. The advantages of such materials are significant. As mycelium-bound building components are organic matter, they can, following a metabolic cycle, simply be composted after their original use. Mycelium-bound components can also act to reverse carbon emissions through the absorption of carbon (Hebel et al., 2017; Vallas and Courard, 2017).

Fig. 4 (a). (Left)Hy-fi muchroom Tower. New York, 2014 and (Right) Mycelium-based bricks. (https://legacy-aia.aiany.org/Honors%20Projects%20HyFi.pdf.)

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Fig. 4 (b). (Left) “Beyond Mining - Urban Growth” exhibition at the 2017 Seoul Biennale of Architecture and Urbanism in Korea. (Right) TNA, RhinoVault as a starting platform for form finding. (https://www.researchgate.net/publication/320443920).

Previous studies and researches show that mycelium is a promising sustainable living material when combining it with agriculture waste, sawdust, or cardboards (Imnof and Gruber, 2015; Hebel et al., 2017). This combination provides nutrients for mycelium to grow, and after a few days, it would begin to transform into a dense and spongy mass.

Then, it would be transferred into molds, where it continue to densify and solidify.

When mycelium is hardened, it has a relatively good compressive strength compared to its tension property. Thus, this property creates a number of possibilities for mycelium to be used in many forms, such as a typical brick form in ‘Hy-fi mushroom tower’ in New York, and a more complex form like ‘Arching Pavilion’ in Kerala (Imnof and Gruber, 2015). However, most of these projects are still new and more research and study need to be conducted. Until recently, a project experimenting on mycelium as building structure has been carried out and was exhibited in South Korea called ‘MycoTree’, (Fig. 4 b) which used geometry to achieve structural stability rather than just focusing on material strength (Hebel et al., 2017). The project utilises TNA as a starting platform to determine form equilibrium and stability through structurally-inform design approach. This enables researchers to find compressive branching structure with a tension structure on top to keep the whole structure from failing. The structure is made mainly from mycelium-based material with bamboo plate at each end on the individual element, providing a clean finish and easy for transportation and re-assembly. For the tension part, it is made from bamboo that held the compressive branching together so that the structure will keep staying as a compression-only form. The structure was able to withstand a considerate amount of loads, the bamboo structure on top weighted about 134 kg in total and the overall weight of the mycelium-bound members was about 182 kg. This experiment combining with TNA and optimisation methods provide a good fundamental to explore the field further. However, there is still some limitations to TNA. The tool is a useful starting point to explore equilibrium form which focusing on forces applying to the structure but the tool does not take material property into account during computing.

This is because it only has to calculate for equilibrium geometry. In order to calculate for buckling and structure deformation, there is a need to further optimise the form with other methodology.

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Part 4 Conclusion This dissertation presents essential impacts a structurally-informed design have in an early form-finding design stage toward the overall design geometry. Introducing structural awareness in the early design stage is not only allow for a more efficient way of working; such as minimisation of resource consumption, reduction in project cost and time, but also providing opportunities for exploration of a new suitable architecture. This design approach provides significant advantages for non-standard building structure, especially funicular form. This type of form demands an early structural consideration since its overall geometry is playing an essential role in building stability. In order to achieve this stability, architects and engineers cannot only rely on the strength and property of materials but form also has a significant contribution as Dieste stated: “The resistant virtues of the structure that we seek depend on their form; it is through their form that they are stable, not because of an awkward accumulation of material.

There is nothing more noble and elegant from an intellectual viewpoint than this: to resist through form.”

There are two main structurally-informed design methods: analogue form-finding and computational form-finding. Analogue form-finding can be traced back centuries ago. It has an essential function in helping to determine equilibrated form by using various approaches, and one of them is a physical approach. This approach relies heavily on using models to find equilibrium form particularly suspended models; hanging chains, string, fabric with attached weights. Initially, the suspended model would be in tension-only structure, but when it is inverted this structure would be compression-only structure due to Hooke’s law of inversion. He was one of the first designers to use a hanging model to find compression-only form. This allows the use of materials that are weak in tension but strong in compression in constructing a large-span space. Moreover, the form that derives from structural consideration is elegant and aesthetic. Later on, this method effects other architects / engineers, among many of them are Antoni Gaudi, Heinz Isler, and Frei Otto. These three architects / engineers recognised the potential of structurally-informed design and developed the form-finding method further into their own style.

However, the method can be relatively tedious, time-consuming and rely significantly on designer’s decades of experience, especially for a much more complex funicular form.

This leads to the rising of a computational form-finding method. This helps to decrease the amount of time consumption during the designing process, and also help to increase the accuracy. One of these programmes is Thrust Network Analysis tool, a three-dimensional representation based on graphic statics and force density method. TNA is a structurally-informed design through the use of geometrical representation utilising reciprocal diagrams of force and form.

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It offers an interactive and flexible form-finding design, allowing for a variety of complex equilibrium designs and an exploration of a compression-only structure. In the combination of TNA with a new emerging sustainable material, mycelium-based material, this computational form-finding method offers a potential of using mycelium-based material in building structure. Based on previous studies and researches, mycelium-based material is weak in tension but relatively good in compression. Thus, TNA can be used to design a compression-only form in the early design stage as a starting platform. There is a necessity for structural optimisation since TNA only offer equilibrium form under applied loads but it does not take the material property into account. Thus, there is further computation and model experimentation to find buckling and any possible deformation that could occur. All these benefits and potentiality will not be realised if structural consideration were not taken into account in the early design stage.

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