Growing Architecture

Growing Architecture

Pavel Hladik EmTech 2005 / 2006

Acknowledgments

I would like to devote this thesis to miss Katerina Juraskova.

The author is very grateful to his advisors Michael Weinstock, Michael Hensel and Achim Menges for their guidance opening mind and also encouragement during the preparation of this thesis.

Contribution from Martin Hemberg, Nikolaos Stathopoulos, Chris Williams and Wolf Mangelsdorf was much appreciated. Thanks also to Guillem Baraut for fruitful discussions.

The research for this book was supported by grants from the Czech Architectural Foundation and company Ce Wood. The author would like to express his genuine gratitude to Ladislav Tucek and his Reprograficke stredisko for collaboration and support.

I would like to thank my family and friends for their love and support during this difficult and yet rewarding year.

Pavel Hladik EmTech 2005 / 2006

Contents

4

Preface

14

Concept

48

Material Properties

68

Form Generation

102

Evaluation

117

Conclusion

118

Areas of Further Research

119

Bibliography

120

Appendix 01

121

Appendix 02

Pavel Hladik EmTech 2005 / 2006

Preface

Concept

Material Properties

Form Generation

Evaluation

Abstract

Recently, there have been introduced digital tools that allow for a simulation of the growth into architectural design. The research in the past decades have placed geometric design representations almost exclusively into the digital design environment without constraints of traditional materials and their fabrication.

In this research it is argued that the generative process driven by growth algorithm could be informed by the behaviour of a material and its production logic. The thesis explores the methodology for the bidirectional approach which links a digitally generated geometry with tectonic articulation. The bidirectional approach is understood as an alternative to the traditional analytical uni-directional approach for the articulation of digital geometry. The proposed methodology therefore takes advantage of form-finding - the behaviour and selfform of material under stress and links it directly to the generated geometry.

The work explores the capacities of laminated wood and its integration into the design in the structural paradigm. The structural scheme is the branching system developed into the complex adaptive system [1].

A key contribution of this thesis is the use of parametric computation techniques in the convergence of structural scheme of branched structures and sensitive growth. The limits of proliferated geometry and behaviour of laminated timber were achieved.

Algorithmic Proliferation - L-system generated proliferation, Pavel Hladik, 2005.

Pavel Hladik EmTech 2005 / 2006

Preface

Concept

Material Properties

Form Generation

Evaluation

Aim and Scope

Having a system allowing for adaptation in diverse structural criteria is advantageous for maintaining the same structural scheme in different geometries. These geometries are produced by the growth algorithm L-system which responds to the requirements of the site through the spread of inputs that are base points for the proliferated branched geometry. The complex branched structure is investigated in terms of structural performance.

The aim of the research is focused on the relationship between vector active branched system and surface active system evolved from branches. The vector active system is explored in physical formfinding models based on dehiscence of water.

The research explores capacities of laminated timber in the structural scheme of branched geometry. Gained knowledge is then instrumentalized by a development of a material system which leads to the evaluation on the scale of the permanent pavilion.

Thesis is based on the research commenced in the institute of Lightweight Structures where related systems were studied and methodology for experiments with branching was outlined.

The scope of the research is divided into two parts.

The first is the generation of form in digital space according to rules gained from physical form-finding of branched structures. This part leads to the self-organisation in the digital environment with a possibility of growth.

The second part is devoted to the integration of self-form of laminated timber and generated branched system. The transition between bending and direct paths is examined and leads to an associative model of the material system.

Layers of plywood exported from the saw mills companies.

Pavel Hladik EmTech 2005 / 2006

Preface

Concept

Material Properties

Form Generation

Evaluation

Hypothesis

The research is based on a premise that complex branched system could perform structurally and compose a self-supporting structure made from laminated wood respecting fibre directionality of the composite.

Timber planks of certain sections could be laminated in order to achieve 3D geometry and then fit into the structural scheme where vector-active system prevails.

A complex system with a structural capacity is achieved by the convergence of computational techniques and inherent material properties.

The material system has extrinsic and intrinsic constrains that are implemented into the system by set of parameters that tune the behaviour of the whole and also provide necessary boundaries. These parameters together with associative parametric modelling provide a base for emergent structure.

Extrinsic constraints: morphology of site, fabrication, loads Intrinsic constraints: structural capacities of geometry, capacities of material, self-load

Studies of Frei Otto for branched supports.

Pavel Hladik EmTech 2005 / 2006

Preface

Concept

Material Properties

Form Generation

Evaluation

Methods of Research

Experiments - Overall analysis and evaluation - page 28

The methods of research involves the formulation of hypothesis which pertains to set of ideas based on certain initial assumptions.

The key points of the research are deployed and evaluated in chapters of the thesis. These approaches are implemented through specific means which include physical and digital experiments.

ing A

Structural Scheme

fig. 01, ex 01, dry threads

fig. 02, ex 01, threads influenced by surface tension of water

fig. 03, ex 02, level 2 threads of II. degree of slack, front view

fig. 04, ex 02, level 2 threads of II. degree of slack, left view

fig. 05, ex 03, level 3 threads of III. degree of slack, front view

B

The first and the most important method is the physical form-finding technique which examines the three-dimensional branching pattern that comes out from experiments with threads immersed into liquid. The threads are affected by surface tension of water and create the structure in tension. The inverted structure therefore act purely in compression without bending moments. The experiments result into models that were studied by architect Frei Otto and his Institute of Lightweight Structures in Stuttgart in 1970’s and 1980’s of the 20th century. The basic research commenced at the IL was considered as the starting point of the thesis.

The experiments of Frei Otto group were extended by variety of input geometry. Rules and pattern of emerged branching were studied. The distance of branching points and also number of threads bundled together were analysed and prepared for the digital model.

The setup for the digital self-organisation was achieved by carefully prepared parameters.

Material Model

fig. 07, ex 04, thick 4 ply threads dipped into water, front view

fig. 08, ex 04, thick 4 ply threads dipped into water, left view

fig. 09, ex 05, threads dipped into water, 4 base “trunks”, topological change from others, front view

fig. 10, ex 05, threads dipped into water, 4 base “trunks”, left view

fig. 11, ex 06, threads with configuration of ex 05, II. degree of slack, front view

C

The second experiment introduced the behaviour of building material into the complex geometry. The material represents the natural composite and was chosen in order to achieve the branched structure according to the biomimetic studies. This knowledge gained by observation of material distribution in natural models was then abstracted into the assembly. The direction of fibres was the most important constraint in the material model. The curvature, flexibility and geometry under stress was studied in form-finding experiments with laminated wood.

Material System

fig. 13, ex 07, 2 ply threads, co-joining of threads, bases oppposite each others, front view

fig. 14, ex 07, 2 ply threads, co- joining threads, bases opposite each others, left view

fig. 15, ex 08, threads dipped into water, bases connected according the random function run in excel, front view

fig. 16, ex 08, threads dipped into water, bases connected according the random function run in excel, left view

fig. 17, ex 09, threads dipped into latex, threads in two layers, 2. layer orinted - fig 02 page 14, top view

The previously described physical experiments converge into the associative digital model that keep structural scheme of branched system and also the behaviour of laminated timber. It results into the material system with its limits of fabrication and structural performance. The digital form-finding of tree-structures within limits of 3D lamination represents the complex geometry that was later evaluated by procedures of finite elements methods. The actual behaviour and flexibility of the structure was studied on physical mod-

Experiments from Nested Form-Finding module 05 - Hladik, Porras, Rabagliati - see appendix of the thesis.

Pavel Hladik EmTech 2005 / 2006

Preface

Concept

Material Properties

Form Generation

Evaluation

els of laminated plywood. The FEA was chosen in order to see the performance of the whole assembly not only of its parts.

Manufacturing possibilities of wooden components learned when visiting these companies are considered as important feedback to the research.

Evaluation The evaluation of the material system is provided both by physical tests and consequently by finite elements analysis (FEA). This provides the feedback to the research. The curvature, deflection and behaviour of the structure was studied. The behaviour of components (laminated planks) and also macrocomponents (branching supports incorporated into a surface) was tested in order to examine the transition between vector-active and surface-active systems.

The assumption which drove experiments of physical form-finding of threads and liquid was evaluated digitally FEA in Ansys. Ansys software was also used for the design of dimensions of laminated branches.

Case Studies Case studies is an essential part of the thesis and provided the feedback at all stages of the research. It aims to review examples of passed and prospective relations between production and conception to discuss relations between particular manufacture paradigms and their associations to related design processes.

The architecture that has designed and been built provide the opportunity to gain knowledge from other teams that dealt with complex curvatures of wooden structures and branched supports.

Scheme of vertical supports in Stuttgart Airport Terminal 1 by Von Gerkan, Marg + Partner feature branched columns that support steel grid of the roof. The branched structure represent merely as a widened head of columns.

Bordeaux Law Court by Richard Rogers Partnership is one of building where the thin shell was introduced as the main structural scheme. Although the structure was build separately as ribs covered by stressed skin the CAD methods developed by the project operte within limits of the material - wooden boards.

ExpoRoof by Thomas Herzog deals with a complex curvature and succesfully introduces the form-finding into the manufacturing process. Although the structural components of the shell are not laminated, the manufacturer (FinnforestMerck) is able to use the similar technique for 3D lamination.

Form-finding, wooden strips - 3D lamination.

Pavel Hladik EmTech 2005 / 2006

Behavior of Planks Curvature

Manufacturing Constraints

Alg. Definition Spatial Requirements

R1

R2

S

Transport Assembly Techniques Geometry - Macro Scale

CS [b]

Geometric Setup

P [1]

CAD CAM Rules, Variables, Logic

CS [1]

Finding of Geometry, Rules

P [0]

Proliferation Methods

Production Logic

Structural Concept Emergent Behavior

CS [0]

Structure

Replication Capacity

Physical Form-Finding 01

1. Growth and Branching Concept of Sensitive Growth derived from natural systems.

The explanation of the concept and relation to the research.

Performative Criteria

Emergence Form Analysis

Top-down Decisions

Common Rules

ture

Hypothesis

Digital Form-Finding

Physical Form-Finding 02

Living, Non-living Na

Diagram of the Work

Evaluation

Structural Requirements

Growth and Branching

Aim

Form Generation

Reset of Criteria

Material Properties

Time, Cost Effectivity

Concept

Material Properties

Preface

2. Physical Form-Finding 01 Research into more complex branched structures that went beyond executed experiments of IL and myself in previous research (viz appendix).

3. Mathematical Model The abstract model of branched structures and its possibility for digital form-finding.

4. Applied Model of Branching Setting rules gained from results of actual Form-Finding and its emergent behaviour.

5. Physical Form-Finding 02 Behaviour of laminated timber and its inherent forces and parameters.

6. Production Logic Available CAM technologies in correspondence with developed CAD.

Model of Material System

Applied Model of Branching Parametric Setup

7. Digital Form-Finding Edge-rewritting L-system and IF statements that drive the model of the complex system. The generic process is informed by capacities of 3D lamination.

Fabrication Tech.

Perform. Capacities

8. Proliferation Methods Set of rules embedded in the digital system controlled by variables.

9. Model of Material System Set of rules and variables that control the performance of continuously laminated wood. Size, thickness, strength and variability of the researched component assembly.

Local Interaction

Global Interaction

10.Performative Criteria Set of constraints that evaluates the final assembly of the material system. The performative criteria are mainly structural.

11.Manufacturing Constraints Strategies for building the larger scale proliferation. The effectiveness within the constraints of performative criteria.

Pavel Hladik EmTech 2005 / 2006

Preface

Concept

Material Properties

Form Generation

Evaluation

Stuttgart Airport, DE

Von Gerkan, Marg + Partner Structural Engineer Weidleplan Consulting

fig 01. Colums are branched into a supporting structure that helps to distribute a load from roof slabs.

fig 02. Section of the structure with a drawing of scaffolding. Each column carries its own slab.

fig 03. Regular distribution of slab beams create grid. Branches are attached to grid intersections.

The characteristic design features of the Terminal 1, which has received several awards – the tree-shaped columns of the loadbearing structure and the dike-shaped building bar orientated towards the apron – were continued throughout the extension. The roof of Terminal 3 was however dissolved into single shed areas, in order to maintain the tree structure with an identical roof incline but a reduced building height. A total of 18 steel trees support the stepped roof (Terminal 1: 12 trees).

All trees are the same construction and size, they vary in trunk length only. The inclination of the roof is also constant.

On the street side, the arrival hall connects Terminal 1 and 3 as a „mall“ over a length of 260 m. The simple and obvious positioning of the access elements and voids allowing vertical visual links guarantee an immediate orientation in the new „Terminal of Clarity“.

fig 04. Spatial organisation of the Terminal 3. Tree-columns decrease its “trunk”. Inclination of the roof is constant.

fig 05. Detail of branched trees are solved by welding and adding an additional piece that serves as a reduction to accomodate diameters of brancehs.

fig 06. Detail of a node. Tree-column is made of steel - anisotropic material.

width 105 m height max. 30 m length 140 m building volume ca.

270 000m3 glazed surface ca.

7 100 m2 number of piers 12 gross floor space 38 000 m2 roof truss structural steel ca. 1 650 t columns structural steel ca.

205 t

fig 07. Construction of tree-columns.

fig 08. Construction of one part of the Terminal 3 - each column supports one slab. Slabs are then bridged by sky-lights.

fig 09. Regular grid of trees, regular grid of roof slabs.

Pavel Hladik EmTech 2005 / 2006

10

Preface

Concept

Material Properties

Form Generation

Evaluation

Bordeaux Law Court

Richard Rogers Partnerships, 1992 - 1998 Design of Geometry: Arup

The individual courtrooms are enclosed within this frame in seven clearly identifiable volumes, tapering in section and rounded in plan.

The courtroom elements were originally conceived as exposed ferrocement structures. The design team has since explored the potential of stressed-skin systems that offer greater flexibility of construction and greater durability, including a lightweight aluminium honeycomb sheet structure (usually employed in the aircraft industry) with a painted epoxy resin finish, which can be prefabricated under factory conditions and easily assembled on site in individual onion like segments.

02. Model of the building. Photograph of the autonomous volumes of courtrooms.

01. Volumes courtrooms are made of wood - structure and interior and exterior cladding.

The technique used for this building was innovative in terms of structural purpose of the skin as a thin shell and its fabrication.

In fact the entire volume and manufacturing was controlled by computer. However the process of the fabrication feature the great loss of the material which could be decreased by following rules of the material properties.

03. Detail of the exterior wooden cladding.

Pavel Hladik EmTech 2005 / 2006

11

Preface

Concept

Material Properties

Form Generation

Evaluation

Bordeaux Law Court

04. Construction of the timber structure. Chambers have concrete bases.

01. Geometry of the chamber. Composition of laminated beams as a prime structure.

02. CAD drawings of the structural elements.

03. Construction of the timber structure. Components are manufactured according to the specific geometry.

05. CAD drawings of volumes of the chambers.

Pavel Hladik EmTech 2005 / 2006

12

Preface

Concept

Material Properties

Form Generation

Evaluation

Expo Roof

Herzog Studio, 2000 Fabrication: Finnforest - Merck

01. Court Covered by shell structure

Each of the 10 upturned umbrellas, over 20m high, consists of a central four-legged tapering pylon of timber and steel supporting a 40 x 40m square crown, which is further divided into four identical square leaves. At the base of each pylon, steel feet are anchored in a 15m deep concrete ring foundation. The leaves of the crown are double curved surfaces made up of a skeletal net of laminated timber struts clad in a weatherproof membrane. Precipitation is conducted to the centre of each umbrella, down a rainwater pipe in the centre of each pylon, and feeds into a grid of 5m wide canals on the piazza which complement the roof geometry. The illusion is of pontoons and pavilions, floating on water, under a substantial billowing cloud.

Changing daylight, the aspect of the sun and sky colour, is filtered through the millimetre thin translucent roofing membrane which is fireproof, self cleaning and, if necessary, recyclable.

The timber originated in the Black Forest, in south-west Germany.

Here grows the biggest concentration of ancient white oaks in western Europe. Used for centuries as ships’ masts, the standard girth of the oaks chosen for the Expo-Roof columns was 1.4m, and some were up to 250 years old. For a forest, the culling of these older trees, up to 50m high, is essential for new growth.

Suitable trees were selected using ultrasonic equipment to reveal any internal structural weaknesses.

02. Plan of the expo square. The image shows the connection of components - supports with shells.

The structure uses advantage of steel joints that provide necessary strength of the structure. The combination of form-found timber planks on a mathematical geometry presents an effective combination of CAD and CAM.

03. Horizontal section of tree-column.

Pavel Hladik EmTech 2005 / 2006

13

Preface

Concept

Material Properties

Form Generation

Evaluation

Pavel Hladik EmTech 2005 / 2006

14

Living, Non-living Na

Behavior of Planks Curvature

Replication Capacity

Manufacturing Constraints

Alg. Definition Spatial Requirements

R1

R2

S

Transport Assembly Techniques Geometry - Macro Scale

CS [b]

Geometric Setup

P [1]

CAD CAM Rules, Variables, Logic

CS [1]

Finding of Geometry, Rules

P [0]

Structure

Proliferation Methods

Production Logic

Structural Concept Emergent Behavior

CS [0]

Performative Criteria

Emergence Form Analysis

Top-down Decisions

Common Rules

Physical Form-Finding 01

Hypothesis

Digital Form-Finding

Physical Form-Finding 02

ture

Evaluation

Structural Requirements

Growth and Branching

Aim

Form Generation

Reset of Criteria

Material Properties

Time, Cost Effectivity

Concept

Material Properties

Preface

Model of Material System

Applied Model of Branching Parametric Setup

Fabrication Tech.

Perform. Capacities

Local Interaction

Global Interaction

Pavel Hladik EmTech 2005 / 2006

15

Preface

Concept

Material Properties

Form Generation

Evaluation

Sub-hypothesis: If woollen threads are immersed into a liquid the branched structure is achieved and this geometry could be analysed and consequently used in digital environment. The result could be used as a model of self-organised tension structure later (inverted) acts in compression.

Different geometry is produced by connecting points from tilted planes than from horizontal ones. By tuning certain parameters could by achieved complex emergent system. Parameters could be summarized and control in digital models as well as in physical experiments.

Gained logic allows for proliferation and differentiation of nested hierarchies in digital environment. Careful observation could also lead to the digital self-organisation [1].

Pavel Hladik EmTech 2005 / 2006

16

Preface

Concept

Material Properties

Form Generation

Methodology

Evaluation

The methodology of understanding the structural concept of material system explores two levels of experiments - physical and digital form-finding. Form-finding is based on the behaviour of material under stress - self-organisation.

a

b

a

a

c

b

b

d

c

e

d

The structural scheme chosen for the material system was branched system that came out from experiments described by Institute of Lightweight Structures in Stuttgart under supervision of Frei Otto [2].

Branched structures are three-dimensional supporting systems used in various materials for buildings. They are ancient and derive from early pole building. Figure 01 shows different supporting systems - column-beam, traditional wooden braces and tree structures, stone structures in bridges. Images 01 f, g shows the recent thinking about supports in tents and suspended roofs - there is a connection of elements in tension and in compression. This way of the scheme is later deployed in this thesis in a way that branched supports are incorporated into the surface where its redundant structure is able to resist both tension and compression forces.

Tree-shape supports are not bionic constructions, as the branches of a tree support nothing heavier than leaves and thus have a lower load-bearing function than the tree-like support structure of shown examples. Threads immersed in liquid are models of constructions that eliminate bending. The structure is not stiffened by any diagonal members. Schemes presented on images 02 b and d deals with branched supports and try to get closer to bionic structures. Branches are interconnected by additional members that stiffen the structure and in terms of topology it creates the closed branching system. Branches are still considered as straight members connected by specially designed nodes similar to that build in columns for Stuttgart airport.

Images on the figure 03 explains the relationship between distances of branches in different conditions. On the figure 03 a there is the direct paths system in a fan structure whereas on the figure 03 f there is a scheme of the minimal path system.

c

f e

d g

01. Schemes of branched structures. Image from [3].

f

02. Branched Supports. Image from [3].

Transition stages between 03 a and 03 f could be studied on physical model of threads immersed in liquid. Bundling of threads in a certain density and distance result in the emergent structure which depends on the surface tension of used liquid. The setup of parameters and the background is widely described in the appendix of this thesis. It was commenced by the author and his colleagues in EmTech Phase 1 as a Nested Form-Finding Module. In the previous work there was also suggested to explore parameters that control the system. Distances between connected points are constant and so parameter tuning the geometry sketched on fig 03 is the length of threads.

03. Relationships of brancehes. Image from [4].

Pavel Hladik EmTech 2005 / 2006

17

Preface

Concept

Material Properties

Form Generation

Evaluation

plane - tension and compression forces

points on the plane C 01 Horizontal plane. Square array of points.

C 03 C 02 Horizontal plane. Points on a Inclined plane. Square array square boundary. of points.

branches

Methodology

In order to understand tree structures and prepare input for the digital models the setup for experiments with liquid and threads was established. Planes with an arrangement of points connected to one base point by threads were studied. There were studied different boundary conditions - planes are not always horizontal and they have different number of points. The other set of experiments is represented by a change of liquid type and the geometrical scheme: from direct paths systems to hanging models with branched supports.

Parameters that influence the structure are:

length of threads arrangement of points

angle of branches - emergent bridge due to surface forces of water

Results gained from experiments are: branch (or trunk)

C 04 Horizontal plane. Square array of points. Bundled threads.

C 05 Horizontal plane. Points on a square boundary. Base point in the middle.

C 06 Vertical arrangement of points and a base point in a plane.

length between points number of bundled threads inclination and curvature of trunk and branches

base point 01. Schemes of the experiment. The initial state represents the distance between points and a base point always as direct paths.

03. Studies for the design of an exhibition hall.

04. Open branching. Diagram shows structural relationships of members.

02. Different boundary conditions as an input for the form-finding experiments.

Frei Otto designed interesting project which goes beyod the scope of the pure vector acting system of branched structure.

The great KOCOMMAS (King’s Office, Council of Ministers, Majilis al Shura) complex in Riyadh, Saudi Arabia, consists of several lattice shells, rope constructions and some solid multi-storey buildings.

The lattice shell cover reception and meeting rooms and inner courtyards. The lattice have a hexagonal mesh with equal-length bars in welded tubular steel and are covered with glass. Specialaluminium umbrellas were developed as shade elements. The three-dimensional form of these bars constructions was arrived at in a suspended model, and the nodal points were also fixed in the suspended position.

The form of the branched supports was itself developed by self-forming processes. The great beuaty of the structure rests on the harmonious combination of two constructions that emerged by self-formation. The project was designed down to the last detail but could not be completed because of political developments. [4] The hybrid system of surface active system and vector active supports was observed on hanging branched structures.

05. K0COMMAS Riyadh - branched columns and lattice shell roof in one structure.

Pavel Hladik EmTech 2005 / 2006

18

Preface

Concept

Material Properties

Form Generation

Evaluation

Methodology

Digital experiments took advantage of the associative models that allows for algorithmic generation. In my particular case it was Generative Components - feature modelling and scripting. The geometry was later postprocessed by other software that allows for complex nurbs geometry (Rhino), 2D drawings (AutoCad, Microstation), data sorting (Excel), rendering (Max).

As an input for the digital generation data were used rules gained from physical form-finding with threads and liquid. Rules put into a model of features allow later algorithmic generation. Simple model of a feature with conditional statements was proliferated according to rules of edge-rewriting L-system. L-system was introduced in 1968 by Lindenmayer as a theoretical framework for studying the development of simple multicellular organisms, and subsequently applied to investigate higher plants and plants organs [9].

The stochastic L-system used for modelling of trees was introduced and served as a scaffolding for further examination.

01. Axial tree - explanation of the L-system algorithm and its basic entities. All Images from [9].

02. Explanation of the edge-rewriting L-system.

03. Context-sensitive L-systems. The predecessor of a tree production (a) matches adge S (b).

02. Different boundary conditions as an input for the form-finding experiments.

The possibility of a growing associative model opens an idea of selforganisation in digital environment. Then just by keeping the rules expressed parametrically the geometry could fit into different input criteria and constraints. Criteria are tuned by parameters until it reaches the crital values and cannot later maintain the form and features of branched system. It is one of important moments in the “life” of complex adaptive system. Constraints are understood as an input coordinates (arrangement) of points and base point (described on the previous page).

Pavel Hladik EmTech 2005 / 2006

19

Preface

Concept

Material Properties

Form Generation

Evaluation

Physical Experiments

Pavel Hladik EmTech 2005 / 2006

20

Preface

Concept

Material Properties

Form Generation

Evaluation

Experiment 00

The aim of this experiment was to document and descirbe the behaviour of threads with different amount of slack. Threads interconnect points and base points when they are crossing each other.

Because of this arrangement threads bundle easier.

On figures 01-03 there are three degrees of slack. It is 10%, 20 % and 30% of the direct length. Branched geometry is very complex and difficult to trace. The pattern of 3D branches is emergent and it varies with every dipp into the liquid.

01. I. degree of slack

02. II. degree of slack.

03. III. degree of slack.

04. The description of the Experiment 00 is expalined in the appendix of the thesis - Nesetd Form-Finding Module.

Pavel Hladik EmTech 2005 / 2006

21

Preface

Concept

Material Properties

Form Generation

Evaluation

Experiment 01

The first experiment examines inclined planes with points. In order to see distances of branching nodes the precise digital model in cartesian coordinate system was built.

Experiments unvail the behaviour of branching system affected by geometrical constraints.There is a certain logic in distances between branching nodes, distances of points and also the length of threads.

01. The image shows the number of bundled threads: 2, 3 and occaisonelly 4

02. Detail of s-o structure. The typical end of the trunk is for inclined plane connected to a base point.

110

[170,125,110] [185,125,110] [200,125,110] [170,140,110] [215,125,110] [170,155,110] [230,125,110] [170,170,110] [170,185,110]

0,0 125 250 x [80,0,-30]

[50,0,-30] [0,50,-30] [0,80,-30]

[125,125,0] [250,170,30] [250,170,15] [250,185,15] [250,200,15] [250,215,15] [250,230,15]

[210,0,-60]

[80,0,-60]

125

[20,0,-60] [0,20,-60]

[50,0,-60]

y

[0,50,-60]

250

[0,80,-60] [20,0,-90]

[80,0,-120]

[0,110,-60]

[0,20,-90]

[50,0,-120] [0,50,-120]

-140 [80,20,-140]

[50,20,-140]

[80,50,-140] [110,50,-140]

[50,50,-140]

[0,80,-120]

[20,50,-140] [20,80,-140]

[50,110,-140] [80,110,-140]

03. The geometry of the boundary conditions: The cube 250 mm. In the middle corner of the cube there was selected a start of the coordinate system.

trunk bifurcated at the base - 90° angle of point bases Pavel Hladik EmTech 2005 / 2006

22

Preface

Concept

Material Properties

Form Generation

Evaluation

Experiment 02

The second experiment with inclined planes explored the behaviour of trees when they affect each other and compose more complex geometry. The special steel “cage” enabling reconfiguration of planes was constructed.

Threads were immersed in liquid - in water and later in water with PVA glue in order to maintain its branching geometry. There was introduced also a hierarchy in the system by adding different thickness of threads. The results were expected according to the research made in Nested Form-Finding Module (see appendix of the thesis).

3D pattern of branches now became clearer.

Points in cartesian coordinate system were later reconstructed digitally.

Planes with points are in these angles: 0°, 90°, 45°.

01. A,B tree structres

02. A,B tree structres

03. C tree structres with influence (variable thickness of threads)

05. 2B

06. 2C

400

[105,115,400] [145,115,400] [185,115,400] [105,155,400] [225,115,400] [105,195,400]

[165,125,195]

[125,95,80] [145,95,80] [125,115,80] [165,95,80] [125,135,80]

[0,110,55] [0,125,55] [0,140,55] [0,110,40]

0,0 [0,110,25] 260 x y

04. 2A

240

Pavel Hladik EmTech 2005 / 2006

23

Preface

Concept

Material Properties

Form Generation

Evaluation

Experiment 03

The Experiment 03 explores the idea of branched hanging model.

There was one branched model nested on the other structure.

Threads are dipped into latex and after solidifying the other tree structure is produced by threads connected to branching nodes of previous branched model.

This approach was not later deployed but it opens an interesting way how to connect two important structural concepts in architecture. The work of IL institute on this topic is documented in the design of KOCOMMAS Riyadh. The vector-active and surface-active systems could be in more equal ratio.

01. Branched hanging model. Branches result into a surface that forms 02. Image shows the connection of trees. a catenoid. The second tree is connected to branching nodes of the first geometry.

03. The tree structure reacts on the distances and geometry of the other tree.

04. Boundary conditions for the nested tree structure.

Pavel Hladik EmTech 2005 / 2006

24

Preface

Concept

Material Properties

Form Generation

Evaluation

Experiment 04

There were executed several experiments that were aimed to study the impact of surface tension of water as a form-finding method for minimal paths between points. Important issue was to study different boundary conditions for branched threads.

These experiments were later used for proliferation of the branched structure on plane an it could be later extended to morphology of a given site. It drives the layout of the pavilion. Presented set of pictures opens a discussion for further development of this strategy.

The outlined strategy goes far beyond of this thesis but deserves further development. The sensitive growth algorithmicaly driven by algorithm L-system that is constraint by rules of minimal paths has been seen as a very innovative and powerful approach for designing.

In this thesis there is a framed possibility to control a spread of a pavilion structure on a given planar site. Later in the chapter Form Generation there are explained my design strategies.

01a. Different boundary conditions and branched structures.

a

01b.

01c.

Figures 01a-01c are photographs focused on the theme of minimal paths and different boundary conditions. There are structures in 2D as well as in 3D. On figures 02a and 02b there are two plans (examples of variations) of the plan of designed pavilion. The branched structure of the building itself is dependent on the triangulated geometry of an area. It comes out from points connected according to rules explained in the chapter Analysis and Evaluation. The self-organised model of minimal paths could have bigger impact and could also influence the environment. At this point it is possible to define and control the notion of nesting and hierarchy in designing.

b

02. Two plans of the pavilion with the same input. Change of parameters of the branched structure in 2D cause the reconfiguration of the building. This has an impact on a built area of the site and also on the pavilion itself.

base - water, variation Pavel Hladik EmTech 2005 / 2006

25

Preface

Concept

Material Properties

Form Generation

Analysis - Experiment 01

Evaluation

txt file: coordinates

[12.5,7.5,-3.0]

[12.5,4.5,-3.0]

[12.5,10.5,-6.0]

[12.5,7.5,-6.0]

[12.5,10.5,-9.0]

[12.5,4.5,-6.0]

[12.5,7.5,-9.0]

[12.5,1.5,-6.0]

Rules that later drove digital experiments were based on relationships of bundled threads. Images show digital reproduction of physical experiments. There are direct paths in red colour on figure 04 which analyse the tree structure with inclined plane of 90° from the horizontal plane. The distance (l1) of branching node “centroid 02” is studied as a variable dependent on distances between points “3”.

The exact mathematical formulae are on consequent pages.

03. txt file with coordinates as an input to the GC associative model.

[12.5,4.5,-9.0] [0.0,0.0,0.0] [12.5,7.5,-12.0]

Experiments were analysed and carefully reproduced (fig. 01 direct paths, fig. 02 minimal paths) in order to understand emergent features. The dipped threads pulled out from water had always different geometry but after repeating of these experiments rules were abstracted.

12.5,7.5,-3.0 12.5,4.5,-3.0 12.5,10.5,-6.0 12.5,7.5,-6.0 12.5,4.5,-6.0 12.5,1.5,-6.0 12.5,10.5,-9.0 12.5,7.5,-9.0 12.5,4.5,-9.0 12.5,1.5,-9.0 12.5,7.5,-12.0 12.5,4.5,-12.0

[12.5,1.5,-9.0] [0.0,0.0,0.0] [12.5,4.5,-12.0]

0 l1

[12.5,4.5,-3.0]

01. Direct paths. The geometry of threads before dipping into water.

Cartesian coordinates of points form external txt file.

3

1

[12.5,7.5,-3.0]

centroid 01 [12.5,7.5,-3.0]

[12.5,1.5,-6.0]

l2

[12.5,4.5,-6.0]

L

centroid 02 1

1

L ... distance centroid of points last level, point first level l1... distance of branching node A>L>B l1... range (L/2, 2L/3)

l2 [12.5,1.5,-9.0] l2

[12.5,7.5,-6.0]

3

[12.5,4.5,-3.0]

[12.5,10.5,-6.0]

[12.5,10.5,-6.0]

[12.5,4.5,-9.0]

1

3 [12.5,7.5,-6.0]

centroid 01

[12.5,7.5,-9.0]

centroid 01 [12.5,4.5,-6.0]

[12.5,10.5,-9.0]

[12.5,10.5,-9.0]

[12.5,1.5,-6.0]

[12.5,7.5,-9.0]

[12.5,4.5,-12.0]

[12.5,7.5,-12.0]

geometric center

geometric center

[12.5,4.5,-9.0] [0.0,0.0,0.0] [12.5,7.5,-12.0]

[12.5,1.5,-9.0]

05. Analysis of geometry as it is modelled in GC. The centroid of points in plane always shows the projection of the line onto this plane. On the hand the geometric center is the center of the circle which goes through all points.

[12.5,4.5,-12.0]

02. Minimal paths. The geometry dipped into water.

04. Reconstruction of the physical model.

Pavel Hladik EmTech 2005 / 2006

26

Preface

Concept

Material Properties

Form Generation

a’2

a’1

a1 a2

a

30

b1

50

20

a’3

110

40

c2 c1

01. Picture of the experiment. There are two structures composed of three trees. One of them was analysed as an experiment 02B.

02. Scheme of the experiment: two prisms and a triangle.

40

80

b

Analysis Experiment 02B

Evaluation

b2

a3

Aim of the experiment was to observe the behaviour of threads in 2D and also in horizontal arrangement of base point and plane with points. The 2D plan was later used for summarizing of rules for branched structure in a plane as rules for minimal paths. The horizontal tree is affected by gravity and could be included into a group of hybrid structures of catenaries and linear branching.

The frame for the experiment of branching in 2D was arranged horizontally in the metal scaffolding so branches were form-found as a by pure tension. This part of the experiment is directly related to the basic research in minimal paths commenced in Institute of Lightweight Structures in Stuttgart. There were significant differences in geometry from experiments in 3D. The regular arrangement of points results in an irregular geometry. There were set parameters that were later used for tuning the plan of the pavilion structure. These parameters drove the complex system consisting of end points of branches with the entrance point of the structure in the plane (base point in my experiments).

The horizontal tree structure affected by gravity results in a very complex geometry that were not later analysed. But curvature introduced into the model could lead to a consequent structural performance where the curvature is beneficial. The feature of the system is documented in a shift of the centroid from c1 to c2.

03. Analysed model of the experiment 02B. The important feature of this model is the change of geometry in central part of the structure. The tree is almost horizontal and therefore all centroids are affected by gravity (c1,c2).

Pavel Hladik EmTech 2005 / 2006

27

Preface

Concept

Material Properties

Form Generation

Evaluation

P1

Analysis Experiment 02C

This experiment was made in order to understand the complexity of nested hierarchical structure. The differentiation of branches was observed. It came out from the experiment and analysis of the Frei Otto group which set dependances of thickness and lenght of branches in columns loaded in compression.

There were two independent base points and points in plane that were shared by threads from two bases. The basic 1ply woollen threads (white on figure 01) were mixed with 3ply threads (blue in figure 01). White threads had bigger slack and due to thickness and slack were nested on blue threads. This fact could have very important impact on the structure if this was considered. The research of Frei Otto confirmed that thicker elements have bigger loadbearing capacity.

The thickness and nesting in the digital model requires advanced skills in modelling and analysing of generated structure. This direction of research could be deployed later as a further area of research. It could result in the model where differentiation plays significant structural role.

P2

01. Picture of the experiment. The experiment 02B is still present in the model.

02. Scheme of the experiment: complex system of threads abstracted into prisms that intersect each other.

03. Model of branched structure with hierarchy. The hierarchy was achieved by threads with different amount of slack and emphasised by various thicknesses of threads. Prisms are distinguished by different colours.

Pavel Hladik EmTech 2005 / 2006

28

Preface

Concept

Material Properties

Form Generation

Evaluation

Analsyis Experiment 01

Branching pattern could be described by a simple equation that serves as an input into a parametric digital model.

The most important is a parameter d which helps to define a distance of a branching node from the previous branching point (or obviously from a centroid of points P).

The experiment unveil that three threads are bundled together and create a branching form. From observation occurred two possibilities of a branching node: dividing into three branches in a single node or node with two branches and the last one is connected to the main branch in a certain distance.

axonometry

G [0.0,0.0,0.0]

The geometry of the first example is presented here the second is elaborated on consequent pages. definition of a geometry:

Y .... distance G, P l1.... distance C01, C02 d .... distance P1, P2, P3 / 3

L P1 [12.5,7.5,-3.0] C02

defining of distances:

Y

(d1+d2+d3) / 3 = d d -> (d1+d/4)

L1

d

L - distance G C01 L1 - distance G C02

C01 P2 [12.5,7.5,-6.0]

defining a branching point:

L1 = L/(d+1)

P3 [12.5,10.5,-6.0] plan of the triangle

P2

d1

additional constants:

P1

d2

d3

S .... amount of slack a .... angle of a plate m ... material of threads

P3

Pavel Hladik EmTech 2005 / 2006

29

Preface

Concept

Material Properties

Form Generation

Evaluation

Analsyis Experiment 01

Emergent properties of the pattern feature a change of the distance of the node from the previous branching node. These distances (L1 and L1’) vary according to the distances between points (P1, P2,P3).

Dependencies are described by if statements included in a digital model.

G [0,0,0]

L - distance G C01 L1 - distance G C02 L1’ - distance G C03

d = (d1+d2+d3) if (d1+d2+d3) [ (d1+d/4) then L1 = L/(d+1) L1’ = L1

L1’ L

Y L1

change form the straight line

C03 plan of the triangle

branching node 02

P2

d1

definition of a branching node:

if (d1+d2+d3) [/ (d1+d/4) then L1 = L/(d1+1) L1’ = L/(((d2+d3)/2)+1)

C02

P1

equation with parameters:

d2

d3 P3 [170,140,110]

C01

d

L = S*L + L/(d1+1) P1 [185,125,110]

P2 [170,125,110] P3

Pavel Hladik EmTech 2005 / 2006

30

Preface

Concept

Material Properties

Form Generation

Evaluation

Prisms of threads represent the influence of branched structure. It is defined by points in plane and a base point. These pyramids could lead to these ideas: _prisms as self-supporting structures _prisms as a vector-active system that supports a slab _prisms as a structure that fluently dissolve into any other type of structural scheme

01 01

01

G1

06

G2

02

G3

02 03

Analysis and Evaluation

02 03 03 04

Each prism is an unique structure according to its position to the main node. These structures could be then used in a space with its type of position.

The inner geometry of prisms (branched pattern) probably does not match with a pattern that could be produced by real building material. Wooden stripes in this case. The next part of research will be devoted to this problem and try to find out what is the range of this difference. Then could be set a criteria (parameters) that allows for fabrication of these branched structures.

05 04

01 a. Outline of the geometry from form-finding experiments 02 B

02 a. Outline of the geometry from form-finding experiments 02 C. Gained geometry of prisms differs according to a plane with points.

03. Geometry of prisms (outlined geometry of trees) and relationship of forces acting on the assembly.

01 b.geometry of trees - prisms without consideration of catenary curves

02 b. Composite trees and their outlined geometry with different inner tree structure.

02 c. Outlined geometry from form-finding experiment 02 C. Pavel Hladik EmTech 2005 / 2006

31

Preface

Concept

Material Properties

Form Generation

Evaluation

Analysis and Evaluation

Geometry of prisms and their equilibrium are studied in this analysis. The position could be balanced only on one point in a distance d0 from a vertical axis. Figure 01 shows a vertical axis arbitrarily chosen on a plane. The model is simplified if we consider a vertical axis in a position of one force.

d2 d1

given points in a plane given points in a plane

G1

moment equilibrium: G2

G1d1+G2d2 = d0(G1+G2) d0 = (G1d1 + G2d2)/(G1+G2)

G1

equilibrium in one point: G2

d0 = (G2d2/(G1+G2)

E 02. Equilibrium of prisms concentrated into one point.

d0 .... length from a point of action G1

given point in a “trunk”

The length of a base of the lower pyramid could vary between two critical numbers. It could be closed to 0 - ideal stable state (fig 02) or it could extend to a distance from forces G1, G2 to E (fig.

03). This will cause more stable structure and provide a range for changing G1 and G2. The structure is therefore more stable under dynamic loads. The base pyramid could be divided into two parts when points of actions of G1, G2 are too far from each other.

G1 known base plane

0

G2

This approach could be extended by knowledge from biomimetic lessons, especially from building structure of trees. The reaction of wood on a sloping terrain with densifying fibers leads to a conclusion about a branched structure of the pyramid.

E

The shape of prisms (for easy understanding now represented as triangles) is informed by consequent series of form-finding. The experiments with laminated wood and possibilities of bending timber between fixed points cause the possible shape of pyramids.

d0

01. Equilibrium of prisms, “tree” structure is generated according to rules obtained from physical model and given planes.

03. Base - plane that cause structure more stable against dynamic load - changing of forces G1 and G2.

Pavel Hladik EmTech 2005 / 2006

32

Preface

Concept

Material Properties

Form Generation

Analysis and Evaluation

Evaluation

angle1

Physical form-finding showed possible configuration of 3D branching pattern. This pattern could be assumed as a pyramidal shape that is made according to position of a plate and a base point. The internal organisation of these pyramidal shapes are unique and could be collected and described and stored to a data set for a consequent proliferation.

angle1 thickness1 thickness1

P1

angle2

P2

P3

The approach of GC modelling by using logic of L-system could achieve pyramids with nodes that could mutate according to certain parameters. These parameters are obtained from physical models and could be extended with if statements. Than this models have emergent properties.

thickness2

no angle2

thickness2

thickness3

GC modelling L-system - node rewriting thickness4

thickness3

thickness5 thickness4

P4

P5

P6

thickness3 + thickness3 newthickness 01. Geometry from physical models (example of the most simple one)

length - length o threads, amount of slack

02. Geometry produced by L-system. The combination of parameters could achieve geometry that is extended beyond physical models. But rules remain the same.

distance from a reference point

03. Geometry of pyramids - these pyramids according to rules and parameters from physical form-finding make together a catalogue. This geometry will later serve as a basic row fro proliferation on certain space.

mutation: branching into 4 lines

branching into 3 lines

04. 3D L-system branching. Different “angle1”, “angle2” could be introduced.

parameters: angle1 - position of final points angle2 - amount of slack thickness - number of threads

05. Rewriting rule creates a pyramidal geometry with a triangular base.

06. Possible strategy for a deviation from a three-branches node.

This is a possible strategy for a non-triangular base of a pyramid.

Pavel Hladik EmTech 2005 / 2006

33

Preface

Concept

Material Properties

Form Generation

Evaluation

Glossary of Terms

Bifurcation The act of splitting into two branches.

Branching The subdivision of offshooting of a structure, developing or diverge from: into a number of elements. In computing: A programming structure that evaluates a condition and then takes one of two actions based on the outcome of condition evaluation.

Dichotomous Branching into two equal structures (stem, veins, etc.) leading to „Y“.

Fork A bifurcation or separation of two or more branches.

Fuse To mix together as if by melting.

Hierarchy A hierarchy is a systém of ranking, categorising, grading or organizing elements of a group or series.

Junction The place where to entities (lines, planes, etc) come together at a connection point.

Merging Act of combining two entities into more.

Nested A material systém, process or activity self-contained within a larger entity, that retains its identity and characteristics. Each nested systém, process or activity can be embedded sequentially within any number of others.

Surface Tension The elastic-like force in a body, especially a liquid, tending to minimize, or constrict, the area of the surface. It is the effect that allows insects (such as the water strider) to walk on water, and causes capillary action. Surface tension is caused by the attraction between the molecules of the liquid, due to various intermolecular forces, which exists in the surface film of all liquids that tends to draw the surface molecules into the bulk of the liquid and causes the contained volume to have a shape of the least surface area.

Tree A path system in which does not contain a closed loop, that is one cannot go in a circle within the system.

Pavel Hladik EmTech 2005 / 2006

34

Preface

Concept

Material Properties

Form Generation

Evaluation

Digital Experiments

Pavel Hladik EmTech 2005 / 2006

35

Preface

Concept

Material Properties

Form Generation

Evaluation

Digital Form-Finding

Aim of these experiments was to find the most efficient way for modelling branched structures in parametricaly controlled environment.

Associative model is based on a given array of points and one base point. The geometry is generic due to setup of relationship between lines and points and operative rules from L-system algorithm. Edge-rewriting method is used for the model. On Figure 01 there are three iterations of the algorithm. Each iteration looks for the central point of arrays of points that are multiplied by three until it ends in points itselfs. When it reaches an input point the algorizhm is terminated.

The model is tuned by parameters that control the distance of branching points and a base point. Parameters are explained on the following page.

1st Iteration 2nd Iteration 3rd Iteration

01. Tree structure generated by edge-rewriting L-system: 27 input points, 3 iterations.

Pavel Hladik EmTech 2005 / 2006

36

Preface

Concept

Material Properties

Form Generation

Evaluation

Digital Form-Finding

Distance Between Points

Presented structure was digitally modelled in order to be physically fabricated as a representative sample of the branched structure. The model represents generation of structure using edge rewriting L-system algorithm. The algorithm include IF statements with variables gained from the physical models of woollen threads immersed into liquid. Components with coded information replace previous branch of the structure. The change of parameters allows for control the lengths of branches and therefore density of the final outcome. Configuration of initial points determine the geometry of branches. The branching node and its position is dependant on the distance of connected points. The technique is developed for the further application with material. The curvature, twist and possibility to bend wood is very closely related to the length of branches.

The executed experiment is considered as a base for further digital experiments. The geometry of points and lines will serve as a scaffolding for the digital form-finding of laminated wooden material.

The choice of the right parameters and its application would serve as an informed model of the branched structure.

Although the geometry does not have any concrete structural application it is considered as a starting point for the self-supporting branched structure. The flow of forces and connection to a plate that connects points are later elaborated in the research.

Distance Between Branching Point and Base Point

Branching Point

Base Point

01. Branched structure geneŕated by edge rewriting L-system. The geometry of crown is different from the geometry of base due to the number of points and values of Z-coordinates.

02a. Configurations of components - the distance of the branching point from the bas e point.

02b. Configurations of components - the distance between points.

Pavel Hladik EmTech 2005 / 2006

37

Preface

Concept

Material Properties

Form Generation

Evaluation

Emergent Structure: Physical Model

Sub-hypothesis: The configuration of points allows for further examination of the emergent structure where the connection of points forms the complex structure of interrelated points and lines. If the boundary condition is changed the geometry of the whole is changed. The physical model opens and deploy the question of actual size and dimension of the final structure.

Pavel Hladik EmTech 2005 / 2006

38

Preface

Concept

Material Properties

Form Generation

Evaluation

Emergent Structure: Physical Model

The digital self-organisation described on previous pages (fig 01) was intended to model physically. The intention was to built physically the relationships between branches, nodes and input points.

There were also explored possibilities of communication between different programes.

The model in scale was important for the next steps in research because it showed the actual dimensions and from that could be estimated also capacity to modulate the environment in structure.

That means dimension of branches and possible manufacturing techniques. The model was build as a cube with a side 300 mm.

01. Generated Branched Structure by edge rewriting L-system.

The procedure starts with strategicaly placed points into the parametric software Generative Components. Strategicaly is understood as a top-down decission or a decission that comes out from other input. The second case was later explored in the thesis. Generated branching points are then sorted according to Zcoordinates in Excel spread sheet and imported to AutoCad. There were several possibilities of constructing trees but for my purpose seemed to be the most accurate threads going through plexiglass plates. Plates were laser cut according to plans drawn in AutoCad.

02. Excel spread sheet exported from GC. There are x, y, z coordinates in columns A, B, C. Column D is prepared for export to AutoCad. Pavel Hladik EmTech 2005 / 2006

39

Preface

Concept

Material Properties

Form Generation

Evaluation

Emergent Structure: Physical Model

Points were concatenated according to their Z-coordinates. Values that varied in an interval of 5mm were interpolated into one plate.

Figure 01 shows the excel spread sheet with 21 plates and coordinates of branching points. There was another sheet with points where branches go through plates as straight lines.

01. Adjusted excel spread sheet. Colours represents plexiglass slabs - points with the same value of the z coordinate. There are x, y, z coordinates in columns A, B, C. Column D is prepared for export to AutoCad. Pavel Hladik EmTech 2005 / 2006

40

Preface

Concept

Material Properties

Form Generation

Evaluation

Emergent Structure: Physical Model

AutoCad model of fabrication plans for the laser cutter. Every level (fig. 01) with circle openings had its own plan that was nested on a plane and prepared for laser-cutting.

01. Elevation, Axonometry and Plan of the Tree Structure. Model is ready for manufacturing.

02. Nested plans ready for laser cutting.

Pavel Hladik EmTech 2005 / 2006

41

Preface

Concept

Material Properties

Form Generation

Evaluation

Emergent Structure: Physical Model

Finished model shows the arrangement of tree structures with 27 and 54 branches.

The manufacturing technique did consider the fiber continuity of material but is not very efficient when scaled up. But the idea of fixing control points could lead to succesful results when is chosen a material that is flexible enough and self-organise itselfs into the required position. This technique was later explored in chapter material properties with 3D lamination of plywood.

01. Finished model of the tree structure: cube 30cm.

Pavel Hladik EmTech 2005 / 2006

42

Preface

Concept

Material Properties

Form Generation

Evaluation

Analysis and Evaluation

Branches got thinner when they were branched out from the base point. It was due to the material - woollen threads and also also there was mainatined a biomimetic approach of continuos fibers.

01. Trees illuminated level by level.

Pavel Hladik EmTech 2005 / 2006

43

Preface

Concept

Material Properties

Form Generation

Evaluation

Analysis and Evaluation

Manufacturing process is different from that used for building the Terminal 1 in Stuttgart Airport. There was a scaffolding but the tree structures were made from isotropic material and then piece by piece welded together. Approach outlined in this research takes benefit from the anisotropic natural material - wood. Wooden planks are form-found and clamped in a position of branching nodes. Then the structure could be constrained by dimensions of manufacturing halls and also by transport means.

The smal cube of 30 cm was not built just for the demonstration of available techniques but it also represented.

01a. Process of building the model. Woollen threads go through opennings in plates.

01b. Process of building the model.

02a. Finished model.

02b. Finished model.

Pavel Hladik EmTech 2005 / 2006

44

Preface

Concept

Material Properties

Form Generation

Evaluation

Branched Structures

Pavel Hladik EmTech 2005 / 2006

45

Preface

Concept

Material Properties

Form Generation

Evaluation

Branched Structures

fractal geometry - comparison to nature Many attractive images and life-like structures can be generated using models of physical processes from areas of chemistry and physics. One such example is diffusion limited aggregation or DLA which describes, among other things, the diffusion and aggregation of zinc ions in an electrolytic solution onto electrodes.

“Diffusion” because the particles forming the structure wander around randomly before attaching themselves (“Aggregating”) to the structure. “Diffusion-limited” because the particles are considered to be in low concentrations so they don’t come in contact with each other and the structure grows one particle at a time rather then by chunks of particles. Other examples can be found in coral growth, the path taken by lightning, coalescing of dust or smoke particles, and the growth of some crystals. Perhaps the first serious study of such processes was made by Witten, T.A. and Sander, L. M. and published by them in 1981, titled: “Diffusion limited aggregation, a kinetic critical phenomena” in Physical Review Letters.

New points are introduced at the borders and randomly (approximation of Brownian motion) walk until they are close enough to stick to an existing black pixel. If a point, during its random walk, approaches an edge of the image there are two strategies. The point either bounces off the edge or the image is toroidally bound (a point moving off the left edge enters on the right, a point moving off the right edge enters on the left, similarly for top and bottom).

In general new points can be seeded anywhere in the image area, not just around the border without any significant visual difference.

01. DLA in 3D from one point seed

02. DLA program - Diffussion-limited aggregation

03. Fractal Geometry - the Mandelbrot Set

04. The Hele - Shaw cell Pavel Hladik EmTech 2005 / 2006

46

Preface

Concept

Material Properties

Form Generation

Evaluation

Branched Structures

Fractal branching could be found both in living and also non-living nature. The experiments with colonies of bacteria have shown complex branching pattern tuned by amount of food (examples of colonies of different species are on fig. 01, 02).

The Interesting comparison with other concepts of branching is that of veins in bodies. The branching angle is dependent on a flow of energy. The topic was observed and worked up by D’Arcy Thompson in On Growth and Form.

01. Growth of bacterial colony of Bacillus.

06. Forewing of a stonefly [3]

02. Growth of bacteria that swarm in a blob-like vortex at the tip of each branch.

07. Dependance distance - diameter - speed of blood vessels [3] Pavel Hladik EmTech 2005 / 2006

47

Preface

Concept

Material Properties

Form Generation

Evaluation

Pavel Hladik EmTech 2005 / 2006

48

Behavior of Planks Curvature

Geometric Setup

Manufacturing Constraints

Alg. Definition Spatial Requirements

R1

R2

S

Transport Assembly Techniques Geometry - Macro Scale

CS [b]

CAD CAM Rules, Variables, Logic

P [1]

Finding of Geometry, Rules

CS [1]

Proliferation Methods

Production Logic

Structural Concept Emergent Behavior

P [0]

Structure

Replication Capacity

Physical Form-Finding 01

CS [0]

Performative Criteria

Emergence Form Analysis

Top-down Decisions

Common Rules

ture

Hypothesis

Digital Form-Finding

Physical Form-Finding 02

Living, Non-living Na

Evaluation

Structural Requirements

Growth and Branching

Aim

Form Generation

Reset of Criteria

Material Properties

Time, Cost Effectivity

Concept

Material Properties

Preface

Model of Material System

Applied Model of Branching Parametric Setup

Fabrication Tech.

Perform. Capacities

Local Interaction

Global Interaction

Pavel Hladik EmTech 2005 / 2006

49

Preface

Concept

Material Properties

Form Generation

Evaluation

Sub-hypothesis: Suitable technique of wood-working helps to find a self-organised structure that follows rules similar (or the same) from those obtained experiments from threads-liquid experiments.

Lamination of wooden layers can record a self-organised curvature of a strip of a certain length between two points. This technique could fulfil task of branched system.

Nodes of branched structure could be bundled into one point and this point have higher structural capacity then a single branch or a straight member of a structure (e.g. column).

Pavel Hladik EmTech 2005 / 2006

50

Preface

Concept

Material Properties

Form Generation

Evaluation

Methodology

tension wood The methodology of the research into material behaviour starts with exploring properties of wood. There are several types of wood dependent on types of trees. It is also possible to distinguish two groups of wood according to the inner distribution of material (fig.

07, fig. 08). In furniture industry there is used a group on fig. 07 because it allows for severe curvature. In building industry the most common wooden material for lamination is from a group on fig. 08.

01. Tension wood in deciduos trees is produced on the inner part of a curved branches or trunks.

03. Splitting of tension wood caused by drying

02. Microphotograph of tension wood

compression wood

A tree itself has its own inner structure which differs according to the function of particular parts of the tree. The structure is distinguished into Reaction wood. Reaction wood is used by trees to modulate shape of a trunk and branches (gravitropism/phototropism). Tension wood is located on the uphill side of trees and compensate inclination of deciduous species. If it is drying it could split along grain. This effect is used by some sculpture-making techniques. Compression wood in coniferous trees (fig. 04) allows for upright position and seeking light.

For initial experiments with wooden components were selected species that are used for lamination of beams in wooden industry.

They belong to a group of trees that have soft wood and are widely available in European forests. To this group belong pine, russian redwood and fir.

04. Compression wood is produced on the downhill side of trees coniferous.

05. Microphotograph of normal wood. This picture is used for a comparison with tension wood (fig. 02).

06. Section of a trunk of a coniferous tree

07. Group of trees suitable for severe curves

Although the usual manufacturing technique is the lamination in a plane it is possible to glue wood in 3D. The next step was to create a set-up for from-finding experiments where the curvature of laminated wood plays important role. Form-finding experiments started with exploring bending and twisting capacities of wooden stripes. These stripes were bent and twisted and documented.

Information from these exercises was used for the set-up of consequent physical experiments with laminated stripes. Firstly a lamination was made in 2D and then a possibility of more complex lamination in 3D was explored.

In order to measure these experiments and input them to the associative model there was made a scaffolding with a fixed position of clamping points in a cartesian coordinate system. The input for the system was a position of clamping points and also the length of stripes - layers of lamination.

fir

Executed experiments were then compared with gained information from visits to companies that work with fiber material. Consultantions with experts from the company Finnforest-Merk were very fruitful and led to better understanding of connection between CAD and CAM. Also problematic of work with wooden composites in products developed in 20th century was also explored. The famous wooden airplanes were studied and analysed as component based products.

ash

beech

pine

elm

spruce

hickory

mahagony

oak

maple

teak

08. Group of trees allows for gentle curves Pavel Hladik EmTech 2005 / 2006

51

Preface

Concept

Geometry

Geometry

Form-finding

Form-finding Methods: Modelling Scripting

Material Properties

Form Generation

Evaluation

Scheme of the work

Methods of Proliferation concept of geometry and structural scheme - branching form-finding experiments - lamination

Material

Material

Material

Material

Material

Material

Material

Form-finding

Form-finding Limits of Wooden Strips Parameters for Digital Experiments

Lamination 2D

Lamination 3D A

Lamination 3D B

Lamination 3D C

Lamination 3D D

concept of branching informed by behaviour of wooden lamination constraints of material

Proliferation

Proliferation

Digital Modelling Nesting of Pyramid Extrinsic Influences Loading Capacities Bearing Capacities

Digital Modelling

Pavel Hladik EmTech 2005 / 2006

52

Preface

Concept

Material Properties

Form Generation

Evaluation

Form-finding Experiments I

Thera are two suitable strategies of form-finding that could be used to fulfill the task of a branched contruction. The first is bending of wooden stripes and later laminate them, the other is splitting of wood. The aim was to achieve desirable structure without any other joining material than glue. This process maintained the fiber directionality of the composite.

Lamination represents one of techniques that allow for bending of wooden components. There is an impact on the curvature by thickness and width of wooden stripes.

Bending of wood Furniture making method which is based on natural curvature of wooden stripes that are laminated in a form-finded position. The executed form-finding was made without any treatment of wood (steam, water, etc.) The composite is made of stripes of wood of different thickness and therefore adaptability to shapes (fig. 01).

01. Form-finding with anisotropic wooden strip. The curvature is achieved by location of two points and length of stripe.

02. Form-finding with anisotropic wooden strip in 2D. This is the first set of experiments that inform physical and consequently digital models with its parameters.

03. Splitting of tension wood. There must be chosen special timber that have specific direction of grain.

04. Piece of hardwood is split along grain. There could be hardly predict nodes of splitting and distance of split branches.

Parameters of the composite are type of wood, length, thicknes, width. The curvature is dependent also on the distance and rotation of axis of clamping points. According to the visit to factories that work with wooden components it is possible to introduce complex curvature to the model.

Pavel Hladik EmTech 2005 / 2006

53

Preface

Concept

Material Properties

Form Generation

Evaluation

Form-finding Experiments I

Pavel Hladik EmTech 2005 / 2006

54

Preface top view bending

Concept

Material Properties top view torsion + bending

Form Generation

Evaluation

Form-finding Experiments I

side view torsion + bending

Form-finding experiments with wooden stripes of pine. The experiment was made with material of these size: thickness: 3 mm, 4 mm width: 30 mm, 40 mm The conclusion is that it is possible to achieve severe curvature with thinner material. There has to be take into acconut also the loss of material for milling and assembling and glueing time. These parameters were explored in consequent studies of laminated form-finding.

thickness: 3 mm, width: 30 mm, length: 800 mm

thickness: 4 mm, width: 30 mm, length: 800 mm

thickness: 4 mm, width: 40 mm, length: 800 mm Pavel Hladik EmTech 2005 / 2006

55

Preface

Concept

Material Properties

Form Generation

Evaluation

A - min. path C1 [0,14]

C2 [9,14]

The digital experiments started with the translation of informtion from physical model to the digital environment. The simple 2D curves were used to understand this logic.

B - optimal path C5 [23,13]

45°

C - max. path

A: Minimal path for a strip of veneer.

C3 [16,7.5]

90°

Experiment examined two stripes of veneer (of length 510 and 456 mm) that were clamped between 5 points. Figure O1 shows the set-up of this experiment: angles of 45°, 90°, and 315°. There were studied three modes of the bent stripe: minimal path, maximal path and optimal path in which the stripe self-organise itself according to the given geometry. Optimal path is a state where one edge of the stripe (fig. 01, C1 [0,14]) is fixed to the position and the other end is left without any fixation.

Digital form-finding was done in parametric model in GC. Curves were controlled by rotation of tangency points. Points were on the X-axis of a coordinate system that aimed to the next clamping point. The angle of rotation was observed from the physical model and then limits of angle were set (fig 04).

01 - TLength 510 02 - TLength 456 C4 16,0]

Digital Experiments

315°

C: Maximal path for a strip of veneer.

01. Composite image of the experiment.

02. Control of BSplines, degree 3.

03. Change of geometry by changing parameters - rotation of tangents.

04. Parameters of tangents controlling BSpline Curves.

Pavel Hladik EmTech 2005 / 2006

56

Preface

Concept

Material Properties

Form Generation

Evaluation

Form-Finding Experiments II

Pavel Hladik EmTech 2005 / 2006

57

Preface

Concept

Material Properties

Form Generation

Evaluation

Form-Finding Experiments II

The aim of described experiments was to test the possibility to glue wooden stripes and later test them. The features of natural composite were observed - flexibility and also shape memory after hardening the glue.

The important issue was to solve branching nodes and alternatives for curved laminated planks. All described experiments xamine form-finding with four given points in space and given parameters.

There is internal force that cause the form - it is a property of the material - natural anisotropic material. The form-finding process involves curvature continuity of geometry.

Curvature of stripes is formed according to certain parameters: position of points - distance between each other position of branching point length of wooden stripes thickness of wooden stripes number of wooden layers

01. 3D lamination in progress.

Pavel Hladik EmTech 2005 / 2006

58

Preface

Concept

Material Properties

Form Generation

Evaluation

Experiment 01 A

4 layers of russian redwood thickness: 1.5 mm width: 15 mm The layers are bent in two directions - curves follow a plane. 4 layers of Russian redwood are used to produce this geometry. The possibility for sending and treatment after laminating are broader because of easily approachable machinery.

The branching node is glued from two parts and there is a higher probability that this glued joint fails. The other disadvantage is gluing two pieces together - it is suitable only in assembly of 90° without additional material.

The ability to retain its shape after lamination is higher then in 3D lamination.

01a. Two laminated pieces glued together. 2D lamination.

01b

01c

01d Pavel Hladik EmTech 2005 / 2006

59

Preface

Concept

Material Properties

Form Generation

Evaluation

Experiment 01 B

3 layers of pine (bad quality wood) thickness: 1.5 mm width: 15 mm The layers are bent in three directions and therefore there is also twisting introduced into the geometry. Branching node of three branches is not in the same position (fig. 01c). This was solved in the digital model by writing an IF statement in the script generated the BSplines geometry. This statement takes into account the distances between end points of curves branched out from the node.

The process is very similar to that explored in the form-finding with woollen threads dipped into a liquid where a branching node emerged in dependance on the distance between points on planes.

The ability to retain its shape after lamination is poor. The central branch relocate itself and tends to get closer to side branch.

Figure 01c shows detail images of the lamination. There is also visible delamination that happened when the structure was loaded.

01a. Curvature and twisting of branches - most significant is the middle branch.

01b.

01c. Detail of the node.

02. Top view geometry of a node (cm).

03. Elevation of a node (cm).

Pavel Hladik EmTech 2005 / 2006

60

Preface

Concept

Material Properties

Form Generation

Evaluation

Experiment 01 C

5 layers of russian redwood thickness: 1.5 mm width: 15 mm The Eperiment 01C is different from the previous one in the bigger number of layers.

Legend: black points - fixation points red points - actual points after lamination blue points - maximum value of Z coordinates, branching nodes Parameters: p - length between branching point and base point A l - length of stripes t - thickness of a branch (stripes have constant thickness t=k*n, n- number of layers) h - height of the highest point of branches

01a. Curvature and twisting of branches - most significant is the middle branch which is twisted by 90°.

01b. Curvature and twisting of branches.

[21.5,42,0] [22.5,42,0]

D D’ C’

[45,36,0] [45,35,0]

C [20,32,25]

h(d)=22.4 [32,29,28]

h(c)=25.3

t l2=78 l2=71.5

[38,22,21]

B =B’ [51.5,16,0]

l3=77

p1=p2=19

h(b)=25

P

A

02a. Top view: geometry of a node (cm).

02b. Top view: geometry of a node (cm).

Pavel Hladik EmTech 2005 / 2006

61

Preface

Concept

Material Properties

Form Generation

Evaluation

Analysis Experiment 01 B + C

[22,45.5,0] [21.5,42,0] [22.5,42,0]

[22.5,42,0]

[45,36,0]

[45,36,0]

[45,35,0]

[20,32,25]

[51,33,0] [20,32,25]

[32,29,28]

[32,29,28]

[38,22,21]

[38,22,21]

[51.5,16,0]

[51.5,16,0]

[55,16,0]

3 layers of pine (bad quality wood) thickness: 1.5 mm width: 15 mm

5 layers of russian redwood thickness: 1.5 mm width: 15 mm

black points - fixation points red points - actual points after lamination blue points - maximum value of Z coordinates

black points - fixation points red points - actual points after lamination blue points - maximum value of Z coordinates, branching nodes

p1= 170 mm p2= 210 mm h1= 200 mm h2= 220 mm h3= 170 mm l1= 785 mm l2= 790 mm l3= 670 mm

p1= 190 mm p2= 190 mm h1= 250 mm h2= 253 mm h3= 224 mm l1= 770 mm l2= 780 mm l3= 715 mm

Pavel Hladik EmTech 2005 / 2006

62

Preface

Concept

Material Properties

Form Generation

Evaluation

Experiment 02 A

3 layers of russian redwood that go in the full distance of a branch thickness: 1.5 mm width: 15 mm There are splits of an outer layer and these stripes go from this point (located arbitrarily on branches) to other branches.

For the geometry analysis is important that these stripes follow curvature of full laminated layers.

This model was made as a result of the negotiation of all involved stripes in branch. This model also proved that there is a similarity in logic of nesting woollen threads. A thread with bigger thickness determine the shape and direction of a system.

Bundling of splitt stripes and layered main branches caused that shape was more stable than simple branched pattern.

The logic of this geometry should follow the self-organised pattern of bridges that occur in the model of threads dipped into latex.

This claim will be also proofed by testing this node by different loads.

01. Image of the complex lamination of the eperiment 02.

Pavel Hladik EmTech 2005 / 2006

63

Preface

Concept

Material Properties

Form Generation

Evaluation

Case Studies: Manufacturing

Pavel Hladik EmTech 2005 / 2006

64

Preface

Concept

Material Properties

Form Generation

Evaluation

Mass Wooden Components, CZ

Ploma, Hodonin Wooden industry degraded wood into a mass production because there was a strong idea that wooden composites would be replaced by synthetic materials. These automated procedures does not require any additional thinking about fabrication of components like CNC. But it leads to simple wooden components that later limits its use in building industry. Final products are then boards made of plywood that very often does not respect important feature of natural product - anisotropy.

fig 01. Storage of trunks - with bark and without bark ready for “peeling” machine.

fig 02. Peeling machine.

fig 03. Production hall - sorting of wet veneer and prepare it for drying.

fig 04. Feeding a drying machine.

fig 05. Dryed veneer.

fig 06. Cutting of plywood boards.

fig 07. Veneer prepared for cabinet-makers.

fig 08. Timber-plywood board in a process of gluing layers.

fig 09. “Architectural” application for housing. Boards are nailed and create panels that will be assembled on site.

Pavel Hladik EmTech 2005 / 2006

65

Preface

Concept

fig 01. Stored boards of plywood. Required quality are ordered from Finnforest company from Finland.

Material Properties

fig 02. Robotic CNC procedures - cutting, milling, drilling.

Form Generation

Evaluation

fig 03. Tools for robot Kuka, initialy developed for car industry.

Individual Wooden Components, DE

FinnforestMerk, Aichach The post-fabrication of wooden products - plywood. The plywood are in two categories - 90°angle and parallel grain. These products are delivered from a similar factory like described in previous analysis but this time from Finland. The analysed fabrication is from company FinnforestMerk.

The company creates components that are used for special architectural application. Fig. 01, 02, 04, 05, 06 show procedures of manufacturing of ceiling and wall components for a theatre to Russia that have to fulfil acoustic and aesthetic requirements of the interior of the auditorium.

Plywood board are treated in a state of flat sheets and boards. Than they are glued and screwed together in order to achieve curved components of single curvature. There are at least two interesting robotic units that can CNC cut and mill wooden components. All the assembly are made by hands.

There is a machinery available to create a flat components in size of one storey walls - fig. 09. There is also a procedure for gluing together timber boards.

fig 04. Assembling ribs and plywood finish - gluing, screwing.

fig 05. Finished component. Curved surface of a second ceiling of a theatre (acoustic and extetic panel).

fig 06. Detail of the panel - work of CNC machines and hand assembly.

fig 07. CNC machine for cutting long timber/plywood pieces.

fig 08. Hammer for joints of “Lidl” trusses.

fig 09. CNC cutter - flat boards.

Pavel Hladik EmTech 2005 / 2006

66

Preface

Concept

Material Properties

Form Generation

Evaluation

Composite Aircraft Manufacturing, CZ

Composite aircraft from synthetic materials follow similar rules as aircraft made form wooden components. The analysed aircraft are designed by structural and mechanical engineers who use FEM (Nastran) to analyse the aircraft and locate parts with high strain.

Composite aircraft is made by a company which create wings and fuselage on its own and incorporate engine and glass lid of a cabin only.

fig 01. Laminate mould of a half of a fusselage of a composite aircraft. The mould is treated by wax or thin film of polyethylen.

fig 02. Construction of a fusselage. Reinforcement of the composite structure result in acting of forces in rectangles - division of the shell.

fig 03. A partition in the fusselage structure. Black colour of the fabric means carbon material.

fig 04. Additional fusselage panel - foam division of layers. The addition is glued by resin in vacuum.

fig 05. Additional reinforcement of a fusselage. Colour of fabric means carbon-kevlar. Kevlar is used for safety of a crew in an accident.

fig 06. Structure of a fusselage - cabin. Massive partitions acts against strain during flight. The continuity of fusselage is interrupted by a crew window.

fig 07. Structure of wings. Wings have one inner beam which continues through fusselage and ends in the opposite wing. There are no fixed joints, just links allows for rotation.

fig 08. Side of the fusselage with holes for control of wing flaps, holes for continuing of wing beam. There are two small holes for fixture of a position of a wing.

fig 09. Ultra light aircraft Lambada. Weight - glass fibres: up to 300 kg, carbon-kevlar: up to 280 kg. Engine: boxer Rotax. Halves of the fusselage are connected by overlaping parts and glueing together.

The procedure of the aircraft making is shown on pictures. Dimensions and weight are constrained by requirements and transport. That is why wings are always constructed for better dismounting and making-up on an airport.

Pavel Hladik EmTech 2005 / 2006

67

Preface

Concept

fig 01. Hand made kayak for speed racing. Disputable German design, Czech konw-how.

Material Properties

Form Generation

fig 02. Inners structure of carbon-kevlar. Tips and ends of boats are reinforced by carbon fabric.

Evaluation

fig 03. Inner structure of the boat. There are two parts of the boats connected by resin and kevlar tape. Together it makes a monocoque structure.

fig 04. Carbon-kevlar fabric.

fig 05. Kevlar tape, glass fibre tape (white).

fig 06. Mould for top part of the boat. Structural reinforcement of problematic areas.

fig 07. French racing sea yacht. Wooden scaffold, laminate finish, mahagony deck.

fig 08. Construction of wooden boat - layers of veneer and plywood in the 45° constitution. Veneer is glued and fixed to ribs. Ribs are not essential - it depends on the boat structure.

fig 09. Reconstruction of the boat of Heidrich. Structural ribs remain in the boat structure. Plywood is fixed by copper rivets.

Boat Manufacturing, CZ

Bohemia Yacht, Hluboka nad Vltavou There are requirements for individual boat production because forms change every year and they could be changed even three times a year. Hand manufacturing is nowadays the most suitable and cheapest solution on a demand from racing teams.

The hull of racing kayaks are monocoque structure and consists of two parts - top and a “belly”. The final assembly is similar to an aircraft technique but requires more fine work. The skin in general consists of several layers (usually up to 6) of fabric that is separated by additional foam divisions. The foam divisions cause higher profile and therefore better structural performance. This approach follows the successful technique used in Mosquito bomber which was made of wood.

Fabrication of replicas of wooden yachts and repairing of wooden yachts consists of layering of plywood and veneer in an angle of 45°.

These layers could be permanently fixed to wooden ribs of the hull or could remain without ribs as a pure monocoque structure. This structure then requires further stiffening partitions.

Pavel Hladik EmTech 2005 / 2006

68

Preface

Concept

Material Properties

Form Generation

Evaluation

De Havelland Mosquito, UK

The most succesfull composite aircraft is made of wood. This aircraft combines th euse of moulded plywood with balsa cored macro composite components. The balso wood core was produced

by Baltek Corporation company which still supplying balsa cores for the construction of boats, planes and buiůlding components.

End grain balsa with its elongated vertical cell structure provides very high compressive stiffness and resistance to crushing. It has a great capacity for handling cyclkic loads and it is possible to obtain very strong skin to core bonds. These panels have the ability to handle excessive dynamic loads with high resistance to fatigue. fig 02.

fig 02. Comparison of forces and moments of the wing. More convenient is a wing that is supported by a rod. But the aircraft pays for worse aerodynamic and additional force into fusselage.

Mosquito fusselage is made from two halves that are connected together by steel linking material. An inner skin of a fusselage is applied onto a mould then the other layers are gloued onto it. The shapoe is then carefully lifted off the mould and connected to the other half.

Each part of the aircraft deserves deeper examination. The fusselage and wings construction represented the cutting edge technologies of its age. Nowadays the indusrty is mainly focused on synthetic materials - carbon, kevlar composites. But there is also possibility to taka into account to combine these techniques and create a hybrid structures that gain advantiges from both sides. The example could be very good ratio of wood in bending performance and ability of connection of synthetic fabrics.

fig 01. Wooden composite aircraft has two main construction parts - fusselage and wings. The aircraft has painted wooden finish.

fig 04. Wing structure: two main girders, mosquito boards form semi-monocoque structure with inner supports.

fig 03. Fusselage of an airsraft made from stripes of venner.

Mosquito has balsa partitions and longitudial reinforcements.

fig 05. Section of the wing - centre, engine area, wing tip. Boards are thicken according to loads. In general there is a compression in the top surface of the wing.

fig 06. Explanation of the equation of the thickness of the board of the wing. Picture shows a veneer connection in a wing board. Czech language is beautiful.

Pavel Hladik EmTech 2005 / 2006

69

Preface

Concept

Material Properties

Form Generation

Evaluation

Pavel Hladik EmTech 2005 / 2006

70

Behavior of Planks Curvature

Geometric Setup

Manufacturing Constraints

Alg. Definition Spatial Requirements

R1

R2

S

Transport Assembly Techniques Geometry - Macro Scale

CS [b]

CAD CAM Rules, Variables, Logic

P [1]

Finding of Geometry, Rules

CS [1]

Proliferation Methods

Production Logic

Structural Concept Emergent Behavior

P [0]

Structure

Replication Capacity

Physical Form-Finding 01

CS [0]

Performative Criteria

Emergence Form Analysis

Top-down Decisions

Common Rules

ture

Hypothesis

Digital Form-Finding

Physical Form-Finding 02

Living, Non-living Na

Evaluation

Structural Requirements

Growth and Branching

Aim

Form Generation

Reset of Criteria

Material Properties

Time, Cost Effectivity

Concept

Material Properties

Preface

Model of Material System

Applied Model of Branching Parametric Setup

Fabrication Tech.

Perform. Capacities

Local Interaction

Global Interaction

Pavel Hladik EmTech 2005 / 2006

71

Preface

Experiment 01

Concept

Material Properties

Experiment 02

Form Generation

Experiment 03

Evaluation

Methodology

The research in the form that leads to the tectonic articulation had been divided into three strategies that are documented in three experiments. Each experiment has its own setup and procedure which had been documented. All three experiments start with digital form-finding that results in the material system.

The first experiment feature surface that is dominant in the structure. The branched supports and a “shell” compose a hybrid structural scheme - mix of arch, beam and shell (fig. 01a - 03a).

The second experiment deploys the possibility of self-supporting branches. The structural stability is based on a hypothesis that components branched out from different bases could interact and support each other (fig. 01b - 03b).

01b. 3D lamination of branches.

01c. Surface + Supports.

02a. Surfaces based on catenary curves from branched supports.

02b. Selfsupporting branches.

02c. Surface + Supports.

03b. Branches are supporting each other.

03c. Supports are incorporated into the surface.

H

01a. Foto of the model. Surface is predominat in the assembly.

The experiment 03 represents incorporated branches into a surface that can act both in tension and in compression. This had been seen as the most efficient connection scheme (fig. 01c - 03c).

03a. Scheme - hybrid structure of arch, beam and shell.

Pavel Hladik EmTech 2005 / 2006

72

Preface

Concept

Material Properties

Form Generation

Evaluation

Experiment 01

Subhypothesis: The branched supports could be incorporated to the surface which span longer distances. By dependance on the distance different hight of the structure is achieved and the structural performance is the same.

Pavel Hladik EmTech 2005 / 2006

73

Preface

Concept

Material Properties

Form Generation

Evaluation

C - 165 mm

B - 135 mm

C - 95 mm

A Length of a strip - 400 mm.

Distance of clamps - 260 mm Opening - 75 mm

B Length of a strip - 400 mm.

Distance of clamps - 200 mm Opening - 83 mm

Form-Finding Experiments

The first experiment started with form-finding of veneer stripe and its behaviour. These experiments document the interest in systems where vector-active system is incorporated into the surface-active system. The model on figure 01 shows heights of the stripe in dependance on the distance between vertical supports. The structure was then compared to the digital model of catenary and chosen geometry that was the closest to the catenoid.

Branched supports featured complex curvature and then they were continuously used as parts of the shell.

C Length of a strip - 400 mm.

Distance of clamps - 140 mm Opening - 55 mm

01. Physical model of form-finding with veneer stripes.

Pavel Hladik EmTech 2005 / 2006

74

Preface

Concept

Material Properties

Form Generation

Evaluation

Pavilion Growth

The model of catenaries had been evolved from set of points generated by L-system algorthm. The algorithm was chosen arbitrarily to test the structure and its proliferation. The structure is generated on figure 01, and 02 is based on the catenary model - fig. 03.

supports generated by algorithmus catenary curve roof 10 m

12 m

5m

01. Points proliferated on a site by an L-system algorithm. Roof is generated according to these criteria: Top curve as catenary with a length: Distance(point1,point2)*1.1, Boundary curves are formfound.

02. Part of the growth of the pavilion. Catenary curves define the hybrid structure - arch, beam, shell.

03. Catenary + boundary curves in GC define the roof.

Pavel Hladik EmTech 2005 / 2006

75

Preface

Concept

Material Properties

Form Generation

Evaluation

Test Model of the Macro Component

Digital data for the physical test model. Model was prepared for structural test of the branching support (red rectangle on the fig.

01). The boundary supports were fixed in space in order to do not allow any horizontal movement (black dots on fig. 01). Then there were studied deflections and flexibility of the structure.

load

fixed supports

01. Test Model. One part of the system was tested - chenge of length and width under applied load. The test was also focused on the movement and deflection of the central support.

02. Curvature analysis of the tested part.

load L

h

H

C

boundary condition - doesn’t allow any movement

03. Scheme of the structure.

Pavel Hladik EmTech 2005 / 2006

76

Preface

Concept

Material Properties

Form Generation

Evaluation

section by a surface that follows the angle of f-f edge

form-found structure catenoid

f-f structure

catenoid

02. Elevation 1 of the comparison f-f structure with catenoid

section plane

Test Model of the Macro Component

Analysis of the digital model explores the structural schemes in detail. Comparison of the surface with catenoid and direct branching paths of the support. There are certain gaps between ideal form-found structure and possible form made by fabrication constraints.

difference between catenary and shell

03. Elevation 2 of the comparison f-f structure with catenoid Pavel Hladik EmTech 2005 / 2006

77

Preface

Concept

Material Properties

Form Generation

Evaluation

Test Model Analysis

Model was built step by step on the metal scaffolding that held laminated bent beams. The bending form-finding was the most prevailing and also determinant concept that form the shape.

Bent form-found guides were glued (PVA glue) from 7 layers of veneer and fixed on the metal scaffolding. Than layers of veneer stripes were laid on ribs that were in perpendicular direction to the guides. Veneer stipes were laid in two layers. It was sufficient to whitstand loads applied to this test model.

Wooden shell structures were inspired by the boat manufacturing and also by wooden aircrafts that were succesfull in the beginning of the 20 th century. Today, wooden composites are still used in the these fields: marine, car industry, aerospace, wind energy.

The famous aircraft Mosquito was made by companies that later fused into the corporation Alcan.

Alcan Composites Core Materials offers you many decades of broad experience not only from one company, but from two leading companies in the composite business. Alcan Airex, Switzerland and Alcan Baltek, U.S.A. are companies that provide support and technical advice.

Baltek is the manufacturer of the core materials based on the balsa wood. www.alcanbaltek.com

01. Picture of the model attached to the construction.

02a. Deatil of the branched column into the shell.

02b. Deatil of the branched column into the shell.

03. Model under construction.

Pavel Hladik EmTech 2005 / 2006

78

Preface

Concept

Material Properties

Form Generation

Evaluation Test Model Analysis Test 01 - Side View Model was loaded by 1 and then 2 kg and then observed deflections and displacement of the central support which was left free.

Model 1:35 h= 17.5 cm d= 16 cm (width of the shell) f (distance the center of the support from the initial position) l1= 41 cm l2= 56 cm Load Case 01 h´= 2 cm d´= 1cm f = 1.5 cm Load Case 02 h´= 3.5 cm d´= 2cm f = 4 cm

h f

Height was smaller but the width was bigger than in the initial position without loads. l2

l1

01. Composite picture of loaded model.

02. Structure without any load.

03. Structure with a load 1kg - Load Case 01.

04. Structure with a load 2kg - Load Case 02.

Pavel Hladik EmTech 2005 / 2006

79

Preface

Concept

Material Properties

Form Generation

Evaluation

Test Model Analysis

Test 01 - Top View

01. Composite picture of loaded model.

02. Structure without any load.

03. Structure with a load 1kg - Load Case 01.

Pavel Hladik EmTech 2005 / 2006

80

Preface

Concept

Material Properties

Form Generation

Evaluation

Test Model Analysis

Conclusion Building and testing of this model proved that the vector-active system of the branching did not perform as the main structural scheme. It was not coherent with the aim of this dissertetion and therefore this way outlined by this experiment is not considered as a desirable path for the further research. The complicated structural scheme of the model together with forcing material to desirable shapes did not satisfied set tasks of this research.

The methods of building this material system could be used for ideas about fabrication of the continuous lamination. The main beams branched out from supports clamped in key positions selforganise to the desirable shape and then were used as guides for other structural layers. All together compose a robust redundant (in biological terminology) structure of natural fiber composite.

The work with porosity of the surface affected by structural scheme was followed by the experiments that followed these sets of models.

01. Composite picture of loaded model. Side view of the model.

02. Structure without any load.

03. Structure with a load 1kg - Load Case 01.

04. Structure with a load 2kg - Load Case 02.

Pavel Hladik EmTech 2005 / 2006

81

Preface

Concept

Material Properties

Form Generation

Evaluation

Experiment 02

Subhypothesis: The branched structure could be self-supporting and by converging branching could achieve stable volume that respond to environment by modulating space in and under the structure. (The branched 3D laminated wood follows the conncept of trees in forest - research by Frei Otto and IL institute.)

Pavel Hladik EmTech 2005 / 2006

82

Preface

Concept

Material Properties

Form Generation

Evaluation

Methodology

input points

The research was directly linked to the form-finding described in the chpter Concept in this thesis. It is branching of threads dipped into water. The digital form-finding took advantage from the associative environment of GC and due to parameters it was possible to define limiting distances between branching nodes. These distances had to fulfill the requirements for the minimal length where the curvature of lamination took place. It was then constrained by the possibility of fabrication. The structural performance was guaranteed by following the rules from form-finding of woollen threads.

base point

The complex branched system is achieved by input x,y,z coordinates of points that are later interconnected by lines. The geometry of input data drove the performance of the final structure.

01. Edge-rewriting L-system algorithm. Three iterations of the algorithm.

02. Geometries achieved by L-system and extensive scripting and sorting algorithms in Excel.

Pavel Hladik EmTech 2005 / 2006

83

Preface

Concept

Material Properties

Form Generation

Evaluation

Methodology

The process of dealing with input data. In this case points generated by spiral phyllotaxis. The spiral phyllotaxis was chosen in order to explore complex pattern. This pattern did not have even distribution of points but it features wider spread with bigger distance from the centre of the distribution.

The process starts with the pattern of points in GC that was later post processed in excel and put back to GC. The excel VBA script divide the x, y, z coordinates of 3D pattern into four quadrants where the number of points was 81. The consequent branched pattern generated by L-system connected points in quadrants with lines. These lines were later materialized by digital setup for the wooden lamination. It was done by digital form-finding based on principles gained from chapter Material Properties. The exact process of the digital procedure is described in the following part - Experiment 03. It was there used for the test model of branches interwoven together.

01. Branched structure generated by edge rewriting L-system between points of phyllotactic pattern and one base point.

02. 4 x 81 = 224 points of spiral phyllotaxis on a plane.

03. Branched structure connected to points in 3. and 4. quadrants.

Pavel Hladik EmTech 2005 / 2006

84

Preface

Concept

Material Properties

Form Generation

Evaluation

button to fire up the sorting macro

Methodology

The process of dealing with input data. In this case points generated by spiral phyllotaxis. Explanation of the process of dealing with input data.

81 points

distances

x y z

QUADRANT IV

01. Excel spred sheet with 81 points generated according to the spiral phyllotaxis.

The 4th quadrant. Distances between points are compared and then sorted.

QUADRANT I QUADRANT III QUADRANT II

02. Excel spred sheet with 81x4 = 324 points. Colured are Quadrants of 81 points. In columns - x, y, z coordinates.

03. Diagram of 4 Quadrants. Points are divided into these Quadrants.

Pavel Hladik EmTech 2005 / 2006

85

Preface

Concept

Material Properties

Form Generation

Evaluation

Methodology

Physical models of possible connection between branches. It seemed to be tho most appropriate for this test to converge branches to one point.

The figure 04 shows the interweaving of stripes. This approach was followed in the last experiment. Branches there reached certain level and then bacame the surface.

01. Overlapping.

02. Convergence 2 elements.

03. Convergence 3 elemnts.

04. Veawing.

Pavel Hladik EmTech 2005 / 2006

86

Preface

Concept

Material Properties

Form Generation

Digital Generation

Evaluation

6

The process of dealing with input data. In this case points generated in a square array of 81 points.

750 mm

6

6

Points have the constant Z coordinate and constant spacing. They form an array of size 6m by 6m.

750 mm 7m

04. Plan of the tip of the tree. Spacing between points 750 mm, top of branches 30 mm plank ply.

Top Points 0.0045 0.0135 0.0405 0.1215 0.3645

2

Base Point 0.3645

2

0.1215 0.1215

01. Three trees sharing the array of 81 points. Dimensions are in m.

02. Top view. One base point is connected to 4 arrays of points.

Bottom Points

05. Schematic section of the structure in m. Numbers represents sections of branches in particular heights.

03. Elevation shows the position of starting branches from the base point.

Pavel Hladik EmTech 2005 / 2006

87

Preface

Concept

Material Properties

Form Generation

Evaluation

centroid of points

In the beginning of the parametric setup was obvious that concept of pure tension in threads-liquid experiment cannot be directly materialized by laminated wood. It could follow the technique of design and fabrication used in the Stuttgart Terminal 1 but it was not the aim of this thesis. Geometry and therefore parameters suitable for associative model does not match and should be revised.

direction of the branching node

01. Geometry of the Component 01 - The component follows the logic of the direct path system.

01a. Result of the L-system by rewriting of the component 01.

Presented pictures show the way how to understand and prepare digital models for fabrication - laser cutting (or saw cutting) of flat wooden material.

One part of the overall hypothesis driving this project was continuity of fibres. These fibres are parallel to cutting lines of an assembly.

Zhe length of fibres could be derived from the digital model of GC.

plane point on the line (centroid-proj.bp) line - plane intersection direction of the branching node

02. Geometry of the Component 02 - The component is informed by the behavior of the laminated wood.

02a. Result of the L-system by rewriting of the component 02.

distance between points

branching points

03. Geometry of the Component 02a - Distance between points is not even and therefore there are two branching points.

Pavel Hladik EmTech 2005 / 2006

88

Preface

Concept

Material Properties

Form Generation

Evaluation

Experiment 03

Subhypothesis: The branched 3D pattern could modulate environment by controling positions of branching nodes. Wooden branches smoothly transmit into the surface. This surface has the smaller ratio in comparisson with direct paths of branching. The negotiation between surface and vectors could be explored.

It is possible to achieve complex design by adapting features of paths systems in 2D and 3D and introducing them to generic Lsystem. The L-system algorithm responds to needs of the site and has impact on the structural scheme as wel on the environment.

Pavel Hladik EmTech 2005 / 2006

89

Preface

Concept

Material Properties

Form Generation

Evaluation

Methodology

The aim was to create generic model of a digital macrocomponent from the self-supporting structure attached to the ground on three or four points. The branching described and analysed in the chapter Concept was always stable due to the attaching to the plexiglass plate. In Experiment 03 the interwoven branches acted as a surface. Later is shown and deployed the strategy for controlling the porosity and manufacturing.

The L-system algorithm drove the whole process of tectonics. Simple parameters and positions of input points and one base point directed the output that result in the macrocomponent with three supports attached to the ground. Figures 01-04 illustrate the possibilities of attaching branched supports to the structure.

01. Connection of points 01. Supports branche out into 9 points that are later connected according to presneted rules.

02. Connection of points 02. Supports branche out into 9 points that are later connected according to presneted rules.

Described macrocomponent was then proliferated on a site on a plan generated by other scaffolding of L-system. The L-system that drove these experiments had evolved from the previous studies. Firstly it was branching pattern informed by the behaviour of wooden laminated planks. The other method was used from studies of branching in 2D - see chapter Concept.

03. Connection of points 03. Supports branche out into 9 points that are later connected according to presneted rules.

Pavel Hladik EmTech 2005 / 2006

90

Preface

Concept

Material Properties

Form Generation

Evaluation

Experiment 03a

4

This experiment followed the logic of a plane and branched supports that have tangency continuity to the plane surface. This surface was a porous surface from laminated planks. These planks were continuous on the surface and cover like a slab the whole area of proliferated geometry. Because of the continuity the whole assembly was very stable against vertical loads. But there was a possibility to asses this structure as a slab and columns. Similar scheme was used in the roof of the Stuttgart Terminal 1.

The advantage of this approach was the possible manufacturing. It was meant to made the surface off-site and then attach it on-site by laminating support tree.

10

01. Three trees with branching out into 9 points. The triangle has all sides 10m long.

02. Plan of the geometry. The triangle was made in order to analyze the structural behavior.

8.66

0.98

0.62

03. Axonometry of the structure. The geometry is considered to be a sample from the structure.

Pavel Hladik EmTech 2005 / 2006

91

Preface

Concept

Material Properties

Form Generation

Evaluation

Experiment 03a

The geometry is constrained by the structural capacity of the macrocomponent. The branched structure supports the layer evaluated by the FEA method.

03. Structural evaluation of the Macrocomponent

The L-system as a scaffolding for the lamination controlled the porosity of the surface. The distance between points determined distances of branches and then distrubution of horizontal planks.

This had a direct impact on the light, air and water permeability.

Within certain limits the structural scheme was the same. The analysis of the finite elements method was set as a feedback for the structural scheme. The deflection of the surface of the macrocomponent in was critical in certain dimensions and distances of supports. These values were also cnfirmed by the physical teset with laminated timber planks.

04. Geometry of the branched structure - digital for-finding of laminated timber.

01. Proliferation of macrocomponents - Bird view

points L-system in supports

points - L-system in plan 05. Detail of the macrocomponent - the porosity of the structure is controlled by two levels of L-system. The first level is the distribution of points on the plane and therefore the geometry of final branching points. The second level is the branching itself. By varying of the distance between branches the porosity of the surface is also afected.

Strategy for the planar distribution is later explained.

02. Proliferation of macrocomponents - Perspective Pavel Hladik EmTech 2005 / 2006

92

Preface

Concept

Material Properties

Form Generation

Evaluation

Digital Form-Finding

P [0] = P[1]

c c/3 c a

a

a

P [0] CS [0] P [0]

c c/3 c a

a

P [1]

a = thickness of layers - number of layers b = constant width of timber c = distance of points in an array - curvature of BSplines

The dialog between surface-active and vector-active systems is deployed into detail by digital form-finding of laminated wood. This experiment ended up with the physical model and outlined the procedure for the manufacturing of larger pieces.

The digital model of lines and points were extended by adding sets of points that controlled the curvature of BSpline curves. Points were generated on coordinate systems placed on branching nodes.

These coordinate systems were rotated according to the distance and position of the next branching node. Nodes from digital formfinding were then used as nodes in physical model as an area of first clamps. Fig 01 and 02 illustrate the strategy for control of BSplines. In fact it was nesting of additional scripts on the script of branching explored early in the thesis.

CS [1] P [1] c

CS [b]

c/3 c a 01. Branching node. Branches split under the influence of the distance of the next branching nodes. The control of the curvature is provided by manipulation of arrays of points.

a

a

02. Details of three possibilities of branching points. The array of points in 3D serves for the cointinuity of BSpline curves determining the volume of laminated wood.

03. Array of points as tangency points for the volume of branches. Branches behaves according to set rules.

Pavel Hladik EmTech 2005 / 2006

93

Preface

Concept

Material Properties

Form Generation

Evaluation

Digital Form-Finding

The digital set-up for the geometry and volume control of laminated wood. Images on this page illustrate step by step how to get and control the geometry for the fabrication. The model was generic and so it could be used in the any branched pattern that came with certain constraints - dimensions - space for later BSplines.

This strategy is based on the premise that a plank board of wood of certain length achieve complex 3D curve by fixing its points.

This curvature could be repeated consequently with the same type of wood and dimensions. This board could be then glued together, fixed by clamps and later milled by advanced CAM. 01. Brancehd structure proliferated by coordinate systems.

04. Detail of the branching node with one coordinate system01.

02. Arrays of points on branching nodes. The tangency continuity is maintained - clamping points.

05. Coordinate system02 rotated around coordinate system01 around X axis. Angle 45°.

03. BSplines Curves through arrays of points.

06. Final coordinate system - rotation around coordinate system02 around Z axis. Angle 20°.

Pavel Hladik EmTech 2005 / 2006

94

Preface

Concept

Material Properties

Form Generation

Evaluation

Model of 3D Laminated Timber

The model of 3D branches was made in order to understand the limits of this technique. The model was built in scale 1:20. It was made of 3 layers of veneer. This model could be scaled up because it is a model made by a composite material but it should be also teste don the bigger scale.

There were 9 clamping points and one base point of the tested model. The two images O1, O2 showed the digital model of the structure with planes that determine clamping points. The figures 03, 04 have shown the finished model and scaffolding that held clamping points. The scarf joint was made because of the space requirements. These joints were also inteded to use in the assembly of pieces for buildings.

01. Model for prepared for the fabrication. The upper branch is made separately and then glued together.

03. Finished model in the scaffolding from paper boards.

02. Model for prepared for the fabrication.

04. Model removed from the paper scaffolding.

Pavel Hladik EmTech 2005 / 2006

95

Preface

Concept

Material Properties

Form Generation

Evaluation

Experiment 03b

The second path of the Experiment 03 was assesed as the most successful. Here, the boundary between surface and support was blurred. Laminated timber branched out from the ground point and form an intervowen surface that can resist both tension and compression.

The design of macrocomponent was similar to the Experiment 03a. Here, there is not a plane that acts as a slab but there are only control points that determine the shape and also theporosity of the surface.

01. MAcrocomponent - setup in associative model - GC.

03. Macrocomponent. Rendering.

03. FEA of the macrocomponent - Deflection in Z-axis.

Pavel Hladik EmTech 2005 / 2006

96

Preface

Concept

Material Properties

Form Generation

Evaluation

Experiment 03b

There was made the test design in which to examine the potential of L-system proliferation.

The significant architectural control is achieved by mastering parameters that determine the proliferation of the structure. This issue consists of the triangulation of the site and also the manipulation and number of control points (also clamp points) in the laminated structure. The triangulation of the site is important for the height of macrocomponent and also for the density of branches.

The material process followed the logic from previous experiments. The idea was to assemble large pieces off-site and then connect them on-site. The connecting could be made by gluing ends in the vacuum sleeve. The space required for the sleeve was also one of constraints of the design.

Structural performance of the pavilion was tested on the macrocomponents and also on a part of the proliferated geometry. The combination of the FEA and physical test gave necessary feedback for the design. The framework outlined in this thesis is open for the high variety of parameters and could be later extended.

01. Elevation of the pavilion.

the density and porosity of the structure is controlled through the manipulation of the parameters in the algorithm

the surface modulates the light and it has an environmental performance

02. Perspective view of the experimental design.

Pavel Hladik EmTech 2005 / 2006

97

Preface

Concept

Material Properties

Form Generation

Evaluation

Proliferation Strategy

border of the site 300m

area of proliferation

program constraints

border of the site 250m

The proliferation strategy of the geometry comes from requirements of the site and a program of the pavilion. The logic of the component is also informed by material, manufacturing technique and branched structure.

Branching nodes represent places where the “tree” structure is placed. These structures have certain properties and tectonics that are in direct influence with proliferated “map”. The behaviour could be a self-organisation with emergent properties.

The surface of an assembly is evolved from a branched geometry and follows two main structural constraints: span and density of branches. The “tree” structures could be also overcome without any porous openings in the area of other trees. As reference could be mentioned branches of mangrove supported by other small trees that emerge from heavy, long span branches.

Input for the proliferation: Topography + Obstacles

angle- input from the site

Spans of the structure Distances of the support Opening for the natural light and air The role of the designer is in choice of the parameters and affection of the proliferated geometry by further strategical steps. One of these strategies is introducing higher degree of attracting paths gained from the nested form-finding. In experiments with threads of various thickness dipped into a liquid is observed that thicker threads bind more threads together and rapidly change the direction of paths.

In case the designer is not satisfied with generated model, it is possible just change values of parameters and run routine again.

01. Site for the pavilion - given constraints by program and by configuration of the site.

R1

R1, R2 Reference points of the influence. The distance from these points influence the proliferated “map” on a site. The distance between branching points is different and therefore span of the final structure varies. Also the angle of the branching node is changing according to the distance from reference points.

R1 R2

R2

S

S

02. Proliferaton strategy 01. Chosen starting point and geometry influenced by program constraints. Change in angle an length.

03. Proliferaton strategy 02. Main path (blue) influences smaller branches and bind other branches.

In this thesis there was the simplest mode explored. It meant Start and End points of the site as “entrance” points.

S Starting point of the proliferation. Designer choose the location according to the “top - down” strategy of the design. There could be several starting points on the site.

Algorithm responds to the borders of site and to the points that are generated by this algorithm. The Start point and end points were as an input. Then paths of branches could not be crossed.

Pavel Hladik EmTech 2005 / 2006

98

Preface

Concept

Material Properties

Form Generation

Proliferation Strategy

Evaluation S1

Example of the proliferation. Fig. 01 represents variety of paths leading from base point to points of branches. The branching lines traced the pavilion area. This area was then meshed into triangles which determined locations of supports. Fig. 03 explains the dependencies of the building on the site.

The design strategy shown on figures 04, 05 explains the aim for the whole pavilion. The site with entrance points S1, S2, S3 and growth of pavilion towards the point R.

01. Various tree structures connecting points with a base point.

R

S2

S3 04. Strategy for the approach from the Start points “S” to the reference point “R”.

S1 02. Triangular site... 1710 m2. Area of pavilions: S1- 704 m2, S2- 764m2.

R

S2

S3 03. Strategy for the proliferation: the grid of “map” (green points) and heights of the macrocomponent.

05. Meshed plan of the pavilion.

Pavel Hladik EmTech 2005 / 2006

99

Preface

Concept

Material Properties

Form Generation

Evaluation

Light Study

003 002 002

002

002 002

003

001

003

003

002 001

002

01. Light study 01 - the direct light onto the pieces of the pavilion. Sharp shadows.

Dimensions of triangles determine the size of the macrocomponent. Macrocomponents consist of laminated planks in certain grid. The size of the grid varied in boundaries constrained by the space for manufacturing and also by the structural performance.

The light studies shows that the impact on environment must be considered and the grid could modulate significantly light under the structure. The more control and more blurred shadows could be achieved by adding more layers and created then multi stored pavilion. The structure could be strong enough to bear the movement of people and could then branch into next level and get the input from the experiments described in chapter Concept.

02. Light study 02 - the direct light onto the pieces of the pavilion. Blurred Shadows.

Gradient of porosity

SUN

002 001 003 002 002

002

001

002

002

003

003 003 001 002 002

03. Plan of the pavilion.

04. Gradient map of the porosity.

Pavel Hladik EmTech 2005 / 2006

100

Preface

Concept

Material Properties

Form Generation

Evaluation

P3 P4

P2

Manufacturing Process

The pavilion was designed as an asembly from macrocomponents.

Each macrocomponent consists of 4 pieces (fig. 02 - P1, P2, P3, P4). These pieces were intended to build off-site according to the transportation possibilities and then gleud together on-site in vacuum sleeve. Timber boards have its own length and dimensions and therefore they could be prefabricated by methods of form-finding- clamped on certain points and then glued together. The Expo Roof by Thomas Herzog is shown in detail on fig. 01. The process of dealing with timber lattice shell made in the company Finnforest Merk was used as the direct reference for this procedure.

P1

02. Macrocomponent. The sections for the off-site assambling.

01. The scheme of the construction of the Expo Roof, T. Herzog, 2000.

03. Rapid-prototyped model of the branched-out support.

Pavel Hladik EmTech 2005 / 2006

101

Preface

Concept

Material Properties

Form Generation

Evaluation

Pavel Hladik EmTech 2005 / 2006

102

Behavior of Planks Curvature

Geometric Setup

Manufacturing Constraints

Alg. Definition Spatial Requirements

R1

R2

S

Transport Assembly Techniques Geometry - Macro Scale

CS [b]

CAD CAM Rules, Variables, Logic

P [1]

Finding of Geometry, Rules

CS [1]

Proliferation Methods

Production Logic

Structural Concept Emergent Behavior

P [0]

Structure

Replication Capacity

Physical Form-Finding 01

CS [0]

Performative Criteria

Emergence Form Analysis

Top-down Decisions

Common Rules

ture

Hypothesis

Digital Form-Finding

Physical Form-Finding 02

Living, Non-living Na

Evaluation

Structural Requirements

Growth and Branching

Aim

Form Generation

Reset of Criteria

Material Properties

Time, Cost Effectivity

Concept

Material Properties

Preface

Model of Material System

Applied Model of Branching Parametric Setup

Fabrication Tech.

Perform. Capacities

Local Interaction

Global Interaction

Pavel Hladik EmTech 2005 / 2006

103

Preface

Concept

Material Properties

Form Generation

Evaluation

Sub-hypothesis: If physical tests with laminated planks preshaped and glued together are executed the important feedback for the relevant structural analysis could be set. The triangle between form, digital geometry and actual physical behaviour could be established.

Pavel Hladik EmTech 2005 / 2006

104

Preface

Concept

Material Properties

Form Generation

Evaluation

Methodology

The dissertation is mainly focused on the structural performance of developed material system. The feedback loop of the design is closed by evaluation methods that are presented in this part of the thesis. It is physical and digital structural analysis. The physical models provide information for the digital tools in terms of actual behaviour of selected components.

There were made 3 tests with laminated timber. These tests studied the strength of lamination, flexibility and limiting curvature.

This information were then compared to deflections of structure plot in FEA analysis of this complex structure. The first test was made in order to explore the flexibility of a single laminated “beam” and its limits the second two experiments represented two laminated pre-shaped beams. The laminations were made from the same type of wood - 3layered ply where the grain was crossed in 90°.

Material for the physical tests: 3 layers of birch ply (1.5 mm thick - 3 layers) glued together width: 30 mm length: 1000 mm PVA glue Digital analysis was made in engineering programe ansys - the tool for the finite elements method. Modeled geometry was imported to the program and then studied the deflection of the structure and compared to the results from physical tests. Although the normative values for buildings made of timber does not allow such high flexibility as were achieved in the physical modelling the interesting results could be made when one considers the flexibility of the structure as an advantage of the design. The structural scheme presented here is the scheme for the pavilion loaded by snow and wind.

Values for the digital analysis: snow: 0.6 kN/m2 wind: 0.5 kN/m2

Pavel Hladik EmTech 2005 / 2006

105

Concept

Material Properties

Form Generation

Evaluation

Test of Wooden Components 01

Material: 3 layers of birch ply (1.5 mm thick - 3 layers) glued together width: 30 mm length: 1000 mm

1000

Preface

PVA glue

100

500

The component was broken when there was applied force from the side of the testing model. The flexibility of the single beam was enormous. The interesting comparison would be when these single beams would be touching each other when load is applied. This scheme is not dissimilar from that in trees in forest. Branches of trees touch each other and that cause the complex whole that from the “distance” could be regarded as one piece. The emergent behaviour is significant.

100

500

1000

Image of all experiments: units are cm.

01. No load.

02. Load 15 N.

03. Load 30 N.

04. Geometry is changed by unspecified force.

05. Extreme change of geometry.

06. The tip was in angle more than 180°.

Pavel Hladik EmTech 2005 / 2006

106

Concept

Material Properties

Form Generation

Evaluation

Test of Wooden Components 02

Material: 3 layers of birch ply (1.5 mm thick - 3 layers) glued together width: 30 mm length: 1000 mm

1000

Preface

PVA glue

100

500

Distance: 180 mm

100

500

1000

Image of all experiments: units are cm.

01. No load.

02. Load 15 N.

03. Load 30 N.

04. Load 45 N.

05. Load 60 N. Test piece is acting mainly in tension.

06. Introduced side force of 20 N. Pavel Hladik EmTech 2005 / 2006

107

Concept

Material Properties

Form Generation

Evaluation

Test of Wooden Components 03

Material: 3 layers of birch ply (1.5 mm thick - 3 layers) glued together width: 30 mm length: 1000 mm

1000

Preface

PVA glue 600 mm

100

500

Distance:

100

500

1000

Image of all experiments: units are cm.

01. No load.

02. Load 15 N.

03. Load 30 N.

04. Load 45 N.

05. Load 60 N.

06. Load 75 N. Pavel Hladik EmTech 2005 / 2006

108

Preface

Concept

Material Properties

Form Generation

Evaluation

Analysis

The physical test proved that laminated timber is highly flexible and can withstand forces that caused deflection that is not allowed in ordinary timber buildings. It was also obvious that dimensions of tested components could be used only as a porous surface of the “roof” of the pavilion not as a floor platform loaded by loads for floors in buildings.

Fig. 01 and fig. 02 presented details of cracks in the laminated timber. The Experiment 02 (fig. 01) had distance between laminated timber beams 18 cm and by applying force 60 N the structure was still flexible. After introducing side force the component broke.

The detail showed that there were torn fibres that acted in tension (upper side of the component) and also in compression (lower part of the component). The other image with a distance of 60 cm was loaded by 60 N and lower part of the component was broken.

These tests presented the potential application of connected branches. And also gave the idea about constraints of distance between branches and attaching them. The structural analysis is based on the premise that glue has the same structural capacity as wood. In reality this has to be reformulated and restated but it is possible to use that for the initial exercises and tests.

01. Test Piece - experiment 01 - detail of the crack. Failure occured on both parts of the component - upper part was in tension and lower part was in compression.

02. Test Piece - experiment 02 - detail of the crack. Fibres broke in the lower part of the laminated component.

Pavel Hladik EmTech 2005 / 2006

109

Preface

Concept

Material Properties

Form Generation

Evaluation

Digital Experiments

Pavel Hladik EmTech 2005 / 2006

110

Preface

Concept

Material Properties

Form Generation

Evaluation

Digital Experiment 01

Digital experiments 01 and 02 were devoted to the models of material system described in the chapter Form Generation in Experiment 02. These experiemnts had their own hypothesis and were assesed as single beams that branched out from a “trunk”.

The images on the left - fig. 01, 02, 03 were analysed under self-load only. The deflection of branches in direction of the Z-axis was enormous. A possibility was to join one tree system to other trees. This assembly was then able to bear itself.

On the following page there are dimensions of sections used for the analysis of the experiment 02a. Experiment 02b was adjusted according to the values gained from enalysis 02a. Branches were shortened to values that were able to bear themselves.

Displacement under the self-load analysed by FEM. E = 7e9 N*m2 vx,y = 0.2 dens: 800 kg*m3

01. Elevation. The colour-coded image of the displacement in direction of Z-axis. The deflection is more than 3 m - viz picture.

03. Top view.

02. Elevation 2.

Pavel Hladik EmTech 2005 / 2006

111

Preface

Concept

Material Properties

Form Generation

Evaluation Digital Experiment 02 Displacement under the self-load analysed by FEM. E = 7e9 N*m2 vx,y = 0.2 dens: 800 kg*m3 Sections: 01... 0.06 x 0.06 m 02... 0.12 x 0.12 m 03... 0.54 x 0.54 m

01. Experiment 01. Top view.

02. Experiment 01. Side view.

03. Experiment 02. Top view.

04. Experiment 02. Side view.

Pavel Hladik EmTech 2005 / 2006

112

Preface

Concept

Material Properties

Form Generation

Evaluation Digital Experiment 02a Displacement under the self-load analysed by FEM. E = 7e9 N*m2 vx,y = 0.2 dens: 800 kg*m3 Sections: 01... 0.06 x 0.06 m 02... 0.12 x 0.12 m 03... 0.54 x 0.54 m

01. Experiment 03. Top view.

02. Experiment 03. Side view.

03. Experiment 04. Top view.

04. Experiment 04. Side view.

Pavel Hladik EmTech 2005 / 2006

113

Preface

Concept

Material Properties

Form Generation

Evaluation

Digital Experiment 03a

The Experiments 03 were executed in order to get precise dimensions for the Experiment 03 in chapter Form Generation. This material system that was found as the most succesful was expressed and analysed as beams that were interconnected. The aim was to create continuous porous surface that is more vector-active than surface-active and these digital experiments proved that it is possible to constraint developed macrocomponent by dimensions. The difference between experiment 03a and Experiment 03b is in the distances between supports in plan. The consequent development of the macrocomponent was made as the dependance between hight of the structure and distances in plan. It maintained the same scheme with the same sections. Due to the complex connections of laminated planks was achieved a redundant structure (redundant in biological terms) this was also proven by FEA.

03. Deflection in Z-Axis. Side view.

01. Plan of the geometry. The triangle was made in order to analyze the structural behavior as the macrocomponent..

02. Deflection in Z-Axis.

Pavel Hladik EmTech 2005 / 2006

114

Preface

Concept

Material Properties

Form Generation

Evaluation

Digital Experiment 03b

Limiting plan dimensions for the macrocomponent. The blue colour and the deflection in the surface between supports is dangerous for the structure and has to be avoid (fig. 01, 03, 04).

1.98

16

0.74

01. Plan of the geometry. The triangle is changed in order to examine the relationship between span, section and configuration of supports.

02. Deflection in Z-Axis.

03. Deflection in Z-Axis. Side view.

04. Deflection in Z-Axis. Axonometry.

Pavel Hladik EmTech 2005 / 2006

115

Preface

Concept

Material Properties

Form Generation

Evaluation

Digital Experiment 03c

THe macrocomponent of the dimension (page 94, fig. 03): L=4-6m H = 2.4 - 3.7 m The deflections and moments showed that the structure had high quality structural performance iven when asambled from small sections: laminated wood of thickness 4 cm and width of 10 cm.

01. Deflection in Z-Axis. Side view.

02. Plan of the geometry.

03. Deflection in Z-Axis.

Pavel Hladik EmTech 2005 / 2006

116

Conclusion

The presented research into the design methods and material behaviour presented powerful tools for architects. The convergence of computation methods and self-form of materials led to the and unique emergent structure. The self-form was explored in extensive use of form-finding and then used as an input data for algorithmic expressions of structure and proliferation on given site.

The potential of L-system proliferation was evaluated on the architectural - structural level and opened other areas which had not been explored (see chapter Further Areas of Research). The L-system was used as a tool for the significant control of space in plan and also in the form generation of components and macrocomponents. The achieved differentiated structure reacted on the site by associative geometry resulting in the successful structural performance. The structure followed the biomimetic approach of fibre directionality and redundancy. The redundancy in structure caused that the complex system was able to withstand dynamic forces in relatively small dimensions of components. The dialog between vector-active and surface-active systems was researched and instrumentalized.

The part Concept introduced important aspects in geometry and in structural scheme. Thanks to the generative parametric software GC very complex hierarchical structure could be developed. This complexity goes beyond physical modelling.

Digital form-finding could be than use directly to the fabrication.

This procedure was successful deployed in the chapter Material Properties and Form Generation. The 3d laminated components were assembled to the macrocomponent and used as an unit for the proliferation. The dimensions of macrocomponent were constrained by specific requirement on a structure and on a site.

The methods of generation of the pavilion on the site was explored in the Experiment 03 in the chapter Form Generation. This test design evolved into one storey of pavilion that had a surface intended for the modulation of the environment only. The possibilities and developed skills and tools in the chapters Concept, Material Properties and Form Generation could lead also to the multi level branched structure. That means that there is a potential also for branching into 3 dimensions.

There was achieved a porous self-supporting surface responding to the plan of the pavilion. The plan was arbitrarily chosen from the wide interval of possibilities that offered parameters of developed algorithm. The surface could be also informed by other aspects that are related to the environment. Architectural concept then could get another layer of complexity to its design procedure.

Pavel Hladik EmTech 2005 / 2006

117

Areas of Furter Research

It is possible to outline further areas of research on the findings of this research. There are issues developed in the thesis that could be used both in multidisciplinar research fields and also in the architectural praxis. The research is regarded as a generic process into methodology that can later evolve in several fields of interest.

Material Level The research into the materials outlined in the thesis could continue with a hypothesis based on combining materials of different qualities into composites. It is possible to pre-stress a curved laminated beams by adding layer with different reaction on the glue. Glue used for lamination dissolves in water and therefore wood could shrink and pre-stress the curved beam. The structural capacity of this component could be later tested and evaluated.

Geometry The work with complex curvature in wooden components has certain limits. Also the manufacturing techniques for continuous lamination have to be revised and match with limits of 3D lamination.

The fibre directionality and continuity is an issue that requires further studies and examples form nature and biomimetic approach.

The whole issue represents the attaching structure to the ground.

In order to maintain the clarity of the structure (timber and glue) these joints are considered with a high degree of importance.

Environment Impact The environment impact was not fully developed in the thesis but it is inseparable feature of the con temporal architectural development. Parameters modulating environment in the structure could be introduced into the material system and requirements on the surface of a pavilion could be stated in the beginning of the design.

The evaluation methods for these issues would consists of digital software and also physical models.

Algorithmic Proliferation The L-system proliferation could be developed into more complex design method by introducing simple statements. The algorithm deployed in the thesis would then serve as a scaffolding for the generic tool for architectural designing. By adding conditions could be achieved powerful emergent generations. The thesis proved that bottom-up approach constrained by material behaviour led to the effective architectural tool.

Pavel Hladik EmTech 2005 / 2006

118

Bibliography

1.

Complexity, Metaphors, Models and Reality, G. A. Cowan, D. Pines, D. Meltzer 2.

Thread model, natural-spontanious formation of branches, Marek Kolodziejczyk, In Natural Structure, volume 7, pages 137-142, Stuttgart, 1991. Universität Stuttgart, Sonderforschungsbereich 230 3.

On Growth and Form, D´Arcy W. Thompson, 1942 4.

Finding Form, F. Otto, 1995 5.

Il 25 - Experiments, 1990 6.

Il 28 - Diatoms I, 7.

Il 35 8.

The Science of Structures and Materials, J. E. Gordon, 1988 9.

Algorithmic Beauty of Plants, P. Prusinkiewicz, E. Linden- mayer, 2004 10.

NOX, L. Spuyerbrook, 2005 11.

Parsimonious Universe : Shape And Form In The Natural World, S. Hildebrandt, A. Tromba, 1995 12.

What is mathematics?, R. Courat and H. Robbins, 1967 13.

Euclidean Steiner Minimum Trees in an Hour, Winter, Zachariasen, Large, 1997 14.

Experimental and Theoretical Static of Liquids Subject to Molecular Forces Only, J. Plateau, 1873 15.

Artefacts and Instruments, M. Weinstock, 1998 16.

The Experimental Determination of Minimal Nets, Institute for Lightweight Structures, 1971 17.

Emergence and Self-Organisation, T. De Wolf, T. Holvoet, 2005 18.

Frei Otto, Complete Works, W. Nerdinger, 2005 19.

Techniques and Technologies in Morphogenetic Design, AD Vol. 76, No 2, 2006 20.

Creating Synthesis Partners, AD Vol. 72 No 1, K. Shea, 2002 21.

Fine Woodworking – Bending Wood, 1985 22.

The International Book of Wood, M. Beazley, 1992 23.

The Self-made Tapestry: Pattern Formation in Nature, P. Ball, 2002 24.

Atlas Of Novel Tectonics, Reiser + Umemoto, 2006 25.

ExpoDach, Thomas Herzog, 2000

Pavel Hladik EmTech 2005 / 2006

119

Appendix 01 Principles of laminated timber structures

Preliminary equation Span

Spacing

Height

Structural Schemes h

Truss 3.6 ~ 9

h ~ l/12-17

3.6 ~ 7.2

h ~ l/15-20

3.6 ~ 6

h ~ l/15-20

4.5 ~ 9

h ~ l/50 f ~ l/6-7

4.5 ~ 9

h ~ l/50 f ~ l/6-7

h

10 ~ 30

Two-pinned frame

h1

15 ~ 30

The structural schemes presented on this page does not match with the structural scheme of the material system presented in the thesis but it is relevant as a comparison. The difference of achieved structural performance of material system and traditional schemes presented on this page is enormous. The required dimensions for single laminated arch are uncomperable to values presented in this thesis.

Three-pinned frame

h

15 ~ 50

f

Two-pinned arch

h

21 ~ 100

f

Three-pinned arch 21 ~ 100

l

Pavel Hladik EmTech 2005 / 2006

120

Appendix 02

Nested Form-Finding

Pavel Hladik EmTech 2005 / 2006

121