Cool Weaving

COOL WEAVING

URBAN FURNITURE WITH EVAPORATIVE COOLING EFFECT

Global 30 Architecture and Urbanism Obuchi Laboratory University of Tokyo Graduate School of Engineering Department of Architecture

V.3, 2014 Obuchi Laboratory Editing Team Miguel Alberto Puig Perezyera Tong Shan Alisha Ivelich

2014, Printed in Tokyo, Japan For more information on Obuchi Lab Visit www.obuchilab.com Obuchi Laboratory University of Tokyo Graduate School of Engineering Department of Architecture 7-3-1 Hongo, Bunkyo-ku Tokyo, 113-8656 Japan

COOL WEAVING Urban Furniture with Evaporative Cooling Effect

Students: Miguel Alberto Puig Perezyera Tong Shan

Professor: Yusuke Obuchi Collaborating Professor: Associate Prof. Jun Sato

Course Assistants: Toshikatsu Kiuchi So Sugita Hironori Yoshida Computational Support: Toshikatsu Kiuchi

Contents Introduction 1.0

Research Targets

01 03

2.0 Background

2.1 Resource optimization for the Olympic Games

2.2 Introduction to bamboo

2.3 Bamboo and environmental advantages

2.4 Moso bamboo

2.5 Bamboo in Japan

2.6 Material flow

05 07 08 09 11 13 15

3.0

A Biomass Source

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4.0

Design Process Overview

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5.0

Background: Tensegrity Systems

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6.0

Background: Woven Architecture 6.1 Case study: The Manheim project 6.2 Biaxial vs triaxial weaving 6.3 Weaving and tensegrity 6.4 Case study: The Pompidou Metz project

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7.0 Weaving

7.1

7.2

7.3

7.4

The current scenario History of traditional weaving Types of triaxial weave Three traditional weaving elements

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8.0

Analog Experimentation 8.1 Analog experimentation 8.1.1 System assumptions and following experiments 8.1.2 Two-dimensional weaving 8.1.3 Bending before weaving 8.2 Triaxial weaving with ropes 8.2.1 Mixed weaving: bamboo and rope 8.2.2 Bamboo and rope weaving 8.3 Conclusions: analog research

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9.0

Design Tool: Flexible Bamboo 9.1 Development of digital design tool 9.2 Strength and flexibility 9.3 Curvature example 9.4 Gap control 9.5 Mesh gradient

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10.0 Geodesics

10.1 Experiments on bamboo surfaces

10.2 Surface experimentation 01

10.2.1 Single curved canopy with grid density increment on surface 01

10.2.2 Single curved canopy with grid density increment on surface 02

10.3 Experiment 02 on bench surface

10.4 Experiment on bamboo surface 03

99 101 103 105 107 109 113

11.0

117

Assembly

11.1

Assembly

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12.0

Surface Curvature Analysis and Tension System: Cho-gen-bari 12.1 Analog Model 12.2 Curve and geometry: computational comparison 12.3 Bow and arrow 12.3.1 Geometry A 12.3.2 Geometry A model: peg length manipulation 12.4 Geometry B 12.5 Control over tension cable 12.5.1 Pegs and spacers 12.5.2 Defining peg lengths

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13.0

14.0

Patterns and Structural Analyses 13.1 Scaling up and structural analyses 13.2 The computational tool 13.3 Structural experiment

153 155 157 159

Computational Tool and Calculation 14.1 Input data 14.2 Input data for geometry position and Hogan initial settings 14.3 Input data for material properties 14.5 Input data for cross section 14.6 Editing input data with Grasshopper 14.7 Experiment 1 14.8 Experiment 2 14.9 Furniture scale and structural analyses 14.10 Experiment 3 14.11 Findings 14.12 Experiment 4 14.13 Findings

171 173 176 178 179 181 191 201 209 211 223 251 253

15.0

Building a Microclimate with Woven Bamboo 15.1 The Rules 15.2 Evaporative cooling 15.3 Capillarity and transpiration 15.3.1 Capillarity in plants and trees 15.4 Bamboo transpiration 15.4.1 Sap flux measurement 15.5 Case study 15.6 Cooling optimization by weaving 15.7 Bamboo cooling test 15.7.1 Evaporative cooling experiment with bamboo 15.8 Surface development and mesh optimization 15.8.1 Anthropometric analysis for form finding 15.8.2 Point manipulation from anthropometric analysis to form finding 15.8.3 Geometry one 15.8.4 Geometry two 15.8.5 Cooling performance

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16.0

Conclusions and recommendations

16.1 16.2

Weaving system design recommendations Conclusion

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COOL WEAVING INTRODUCTION Material research is becoming one of the most important issues in the construction and design industry, especially as technologies become cheaper but resources become increasingly scarce. It is in this context that we examine the possibilities of temporary structures for which material qualities are considered the core part of the design.

Tokyo will hold the 2020 Olympic Games, thus providing a perfect scenario for improvement of current knowledge on temporary structures.

This is because the games require new buildings.

Both computational analysis and research of real case studies can allow us to update our knowledge of temporary structures, therefore assisting designers in improving efficiency.

Collaborative methods through which material research, computational design technologies, and traditional and artisanal methods work together can create understanding and lead to efficiency and design optimization.

With this in mind, this thesis presents a study on weaving techniques which was inspired by Japanese artisans.

Bamboo is the fastest growing woody plant. It has been widely used throughout Asia and Japan for many different practices over the centuries. Our team was interested in bamboo because it is a material characterized by tension, compression, and flexibility. These properties suggested the material may have potential for use in a nonlinear woven tensegrity system.

We explored the limits of the material as a temporary structure. The proposal examines the possibilities of bamboo post-use to offer benefits to the community, the economy, and the environment. This thesis aims to pave the way for new computational design strategies through which quality of life can be improved and sustainable building methods can be implemented.

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Image: Bench prototype

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1.0 Research Targets

Our research proposes the development of a triaxial weaving system which is supported by the creation of a computational design tool. This tool would make it possible to simulate and mimic the bending qualities of bamboo in order to improve design flexibility.

To develop the tool, our team first studied contemporary architectural gridshell systems, traditional weaving systems, and material qualities before moving on to simulation tests.

Through a simulation process, the proposed digital tool would be capable of analyzing the strength and flexibility of bamboo to adapt different bamboo thicknesses to a given designed geometry.

The computational tool can output the dimensions of the bamboo pieces required to produce a woven system which can be manipulated to obtain an improved weaving pattern in terms of structural stability and cooling performance.

Parallel with this study, and with help of the “Hogan� software, a structural analysis method, (designed by Prof. Jun Sato) is that the structural behaviour of the weaving system can be analysed.

The Hogan software was utilized to explore the relationships between scale, pattern, geometry, and structural stability, this allow us to obtain an efficient database to be used as an approach during the design process of the project.

On the side, we analyses the capillarity qualities of bamboo and its evaporative abilities in order to obtain a convection cooling system that capitalizes by the increment of bamboo components from the weaving systems creating a cooling effect.

The result is a tool that allows a designer to predict the thickness of bamboo pieces required to achieve a desired geometry while it provides a cooling microclimate performance.

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computational tool

Fig. 1.0: Research diagram

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2.0 Background

Our research team is interested in the tensile, compressive, and flexible properties of bamboo because it suggests potential for use in a nonlinear woven tensegrity system. This approach to tensegrity, inspired by the work of Frei Otto, aims to produce light structures which require a minimal amount of material.

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Fig. 2.0: Bench prototype (computational visualization)

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2.1 Resource optimization for the Olympic Games Today resource optimization and material research are two of the most important topics in the construction industry.

Tokyo has been selected to host the 2020 Olympic games. When cities are conscious of the ecological footprint of the Games and consider this in their planning, the cost of the investment reduces.

16 days

The Games also come with requirements for new buildings, the great majority of which will only be used for a temporary period of time.

London hosted the most ecological Olympic Games, by far.

Fig. 2.1: Cost of the Olympics, by city.

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2.2 Introduction to bamboo Bamboo, a grass with properties similar to timber, has been used for centuries as a material for construction, for utensils, as medicine, and even for food. It is a plant which has recently been of great interest in the construction industry due to its fast growth, flexibility, sturdiness, and aesthetic qualities.

Bamboo grows in many countries, especially in Asia, Africa, and Latin America. The INBAR indicates that global bamboo resources cover more than 36 million hectares. Asia is the continent richest in bamboo. With a total of 24 million hectares of the material, it makes sense to consider bamboo as a construction material in Asia.

Fig. 2.2: Bamboo distribution in Asia

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2.3 Bamboo and environmental advantages

Bamboo forests present a large number of environmental benefits. One of these benefits is related to bamboo’s ability to work as a carbon absorber. Over the first seven years of its life, bamboo captures 149.9 tons of carbon dioxide (CO2) from the atmosphere per hectare [1].

This carbon fixation is about two times more than normal trees. After harvesting, the CO2 trapped in bamboo stays captured in the bamboo that is used to create products, furniture etc. It is released only if burned, but still will be carbon neutral, as it will put in the atmosphere the same amount that it absorbed from the atmosphere. In terms of biomass, some bamboo can produce up to 5 times more biomass than some trees. Other benefits of bamboo are its ability to increase soil fertility and the structure of the soil due to it’s root network.

In an effort to adhere to the conditions of the Kyoto Protocol, many countries aiming to reduce their greenhouse gas emissions see bamboo as a good strategy for decreasing CO2 and other gas emissions [2].

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Fig. 2.3: The Carbon Cycle Diagram Source: California Forestry Association

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2.4 Moso bamboo Two species of bamboo exhibit the strength required for structural work: Guada bamboo, which grows in Latin America, and Moso bamboo, which grows in Asia.

This thesis seeks to address the issue of abandoned forests and propose a method for bamboo utilization.

The proposal will help control the current problem of the growing size of abandoned forests in Japan.

For the purposes of structural analysis, our team studied characteristics of Moso bamboo. Madake bamboo (a bamboo also abundant in abandoned forests) was also investigated for its structural qualities. Analyses of the maximum deflection and flexibility of the bamboo will be included in the coming chapters.

Characteristics of Phyllostachys Pubescens (Moso) Latin name: Phyllostachys heterocycla var. pubescens Mazel ex J.Houz.

Common synonym: P. edulis (Carrière) J. Houz Common names: Moso bamboo, Mao Zhu (China) Characteristics Length (average): 11-25 m Diameter (average): 6-18 cm (breast height) Rate of growth: up to 119 cm in 24 hours, and 24 m high in 40-50 days Rhizome: monopodial (runner) Other: cylindrical green internodes, length 25 cm on average. Leaves are 0.9-1.3 cm wide and 5-8 cm long [3].

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2.5 Bamboo in Japan At one time, bamboo was the most commonly used plant in Japan. Planted in forests near villages, it was used for basketry, construction, and seasonal provisions. Due to economic changes, however, a large majority of such forests are now abandoned.

Without proper human control, the propagation of bamboo has become a social and environmental issue for Japan. Bamboo cultivation in Japan has been drastically reduced overall. From 1990 to 2009 bamboo cultivation decreased by 38% nationwide. Moso bamboo culm production dropped from 150,000 tons in 1990 to approximately 40,000 tons in 2009.

According to Masatoshi Watanabe, Doctor of Agriculture, specialist at the Japan Bamboo Society, and member of the Japan Bamboo Association, this dramatic change has occurred due to several factors which include the introduction of substitute plastic materials, the import of bamboo products from China, the aging of laborers and skilled craftsmen, and issues related to labor-intensive cultivation [4].

The problem is that Japan continues to use bamboo as a primary material for many products, but imports most of it. As a result, many bamboo forests have been abandoned, thus creating a secondary problem. Bamboo forests are now taking over woodland areas.

Japan has the land, the resources, and the technology to stop relying on imported bamboo.

Through the use of strategies that consider economic, ecological, and social factors, utilization of Japan’s domestic bamboo resources could be possible. Such measures have potential to improve local economies and lifestyles for local farmers and small business owners.

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Fig. 2.4: Bamboo cultivation areas declining in Japan

Fig. 2.5: Present Status of culm production in Japan.

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2.6 Material flow

This project aims to utilize bamboo from abandoned forests by bringing it into the city to serve as urban furniture for the 2020 Olympic Games. This strategy is expected to provide a place of rest while encouraging visitors to experience the city of Tokyo by walking through different venues.

This initiative could be adopted by local governments to help keep forests under control. At the same time, such an initiative could offer Tokyo residents new opportunities for outdoor interactions during the summer.

At the end of its use period, the bench can be shredded into briquettes to be used as a local biomass. New bamboo growing in forests will again sequestrate CO2 emissions. In this manner, the project offers not only a way to control forests but also a source of energy for certain areas of Tokyo.

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Fig. 2.6: Material flow of the project

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3.0

A Biomass Source

The cooling bench aims to provide an area to sit and cool down during the 2020 Tokyo Olympic Games.

After analyzing the venues around Odaiba beach, our team noticed 1000 linear meters of beach that could potentially accommodate 250 bench pieces in a line, or 500 pieces distributed in two to three rows. Including the Odaiba beach zone and strategic locations between venues, we estimated a total of 3000 benches could be successfully placed in the area.

Approximately 12 linear kilometers in the Odaiba area offer potential locations for the cooling bench. Filling the space with benches would require approximately 4800 cubic meters of bamboo. This bamboo would then become pellets for a biomass at the end of its life as a bench.

The biomass capacity of Japan is of 361 billion kWh, but Japan currently imports nearly 76,000 tons of pellets annually.

Local biomass production grew from 21,500 tons in 2005 to 78,000 tons in 2011 (data from 2012) [5].

In recent years, approximately 12,000 pellet stoves were installed throughout Japan.

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“On September 22, 2009, Japan’s then Prime Minister, Yukio Hatoyama, announced at the United Nations Climate Change Conference that Japan would aim for a 25% cut in CO2 emissions by 2020” [6].

Japan will triple the amount of power it generates from renewable energy technologies to 300 billion kWh by 2030.

Fig. 3.0: Bench prototype computational visualization

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Fig. 3.1: Venues for the Olympic games in Odaiba, Tokyo. Photo via Google Earth.

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Potentially 12 linear kilometres of area from between venue locations in the Odaiba area.

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3,000 benches potentially distributed around the Odaiba area

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4800 m3 of bamboo required to build; can be utilized post-use as biomass

Fig. 3.2 - 3.5: Analysis of feasibility for the location of the cooling bench project.

Photo via Google Earth.

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Fig. 3.6 - 3.7: Analysis of feasibility for the location of the cooling bench project.

Photo via Google Earth.

On September 22, 2009, Japan’s then Prime Minister, Yukio Hatoyama, announced at the United Nations Climate Change Conference that Japan will aim for a 25% cut in CO2 emissions by 2020 [7].

Fig. 3.8: Planned renewable energy sources in Japan through 2030

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Odaiba beach: 1000 linear meters. Potentially 250 bench pieces in a line or 500 pieces distributed in two to three rows.

Japan will triple the amount of power it generates from renewable energies to 300 Billion kWh by 2030 [8].

Fig. 3.9: Utilization of bamboo as a by-product.

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Fig. 3.10: Rendered visualization of the bench placed at Odaiba beach.

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This thesis aims to pave the way for new computational design strategies and promotes the implementation of technologies which will improve both the quality of life and sustainable building methods.

Fig. 3.11: Rendered visualization of a bench placed in the Odaiba area.

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4.0

DESIGN PROCESS OVERVIEW 15.00

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Fig.4.0: Design process

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5.0

BACKGROUND: TENSEGRITY SYSTEMS Frei Otto’s ideal is that ethically good architecture is also aesthetic.

“Buildings are an exercise of power, even if we do not intend.”

Our times demand lighter, more energy saving, more mobile and more adaptable, in short more natural buildings.”

Frei Otto pointed out at an early stage that every environmental project can only be judged if one considers the overall energy balance involved in manufacturing and using an object (through to the point of disposal).

Otto states that the forms of relatively lightweight constructions “are rarely coincidental. Usually, they are the result of development and optimization processes which, for whatever reason, follow the principle of the reduction of mass. We call this principle the lightweight construction principle” [9].

Light, filigree objects have a more luminous atmosphere than heavy, ungainly structures. A meticulously formed lightweight structure reveals the flow of forces, gives buildings a logical and understandable appearance, exposes that which is essential, and thus appears open and likeable.

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• Lighter • More mobile

• Adaptable

• Light weight construction

• Optimization processes

Fig.5.0: Tensegrity model study

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6.0

BACKGROUND: WOVEN ARCHITECTURE

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Fig. 6.0: Triaxial weaving, physical model

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6.1 Case Study: The Manheim project

Constructed in Mannheim in 1975, Frei Otto’s gridshell project is a structure which derives its strength from a doubly curved surface.

It was assembled on the ground and very carefully put into place. Due its dimensions, the process required a great deal of scaffolding and time.

Also of great importance was the stiffness of the structure. It was composed of hundreds of small joints which gave the structure the necessary strength [10].

Frei Otto mentions that the Gridshell is a structure which derives its strength from a double curvature surface and that “One of the most important things about this kind of membranes is the perimeter, which has to be rigid enough to support the deadweight of the structure and most important, all the loads sitting above it” [11].

One of the objectives of our team’s research was to look into potential methods for improving the efficiency of the construction method; to avoid the use of scaffolding and utilize the material in a smart manner (in accordance with its intrinsic qualities).

Our project has also made efforts to avoid the utilization of a contention ring. Instead, the system uses a woven method and a tensegrity strategy. This produces a geometry and the necessary tensioncompression system. The method allows for the production of stable structures.

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Fig. 6.1: Construction of the Manheim project

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Despite being a masterpiece of architecture and engineering, the Manheim project included hours of extra labor after initial construction.

• Joint adjustments in each connection • Scaffolding to keep the geometry in place • Rigid ring to support the building How can labor be reduced?

Can the scaffolding and rigid ring be removed?

Fig. 6.2 - 6.6: Construction of the Manheim Project

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6.2 Biaxial vs triaxial weaving

Triaxial weaving was of particular interest to this research due to its structural superiority (in contrast to biaxial weaving).

In 1981, Frank Scardino and Frank K. Ko at the Philadelphia College of Textiles and Science analyzed the behavior of triaxial woven fabrics. Tensile, shear, and burst deformations were tested and the results were compared on triaxial and biaxial grids. The results indicated that a triaxial grid possesses a stronger and more uniform resistance to extension, shear deformation, and burst than biaxial grids [12].

Their results demonstrated that through triaxial weaving, interlacing elements at a 60 degree angle presents a greater degree of isotropy in mechanical properties than the biaxial system. In tensile deformation and in shear deformation under normal and biaxial loading, triaxial fabrics do not exhibit as low a directional minimum resistance as biaxial fabrics. This indicates that triaxial systems are strained more uniformly than biaxial structures because the loads are distributed more evenly throughout the plane of the structure.

Results also suggest that triaxial systems become more resistant to shear deformation as the tension increases.

Accordingly, triaxial structures should provide superior performance in applications where loads come in all or several directions rather than uniaxially.

Because of this, and also due to the implicit aesthetic qualities, it makes sense to choose the triaxial weaving method to explore our tensegrity system. Hexagonal plaiting produces light, robust structures that use less material than those of biaxial close-woven works.

They can be quickly constructed to produce interesting aesthetic pieces.

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Fig. 6.7: Triaxial and biaxial comparison

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6.3 Weaving and tensegrity Kenneth Snelson analyzes weaving as one of the steps to understanding tensegrity. Snelson mentions that there is no difference between weaving and tensegrity, and that “...weaving reveals in a direct way the basic and universal properties of natural structures”: modularity, helical symmetry and structural geometry [13].

According to Snelson, there are only two fundamental woven structures: the standard two way weave and the three way weave. Both are capable of creating rectangles, triangles, and hexagons.

Each woven interaction produces its rotational complement. Just as the individual crossings of filaments have their helical axes so each square in a plain weave has its opposite. Each cell’s neighbours are its mirror form like a alternate squares on a chess board. In three-way weaving, hexagons alternate with triangles. The weave can be set in two distinct forms like right and left-handed gloves. If the hexagons are constructed clockwise the triangles are counterclockwise and vice versa [14].

Fig. 6.8: Biaxial system and triaxial system concept diagram

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Weaving and tensegrity share the same grounding principle of alternating helical directions; of left to right; of bypasses clockwise and counterclockwise. In these figures, the column on the left shows the primary weave cells.

To their right are the equivalent basic tensegrity modules. By transposing each weave filament to become a strut (stick, tube or rod) the cells transform into arrays of two, three, four, etc.

Compression members. They retain their original form and helical direction [15].

Fig. 6.9: Comparison of tensegrity and weaving systems

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6.4 Case study: The Pompidou Metz project “A simpler surface mapping technique was developed during the concept design of the Pompidou Metz roof to investigate basket-weaving techniques on a large scale. The technique simulates the wrapping of (geodesics) over an arbitrary surface and is a method that can also be used for investigating trajectories for seam lines on fabric structures� [16].

The Pompidou Metz was developed by Arup to create a woven system that would allow basket-weaving techniques to be used for design on the architectural scale. The system can create a structure that works as a woven system, but it must be built in sections as a traditional panelling system.

With base pieces 2.6 meters in length and pieces connected at the end boundary, the system allows wood to be bent and kept in position with multiple bolts.

Arup mentions that woven systems are a clever strategy for designing lightweight structural systems, but when the scale grows, the components grow accordingly and this makes it impossible to weave systems in a traditional manner. As a result, construction requires the system be subdivided into panelling. When complete, the connected systems work much like hexagonal mesh.

Fig. 6.10 - 6.15: Construction of the Pompidou Metz project

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7.0 WEAVING

7.1 The current scenario Weaving is an activity that has been present in all cultures, and it has continued through centuries because cultures have passed traditional methods from generation to generation. Japan has been developing weaving techniques for approximately 1500 years. Weaving techniques in Japan are traditional art forms. Patterns are well known by the local artisans and are developed into contemporary geometries which challenge the limits of the artists and the traditional patterns.

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7.2 History of traditional weaving “Bamboo is a quintessential part of Japanese culture, shaping the country’s social, artistic, and spiritual landscape” [17].

Between the 15th and 16th centuries, bamboo vases, tea scoops, ladles, and whisks became important features of Japanese traditions such as flower arranging (ikebana) and the tea ceremony (chanoyu and senchado). By the 8th century, bamboo baskets filled with flowers were incorporated into Buddhist ceremonies, and gave birth to bamboo as a sculptural art form with religious roots.

Today, contemporary artists challenge the limits of woven bamboo to create exquisite objects that demonstrate cultural heritage and years of study.

Fig. 7.0: Hiroshima Kazuo’s basket

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Fig. 7.1: Hiroshima Kazuo, a basket maker in rural Japan.

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7.3 Types of triaxial weave Hexagonal plaiting (in Japanese weaving, mutsume ami) is explained in the following manner on Basketry and Beyond: Hexagonal plaiting, often called hex weave, involves elements that move in three directions at once, a horizontal and two diagonals at 60 degrees to each other.

Open hexagonal plaiting produces light, robust structures that use less material than close woven work. They can be quick to construct from rough materials but there are also beautiful and fine.

To produce baskets where sides and openings are needed, corners must be created. Here, the weave structure changes and elements are linked together to form the shapes. Basket sides usually rise from hexagonal or triangular bases.

Patterning: by weaving extra elements between the gaps, complex star, diamond, and snowflake patterns may be achieved such as those seen on food covers from China and Indonesia [18].

Fig. 7.2: Traditional Japanese basket

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The other styles of hexagonal plaiting mentioned on the Basketry and Beyond website are netting, knotting, and looping.

These techniques, often thought of as more textile than basketry, generally result in soft flexible structures. When stronger materials than the usual soft string/twine are employed, potential for more intriguing forms increases. They offer opportunities for exploring structural combinations and experimenting with properties that allow them to be squashed, stretched, and manipulated into interesting forms. For example, the Nassau fish traps of the Mediterranean combine knotting with a grass or cane trellis and a spiral structure [19].

Fig. 7.3: Nassau Traditional fish trap

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7.4 Three traditional weaving elements

Three elements are ubiquitous in traditional weaving methods.

1) Ribs 2) The soft “weaver�

3) Ring

The friction between components produces stability in woven systems. Through an analysis of the basketry knowledge of artisans and implementation in the following experiments, our team worked to recreate and expand upon this to develop our weaving system.

Part of our research during the analog experimentation phase was to determine whether or not it was possible to develop a system capable of functioning without requiring a joint for every connection in the gridshell.

Additionally, we sought to find a replacement for the ring.

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1) Ribs: Weaving systems often are created using rigid main elements that will guide construction while also dictating the geometry of the system.

Fig. 7.4 Basket making

Fig. 7.5 Basket making

Fig. 7.6 Basket making

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2) The soft “weaver� is a secondary element that can be manipulated by hand. The weaver helps creates the friction required to keep the elements together and create a surface.

Fig. 7.7 - 7.9: Rigid element and rope weaving examples

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3) A rigid ring is commonly used to keep the geometry in place.

Fig. 7.10 - 7.12: Woven baskets with rigid ring examples

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8.0

ANALOG EXPERIMENTATION Analog experiments allowed our team to better develop our understanding of weaving on an architectural scale.

These experiments indicated that increasing the scale of the woven material makes the classic weaving process nearly impossible. To develop an improved system, we therefore changed construction methods and placed the first two axes on top of one another. A third element was then woven through the initial two elements.

This offered improved control during the construction process.

Fig. 8.0: Detail on woven analog model

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8.1 Analog experimentation The first analog test (chapter 8.1.2, test 01) was conducted by developing a two-dimensional weave and pushing its edges.

Although this process creates a geometry, it only allows for developable surfaces to be created (because all elements become locked). To develop a triaxial system with enough flexibility to create developable surfaces from a two-dimensional weave, our team replaced the third component in the weave with flexible ropelike material. Our hypothesis was that this process would hold the weave loosely in place until tension was applied to the rope, at which point the surface would lock into place.

This would allow for surface manipulation and for construction feasibility. The photos on the right illustrate the experiments utilizing a “rope� to successfully obtain a non-developable surface.

Fig. 8.1 - 8.2: Single curvature analog model

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Fig. 8.3 - 8.6: Analog models of hexagonal grid systems with rope

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8.1.1 System assumptions and the following experiments

Is it possible to develop a doubly curved system through the use of a weaving system?

Can we achieve a doubly curved system by transforming a two-dimensional weave into a threedimensional geometry?

Could the utilization of a rope as the “weaver� component help our team achieve this?

How can the system avoid the utilization of a rigid ring (as in classic basketry)? Is it possible to create the necessary locking geometry without interlocking each bamboo intersection?

Our team assumed that the system would only develop a surface, and that the weaving system would not keep the geometry in position. To create order a geometry without the use of a ring, a bow and arrow tension system called cho gen bari was tested.

Analog experimentation indicated that woven patterns in two dimensions are non-developable surfaces due to the friction between components.

To develop three-dimensional geometry from a twodimensional surface, our team needed to explore methods of creating two-dimensional patterns that would remain in tact when transformed into three dimensions.

This chapter will present a number of analog experiments and further computational simulations which our team used to obtain a better understanding of the potential strategies for addressing these issues.

Fig. 8.7: Analog model with a single curvature

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8.1.2 Two-dimensional weaving The systems lock into a developable surface.

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Fig. 8.8 - 8.16: Construction process, analog model with single curve

The first analog test was conducted by developing a weave in two dimensions and pushing its edges.

Although this created a geometry, it only allowed for developable surfaces to be created (because all elements become locked).

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8.1.3 Bending before weaving Pre-bending the rigid components and attaching them to the ground for weaving allows for the production of a double curvature, however, our team

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noticed that as the scale of the project increased, our ability to weave hard elements became much more difficult, up to the point that it became practically impossible. Therefore, because our aim was to produce a system capable of scaling up beyond traditional baskets, we chose to utilize a rope as a flexible element in the system. Through this, we attempted to develop a doubly curved surface.

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8.2 Triaxial weaving with ropes

Triaxial weaving is a method of plaiting that involves three elements: two elements at 60 degree angles and a third horizontal element. Initial analog experiments indicated that weaving a pattern in two dimensions locks the form into a non-developable surface.

Our team altered the traditional weaving method by allowing movement between the two crossed components and the third component. To do this, a flexible rope component was used for the third element. The two bamboo elements acted in tension, and the flexible component acted in compression. The system locked the weaving system into a surface.

Friction in the system can be controlled by manipulating grid density and by altering the parameters of component thickness.

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Fig. 8.26: Triaxial weave steps

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Fig. 8.27: Diagram for traditional triaxial weave

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8.2.1 Mixed weaving: bamboo and rope Using a rope for the third component in the system allows the surface to be transformed from a non-developable surface even after being woven in two dimensions.

Our team’s hypothesis for this experiment was that by using a rope as an

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element, the weave would be loosely maintained, and would allow for temporary flexibility and surface manipulation to determine construction feasibility. When tension is applied to the system, we believed the surface would lock into the desired geometry.

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Using a rope in the system proved successful. The system was transformed into a non-developable surface, even after being woven two-dimensionally.

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Fig. 8.28 - 8.36: Triaxial weave using rope analog model.

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8.2.2 Bamboo and rope weaving

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The determined construction strategy was to weave each component in a two-dimensional configuration, and then push the edges into a threedimensional geometry. The geometry would then be locked through the use of a rope component.

A computational model was generated in Grasshopper to compare with the analog model. This experiment was conducted under the assumption that small variations in the pattern occurred in the analog model due to sliding of the bamboo elements. These variations would then result in variations on the overall surface. These variations were not incorporated into the digital model.

The potential for such variation, however, indicates the need for a secondary system which allows for better control of the geometry. The secondary system should also correct any variations by controlling tension in the cable or strategically joining specific nodes of the gridshell (this will be analyzed in the following chapters).

Fig. 8.37 - 8.39: Digital development for construction of triaxial weaving system.

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03a A “foundation� is created where the edge of each component can be placed.

This allows for accurate geometries to be created. After the geometry is formed (in the locked position), the entire form can be released.

The components adopt a spline curve when the edges are pushed.

Each component can be pushed independently. This facilitates the construction process. The third element can be added to the weave following this step.

The first two rows are placed in a flat position, and by pushing the edges, each component adopts a spline curve. This process provides a feasible assembly method with little required labor.

In this example, the rope edges are attached to the ground. When tension is applied to the rope, the forces increase and the system begins to have structural strength. As a consequence, the final form appears.

In this experiment, the wood strips chosen were not flexible enough to obtain the desired geometry. This created difficulties in working toward the final shape and resulted in the structural failure of some components.

These results indicated a need for an analysis of the bending capabilities of the chosen material.

Fig. 8.40 - 8.45: Assembly process, physical model of digital design (using wood)

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03b In this experiment, weaving was completed in the two-dimensional stage with the rope components attached to the ground. The bamboo components were able to “move� because the rope offered very little friction.

Because the rope component is attached to the ground, when tension was applied, the forces increased and the system began to have structural strength.

The method of attaching the rope to the other two woven elements, therefore, must be strong enough to hold all interconnected components together.

In this experiment, the wood strip components were not flexible enough to achieve the desired geometry. Further studies were conducted to analyze the bending qualities of each component.

06

Fig. 8.46 - 8.51: Physical model of the digital design using wood and rope

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03c

This experiment began by selecting the components which would be involved in the inverted curvature part of the weave. These components were attached to the ground.

In the second step, the bamboo components were pushed into their position to transform the structure from two dimensions to three dimensions. This successfully produced a double curvature. The rope successfully bent the strips into the desired position.

The weave is carried from the ground to higher points on the structure.

By using a material with a greater degree of flexibility, our team noticed that the geometry was able to transform into the desired position with the addition of tension on the rope component.

To further develop the system, an flexibility analysis of the bamboo qualities was required to ensure successful structural performance.

Fig. 8.52 - 8.59: Physical model of the digital design using paper and rope.

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The final analog experiment indicated that when the gaps between components were smaller there was very little room for the bamboo to slide, and therefore the accuracy of the system increased.

Fig. 8.60 : Physical model of final bench prototype

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8.3 Conclusions: analog research •

•

•

•

•

Although further studies will explore potential methods of removing the perimeter ring, the experiment included in this chapter were carried out by attaching the structure to the ground. The experiments indicated that the bamboo needed to be attached to the ground during the construction processes, and the accumulated force of all the bamboo caused stress on the system overall. Tension applied to the rope element increases the tensioning forces of the geometry overall.

After several experiments, our team determined that the geometry should aim to produce a smooth curvature rather than strong peaks. Extreme curvatures will cause components to break, particularly during the construction process. Smoother geometries will offer an easy transition from two-dimensional surface to three-dimensional form, and will reduce stress at the edges which can cause the bamboo to break.

Using a stronger bamboo element results in a smaller degree of curvature, and could lead to easy breakage. For this reason, our team chose to use a thinner component (the following chapter will analyze the bending qualities of the chosen bamboo).

Experiments indicated a need for a system capable of allowing adjustments to the rope element for tension (after the system is woven into position).

Obtaining adequate tension from the beginning of the process is difficult due to sliding bamboo pieces during construction.

Note: These experiments were conducted prior to analysis of the bamboo bending qualities. Following analysis studies, our team gained a greater

The system is temporarily attached to the ground.

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understanding of the bending capacities of bamboo. This was then applied to the computational tool.

The system is woven and tension is applied to the rope.

Adjust the tension rope for optimization of the geometry

Fig. 8.61 - 8.63: Physical model of the digital design using paper and rope

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9.0

DESIGN TOOL: FLEXIBLE BAMBOO 9.1 Development of digital design tool

Through an analysis of the bending qualities of bamboo, our team obtained the maximum deflection in accordance with the diameters of given bamboo strips. The analysis of flexibility at the curve inflection points provided the data required to feed the computational algorithm.

This system made it possible to predict the diameters of the bamboo components required to populate a given geometry through the use of our weaving system.

The analysis allowed for direct feedback between the design tool and the necessary bamboo diameters during the design process.

It assisted our team in visualizing the bamboo required to achieve a desired geometry.

Fig. 9.0: Prototype #01 for cooling bench

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9.2 Strength and flexibility performance

Though an analysis of the maximum deflection of bamboo, the computational design tool was able to predict the bamboo required to achieve a certain geometry as well as the diameter(s) required achieve the necessary flexibility.

Fig. 9.1: Bamboo maximum deflection and diameters

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MAXIMUM CURVATURE Length Maximum deflection Modulus of elasticity Moment of inertia

Fig: 9.2: Maximum deflection diagram

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R4195.4 R4666.3 R4195.4 R5216.7 R4666.3 R5877.5 R4195.4 R5216.7 R6645.7 R4666.3 R5877.5 R7566.3 R5216.7 R6645.7 R8728.2 R5877.5 R7566.3 R10036.9 R6645.7 R8728.2 R11510.6 R7566.3 R10036.9 R13363.2 R8728.2 R11510.6 R15685.6 R10036.9 R13363.2 R18777.9 R11510.6 R15685.6 R13363.2 R23219.7 R18777.9 R15685.6 R30447.7 R23219.7 R44718.4 R18777.9 R30447.7 R87936.9 R23219.7 R44718.4 R30447.7 R87936.9 R44718.4 R87936.9

R6876 R706 R78 R8 R

curves from 1 to 16 m 7 cm diameter curves from 1 to 16 m 7 cm diameter curves from 1 to 16 m 7 cm diameter

curves from 1 to 16 m 9 cm diameter curves from 1 to 16 m 9 cm diameter curves from 1 to 16 m 9 cm diameter

1m

1m 1m

R9639.7 R10499.9 R12274.9 R9639.7 R13462.2 R10499.9 R14807.5 R12274.9 R9639.7 R16384.1 R13462.2 R10499.9 R18251.7 R14807.5 R12274.9 R20516.1 R16384.1 R13462.2 R23367.8 R18251.7 R14807.5 R27081.0 R20516.1 R16384.1 R32213.6 R23367.8 R18251.7 R39854.7 R27081.0 R20516.1 R52560.7 R32213.6 R23367.8 R78072.4 R39854.7 R27081.0 R155016.2 R52560.7 R32213.6 R78072.4 R39854.7 R155016.2 R52560.7 curves from 1 to R78072.4 R155016.2 10 cm diameter curves from 1 to

10 cm curves from 1 todiameter 16 m 10 cm diameter

4m

5m

4m 4m

5m

6m

curves from 1 to 16 m 10 cm diameter curves from 1 to 16 m 10 curves fromcm 1 todiameter 16 m 10 cm diameter

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6m

5m

7m

6m

7m

8m

7m

8m

9m

8m

9m

9m

10m

11m

10m 10m

12m

11m 11m

12m 12m

R10679.

R11594 R1260 R137 R15 R1 R

16 m 16 m

13m 14m

15m

13m 14m

15m

13m 14m 15m

16m

R6876.8 R7062.4 R6876.8 R7863.0 R7062.4 R8710.3 6.8 R7863.0 R9670.2 62.4 R8710.3 R10760.6 R9670.2 863.0 R12009.4 8710.3 R10760.6 R13468.0 R9670.2 R12009.4 R15186.8 R10760.6 R13468.0 R17327.1 R12009.4 R15186.8 R20050.3 R13468.0 R17327.1 R23789.5 R15186.8 R20050.3 R29257.6 R17327.1 R23789.5 R38307.5 R20050.3 R29257.6 R56553.5 R23789.5 R38307.5 R111701.1 R29257.6 R56553.5 R38307.5 R111701.1 R56553.5 R111701.1

R7803.0 R8567.4 R7803.0 R9411.6 R8567.4 R10365.6 R7803.0 R9411.6 R11430.8 R8567.4 R10365.6 R12665.4 R9411.6 R11430.8 R14130.7 R10365.6 R12665.4 R15811.9 R11430.8 R14130.7 R17824.6 R12665.4 R15811.9 R20332.3 R14130.7 R17824.6 R23597.2 R15811.9 R20332.3 R28062.9 R17824.6 R23597.2 R34649.5 R20332.3 R28062.9 R45575.0 R23597.2 R34649.5 R67520.5 R45575.0 R28062.9 R133799.8 R67520.5 R34649.5 R45575.0 R133799.8 R67520.5 m R133799.8

R10679.0 R11594.7 R10679.0 R12604.8 R11594.7 R13756.5 R12604.8 .0 R15063.4 R13756.5 R16586.6 4.7 R15063.4 R18356.1 04.8 R16586.6 R20462.3 756.5 R18356.1 R23021.1 5063.4 R20462.3 R26233.2 16586.6 R30422.1 R23021.1 R18356.1 R36237.8 R26233.2 R20462.3 R44916.8 R30422.1 R23021.1 R59367.8 R36237.8 R26233.2 R88353.5 R44916.8 R30422.1 R59367.8 R175694.6 R36237.8 R88353.5 R44916.8 R175694.6 R59367.8 R88353.5 R175694.6

R12068.6 R13049.9 R14143.3 R12068.6 R15389.9 R13049.9 R16800.0 R14143.3 R12068.6 R18447.2 R15389.9 R13049.9 R20361.0 R16800.0 R14143.3 R22652.0 R18447.2 R15389.9 R25448.6 R20361.0 R16800.0 R29001.5 R22652.0 R18447.2 R33681.6 R25448.6 R20361.0 R40184.5 R29001.5 R22652.0 R49881.8 R33681.6 R25448.6 R66044.9 R40184.5 R29001.5 R98447.0 R49881.8 R33681.6 R195995.4 R66044.9 R40184.5 R98447.0 R49881.8 R195995.4 R66044.9 R98447.0 R195995.4

m

m

m

curves from 1 to 16 8 cm diameter curves from 1 to 16 m 8 cm diameter curves from 1 to 16 m 8 cm diameter

curves from 1 to 16 m 10 cm diameter curves from 1 to 16 m 10 cm diameter curves from 1 to 16 m 10 cm diameter

WHAT DOES THIS MEAN? An increasing modulus of elasticity means a decreasing bend radius. Therefore, stronger bamboo are more likely to fail than weaker pieces. Bamboo pieces with smaller diameters are able to bend more than pieces with thick diameters.

16m 16m Fig. 9.3: Comparison of modulus of elasticity for different bamboo diameters

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maximum deflection

Through the use of the computational tool, it is possible to analyze each bamboo component for: Inflection points Maximum deflection Length

inflection point

Fig. 9.4: Computational analysis visualization of a curve’s inflection points and maximum deflection

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The computational tool is capable of obtain the bamboo diameter required to produce each curve.

inflection point

inflection point

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Diameter = (allowable stress * Length ^2 ) / (6* E *max deflection) allowable stress = 80% of (MOR module of rupture 85 N/mm^2) E=12000 N/mm^2

maximum deflection

6 cm diameter

7 cm diameter

Fig. 9.5: Computational analysis visualization of curve’s inflection points and prediction of diameters

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As visualized in this image, the computational tool makes it possible to determine he maximum diameters of the bamboo required to produce the designed geometry. The next step in the design process is to optimize the system in terms of cooling and structural performance.

12 cm diameter

8 cm diameter

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Curve versus diameter: computational manipulation The tool allows us to examine the curvature of each component individually or to examine the entire geometry. The process makes it possible to visualize where the geometry has a high degree of curvature, and correct this if required to utilize the bamboo available.

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This indicates that direct feedback from the design tool is possible, and the required bamboo for a given geometry can be visualized in real time.

Note: trying to increase the minimum diameter of the bamboo component results in changes in neighboring curves Fig. 9.6 - 9.8: Computational analysis of bamboo diameters and curve optimization process

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9.3 Curvature example The following examples illustrate visualization of the design tool outputs.

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Fig. 9.9: Analysis of curvature to obtain bamboo diameters

This diagram shows how an increment in curvature throughout the surface will directly affect a decrement in the diameter and allow the bamboo to bend enough to achieve the desired shape. Because bamboo is available in different diameters according species and growth conditions, an analysis of the types, quantities, and sizes of collected bamboo is necessary to ensure utilization in the most efficient manner.

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9.4 Gap control The number of bamboo pieces in the system can be increased to maintain control and avoid collapse of the structure.

The computational tool maintains a distance relative to the bamboo radius to allow for creation of a proportional mesh system.

•

Increasing gaps between bamboo pieces and reducing radius

Fig. 9.10: Analysis gaps on grid to obtain adequate air flow optimization

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9.5 Mesh gradient Gradually changing the mesh density allows for control of a gradient of bamboo diameters which can potentially contribute to structural stability and concentration of cooling areas (the cooling capacities of bamboo are examined in the following chapters).

Fig. 9.11: Visualization of grid density optimization

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10.0 ANALYSING GEODESICS

Our research team explored alternative methods of populating geometries through use of the weaving system, and researched possibilities related to geodesic linearity. A geodesic path is a straight line between two points on a curvature. An example of this concept is the direction chosen by an airplane to cross the globe (using the shortest path). The subject of geodesic linearity has been a recent research focus by desiners for the improvement of material utilization through geometric optimization.

Because our research aims to bend bamboo, our studies examined geodesic linearity to determine what potential geodesics could hold for our system. We hypothesized that bending bamboo on a geodesic path could simplify the forces needed to maintain its shape (compared to a basic grid on a surface).

This chapter analyzes the use of a geodesic curve for bamboo bending.

Through a series of computational experiments, we aimed to increase our understanding of geodesic components. This included the pros and cons of the use of geodesics in terms of construction, cooling, and form finding.

Fig. 10.0: Geodesic path

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Fig. 10.1: Geodesic paths produced by planes.

Fig. 10.2: Geodesic path on surface

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10.1 Experiments on Bamboo Surfaces Several trials were conducted with the geodesic component included in our computational tool. The tool was used to create bamboo surfaces which utilize the same footprint (indicated in the below images).

Because the geodesic component works to modify the normal path of grids, the woven patterns are also modified. These experiments were conducted in part to increase geodesic control as part of the design process, and also to explore potential forms.

Fig. 10.3: Experiment 03, A geodesic path on a surface with different iterations on its topography.

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10.2 Surface Experiment 01

The below image indicates an area of 10 m x 30 m with changes in curvature on the two edges of the “y� axis. Applying increments of one meter to five meters between the highest and lowest points of a sine curve at the edge produce different surfaces.

The resulting iterations of the combination of these different curvatures were analysed in terms of how increments in curvature on the bamboo shape can directly affect the percentage of bamboo area and therefore increase temperature exchange capabilities.

Fig. 10.4: Geodesic experiment 01.1

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10.2.1 Singly curved canopy with grid density increment on undulated surface 01. (10 x 40 grid)

Different iterations with a regular grid of 10 x 40 presented a range on the bamboo surface from 646 m2 to 900 m2

Fig. 10.5: Geodesic experiment 01.2

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10.2.2 Singly curved canopy with grid density increment on undulated surface 02. (10 x 40 grid)

Different iterations with an irregular grid of 10 x 40 that densify from the center concentration on the zigzag area presented a range on the bamboo surface, from 716 m2 to 1006 m2.

We observed via the sine curve that as the area on the surface increases, the geodesic component (in most caes) modifies the regular grid. Through this, we were able to observe some of the geometries that presented a pattern of openness on one side and density on the other.

Fig. 10.6: Geodesic experiment 01.3

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Density increment applied on the undulating zone of surface.

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10.3 Experiment 02 (bench surface) After adding the geodesic component to our computational tools, we made changes to the topography of the surface by adding textures. This increased the area of the footprint (see below images for overall process).

As the geodesic component tries to modify the regular path of the grid, the bamboo components modify the route through the surface, resulting in unpredictable patterns.

Fig. 10.7: Geodesic experiment 02

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Although we can see that on a smooth surface with a shallow curvature the geodesic path draws a nice curve, when the surface becomes more “challenging� in terms of pitch or texture, the resulting weaving pattern becomes nearly unpredictable.

The following experiment will analyse the boundaries of our system in order to allow the utilization of geodesics.

Fig. 10.8: Geodesic experiment 02.1

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10.4 Experiment on bamboo surface 03 Deeper levels of experimentation with different grids and different levels of corrugation indicated limits to the designs (when the geodesic component was used). The design team thus decided to remove the geodesic component of the computational algorithm to work with parameters that offered more predictable data in terms of pattern manipulation.

Nevertheless, it is important to consider the qualities of the geodesic path in terms of material optimization. Although never tested in this research, this includes the possible structural performance for gridshells and weaving systems.

Fig. 10.9: Geodesic experiment 03

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Fig. 10.10: Geodesic experiment 03.1

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11.0 ASSEMBLY

Through several attempts to find an adequate process for construction, the analog experiments explored different ways of developing the geometry, with four goals taking priority: •

To provide a method that allows components to lock on the edges in 2D, and after that to bend the geometry into a 3D form.

•

To allow maximum accuracy in terms of form finding.

•

To obtain adequate tension.

•

To allow for control in order to overcome cable displacement and amend forces on the tension cable

Fig. 11.0: Digital representation of the components for the triaxial system.

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As described earlier in this document, Frei Otto commented that “one of the most important things about this kind of membrane is the perimeter, which has to be rigid enough to support the structure.� Grid shell systems are great examples of architecture and engineering working together, but they are restricted by a ring perimeter and the extensive use of scaffolding for their construction.

Is it possible to have a woven lattice that can avoid the utilization of rigid rings and scaffolding in order to reduce the amount of labor required while improving material efficiency?

Fig. 11.1: Manheim project, Frei Otto.

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11.1 Assembly In contrast to the previously introduced analog experiments in which the presented woven system was attached to a base, our bench project was developed to be independent from any ground attachment, thus achieving mobility and transportability.

A new approach was to develop a “foundation” wherein each bamboo component was locked into position at the adequate height (photos on the right). This provided the right setting for pre-bending before weaving.

We hypothesized that once the bamboo edges were attached to one another a series of ropes could make it possible to bend the bamboo chair into position.

The images on the right present the first approach to this strategy. A temporary structure was first created in order to place the weave. Although this strategy was successful, our research aimed to develop the project while avoiding the use of extra infrastructure.

We also hypothesized that using a “bow and arrow” strategy could potentially aid in the creation of the foundation. The previous construction process, which consisted of (1) a ring, (2) a woven pattern, and (3) a tension cable, changed to utilize weaving as the last step in the system.

This change in the process could also be beneficial because the small sliding motions of the bamboo are due to forces acting upon places where the weave has become loose.

Therefore, making weaving the final step in the process may provide added stability.

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Fig. 11.2 - 11.7: Construction process of analog model.

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A second developed strategy intended to avoid the creation of any extra infrastructure for the weaving of the gridshell. The strategy joined the edges of the model in 2D, and through a series of triangulations, attached the corner points for the final shape. This allowed us to visualize the final output and weave the system. The process indicated that the geometry was susceptible to changes.

If this method is chosen, close care during the construction process must be taken, and periodic revisions must be carefully made to avoid a change of form.

Fig. 11.8: 2D representation of bamboo pieces for assembly.

The pattern above shows the elements presented in 2D with the computational tool. With this, it is possible to print the lengths of each bamboo element and mark them before construction.

The images on the right present the first steps of the construction process for one of the design research models.

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Fig. 11.9 - 11.14: Assembly process from 2D to 3D before weaving.

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Our final prototype was developed trough this triangulation system. It presented very little displacement and a high grade of accuracy.

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Fig. 11.15 : Physical model of final bench prototype.

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12.0 SURFACE CURVATURE

ANALYSIS and TENSION SYSTEM: “cho-gen-bari” As previously mentioned, traditional weaving systems are kept in place through use of a rigid ring. Utilizing a ring keeps the geometry in position, but also removes any opportunities for the geometry to be flexible.

Our intention aimed to avoid the use of a rigid ring.

A tension system called “cho-gen-bari,” wherein a bow and arrow formation shows a possible way of maintaining the geometric curvature, was used. Through the utilization of a Grasshopper definition, it is possible to analyse surface curvatures in order to choose points where “pegs” will be placed to maintain the geometry.

A bottom-up approach to this system was analyzed to determine the adequate length of “pegs.”

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Fig. 12.0: First trial using pegs, analog experimentation.

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12.1 Analog model A small test of the latest model indicated that a tension system using pegs for positioning was a viable alternative to the ring that traditional weaving systems use.

The following experiment examined how the peg system could be improved, and also explored possible methods of adjusting tension on the cable.

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Fig. 12.1 - 12.7: Building process of analog model and pegs in position.

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12.2 Curve + Geometry Computational Comparison The images on the right present different geometries.

A curvature analysis has been applied to the geometries; the result is a graphic representation with bigger circles representing the peak points of curvature along the bamboo at the nodes intersection.

Through this analysis, it is possible to locate the best position for the pegs in the tension system.

Fig.12.8 - 12.10: Computational visualization for curvature analysis.

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12.3 Bow & Arrow In this experiment, we developed grids of different densities. One grid concentrated density in the center while the other geometry concentrated density at the edges.

This experiment aimed determine the following:

to

Density optimal for maintaining geometric position in the tension system.

Density optimal for creation of a woven surface.

A previous model was designed using a grid of 40 x 40 bamboo pieces. This produced a dense mesh and did not allow much space for the bamboo to slide.

This also produced a very strong surface.

The following models present a more open grid in order to visualize and enhance possible problems through the construction phase.

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Fig. 12.11: Detail of peg on physical model during first peg trial.

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12.3.1 GEOMETRY A Geometry A is dense at the edges, creating an open grid in the center where the curvature of the geometry intensifies.

This is compared with geometry B, which is densified in the center.

These two examples serve to illustrate which strategy is better suited to the utilization of the bow-and-arrow tension system to manipulate the geometry’s curvature.

Fig. 12.12: Computational visualization for curvature analysis.

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1.5 cm length peg

geometry opening 925 mm

2.5 cm length peg

geometry opening 830 mm

3.5 cm length peg

geometry opening 740 mm

Fig. 12.13 - 12.18: Adjusting curvature with peg lengths.

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12.3.2 Geometry A model: Peg length manipulation By following the location of the pegs with a computational analysis, it is possible to maintain the position of the geometry, however, we noticed that as the geometry moves (when changing the pegs), the bamboo slides along the surface and results in places where the weave becomes loose.

To avoid this, we implemented a system that would allow us to have more control over the tension cables and the weaving rope.

3.5 cm length peg

2.5 cm length peg

1.5 cm length peg Fig. 12.19: Pegs of different lengths for experiments.

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12.4 Geometry B Geometry B shows a densification in the center. The circles indicate the peak points on the curvature. Through this analysis, we can choose peg locations along the surface. As described previously, the bamboo slides along the surface, affecting tension through both the tension cable and within the weave pattern. In further developments of this experiment, we examined construction strategies and pursued further tension adjustability.

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Fig. 12.20: Computational visualization for curvature analysis.

Fig. 12.21.

Computational visualization for peg locations.

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12.5 Control over tension cable

Finally, in order to improve control over the tension cable, a strategy similar to the one used in the 99 Failures pavilion project was applied to adjust any possible inaccuracies in tension caused by sliding bamboo. The project utilized a double cable system to allow a system of pegs (or sticks) which served to potentially counteract the sliding effect.

Fig. 12.22: “99 Failures� pavilion

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Fig. 12.23: Detail of tension cable and peg system (bow-arrow)

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12.5.1 Pegs and spacers

The strategy of the bow-arrow system is: 1. To follow the computational analysis by plaing pegs into strategic locations on the model.

2. To utilize three different sizes of pegs: 1.5 cm, 2.5 cm, and 3.5 cm. the tension system will first be placed in position without any spacers.

3. To utilize a double cable for greater accuracy in determining an adequate distance for the “local� curvatures at each bow-arrow point. 5 different spaces are used in this system, ranging in size from 0.5 cm to 3 cm.

These strategies produce an improved system that can fix variations in curvature and tension by applying a spacer in the bow-arrow cable.

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Fig.12.24: Detail of pegs and spacers working together.

Fig. 12.25: Pegs and spacers

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12.5.2 Defining Peg Lengths The aim is to utilize pegs which are as small as possible to ensure efficient utilization of the space.

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There are three potential cases in which the bow and arrow system can be utilized. In the first case, a peg that is smaller than the maximum deflection length on the curvature pulls the tension cable inwards. While this works well, it is dependent on competition between bamboo and tension cable forces. The formation could, however, turn into a flat cable and produce a buckling effect on the bamboo curvature.

In the second potential case, the cable is at a 90 degree angle to the maximum deflection line. This holds the system in position, but also produces major compression forces on the bamboo and applies more tension to the cable.

The third case results in less compression force and offers an easier assembly method in terms of labor, but also requires the longest peg in order to function.

To operate the system with a minimal amount of material, our research chose to further investigate the second case scenario, in which the cable is held as close as possible to 90 degrees from the maximum deflection length.

Fig. 12.26: Diagram for different scenarios on the use of pegs.

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L

L

Fig. 12.27: Visualization of the use of different sizes of spacers.

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As seen in the analog test, an increment on the “spacer” length produces a reduction in “L.” Therefore, when comparing “L” in the analog process with the digital model, we can adjust the tension cable accordingly to determine the adequate length for an increment to improve accuracy during the assembly process.

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No spacer

1 cm spacer

1.5 cm spacer Fig. 12.28: Experiment showing how through the use of longer spacers, the length of the cable decreases, thus improving control over the whole curvature.

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13.5 cm length

13 cm length

12.5 cm length 150

Fig. 12.29: A stable model which uses the bow-arrow tension system.

Figs. 12.30 - 12.33: Close up detail of the model.

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13.0 PATTERNS AND STRUCTURAL ANALYSIS 1 Two Different Systems Due to subtle differences in the application of the materials, two different systems were used.

2 Triaxial Kagome Bamboo Weaving System The triaxial Kagome bamboo weaving system is a system which utilizes bamboo for the three-direction al weaving elements.

The woven works presented in the previous section are examples of this system.

3 Triaxial Kagome Bamboo-Rope Weaving system The Triaxial Kagome bamboo-rope weaving system is a system wherein two of the weaving elements are bamboo and one element is an elastic rope. Using an elastic material as the third element allows all elements to lock together securely.

Our research team used different rope materials to make physical models and test the system.

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Fig. 13.1. Bamboo Basket Kagome Weaving System.

Fig. 13.2. Bamboo-Rope Basket Kagome Weaving System.

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13.1 Scaling up and structural analyses Weaving techniques are commonly applied to small scale products such as woven baskets and benches. Our research team considered the possibility of scaling up woven patterns.

Precent examples of woven projects do not indicate that sole use of a woven system can produce three-dimensional structural stability.

In the Centre Pompidou-Metz project, a special secondary structure holds up woven wood elements which form the huge roof of the building. The Sunny Hills project is similar; the actual structural support forms are not woven, but produce a woven effect. In a woven pavilion in downtown Beijing, the structural technique used created only the effect of a Kagome weave, despite the fact that the sketches for the models strictly followed the woven Kagome form.

155

Fig. 13.3. Centre Pompidou-Metz Project.

Fig. 13.5. Sunny Hills Project

Fig. 13.7. Woven Pavilion Project.

Fig. 13.4. Roof Details.

Fig. 13.6. Structural Details.

Fig. 13.8. Woven Pavilion Sketch Model.

156

13.2 The computational tool Simulation of the geometries of large-scale woven structures is possible through the use of a digital structural analysis program. These simulations enabled stability tests in a computational environment. The tool utilized for simulation and testing was the Finite Element Method (FEM) within the Hogan software (developed by Professor Jun Sato2).

The following operation flow was used for tests: 1. Geometries were modified using the “line segment� property in the Rhinoceros program.

2. Three-dimensional data indicating geometry and material were converted into two-dimensional data via the Rhino-to-Hogan converter. The two-dimensional data was subsequently input to the Hogan software. During this process, Grasshopper was used for sophisticated and accurate calculations and simulations.

3. Outputs of the structural tests indicated whether or not the tested system was structurally stable.

Structural stability of a system was expressed visually following each test via colors on each structural element. The colors corresponded to relevant safety ratio index ranges.

157

Fig, 13.9. The output in the program.

Safety Ratio Index Red Orange Yellow Yellow-Green Green Lime Blue

>=1.0 0.9-1.0 0.71428-0.9 0.7-0.71428 0.6-0.7 0.5-0.6 <0.5

Not Safe Safe

Very Safe

158

13.3 Structural Experiments A physical structural experiment on the Moso bamboo material was conducted prior to the computational simulation. This experiment illustrated some of the key characteristics of Moso bamboo, including Young's modulus and the allowable bending stress.

159

Fig. 13.10 "Moso Bamboo".

160

1. Preparation 1) Experiment Subject The subject for the experiment was one Moso bamboo strip with an average cross section size of 15 mm x 10 mm.

2) Experiment Setting As shown in Figure 21, the two edges of the bamboo strip were fixed. The span of the bamboo strip, measured as the distance between the edges of the two pictured desks, was 600 mm.

161

b d b = 15 mm d = 10 mm

Fig. 13.11. Experiment Subject.

Span = 600 mm

Fig. 13.12. Experiment Scene.

162

3) Experiment Formation For experiment accuracy and integrity, two situations were tested. The recorded data includes these two situations.

Situation 1 The exterior surface of the bamboo strip (green surface) was placed face up in the experiment setting.

Situation 2 The internal surface of the bamboo strip (light yellow surface) was placed face up in the experiment setting.

163

Fig. 13.13. Situation 1.

Fig. 13.14. Situation 2.

164

2. Process

Situation 1 is used here as an example for explaining the experiment steps.

1) STEP 1 An observation point is marked near the center of the bamboo strip. This point is also the position where we put the dyno.

A steel ruler measuring vertical movement of the observation point is fixed in position near the bamboo strip.

2) STEP 2 The power of the dyno and the original position of the observation point are recorded.

165

Fig. 13.15. STEP 1.

Fig. 13.16. STEP 2.

166

3) STEP 3 The dyno is pulled vertically, while the power remains at 5 kgf. The position of the observation point is recorded.

4) STEP 4 Step 3 is repeated, and the power of the dyno is increased by 5 kgf with each s u b s e q u e n t o p e r a t i o n . T h i s p ro c e s s continues until the bamboo element reaches its breaking point.

167

Fig. 13.17. STEP 3.

Fig. 13.18. STEP 4.

168

3. Data Records

In Situation 1 tests, seven sets of data were recorded. In Situation 2 tests, six sets of data were recorded.

Situation 1 Original position: 750 mm No. postion Distance (δ) Power 5kgf

1 2 3 4 5 6 7

760mm

770mm 780mm 795mm 805mm 820mm 850mm

10mm

20mm 30mm 45mm 55mm 70mm 100mm

10kgf 15kgf 20kgf 25kgf 30kgf 35kgf

Situation 2 Original postion=725mm No. postion 1 2 3 4 5 6

755mm 770mm 780mm 790mm 795mm 800mm

Distance (δ) Power 30mm 45mm 55mm 65mm 70mm 75mm

10kgf 15kgf 20kgf 21kgf 22kgf

5kgf

4. Results After collecting records and comparing the results, the data indicated the following: 1. Young’s modulus: E =120 tf/cm2 2. Allowable bending moment: δby = 10 kgf/mm2 169

Fig. 13.19. Breaking moment.

Fig. 13.20. Breaking position of the bamboo.

170

14.0 COMPUTATIONAL TOOL AND CALCULATION

The primary computational tool used for experiments was Hogan, a gravity-based analysis program. The program was combined with the Grasshopper software.

Grasshopper had an essential supporting role throughout the process of calculating material properties.

1. Program Principle In the Hogan program, the analysis process is based on a gravitational analysis of the input geometry. Gravity types include longterm gravity and short-term gravity (in both X and Y directions).

171

Fig. 14.1. Hogan Interface.

172

2. Input Data The input data included the geometric information and material information in two text files: a .lst file and a .inp file. The Grasshopper program and a Rhino-Hogan converter were used to convert the three-dimensional model information to text information. Grasshopper also played a supporting role in some of the calculation processes. In Figures 31 and 32, Test 074 is used as an example for indicating both the input data and the subsequent output.

14.1 Input Data Information

for

Geometry

Node Position â&#x20AC;&#x153;NODE 101 CORD 2.819 8.475 1.276 ICON 0 0 0 0 0 0 VCON 0.0 0.0 0.0 0.0 0.0 0.0 NODE 102 CORD 2.506 9.000 0.000 ICON 1 1 1 0 0 0 VCON 0.0 0.0 0.0 0.0 0.0 0.0 NODE 103 CORD 4.072 8.475 1.276 ICON 0 0 0 0 0 0 VCON 0.0 0.0 0.0 0.0 0.0 0.0 NODE 104 CORD 3.758 9.000 0.000 ICON 1 1 1 0 0 0 VCON 0.0 0.0 0.0 0.0 0.0 0.0 NODE 105 CORD 5.324 8.475 1.276 ICON 0 0 0 0 0 0 VCON 0.0 0.0 0.0 0.0 0.0 0.0 NODE 106 CORD 5.011 9.000 0.000 ICON 1 1 1 0 0 0 VCON 0.0 0.0 0.0 0.0 0.0 0.0 NODE 107 CORD 6.577 8.475 1.276 ICON 0 0 0 0 0 0 VCON 0.0 0.0 0.0 0.0 0.0 0.0 NODE 108 CORD 6.264 9.000 0.000 ICON 1 1 1 0 0 0 VCON 0.0 0.0 0.0 0.0 0.0 0.0

NODE 316 CORD 0.000 8.475 0.000 ICON 1 1 1 0 0 0 VCON 0.0 0.0 0.0 0.0 0.0 0.0 NODE 317 CORD 10.000 8.475 0.000 ICON 1 1 1 0 0 0 VCON 0.0 0.0 0.0 0.0 0.0 0.0 NODE 318 CORD 0.022 9.000 0.000 ICON 1 1 1 0 0 0 VCON 0.0 0.0 0.0 0.0 0.0 0.0 NODE 319 CORD 10.000 2.260 0.000 ICON 1 1 1 0 0 0 VCON

173

Fig. 14.2. Test 074, geometry perspective.

Fig. 14.3. Test 074, geometry elevation.

174

Element Position “ELEM 1001 ESECT 202 ENODS 2 ENOD 101 102 BONDS 0 0 0 0 0 0 0 0 0 0 0 0 CANG 0.00000 CMQ 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 TYPE COLUMN ELEM 1002 ESECT 202 ENODS 2 ENOD 103 104 BONDS 0 0 0 0 0 0 0 0 0 0 0 0 CANG 0.00000 CMQ 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 TYPE COLUMN

ELEM 1388 ESECT 203 ENODS 2 ENOD 295 321 BONDS 0 0 0 0 0 0 0 0 0 0 0 0 CANG 0.00000 CMQ 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 TYPE COLUMN ELEM 1389 ESECT 202 ENODS 2 ENOD 321 226 BONDS 0 0 0 0 0 0 0 0 0 0 0 0 CANG 0.00000 CMQ 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 TYPE COLUMN ELEM 1390 ESECT 202 ENODS 2 ENOD 159 160 BONDS 0 0 0 0 0 0 0 0 0 0 0 0 CANG 0.00000 CMQ 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 TYPE COLUMN ELEM 1391 ESECT 203 ENODS 2 ENOD 126 264 BONDS 0 0 0 0 0 0 0 0 0 0 0 0 CANG 0.00000 CMQ 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 TYPE COLUMN ELEM 1392 ESECT 202 ENODS 2 ENOD 153 154 BONDS 0 0 0 0 0 0 0 0 0 0 0 0 CANG 0.00000 CMQ 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 TYPE COLUMN”

175

14.2 Input Data for Geometry Position and Hogan Initial Settings ""CREATED ORGAN FRAME." NNODE 221 NELEM 392 NPROP 1 NSECT 4 BASE 0.200 LOCATE 1.000 TFACT 0.030 GPERIOD 0.600 GFACT 1.0 FOCUS 5.0 4.5 2.0 ANGLE 50.8 -105.2 DISTS 1000.0 50000.0"

14.3 Input Data for Material Property "PROP 101 PNAME BAMBOO(1/100) HIJU 0.00587778 E 12000.000 POI 0.25000 PCOLOR 0 255 255 " E is young's modulus, the one of the results of the structural experiment.

176

Yellow Node: node hinged to the ground

Fig. 14.4. Test 074, Hogan settings.

Red element: CODE 201 Blue element: CODE 202 Brown element: CODE 203

Fig. 14.5. Test 074, geometry top view.

177

14.4 Input data for Scan Rate Test

“ “INPUT DATA” CODE 201 WOOD COLUMN “=C1” PLATE 5.0 5.0 SUGI “FB60x60[mm]” XFACE 0.0 0.0 “FACE LENGTH Mx:HEAD= 0,TAIL= 0[cm]” YFACE 0.0 0.0 “FACE LENGTH My:HEAD= 0,TAIL= 0[cm]” BBLEN 400 400 “BUCKLING LENGTH Lkx=400 Lky=400[cm]” BTLEN 400 400 “BUCKLING LENGTH Lkx=400 Lky=400[cm]” CODE 202 WOOD COLUMN “=C1” PLATE 5.0 5.0 SUGI “FB60x60[mm]” XFACE 0.0 0.0 “FACE LENGTH Mx:HEAD= 0,TAIL= 0[cm]” YFACE 0.0 0.0 “FACE LENGTH My:HEAD= 0,TAIL= 0[cm]” BBLEN 400 400 “BUCKLING LENGTH Lkx=400 Lky=400[cm]” BTLEN 400 400 “BUCKLING LENGTH Lkx=400 Lky=400[cm]” CODE 203 WOOD COLUMN “=C1” PLATE 5.0 5.0 SUGI “FB60x60[mm]” XFACE 0.0 0.0 “FACE LENGTH Mx:HEAD= 0,TAIL= 0[cm]” YFACE 0.0 0.0 “FACE LENGTH My:HEAD= 0,TAIL= 0[cm]” BBLEN 400 400 “BUCKLING LENGTH Lkx=400 Lky=400[cm]” BTLEN 400 400 “BUCKLING LENGTH Lkx=400 Lky=400[cm]” “ CODE 201, CODE 202, and CODE 203 respectively correspond to the three directional elements.

178

14.5 Input Data for Cross Section Information

" SECT 201 SNAME 50x9 NFIG 1 FIG 1 FPROP 101 AREA 0.25716600 IXX 0.00026880 IYY 0.00026880 VEN 0.00026880 EXP 1.500 NZMAX 1.000000 NZMIN QXMAX 1.000000 QXMIN QYMAX 1.000000 QYMIN MZMAX 1.000000 MZMIN MXMAX 1.000000 MXMIN MYMAX 1.000000 MYMIN COLOR 0 150 255

-1.000000 -1.000000 -1.000000 -1.000000 -1.000000 -1.000000

SECT 202 SNAME 50x9 NFIG 1 FIG 1 FPROP 101 AREA 0.25716600 IXX 0.00026880 IYY 0.00026880 VEN 0.00026880 EXP 1.500 NZMAX 1.000000 NZMIN -1.000000 QXMAX 1.000000 QXMIN -1.000000 QYMAX 1.000000 QYMIN -1.000000 MZMAX 1.000000 MZMIN -1.000000 MXMAX 1.000000 MXMIN -1.000000 MYMAX 1.000000 MYMIN -1.000000 COLOR 150 0 255

179

SECT 203 SNAME 50x9 NFIG 1 FIG 1 FPROP 101 AREA 0.25716600 IXX 0.00026880 IYY 0.00026880 VEN 0.00026880 EXP 1.500 NZMAX 1.000000 NZMIN QXMAX 1.000000 QXMIN QYMAX 1.000000 QYMIN MZMAX 1.000000 MZMIN MXMAX 1.000000 MXMIN MYMAX 1.000000 MYMIN COLOR 255 0 150

Fig. 14.6. Calculation by Means of Grasshop-

-1.000000 -1.000000 -1.000000 -1.000000 -1.000000 -1.000000

SECT 900 SNAME HojoPlate SROLE HOJO COLOR 0 0 255 " As shown in Fig. 35, calculations were conducted in the Grasshopper program, through which area (AREA), moment of inertia (IXX and IYY), and torsion (VEN) were determined. Data in Test 074 is here used as an example. In Test 074, a 50 mm radius pipe was used as the structural element and the cross section shape consisted of concentric circles. After input of the radius dimensions to the program, the results were subsequently obtained: AREA = 0.002573m2 IXX = IYY = VEN = 2.6894e-6m4 More information about the calculation of the three indexes' can be found in section 2.7, Calculations for Geometric and Material Properties.

180

14.6 Editing Input Data with Grasshopper As previously indicated, the Grasshopper tool served as a flexible helper in managing data. Figure 36 indicates the Grasshopper program from which our research team obtained text, including bamboo cross section data and material data (for structural simulations).

181

Fig. 14.7. Editing input data with Grasshopper.

182

Calculations for Geometric and Material Properties To input the geometric and material data to the structural simulation program, sophisticated and accurate calculations were required to convert three-dimensional information to twodimensional information.

Two calculations are required: one of the general geometry, and the other of a single structural element.

In the calculation of the general geometry, the buckling length from the span of the geometry was determined as: Buckling length: BBLEN (BTLEN) = 0.4 x Span.

When calculating data on each single structural element, the values determined were area (AREA), moment of inertia (IXX and IYY), and Saint-Venant's torsion (VEN) of the cross section. The material data was illustrated with a cross-section shape.

Three types of cross-section shapes were used to present the bamboo element crosssection shapes: rectangles, arches, and concentric circles. When the element cross section used an arch shape, it indicated that the cut bamboo pieces were system elements. When the element cross section was composed of concentric circles, it indicated that the complete bamboo pipe was the system element. Rectangles were used to illustrate simplified versions of the "arch" shape indicator.

1. Cross Section Type 1: Retangle For rectangle B x H, three index values were determined via substituion of B and H in the formula3.

AREA = B x H IXX = B X H3 / 12 IYY = B3 X H/ 12 183

SCALING UP AND STRUCTURAL ANALYSES

B H

Fig. 14.8. Rectangle B x H.

Fig. 14.9. Test 027 Calculation.

184

2. Cross Section Type 2: Arch For Arch R x t, by applying a formula examining the relationship between the thickness (t) and the exterior radius (R) of bamboo,

t = 0.18R22; we can arrive at a formula which relates the interior radius (r) and the exterior radius(R):

r = 0.82R For an arch with a known α, the index value can be determined via substitution of r and t in the formula3 below.

AREA = π*(R2-r2)/6 IXX = (α+sin α*cos α-16*sin2α/9/α)*(R4-r4)/4 4*sin2α*R2*r2*(R-r)/(9*α*(R+r)) IYY = (R4-r4)*(α-sin α*cos α)/4 VEN = 2*R*α*t3 / 3

185

α

r R

t

SCALING UP AND STRUCTURAL ANALYSES

Fig. 14.10. Arch R x t.

Fig. 14.11. Test 052 calculation.

186

3. Cross Section Type 3: Concentric Circles For Concentric Circles R x t, Combining the formulas for the relationship between the interior radius (r) and the exterior radius (R), the formula3 below was determined.

AREA = Ď&#x20AC;* [R2-(0.82*R)2] IXX

= IYY = VEN = Ď&#x20AC;*[(2*R)4-(1.64*R)4]/64

This process produces the index values.

187

SCALING UP AND STRUCTURAL ANALYSES

r

R

t

Fig. 14.12. Concentric circles R x t

Fig. 14.13. Test 081 calculation.

188

3. Output Data

The output data of the test is the safety ratio of each structural element. The stability of every element can be intuitively judged based on colors assigned to each element (determined by the analysis).

The below data was obtained from Test 074 and is used an example.

ELEM: ELEM: ELEM: ELEM: ELEM: ELEM: ELEM: ELEM: ELEM: ELEM: ELEM: ELEM: ELEM:

1001 SECT: 1002 SECT: 1003 SECT: 1004 SECT: 1005 SECT: 1006 SECT: 1007 SECT: 1008 SECT: 1009 SECT: 1010 SECT: 1011 SECT: 1012 SECT: 1013 SECT:

202 202 202 202 202 202 203 203 203 203 203 203 202

0.00145 0.00000 0.00743 0.00000 0.00174 0.00000 0.01094 0.00000 0.00183 0.00000 0.01279 0.00000 0.00178 0.00000 0.00968 0.00000 0.00182 0.00000 0.00742 0.00000 0.00212 0.00000 0.00778 0.00000 0.00088 0.00000 0.00359 0.00000 0.00141 0.00000 0.00720 0.00000 0.00171 0.00000 0.01073 0.00000 0.00181 0.00000 0.01269 0.00000 0.00177 0.00000 0.00966 0.00000 0.00178 0.00000 0.00729 0.00000 0.00085 0.00000 0.00370 0.00000

ELEM: ELEM: ELEM: ELEM: ELEM: ELEM: ELEM: ELEM: ELEM: ELEM: ELEM: ELEM: ELEM: ELEM: ELEM: ELEM: ELEM: ELEM:

1373 SECT: 1374 SECT: 1375 SECT: 1376 SECT: 1377 SECT: 1378 SECT: 1379 SECT: 1380 SECT: 1381 SECT: 1382 SECT: 1383 SECT: 1384 SECT: 1385 SECT: 1386 SECT: 1387 SECT: 1388 SECT: 1389 SECT: 1390 SECT:

201 201 201 201 201 201 201 201 201 201 202 203 202 203 202 203 202 202

0.01301 0.00000 0.01123 0.00000 0.00994 0.00000 0.00946 0.00000 0.01309 0.00000 0.01147 0.00000 0.01027 0.00000 0.00992 0.00000 0.01318 0.00000 0.01191 0.00000 0.00995 0.00000 0.01168 0.00000 0.01257 0.00000 0.01159 0.00000 0.01452 0.00000 0.01638 0.00000 0.01617 0.00000 0.02194 0.00000 0.01002 0.00000 0.02252 0.00000 0.00365 0.00000 0.01098 0.00000 0.00307 0.00000 0.00723 0.00000 0.00270 0.00000 0.00965 0.00000 0.00312 0.00000 0.01336 0.00000 0.00311 0.00000 0.01330 0.00000 0.00267 0.00000 0.00958 0.00000 0.00319 0.00000 0.00752 0.00000 0.00932 0.00000 0.01314 0.00000 a

Safety ratio = max[a,b]

189

b

Fig. 14.14. Test 074 in Hogan.

Number: Safety Ratio of Each Element

Fig. 14.15. Test 074 result in Hogan.

190

14.7 EXPERIMENT 1 Four total experiments were conducted and were divided into two rounds in terms of scale.

During the trial and error process of structural tests of the pattern system, three variables were changed (pattern, element shape, and element size) in order to produce a certain specific base geometry. The aim of these experiments was to create a database of structurally stable pattern systems. Structural stability required efficient combination of four factors: geometry, pattern, element cross-section shape, and element size.

In two experiments in the first round of tests, experimentations focused on relatively largescale Kagome weaving systems.

Experiment 1 examined grid patterns and different element spacings. The base geometry of Geometry 1 was a symmetric done with a span of approximately 10 meters.

Experiment 1 included 82 tests in total. The tests were divided into three stages which were determined in accordance with differences in cross-section shapes.

The first stage consists of 37 tests with rectangles as cross-section shapes. The second stage is 30 tests, and the arch is the cross-section shape.

The third stage, composed of 9 tests, uses concentric circles as the cross-section shape.

191

Height

Width

Length

Fig. 14.16. Experiment 1 Pattern Example.

192

Stage 1: Test 001 to Test 037 In Stage 1, the base geometry was fixed to a symmetric dome 4 meters high, 9 meters wide, and 10 meters long on a horizontal projection plane. In the pattern tested on this dome, element spacing was fixed to 1100 mm in all three directional elements.

1. Process Using the fixed test pattern, we changed crosssection dimensions by increasing the length of the square sides 10 mm by 10 mm from 50 mm. By substituting related variable values in the calculations, structural safety ratio tests were conducted in the Hogan program. When the side length of the cross-section square reached 60 mm, the pattern was able to stand independently.

The pattern remained stable throughout further increases in square side length until reaching 110 mm. Following this test, the side lengths of the squares were next decreased by 1 mm until the system reached stability once more. These tests allowed our research team to determine a range of efficient cross-section dimensions which were capable of allowing the system to stand.

2. Result A grid pattern system with 1100 mm-spacing elements based on a 4-meter-high symmetric dome reaches stability when the element cross section dimensions are near that of the square with side lengths of 60 mm to 100 mm.

These tests provided a range of efficient square side lengths which allowed the pattern to stand.

These results, however, were not realistic when compared to the actual dimensions of bamboo.

193

Fig. 14.17. Stage 1 Pattern (Perspective).

Spacing = 1100 mm

Fig. 14.18. Stage 1 Tested Pattern (Top).

194

Stage 2: Tests 038 to Test 067 In Stage 2 of the tests, calculation accuracy was improved by applying arches instead of squares as cross-section shapes in the calculations. To ensure bamboo could be applied to the pattern system, our research team examined the dimensions of bamboo pipes. Research statistics indicated Moso bamboo exterior radius measurements ranged from 30 mm102mm5-8, including the dimensions of both common and uncommon Moso bamboo. Element crosssection dimensions chosen for tests were within this range of dimensions.

The Stage 2 research tests examined grid patterns with three different element spacings: 1150 mm, 560 mm, and 340 mm. The base geometry was a 3.8 meter high symmetric dome 10 meters wide and 11 meters long on a horizontal project plane.

1. Process To acquire an efficient dimension set while maintaining the pattern system stability (which consisted of bamboo element exterior radii and element spacing), our research team contined structural tests by applying different dimension sets until a stable pattern system occurred.

Stage 2.1: Tests 038 to 046 Invalid tests in hindsight.

Stage 2.2: Tests 047 to 067 In Stage 2.2, as shown in Fig. 48, the angle in the arch cross section: Îą = PI/6 The tested exterior radii (R): 30 mm, 40 mm, 50 mm, 60 mm, 70 mm, 80 mm, 90 mm, 100 mm, and 102 mm.

2. Results No efficient dimension sets were found. Our research team spectulated that pattern systems could possibly appear if complete bamboo pipes were chosen as elements instead of pre-cut bamboo strips.

195

R

Îą=

PI /

6

t

SCALING UP AND STRUCTURAL ANALYSES

Fig. 14.19. Stage 2 cross-section shape.

Element Spacing = 1150 mm

Element Spacing = 560 mm

Element Spacing = 340 mm

Fig. 14.20. Stage 2 patterns (Perspective).

196

Stage 3: Tests 068 to Test 082 In this stage, a complete bamboo pipe was used as the element for the pattern system. The base dome was the same as that used in Stage 1 (with the same dimensions). There were two versions of element spacing: 1600 mm and 1100 mm. Also, to ensure availability when applying the Moso bamboo material, the cross-section dimension and the exterior radius of bamboo pipes were organized within a confined range of 30 mm and 102 mm.

1. Process Stage 3 tests were conducted in a process similar to the tests in Stage 2.

2. Result The data set below was tested: Exterior radius range of 30 mm to 102 mm with 1100 mm element spacing.

2.2.4. Results and Findings In Experiment 1 of the grid geometry (four meters high), a group of Moso bamboo pipe elements at a controlled spacing of around 1100 mm were capable of effectively holding the geometry up.

197

R

t

Fig. 14.21. Stage 3 cross-section shape.

Element Spacing = 1100 mm

Element Spacing = 1600 mm Fig. 14.22. Stage 3 tested patterns (Perspective).

198

Results and Findings Experiment 1, indicated that a triaxial Kagome bamboo weaving patten system applied to a four meter high dome is stable when Moso bamboo pipe elements are used within controlled spacing of approximately 1100 mm.

199

Fig. 14.23. Efficient element demonstration.

Spacing = 1100 mm

Fig. 14.24. Efficient element spacing

Fig. 14.25. Efficient patterns (perspective).

200

14.8 EXPERIMENT 2 Introduction of Third-Direction Elastic Elements to the Simulation In Experiment 2, a bamboo-rope triaxial Kagome weaving system was first introduced to the structural simulation process.

Responsive to Hogan Program Within the Hogan program, an introduced thirddirection rope element was integrated as a rigid joint to lock the other two directional bamboo elements. For this reason, patterns consistng solely of two lines illustrated the triaxial bamboorope weaing pattern in the computational structural analysis.

201

Experiment 1 Pattern System Demonstration.

↓

Experiment 2

Introduction of the Third-direction Elastic "Rope" Element

↓

Pattern in the Rhino Program.

↓

Pattern in the Hogan Program.

Rope or other elastic material Bamboo

↓

NUMBER: rigid node serial Number Bamboo Fig. 14.26. Comparison of two systems in two programs of geometrical simulation and structural simulation.

202

Base Geometry and Tested Patten Experiment 2 was based on a new input geometry: a developable curved surface distributing a certain quantity of bamboo pipes. The geometry reached 7.3 m with a span of 12 m.

203

Height

Span

Illustration of hinged-toground parts in geometry Fig. 14.27. Experiment 2 Geometry.

204

Radius Distribution and Spacing Distribution Bamboo pipe elements become thinner as they move from the outside of the geometry to the inside. The exterior radii of the bamboo pipes range from 30 mm to 90 mm. The distribution of element spacing exhibits similar parameters; as the elements get closer to the center, the spacing of the pipes becomes looser.

205

R = 30 mm R = 40 mm R = 50 mm R = 60 mm R = 70 mm R = 80 mm R = 90 mm

Fig. 14.28. Illustration of distribution of bamboo pipes of different exterior radiuses.

Fig. 14.29. Illustration of element spacing distribution.

206

Test Results and Findings The test results are indicated in the 2nd and 3rd diagrams on the right. Results showed that Part A and Part B of the geometry were two parts that included a concentration of unsafe pipe elements.

Additional findings and speculations were as follows: 1. A and B were hinged to the ground.

2. The exterior radii of the unstable pipes were checked in Part B to determine whether the pipe was capable of becoming stable when set with a larger radius. Results showed that this was possible, and thus, our team hypothesized that for the chosen curved surface pattern, thicker bamboo pipes could be used in unstable areas to contribute to system stability.

3. The curvatures of geomtry A and B were checked. A large curvature was observed in part A. Our team hypothesized that A required greater strength due to this curvature because shapes with large degrees of curvature necessitate greater structural support. Part B was near the highest point in the entire pattern system and was also located near an area with a great degree of curvature.

In terms of the above findings and related analysis, we concluded with the following advice on geometry: 1) The extent of the geometric curvature could be reduced in Part A, or another more gentle curvature could be introduced.

2) The height of geometry can be decreased to some extent.

3) Regarding the distribution of bamboo elements with different exterior radiuses: we recommended using bamboo pipes with much larger dimensions or placement of a greater number of bamboo pipes in and around the center areas.

207

R = 30 mm R = 40 mm R = 50 mm R = 60 mm R = 70 mm R = 80 mm R = 90 mm

B

Relation of Color and Safety Ratio Index Red Orange Yellow YellowGreen Green Lime Blue

> 1.0 0.9-1.0 0.71428-0.9 0.7-0.71428 0.6-0.7 0.5-0.6 < 0.5

A

A

B Fig. 14.30. Experiment 2 results.

208

14.9 Furniture scale and structural analyses

Produce Geometries by the design t This section includes data relating to the variations second design round of tests, which, like previously introduced experiments, included two tests. The scale for these tests was determined to be the size of a single-person bench (to test the cooling effects of bamboo). The related dimensions, including the exterior radius measuremts of bamboo, also changed accordingly.

original geometry

In addition to changes in scale, another progression from the first round of experiments included use of an algorithm designed by the Grasshopper program. Variant pattern systems were all based on the same pre-determined geometry.

The work flow for these experiments is included on the right. The input is an original geometry which is determined as the base for the pattern systems. Structural tests are conducted on variant pattern systems, which are obtained via the input geometry in the Grasshopper program.

This process allows stable pattern systems and efficient dimension sets to emerge. In addition to these data sets, our team also aimed to find connections between scale, pattern, geometry, and structural stability.

209

Variations of pattern that are strucGeometryturally stable

e design tool based on structural stability and

al try

Variant Patterns

design scheme

Fig. 14.31. Work flow.

210

14.10 EXPERIMENT 3 Base Geometry Experiment 3 begins with two similar original geometric surfaces: Geometry 3-1 and Geometry 3-2.

Both surfaces are similar in shape to a petal and incorporate a number of different curvatures in different positions. Seen from the side, Part A of the shape (circled in blue in Fig. 62) tends to extend upwards in a ramp-like formation. In Geometry 3-2, the extent of this extension is greater than that shown in Geometry 3-1.

This difference could be due to differences in the dimensions of the geometries. The two have the same span and are similar in length on the horizontal projection plane. The height of Geometry 3-1, h owever, is 730 mm; Geometry 3-2 is 1038 mm high (308 mm higher than Geometry 3-1).

Geometry 3-1

Geometry 3-2

1875 mm

1620 mm

1038 mm

730 mm

1743 mm

1620 mm

Fig. 14.32. Dimensions of the geometries.

211

A

Fig. 14.33. Input geometry 3-1 in the Rhino program.

A

Fig. 14.34. Input geometry 3-2 in the Rhino program.

212

Patterns To acquire variant pattern systems, pattern densities were changed in the Grasshopper program. In both the geometries, five patterns were produced (from smaller densities to larger densities). A a result, 10 total pattern systems were produced.

Pattern Series 3-1

Pattern Series 3-2

Density 1 6 lines in each direction

Density 2 8 lines in each direction

Density 3 10 lines in each direction

Density 4 12 lines in each direction

Density 5 14 lines in each direction

Rope bamboo

Fig. 14.35. Pattern variations In the Rhino program.

213

When input to the structural analysis program, the 10 patterns formed without the appearance of flexible elements and were called an "analysis pattern," as shown in the below diagram.

Analysis Pattern 3-1

Analysis Pattern 3-2

Analysis Pattern 3-1-1

Analysis Pattern 3-2-1

Analysis Patttern 3-1-2

Analysis Pattern 3-2-2

Analysis Pattern 3-1-3

Analysis Pattern 3-2-3

Analysis Pattern 3-1-4

Analysis Pattern 3-2-4

Analysis Pattern 3-1-5

Analysis Pattern 3-2-5

Fig. 14.36. Pattern variations In the Hogan program.

214

Exterior Radius Setting To accommodate furniture scale, the exterior radius range was determined as being between 5 mm and 10 mm. For one test, all the elements were set with the same radius pipes.

Test Results Structural analyses on Analysis Pattern 3-1-1 to Analysis Pattern 3-2-5 were conducted and the results of each test are shown in the chart below.

Analysis Pattern 3-1 -1

Analysis Pattern 3-1-2

Analysis Pattern

Radius (mm)

215

5

Ineffi-

Efficient

6

Efficient

Efficient

7

Inefficient

Efficient

8

Efficient

Efficient

9

Efficient

Efficient

10

Efficient

Efficient

Analysis Pattern 3-1-3

Analysis Pattern 3-1-4

Analysis Pattern 3-1-5

Efficient

Efficient

Efficient

Efficient

Efficient

Ineffi-

Ineffi-

Efficient

Efficient

Efficient

Efficient

Efficient

Efficient

Efficient

Efficient

Efficient

Efficient

Efficient Fig. 14.37. Analysis Result 1.

216

Analysis Pattern 3-2-1

Analysis Pattern 3-2-2

Analysis Pattern

Radius (mm)

217

5

Efficient

Ineffi-

6

Efficient

Efficient

7

Efficient

Efficient

8

Ineffi-

Ineffi-

9

Efficient

Efficient

10

Efficient

Efficient

Analysis Pattern 3-2-3

Analysis Pattern 3-2-4

Analysis Pattern 3-2-5

Efficient

Ineffi-

Efficient

Ineffi-

Efficient

Efficient

Efficient

Efficient

Efficient

Ineffi-

Efficient

Efficient

Efficient

Efficient

Efficient

Efficient

Efficient

Efficient Fig. 14.38. Analysis Result 2.

218

Analyzing Test Results Inefficient pattern systems with unstable elements were removed from the results. Specifically, unstable elements were defined as those elements which did not qualify as "very safe" (less than 0.5 safety ratio). By analyzing the unstable parts of the efficient systems, we aimed to: (1) find the relationship between the degree of curvature in certain parts of geometry and the weak or unstable parts of the structure to recommend changes to the geometry, and (2) find the relationship between the exterior radius setting for each bamboo element and pattern structural stability so as to provide recommendations for methods of changing the exterior radius setting.

Analysis Example 1: The findings from Analysis Pattern 3-1-1 (R=5 mm) indicated that the unstable portion of the pattern was concentrated largely near the center of the base surface, where a depression is formed as a result of the interation of curvatures on a curved surface. In cases where there is a small exterior radius setting, the curvature could be made more gentle to achieve pattern system stability.

Analysis Example 2: The findings from Analysis Pattern 3-1-1 (R=8 mm) indcated that the weak areas are situated at the edges of the curved surface. To include diversity among the radii of bamboo elements in this pattern system, columns a, b, c, and d (where non-blue structural members exist) would need to be composed of elements with larger radii than other columns.

Analysis Example 3: The results of Analysis Pattern 3-1-3 (R=7 mm) show that Part A is unstable. We find that Part A has a relatively large curvature and is also situated in a relatively high position. Decreasing the curvature extent around Part A was recommended.

219

Fig. 14.39.Example 1: Analysis Pattern 3-1-1 R=5 mm.

a c

b

d

Fig. 14.40. Example 2: Analysis Pattern 3-1-1 R=8 mm.

A

A

Fig. 14.41. Example 3: Analysis Pattern 3-1-3 R=7 mm.

220

Database of Stable Patterns based on Geometry 3 R refers to the efficient exterior radius of each element.

Analysis Pattern 3-1-1

Analysis Pattern 3-1-2

Analysis Pattern 3-1-3

Analysis Pattern 3-1-4

Analysis Pattern 3-1-5

R= 6mm

R= 5mm

R= 5mm

R= 5mm

R= 5mm

R= 8mm

R= 6mm

R= 6mm

R= 6mm

R= 7mm

R= 9mm

R= 7mm

R= 8mm

R= 7mm

R= 8mm

R= 10mm

R= 8mm

R= 9mm

R= 8mm

R= 9mm

R= 9mm

R= 10mm

R= 9mm

R= 10mm

R= 10mm

R= 10mm

Analysis Pattern 3-2-1 3-2-5

Analysis Pattern 3-2-2

Analysis Pattern 3-2-3

Analysis Pattern 3-2-4

R= 5mm

R= 6mm

R= 5mm

R= 6mm

R= 5mm

R= 6mm

R= 7mm

R= 7mm

R= 7mm

R= 6mm

R= 7mm

R= 9mm

R= 9mm

R= 8mm

R= 7mm

R= 9mm

R= 10mm

R= 10mm

R= 9mm

R= 8mm

R= 10mm

R= 9mm

R= 10mm

Analysis Pattern

R= 10mm

14.11 Findings 1. The geometries explored in Experiment 3 (furniture-scale) indicated that as the utilized bamboo pipes grow thicker, the pattern system grows more stable.

2. Different pattern densities allow checks and analyses for more information about the curvatures of different parts of the shape.

3. The shape of an unstable pattern can be changed subtly (in accordance with test results) to become stable. For example, in some unstable or weak portions, curvatures can adopt one-way changes.

223

Fig. 14.42. Moso Bamboo.

224

14.12 EXPERIMENT 4 Geometry The input geometry of Experiment 4 is a symmetrical doubly-curved surface. As shown from the side elevation and the front elevation at right, the two curves in red (as the isoparms), determine the bending of the whole geometry in U and V directions.

Fig. 14.43. Doubly curved surface base.

225

Side Elevation

Front Elevation

Perspective

226

Creating Variant Patterns with Grasshopper With the help of the Grasshopper program, variant patterns were created with different control settings, as indicated below: 1. Pattern density can be controlled with (1). Differences in quantities of elements in U and V directions lead to different pattern densities; 2. The general density distribution in the pattern can be controlled with (2); 3. Subtle density variations in the pattern can be controlled with (3). The existence of point attractors leads to subtle loosening of the pattern density. Differences in the quantity and position of the attractors lead to different subtle changes in output patterns.

Variant patterns are output afterwards.

(2) Pattern Density Distribution Control

(3) Point Attractors

(1) Pattern Density Control

227

Output: The pattern

Fig. 14.44. The Grasshopper program creating variant patterns.

228

Pattern Variations Using the same base geometry and different control settings in the computational program, eight patterns were output.

Pattern 1: This pattern has 17 elements in both directions. Parts of greater density are distributed around the four ends and the loose parts in the center. One point attractor was also set approximately in the center.

Pattern 2: This pattern has 21 elements in two directions and a similar density distribution to Pattern 1. The positining of the attractor point from Pattern 1 was maintained, and two additional attractors were added symmetrically in the looser below-center areas.

Fig. 14.45. Geometry Top View.

229

Density: 17x17 Attractor quantity: 1

Density: 21x21 Attractor quantity: 3

Fig. 14.46. Patterns.

Pattern 1

Pattern 2

Point Attractor Placement Pattern

230

Pattern 3: This pattern has 26 elements in two directions, and is similar to Pattern 2 in terms of density distribution. The position and quantity of point attractors remains the same as Pattern 2: 3 point attractors were situated; one in the loose center and two symmetrically in the relatively loose below-center areas.

Pattern 4: This pattern has 26 elements in two directions, and is similar to Pattern 3 in terms of density distribution. The positioning of the three point attractors from Pattern 3 is maintained, and six additional point attractors are added symmetrically in upper left, upper right, lower left, and lower right parts of the pattern.

Fig. 14.47. Geometry Top View.

231

Density: 26x26 Attractor quantity: 3

Density: 26x26 Attractor quantity: 9

Fig. 14.48. Patterns.

Pattern 3

Pattern 4

Point Attractor Placement Pattern

232

Pattern 5: This pattern has an even density distribution, with 17 elements in each direction. Instead of single attractors, we set a point attractor group. Three groups of attractors are added, one in the center and two symmetrically on the upper part between the center and two ends.

Pattern 6: This pattern also has an even density distribution and 17 elements in both directions. The three attractor groups from Pattern 5 were maintained, and two additional point attractor groups were placed in the upper and lower regions of the pattern.

Fig. 14.49. Geometry Top View.

233

Density: 17x17 Attractor group quantity: 3

Density: 17x17 Attractor group quantity: 5

Fig. 14.50. Patterns.

Pattern 5

Pattern 6

Point Attractor Group Placement Pattern

234

Pattern 7: This pattern has 17 elements in two directions. The density distribution is the opposite of the distribution indicated in Patterns 1 to 4, with elements concentrating in the center and loosening as the pattern moves to the ends.

One point attractor was placed in the dense center of the pattern.

Pattern 8: This pattern shares the same density set and the same density distribution regularities as Pattern 7. The difference lies in the attractor. Maintaining the position of the attractor in the dense center, a second point attractor is added at the bottom.

Fig. 14.51. Geometry Top View.

235

Density: 17x17 Attractor quantity: 1

Pattern 7

Density: 17x17 Attractor quantity: 2

Pattern 8

Fig. 14.52. Patterns.

Point Attractor Placement Pattern

236

Structural Test of Patterns Just as in Experiment 3, in order to make the bamboo pipe element dimensions in accordance with the furniture scale, the exterior radius was set between 5 mm and 10 mm. For one test, all the elements were set at the same radius.

Test results

Analysis Pattern 1 Analysis Pattern 2 Analysis Pattern 3 Analysis Pattern 4

Analysis pattern

Exterior Radius (mm)

237

5

Inefficient

Efficient

Efficient

Inefficient

6

Inefficient

Inefficient

Inefficient

Inefficient

7

Inefficient

Efficient

Inefficient

Inefficient

8

Efficient

Efficient

Inefficient

9

Efficient

Efficient

Efficient

Efficient

10

Efficient

Efficient

Efficient

Efficient

Ineffi-

Analysis Pattern 5

Analysis Pattern 6

Analysis Pattern 7

Analysis Pattern

Inefficient

Efficient

Efficient

Efficient

Efficient

Efficient

Efficient

Inefficient

Efficient

Efficient

Inefficient

Inefficient

Efficient

Inefficient

Inefficient

Inefficient

Efficient

Efficient

Efficient

Efficient

Efficient

Efficient

Efficient

Efficient Fig. 14.53. Test Result.

238

Test Result Analysis Exterior Radius (mm)

5

6

7

8

9

10

239

Analysis Pattern 1

Analysis Pattern 2

Analysis Pattern 3

Analysis Pattern 4

Analysis Pattern 5

Analysis Pattern 6

Analysis Pattern 7

Analysis Pattern 8

Fig. 14.54. Test Result

240

Overall, the test results indicate that as the exterior radius grows larger (or the pipe elements grow stronger) the pattern systems tend to become more stable.

During the testing process, four different groups of patterns were determined. Each group included two types of pattern.

1. Pattern 2 and Pattern 3: The sole difference between Pattern 2 and Patten 3 is that the density of the latter is greater. When we compare the two patterns using the same size elements in each line, we find that besides the exceptions of the third line, the patterns tend to become stable as the element dimension increases.

241

Analysis Pattern 2

Analysis Pattern 3

Exterior Radius (mm)

5

6

7

8

9

10

Fig. 14.55. Test Result Analysis 1

242

2. Pattern 3 and Pattern 4: The difference between Pattern 3 and Pattern 4 is that the latter is created as a result of adding more point attractors in some less dense areas.

When we compare the two patterns with the same size elements in each line, we can hypothesize that pattern stability can be disturbed by placing new point attractors.

Given the positioning of the point attractors which disturb pattern stability, we analyzed that as these points affected the density of the four ends, the pattern became progressively less stable.

Nevertheless, when unit elements grow stronger, the increasing unit strength counteracts any destruction caused by the attractor points, and aids in returning the pattern to stability.

Analysis Pattern 3

Analysis Pattern 4

Exterior Radius (mm)

5

6

7

8

9

10

Fig. 14.56. Test Result Analysis 2

244

3. Patterns 6 and 7 Patterns 6 and Pattern 7 have the same number of elements. As indicated from left to right in Figure 85, we observed the transferring of density from the two ends to the center (from Pattern 6 to Pattern 7).

As the transfer occurs, the pattern is only able to maintain stability if the elemnts in the system do not grow larger. The first portion of the system to become unstable is the intersection point where two isoparm curves create a large curvature.

Similarly, increasing the size of the units can help counteract changes in structural stability via transferring of the density center.

245

Analysis Pattern 6

Analysis Pattern 7

Exterior Radius (mm)

5

6

7

8

9

10

Fig. 14.57. Test Result Analysis 3

246

4. Patterns 7 and 8: The sole difference between Patterns 7 and 8 is that the latter is created using an additional point attractor setting near the lower-bottom part of the geometry.

The added point attractor was placed with the aim of changing the density distribution of the pattern. As shown in lines 2, 3, and 4, if elements of larger size are used, either the system becomes less structurally stable, or the density distribution changes (from Pattern 7 to Pattern 8).

If unit element sizes are larger, elements in danger of breaking will be neutralized, and the pattern system will regain stability.

247

Analysis Pattern 7

Analysis Pattern 8

Exterior Radius (mm)

5

6

7

8

9

10

Fig. 14.58 Test Result Analysis 4

248

Database of Stable Patterns based on Geometry 4

R refers to the efficient exterior radius of each element.

Analysis Pattern 1

Analysis Pattern 2

Analysis Pattern 3

R= 8mm

R= 5mm

R= 5mm

R= 9mm

R= 9mm

R= 7mm

R= 6mm

R= 10mm

R= 10mm

R= 9mm

R= 8mm

R= 10mm

R= 9mm

R= 10mm

249

Analysis Pattern 4

Analysis Pattern 5

Analysis Pattern 6

Analysis Pattern 7

Analysis Pattern 8

R= 6mm

R= 5mm

R= 5mm

R= 5mm

R= 7mm

R= 6mm

R= 6mm

R= 9mm

R= 8mm

R= 7mm

R= 9mm

R= 10mm

R= 9mm

R= 9mm

R= 10mm

R= 10mm

R= 10mm

250

14.13 Findings 1. Within an exterior radius range of 5-10 mm, as the exterior radius grows larger, the pattern systems tend to gain stability.

2. The portion created as a result of the intersection between the two isoparm curves is structurally weak due to the extent of the curvature. The curvature can be made flatter to allow the system to stand (within a certain exterior radius).

3. Following structural analyses conducted on a

series of systems with various scales, patterns, and geometries, our research concluded that all of these issues (scale, pattern, and geometry) will affect structural stability. Certain material dimensions also affect structural stability. The system is only stable when a certain combination of these factors is applied.

Due to limitations in the number of geometries and patterns that were tested and constrictions in the dimensional range of each element (as related to the project theme), our research team concluded that the relationship between the four factors was still incomplete, but the digital analysis tool method could still be used as a reference for future studies.

251

Fig. 14.59. Moso Bamboo.

252

15.0

BUILDING A MICROCLIMATE WITH WOVEN BAMBOO A semi-controlled microclimate can be created by utilizing the woven bamboo system and manipulating the density of the weave on an architectural scale.

Fig.15.0: Cooling bench prototype

253

254

15.1 Building a microclimate

CAPILLARITY & TRANSPIRATION

Bamboo has capillary and transpiration qualities which are present even in harvested bamboo culms.

By taking advantage of these qualities, we can improve comfort on our urban bench by recreating a heat exchange system through evaporative cooling.

This is made possible by controlling densities in the bamboo canopyâ&#x20AC;&#x2122;s fabric.

WEAVING

Evaporative cooling is not possible without solar radiation.

Solar control plays a part in this strategy.

Our experiments aimed to determine the solar control required along with the percentage of controlled open mesh.

Fig. 15.1: Cooling strategy diagram

255

DENSITY MANIPULATION

MICRO CLIMATE PRODUCED THROUGH EVAPORATIVE COOLING

15.2 Evaporative cooling Evaporative cooling occurs when water vapor is added to the surrounding air.

To create evaporation on the bamboo surface, temperatures on the surface must be exchanged. When the difference between temperatures is large, the evaporative cooling effect is proportionally better than if the difference between temperatures is very small. If both air and surface temperatures are the same, evaporation does not occur, and therefore there is no cooling outcome.

Air on hot days will quickly cool the bamboo because the air currents cause quick evaporation. The heat required from this evaporation is taken from the bamboo culms.

evaporation

warm air stream

ev

cool air WOVEN BAMBOO MESH

Fig. 16.2: Evaporation cooling process.

Fig. 15.3: Cooling bench prototype 01

256

15.3 Capillarity and Transpiration Capillary and transpiration qualities are present in harvested bamboo culms.

By taking advantage of these qualities, we can improve the comfort of the bench microclimate by recreating a heat exchange system through evaporative cooling. These qualities can be enhanced by controlling the densities of the woven bamboo system.

Fig 14.4: Bamboo capillary bundles microscopic view.

257

15.3.1 Capillarity in plants and trees Capillary action in trees increases when transpiration occurs at the leaves, thus creating depressurization. Atmospheric factors affect transpiration in plants. Temperature, humidity, and wind movement all directly affect the efficiency of evaporative air cooling efforts.

Temperature: Transpiration rates go up as the temperature goes up.

Relative humidity: As the relative humidity of the air surrounding the plant rises the transpiration rate falls.

Wind and air movement: Increased movement of the air around a plant will result in a higher transpiration rate. 28

Fig. 15.5: Capillarity on plants

258

15.4 Bamboo transpiration Studies by the National Taiwan University, Kyushu University and the National Agricultural Research Center in Ibaraki indicated bamboo culms retain their evaporative qualities even after being cut.

Bamboo culm measurements: sample #1 of 13.5 m sample #2 of 16.7 m sample #3 of 15.2 m sample #4 of 15.6 m

CAPILLARITY

design for stand-scale transpiration estimates in a Moso bamboo forest.

A crane truck and scaffold were placed near the samples. The samples were roped to the end of the cranes and then cut 0.1 m above the ground at predawn. The lower ends of the cut bamboo stalks were put into a tank filled with water and were recut underwater with a handsaw.

The bamboo was then raised with the cranes and fixed to the scaffold. As the bamboo stalks absorbed water, the supply was replenished (every 30 minutes), and the amount of water added was recorded. The tops of the water tanks were covered with plastic bags to prevent evaporation. 29

Evaporation

This study was conducted between 2007 and 2008 to establish an optimal and effective

evaporation

with a DBH of 10.1 cm and height with a DBH of 16.7 cm and height with a DBH of 11.2 cm and height with a DBH of 12.0 cm and height

Fig. 15.6: Diagram of cut bamboo culms after being placed in water tank.

259

Fig.15.7: Diurnal variations in (a) rainfall ( P ), (b) solar radiation ( Rs ; thin line), vapour pressure deficit (VPD; bold line) and (c) sap flux ( F d ) averaged over 16 individuals in August 2008.

260

Fig.15.8: Relationship between 30 min estimates of sap flux ( F d ) and observed water loss from the reservoir ( F d _up ). The black line is the regression line ( F d _up = 1.35 F d ( R 2 = 0.84)). The dashed line is a 1:1 line. Data symbols in...

Fig.15.9: Relationship between 30 min estimates of sap flux ( F d ) and observed water loss from the reservoir ( F d _up ). The black line is the regression line ( F d _up = 1.35 F d ( R 2 = 0.84)). The dashed line is a 1:1 line. Data symbols in...

261

15.4.1 Sap Flux Measurement The method presented is one of the most common systems used to measure sap flux in trees and has gained widespread acceptance in studies of water use at the tree level (e.g Meinzer et al., 2005; Giambelluca et al. 2003).

Thermal dissipation probes were originally developed by Granier (1985) and used heat as a tracer for the detection of water movement in the sapwood of a tree. 30

Fig 15.10: Sap Flux measurement

Fig. 15.11: Sap Flux measurement diagram.

262

15.5 Case study A study conducted by the Tokyo Institute of Technology examined cooling walls which present evaporative and capillary qualities similar to the present bamboo project. 31 The study was carried out on a summer day in August in Tokyo. Average temperatures were 30-31 degrees Celsius.

A perforated brick lattice was used as the cooling wall. Air temperature was measured both before and after passing through the brick channels.

Different densities of openings presented different readings. The brick form produced cooling effects by subdividing the the lattice into a number of major openings, therefore increasing the total area capable of producing a surface-heat exchange.

The soaked bricks presented a surface temperature of 20-25 degrees Celsius, a temperature 10 to 15 degrees cooler than the average air temperature on the day the study was conducted (Brick thermal conductivity 0.8W/mK).

Opening ratios of 34% and 48% presented differences of 1 degree and 3 degrees, respectively. Air inlet areas and heat exchange surface areas were calculated.

The results indicated that air temperatures dropped by one degree on inlet areas and three degrees on heat exchange surface areas.

In this experiment, a brick cooling wall was created.

By controlling differentiations in the densities of the brick lattice, air was allowed to flow, and an improvement in cooling performance was achieved.

This study indicated that by controlling openings in the system, optimization of the cooling effect could be possible. This same strategy was applied to our research project in terms of considerations of grid density.

263

Fig. 15.12: Air flow visualization

Fig. 15.13: Air flow cooling analysis

Fig. 15.14: Detailed brick design.

264

15.6 Cooling optimization by weaving Bigger bamboo diameters offer greater amounts of heat exchange. To maintain a good air flow, creating an opening that is 30% to 50% of the diameter of the bamboo allows enough space to weave the rope element in place while also creating a triaxial weave.

Fig. 15.15:. Air flow through bamboo weave

265

Diameter decrement: Bigger diameters offer greater potential for heat exchange

EDGES TO SUPPORT THE CANOPY Fig. 15.16: Optimized pattern for bench prototype 01

266

15.7 Bamboo Cooling Test By analyzing the convection cooling of the bamboo we can predict the cooling efficiency of the woven system. The images here demonstrate the process; constant air flow through a piece of bamboo at the maximum humidity level demonstrates bamboo surfaces can achieve high degrees of cooling.

BAMBOO ANEMOMETER

Fig. 15.17: Tools used in the bamboo cooling test.

267

Fig. 15.18: Humidity measurement of bamboo

FAN

268

15.7.1 Bamboo evaporative cooling experiment We tested bambooâ&#x20AC;&#x2122;s evaporative cooling effects through a series of experiments on different lengths of bamboo. A wind speed of 2.0m/s was chosen for this experiment because it is the average wind speed for Tokyo during the summer.

The bamboo utilized for this experiment had a diameter of 55 mm, meaning that the inlet area was 23.7 cm 2. The external temperature at the time of the test was 27.8 celsius.

269

Fig. 15.19: Diagram showing the bamboo lengths tested for evaporative cooling.

Trough variations on the bamboo lengths it is possible to compare the bamboo surface in contact with the air flow against the inlet area. Therefore we can have a rule that allow us to calculate the evaporative cooling effect of the bamboo bench and optimise the openings of the mesh for better performance.

Fig. 15.20: Bamboo section and air flow visualization

Fig. 15.21: Air temperature decrement directly proportional to bamboo surface increment. Results from experiment.

270

15.8 Surface Development & Mesh Optimization

THE AIM: The following tests illustrate a method for optimizing the cooling effect. This method increases the number of bamboo components in accordance with the bending behavior of the bamboo along the surface.

Fig. 15.22: Form finding with digital tools.

271

272

15.8.1 Anthropometric Analysis and Form Finding

Fig.14.24: Anthropometric sitting positions for chart (fig 176)

Fig. 15.26: Form finding through anthropometry

To achieve a form, we researched and analyzed studies in anthropometric behavior in sitting postures (according to age). The data aided in producing a set of iterations that would allow one to three people to sit on the produced benches. A geometry designed for two people was used to further progress the research.

273

Fig.15.25: Anthropometric sitting positions according to age

274

15.8.2 Point Manipulation: From Anthropometric Analysis to Form Finding A tripod canopy was determined for the geometry of the bench canopy. The geometry was determined using four coordinates. Three coordinates will touch the ground, and one will remain open to allow access to the bench.

In locations where the curve points are too pronounced, the bamboo breaks due to the forces applied during construction. The final versions of the bench will incorporate this knowledge.

Fig.15.27: Coordinates for scale and proportion of bench (part of form finding process).

275

276

15.8.3 Geometry one, changing the footprint angle

Diameter decrement due to curvature increment.

Experiment one: Bamboo diameters affected by geometry.

By creating changes in the foot print angle, we can increase the curvature of the overall geometry, thus directly affecting the diameter of the bamboo.

Fig. 15.28: Bench prototype 01 from above.

Fig. 15.29: Experiment on bamboo diameters through changes in surface area, and curvature, or perimeter.

277

NOTE: The numbers on the chart refer to the range of bamboo diameters.

278

15.8.4 Geometry Two: Surface Manipulation INCREASE QUANTITY OF BAMBOO

GRID DENSITY MANIPULATION

Experiment two: the images above illustrate the design process of bamboo optimization in terms of bamboo surface increments to improve convection cooling. Increments in bamboo area are achieved through changes to mesh density manipulation and geometry modification.

279

IMPROVE SHAPE BY MANIPULATING ENDPOINTS

System-optimized bamboo pieces ranging from 17 mm radius to 2.7 mm radius. These offer areas of 16 square meters on a geometry of 3.5 m2.

Fig. 15.30: Optimization process through a series of steps (bamboo quantity, grid manipulation, and shape optimization).

280

15.8.5 Cooling Performance

Following analysis of the bamboo surface and utilization of the results from the previous experiment, we determined that the air cooling qualities of bamboo are as follows: 1) Considering an average wind speed of 2.0m/s to 2.6m/s for August in Tokyo, the developed bench can cool down the air in the local environment by an average of 1.0 degree Celsius.

2) A reduction in solar radiation of 59 w/m2 (solar radiation in summer in Tokyo is 208 w/m2) in combination with wind speed increments of 0.35 m/s could create a drop of 1.0 degree Celsius. 32 Our bench offers a 70% reduction in direct solar radiation. In combination with sporadic wind breeze increments, the bend could result in a cooling effect of up to 4-5 degrees Celsius (in optimum conditions).

Note: sweat rate, skin temperature, and skin moisture can also influence comfort parameters.

AVERAGE AMOUNT OF COOLING (WITH BOTH CONVECTION AND SHADE): 6 DEGREES CELSIUS

281

Optimal measurements for comfort are: 48%-55% humidity and 24-28 degrees Celsius.

Fig. 15.31: Cooling bench final prototype, computational visualization.

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16.0

CONCLUSIONS & RECOMMENDATIONS

Image: Weaving elements shown independently.

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16.1 Recommendations: Woven Design System Traditional grid shell systems develop their structural stability and reach equilibrium through interconnections between their nodes. This produces a structurally efficient transformation from a series of slender arches to a shell behavior. Our woven system differs from this traditional shell type structure in that the components are woven and interlaced but are never welded or connected with anything other than a tension cable. Due to this, bamboo components were observed sliding (in a way that is difficult to predict) to resting positions when forces were applied and the geometry took form. This behavior is more evident when the mesh is open rather than dense. Therefore, the developed system was observed to be more efficient when applied to denser meshes where sliding potential is minimized.

Our research also indicated that the woven cables became loose as the bamboo slid, even if the cables were set in adequate tension from the beginning. As a result, we recommend implementation of a system where the tension cable can be adjusted to accommodate any final movements of the bamboo. The tension cable (bow and arrow) strategy offered improvements in terms of control of the geometry via tensioning. It offered changes to the assembly method by putting tension cables and pegs into position and providing strategic points for the form to develop from two dimensions. This also allowed the bamboo to bend and reach the desired shape. We also recommend that weaving begin from the outer edges and move internally because we observed that other approaches allow larger potential for error on the tension cable.

In terms of geometry, it is important to mention that although a system capable of predicting the required flexibility of bamboo was used, the majority of the breaking that occurred during design development happened not due to curvature but due to manipulations of the material. In order to place the material in position, it was occasionally necessary to bend the material more than ultimately required.Therefore, a larger margin of tolerance must be considered to compensate for human force during assembly.

Smooth changes in the geometry produce better surfaces than strong curvatures. The computational tool indicated that sliding forces at points of strong curvature in the surface make the labor process much more difficult and reduce the aesthetic results.

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16.2 Conclusion: This thesis aims to pave the way for reflective architectural design.

We must look deeper within the architectural discourse to explore the foundations of materiality, computational tools, and vernacular strategies to optimize the creative process. This is not possible without collaboration between disciplines.

A project as small as a bamboo bench can teach us the vast potential of traditional methods that have existed throughout the history of humanity. A system like weaving can be examined on a vast level and can become better understood to produce possibilities in terms of resource optimization, energy creation, and structural performance.

Efficiency should be the word used for design, but the word should also carry a deeper understanding. Efficiency should consider material qualities capable of satisfying human needs, much in the beautiful way that nature does.

Analog and digital experimentation showed potential for seamless integration of new technologies and old methods, however, but it is only through constant improvements of the system through further experimentation that the technique will grow in terms of efficiency.

This thesis explored the first layers within a huge number of possibilities regarding the utilization of woven systems for the benefit of an architectural dialogue concerning material, structure, and form.

Our research team hopes that this document is a positive influence and a source of inspiration for future research into the computational potential of tomorrow. We also hope it serves as a reminder not to ignore the past in the field of architecture.

In conclusion, we believe that in order to achieve architectural excellency, collaboration between disciplines is necessary. New ways of nurturing knowledge within the architectural discourse are also required.

To optimize the creative process in both the digital and physical realm, and to play an essential role, the two mediums complement each other.

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2. United Nations. “Kyoto Protocol.” Kyoto Protocol. http://unfccc.int/kyoto_protocol/ items/2830.php (accessed July 24, 2014).

3 BAMBOO FOR EXTERIOR JOINERY A research in material properties and market May 2010 Valentijn de Vos Thesis report of Larenstein University BSc ‘International Timbertrade’ Source: http://www.guaduabamboo.com/support-files/bamboo_for_exterior_joinery.pdf 4 Watanabe, Masatoshi. “Present Status of Bamboo in Japan.” http://www.worldbamboo. net/wbcix/presentation/Watanabe,%20Masatoshi.pdf.

Masatoshi WATANABE, Dr.Agri, n.d. Web. 8 July 2014. <http://www.worldbamboo.net/wbcix/presentation/ Watanabe,%20Masatoshi.pdf>.

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8 Ibid.

9 “OttoMultihalle ext_view - SMD Arquitectes.” SMD Arquitectes RSS. SMD Arquitectes RSS, n.d. Web. 8 July 2014. <http://www.smdarq.net/case-study-mannheim-multihalle/ ottomultihalle-ext_view/>.

10 “OttoMultihalle ext_view - SMD Arquitectes.” SMD Arquitectes RSS. SMD Arquitectes RSS, n.d. Web. 8 July 2014. <http://www.smdarq.net/case-study-mannheim-multihalle/ ottomultihalle-ext_view/>.

11 “OttoMultihalle ext_view - SMD Arquitectes.” SMD Arquitectes RSS. SMD Arquitectes RSS, n.d. Web. 8 July 2014. <http://www.smdarq.net/case-study-mannheim-multihalle/ ottomultihalle-ext_view/>.

12 Philadelphia College of Textiles and Fabrics, Frank L. Scardino. Frank. K. Ko. “http://

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www.triaxial.us.” Triaxial Woven Fabrics. http://www.triaxial.us/Papers/Textile%20 Woven%20Fabrics%20Part%201.pdf (accessed July 25, 2014).

13 Kenneth Snelson. “Kenneth Snelson.” Tensegrity & Structure. http://www. kennethsnelson.net/tensegrity/ (accessed July 25, 2014).

14 Kenneth Snelson. “Kenneth Snelson.” Tensegrity & Structure. http://www. kennethsnelson.net/tensegrity/ (accessed July 25, 2014).

15 Ibid.

16 “Woven Surface and Form.” http://onlinelibrary.wiley.com/doi/10.1002/ad.366/ pdfFind a website by URL or keyword.... Anish Kapoor, Cecil Balmond and Arup AGU,, n.d. Web. 10 July 2014.

17 International arts and artists.org Modern Twist Contemporary Japanese Bamboo Art Andreas Marks with contribution by Margalit Monroe.

18 “basketry and beyond.” basketry and beyond.org.uk. N.p., n.d. Web. 16 July 2014. <http://www.basketryandbeyond.org.uk/wp-content/uploads/2014/04/TechniquesPanels2-with-BB-logo.pdf>.

19 “basketry and beyond.” basketry and beyond.org.uk. N.p., n.d. Web. 16 July 2014. <http://www.basketryandbeyond.org.uk/wp-content/uploads/2014/04/TechniquesPanels2-with-BB-logo.pdf>.

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20. Jun Sato, Jun Sato: Items in Jun Sato Structural Engineers (1st edition), (Tokyo: Inax, 2010).

21. Compile Group of A Handbook of Static Calculation for the Architectural Structure, eds. A Handbook of Static Calculation for the Architectural Structure ( 建筑结构静力 计算手册 ), (Beijing: China Architecture and Building Press, 1974), 82, 83, 87, and 90.

22. Oscar Antonio Arce-Villalobos, "Fundamentals of the Design of Bamboo Structures," English ed. S. Ralston (Doctor diss., Eindhoven University of Technology, 1993), 248.

23. Jinhe Fu, "Chinese Moso Bamboo: Its Importance," BAMBOO, October, 2001, 5-6.

24. "Phyllostachys Edulis 'Moso'," http://www.lewisbamboo.com/favmoso.html [accessed February 24, 2014].

25. "Mechanical Property of Bamboo," http: //www. bambus/new/eng/reports/ mechanical_properties/referat2.html [accessed February 24, 2014].

290

26. Jinghe Fu, "The Competitive Strength of Moso Bamboo (Phyllostachys pubescens Mazel ex H. de Lehaie) in the Natural Mixed Evergreen Broad-Leaved Forests of the Fujian Province, China," (Diss., Göttingen, University, 2001).

27. Zheng Rong Jiang, Mu Xu, Wei Ning Duan, Kai Rong Shi, Jian Cai, and Shi Tong Wang, "Nonlinear Finite Element Analysis of Beam String Structure," Advanced Materials Research (December 2010).

-------------28 “Evapotranspiration - The Water Cycle.” , from USGS Water-Science School. N.p., n.d. Web. 1 Sept. 2014. <http://water.usgs.gov/edu/watercycleevapotranspiration. html>.

29 “Stand-scale transpiration estimates in a Moso bamboo forest: (I) Applicability of sap flux measurements.” Stand-scale transpiration estimates in a Moso bamboo forest: (I) Applicability of sap flux measurements. N.p., n.d. Web. 8 July 2014. <http://www. sciencedirect.com/science/article/pii/S037811271000383X>.

30 “Measuring sap flux, tree water use and transpiration.” https://www.bgc-jena.mpg.de/ bgp/index.php/NorbertKunert/SapFlux. https://www.bgc-jena.mpg.de/bgp/pmwiki.php, n.d. Web. 8 July 2014. <https://www.bgc-jena.mpg.de/bgp/index.php/NorbertKunert/ SapFlux>.

31 “A 3D CAD-based simulation tool for prediction and evaluation of the thermal improvement effect of passive cooling walls in the developed urban locations.” A 3D CAD-based simulation tool for prediction and evaluation of the thermal improvement effect of passive cooling walls in the developed urban locations.

Jiang He, Akira Hoyano, n.d. Web. 8 July 2014. <http://www.sciencedirect.com/science/article/pii/ S0038092X09000085>.

32 “Outdoor comfort research issues.” Outdoor comfort research issues. http://www. sciencedirect.com/science/article/pii/S0378778802000828 (accessed July 18, 2014).

Figures: 2.1. Taylor, Adam. “http://www.businessinsider.com/why-sochi-is-by-far-the-mostexpensive-olympics-ever-2014-1Find a website by URL or keyword....” Why Sochi Is

By Far The Most Expensive Olympics Ever. Business Insider, 17 Jan. 2014. Web. 8 July 2014. <http://www.businessinsider.com/why-sochi-is-by-far-the-most-expensiveolympics-ever-2014-1Find a website by URL or keyword...>.

2.2. Bamboo distribution in Asia Source: ftp://ftp.fao.org/docrep/fao/010/a1243e/a1243e00.pdf Contribution of world bamboo resources per continent (Lobovikov, 2007) 2.3. California Forest Foundation. “Critical Thinking.” :: The Forest Foundation. http://

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calforestfoundation.org/Critical-Thinking/index.htm (accessed July 25, 2014).

2.4 Watanabe, Masatoshi. “Present Status of Bamboo in Japan.” http://www. worldbamboo.net/wbcix/presentation/Watanabe,%20Masatoshi.pdf.

Masatoshi WATANABE, Dr.Agri, n.d. Web. 8 July 2014. <http://www.worldbamboo.net/wbcix/ presentation/Watanabe,%20Masatoshi.pdf>.

2.5 Watanabe, Masatoshi. “Present Status of Bamboo in Japan.” http://www. worldbamboo.net/wbcix/presentation/Watanabe,%20Masatoshi.pdf.

Masatoshi WATANABE, Dr.Agri, n.d. Web. 8 July 2014. <http://www.worldbamboo.net/wbcix/ presentation/Watanabe,%20Masatoshi.pdf>.

2.6. TU Vienna. “Efficiency of Lightweight structural forms.” http://publik.tuwien.ac.at/ files/pub-ar_7968.pdf. http://publik.tuwien.ac.at/files/pub-ar_7968.pdf (accessed July 25, 2014).

3.1. Google Earth image.

3.2. Ibid.

3.3. Ibid.

3.4. Ibid.

3.5. Ibid.

3.8 “Japan Will Triple the Amount of Power It Generates from Renewable Energies to 300 Billion kWh by 2030 / Asia Biomass Energy Cooperation Promotion Office - Asia Biomass Office.” Japan Will Triple the Amount of Power It Generates from Renewable Energies to 300 Billion kWh by 2030 / Asia Biomass Energy Cooperation Promotion Office - Asia Biomass Office. http://www.asiabiomass.jp/english/topics/1212_03.html (accessed July 26, 2014).

3.9 Ibid.

7.2 - 7.6 “OttoMultihalle ext_view - SMD Arquitectes.” SMD Arquitectes RSS. SMD Arquitectes RSS, n.d. Web. 8 July 2014. <http://www.smdarq.net/case-study-mannheimmultihalle/ottomultihalle-ext_view/>.

6.7. Philadelphia College of Textiles and Fabrics, Frank L. Scardino. Frank. K. Ko. “http://www.triaxial.us.” Triaxial Woven Fabrics. http://www.triaxial.us/Papers/Textile%20 Woven%20Fabrics%20Part%201.pdf (accessed July 25, 2014).

6.8 Kenneth Snelson. “Kenneth Snelson.” Tensegrity & Structure. http://www. kennethsnelson.net/tensegrity/ (accessed July 25, 2014).

6.9 Kenneth Snelson. “Kenneth Snelson.” Tensegrity & Structure. http://www. kennethsnelson.net/tensegrity/ (accessed July 25, 2014).

6.10 - 7.15 “Woven Surface and Form.” http://onlinelibrary.wiley.com/doi/10.1002/ ad.366/pdfFind a website by URL or keyword.... Anish Kapoor, Cecil Balmond and Arup AGU,, n.d. Web. 10 July 2014.

7.0 nternational arts and artists.org Modern Twist Contemporary Japanese Bamboo Art Andreas Marks with contribution by Margalit Monroe.

292

7.1 Hiroshima Kazuo basket maker in rural Japan. http://huntingtonarchive.osu.edu/Exhibitions/basketMakerExhibit.html 7.2 “basketry and beyond.” basketry and beyond.org.uk. N.p., n.d. Web. 16 July 2014. <http://www.basketryandbeyond.org.uk/wp-content/uploads/2014/04/TechniquesPanels2-with-BB-logo.pdf>.

7.3 “basketry and beyond.” basketry and beyond.org.uk. N.p., n.d. Web. 16 July 2014. <http://www.basketryandbeyond.org.uk/wp-content/uploads/2014/04/TechniquesPanels2-with-BB-logo.pdf>.

7.4 “Woodland Skills Centre ... 01745 710626.” Woodland Skills Centre 01745 710626. http://woodlandskillscentre.co.uk/ (accessed July 25, 2014).

7.5 “PART III. SMALL-SCALE ENTERPRISE DEVELOPMENT.” PART III. SMALL-SCALE ENTERPRISE DEVELOPMENT. http://www.fao.org/docrep/004/ad453e/ad453e06.htm (accessed July 25, 2014).

7.6 “Making Baskets, Central Highlands, Vietnam.” Flickr. https://www.flickr.com/photos/ lonqueta/3975037907/ (accessed July 25, 2014).

7.7 Demand Media. “Basket Weaving Directions for a Market Basket.” eHow. http://www. ehow.com/how_7856095_basket-weaving-directions-market-basket.html (accessed July 25, 2014).

7.8 Jessica M. Winder “photosalmagundi.wordpress.com.” photosalmagundi.wordpress. https://photosalmagundi.files.wordpress.com/2013/01/p1150883asalmagundi.jpg (accessed July 26, 2014).

7.9 “Basket Weaving 101 : The Flat-Bottom Egg Basket.” Some owls talk a lot some are quieter. http://owlnet.wordpress.com/2010/10/10/basket-weaving-101-the-flat-bottomegg-basket/ (accessed July 25, 2014).

7.10 “Studio KotoKoto | Baskets.” Studio KotoKoto. http://www.studiokotokoto.com/category/baskets/ (accessed July 25, 2014).

7.11 Ibid.

7.12 Ibid.

10.0 “Geodesic PolyLine Path.” Geodesic PolyLine Path. http://www.mapwindow.org/ phorum/read.php?3,4171,4261 (accessed July 26, 2014).

10.1 “4 Planet Multicast: Geographic MBone Maintenance.” 4 Planet Multicast: Geographic MBone Maintenance. https://graphics.stanford.edu/papers/munzner_ thesis/html/node9.html (accessed July 26, 2014).

10.2 “Gridshell Fabrication: Parametric Analysis | Aaron Grey.” Aaron Grey. http://www. aaron-grey.com/archives/560 (accessed July 26, 2014).

11.1. “OttoMultihalle ext_view - SMD Arquitectes.” SMD Arquitectes RSS. SMD Arquitectes RSS, n.d. Web. 8 July 2014. <http://www.smdarq.net/case-study-mannheim-

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multihalle/ottomultihalle-ext_view/>.

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Fig. 13.3. “Centre Pompidou-Metz Project,” Roland Halbe photograph, http://www. stylepark.com/en/news/the-return-of-the-curved/309264.

Fig. 13.4. “Roof Details,” http://www.centrepompidou-metz.fr/en/roofing.

Fig. 13.5. “Sunny Hills Project,” 设计时代 Photograph, http://www.thinkdo3. com/s/16572.

Fig. 13.6. “Structural Details,” com/s/16572.

设计时代

Photograph, http://www.thinkdo3.

Fig. 13.7. “Weaving Pavilion Project,” Max Gerthel photograph, http://davidgarciastudio.blogspot.jp/2009/04/weaving-project.html.

Fig. 13.8. “Weaving Pavilion Sketch Model,” Max Gerthel photograph, http://davidgarciastudio.blogspot.jp/2009/04/weaving-project.html.

15.4 “Biocanvas - A cross section of a bamboo stem, showing the....” Biocanvas - A cross section of a bamboo stem, showing the.... http://biocanvas.net/post/11594583840/across-section-of-a-bamboo-stem-showing-the (accessed July 26, 2014).

Fig. 13.10. “Moso Bamboo,” http://www.nipic.com/show/1/70/02fd6c7492d7ca42. html.

Fig. 13.42. “Moso Bamboo,“ http://nicolelbates.com/news/putting-down-roots-lifelessons-from-the-moso-bamboo.

Fig. 13.59. “Moso Bamboo,“ http://nicolelbates.com/news/putting-down-roots-lifelessons-from-the-moso-bamboo.

--------15.5 UIC. “http://www.uic.edu/classes/bios/bios100/lecturesf04am/model.gif.” http:// www.uic.edu/classes/bios/bios100/lecturesf04am/model.gif. http://www.uic.edu/ classes/bios/bios100/lecturesf04am/model.gif (accessed July 26, 2014).

15.7 “Stand-scale transpiration estimates in a Moso bamboo forest: (I) Applicability of sap flux measurements.” Stand-scale transpiration estimates in a Moso bamboo forest: (I) Applicability of sap flux measurements. N.p., n.d. Web. 8 July 2014. <http://www. sciencedirect.com/science/article/pii/S037811271000383X>.

15.8 Ibid.

15.9 Ibid.

15.10. “Biological Posteriors: The pulse of a tree.” Biological Posteriors: The pulse of a tree. http://biologicalposteriors.blogspot.jp/2012/01/pulse-of-tree.html (accessed July 26, 2014).

15.11. “Measuring Sap Fluz, tree water use and transpiration . Buogeochemical

294

processes.” Biogeochemical processes. https://www.bgc-jena.mpg.de/bgp/index.php/ NorbertKunert/SapFlux (accessed July 26, 2014).

15.12. “A 3D CAD-based simulation tool for prediction and evaluation of the thermal improvement effect of passive cooling walls in the developed urban locations.” A 3D CADbased simulation tool for prediction and evaluation of the thermal improvement effect of passive cooling walls in the developed urban locations. Jiang He, Akira Hoyano, n.d. Web. 8 July 2014. <http://www.sciencedirect.com/science/article/pii/S0038092X09000085>.

15.12 Ibid.

15.14 Ibid.

15.24 Generative and Parametric Design -eCAADe 29493 Anthropometric and behavior data applied to a generative design system A study of public benches Ana Claudia Vettoretti1, Pablo Resende2, Mário Guidoux Gonzaga3, Benamy Turkienicz4.1,2,3,4UFRGSBrazil.

15.25 Ibid.

Works Consulted “OttoMultihalle ext_view - SMD Arquitectes.” SMD Arquitectes RSS. SMD Arquitectes RSS, n.d. Web. 8 July 2014. <http://www.smdarq.net/case-study-mannheim-multihalle/ ottomultihalle-ext_view/>

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