Arboreal Formations

ARBOREAL FORMATIONS

EMERGENT TECHNOLOGIES AND DESIGN MSC DISSERTATION PROJECT 2011-2012 ARBOREAL-FORMATIONS.BLOGSPOT.CO.UK

EMERGENT TECHNOLOGIES AND DESIGN TUTORS

MICHAEL WEINSTOCK

DR. GEORGE JERONIMIDIS

EVAN GREENBERG

MEHRAN GHARLEGHI

WOLF MANGELSDORF

DIRECTOR

DIRECTOR

STUDIO MASTER

STUDIO TUTOR

VISTING PROFESSOR

MSC CANDIDATES

BARTEK ARENDT (PL)

CHRIS HILL (GB)

ELENI MELADAKI (GR)

GRADUATE SCHOOL PROGRAMMES

COVERSHEET FOR SUBMISSION 2011-2012

PROGRAMME:

TERM:

STUDENT NAME(S):

SUBMISSION TITLE:

COURSE TITLE:

COURSE TUTOR:

SUBMISSION DATE:

DECLARATION:

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EMTECH 04

BARTOSZ ARENDT CHRISTOPHER HILL ELENI MELADAKI

ARBOREAL FORMATIONS

DISSERTATION

MICHAEL WEINSTOCK

14.07.2012

DATE:

“I CERTIFY THAT THIS PIECE OF WORK IS ENTIRELY MY/ OUR OWN AND THAT ANY QUOTATION OR PARAPHRASE FROM THE PUBLISHED OR UNPUBLISHED WORK OF OTHERS IS DULY ACKNOWLEDGED.”

“WE CERTIFY THAT THIS PIECE OF WORK IS ENTIRELY OUR OWN THAT ANY QUOTATION OR PARAPHRASE FROM THE PUBLISHED OR UNPUBLISHED WORK OF OTHERS IS DULY ACKNOWLEDGED.”

14.09.2012

BARTOSZ ARENDT ELENI MELADAKI

CHRISTOPHER HILL

ACKNOWLEDGEMENTS

TO OUR FAMILIES, FRIENDS AND TUTORS

TABLE OF CONTENTS

ARBOREAL FORMATIONS

SHRINKAGE AND SWELLING

USING VENEERS FOR MATERIAL CONTROL

VARIABLE MOISTURE CONTENT BY CLIMATE

TIMBER DIMENSIONS BY LOCAL ENVIRONMENT 031

PROCESSING OF TREES TO TIMBER 0 32 USING VENEERS FOR MATERIAL EFFICIENCY

FABRICATING LARGE COMPLEX GEOMETRIES 035 GEOMETRY

STRUCTURAL PERFORMANCE

BENDING WOOD TECHNIQUES

KEYSTUDY : CHAISE LOUNGE

FABRICATION OBSERVATIONS 0 45

TIMBER APPLICATIONS SCALE 0 47

PROJECT SCALE AMBITION 0 47

MATERIAL SYSTEM AMBITION

METHODS

‘ARBOREAL’

IS DEFINED AS RELATING TO TREES.

ABSTRACT

Arboreal Formations is a research project that investigates how specific properties of wood may be a driver for curving pieces of timber. The thesis documents an approach for generating design solutions that capitalise on the investigation and understanding of wood’s inherent properties. The work aims to create a generative process for a holistic building system implementing a methodology that prioritises materiality to enhance the relationship between material, structure and geometry.

The process investigates the calibration of physical experiments and digital simulations to define a component which may aggregate to form a system that is structurally coherent, fabrication efficient and expresses spatially dynamic morphologies. The characteristics of the component are integral to the material system and using an associative geometry is revealed in the design of a twenty storey timber residential block in New York City.

A novel fabrication technique and understanding of materiality are combined through the research to conceive a timber component that can be programmed to create a range of curvatures and be structural depending upon its thickness. The innovation presents an opportunity for new architectural spaces and forms to be created in wood.

KEYWORDS: INTEGRATED SYSTEMS, WOOD, HYGROSCOPIC BEHAVIOUR, ANISOTROPIC CHARACTERISTICS, MATERIAL COMPUTATION INFORMATION, VARIANT MORPHOLOGIES, ASSOCIATIVE MODEL

“Arboreal Formations is a research project that investigates how specific properties of wood may be a driver for curving pieces of timber.”

WOOD-CUT PRINT OF A WILLOW TREE BY BRYAN NASH GILL, 2011

RACHEL BEACH STACK, 2010; OIL AND ACRYLIC ON PLYWOOD, RECLAIMED LUMBER; 51 X 17 X 10 INCHES

INTRODUCTION

Nature exemplifies materiality, structure and morphology as three interwoven themes that contribute to the operation, performance and survival of an organism. Architecture often neglects the opportunity to unite these elements of design and instead separates them through a hierarchical approach that prioritises the overall project vision first. In turn this defines a process without interdependency or conviction as geometry, structure and material combine only to manifest the project outcome.

The aim of this project is to create a holistic building system, the logic of which is built upon the associated relationships of material, structure and morphology. Considering that materiality is often acknowledged last in a design process, the ambition of the work is to reverse that sequence and investigate how basic material properties can inform structure and geometry as an integrated material system.

Wood is a natural, cellular and fibrous material which when exposed to direct moisture or humidity changes is susceptible to movement. The Hygroscopic behaviour (ability to absorb moisture) and Anisotropic characteristics (direction dependent physical properties) of wood may be studied with incite to developing new fabrication techniques for the manufacture of curved pieces of timber.

The research initially explores through physical material testing the ability to predict the expanding and shrinking affects of moisture applied to thin veneer pieces of wood. This phenomenon is further investigated through fabrication processes for creating thicker elements. A principle discovery is made that when many veneer layers are differentially soaked, laminated together and left to dry, curvature and dependent upon grain direction twisting is induced into the piece. The physical experimentation is then transposed to computational simulations to run increased number of quicker tests. Focused on the curving behaviour of the component a process of calibration between physical and digital

workspaces is pursued determining which parameters influence the fabrication process and are quantifiable. This is a vital step for progressing with material information data that determines the potentials and limitations of proceeding application studies. The findings show that thinner timber elements can be fabricated with tight and more articulated curvatures and also thicker members be produced within a more limited range of curvatures.

Before the material component is applied in a material system for application at the building scale, an analysis of the component assesses its structural integrity and how it may be deployed as part of a structural system. The project considers a residential tower as the appropriate application as variations in both apartment sizes and overall massing scales may show the range of curved structural timber elements that can be achieved. A detailed knowledge of the components behaviour and structural studies suggest its suitability as both the walls and beams within a stacked arrangement. Geometrical studies investigate how the elements may then be organised to define space while reinforcing the structural logic. With the demands for controlling the relationships between material information, structural constraints and geometrical organisation strategies an associated model is employed with the use of computation code. This creates a dynamic yet controllable environment in which variables and constraints may iterate to produce different morphologies.

The model is finally tested by adjusting its input parameters to the context and criteria for the competition design proposal of a twenty storey timber residential tower in New York City. The ambition of the proposal is to showcase a systematic design approach in which rigorous material research, structural understanding and geometrical exploration integrate and enrich each other in response to the variable functional demands of residential living and site context.

The thesis research is documented through six chapters that explain the context, conception, development and application of a material system:

- Domain explains why wood and its properties deem it a prominent material for the future, why non-rectilinear geometries have benefits, the advantages of veneers and laminated fabrication techniques and the current practice for manufacturing curved pieces of timber.

- Methods set seven key aspects that the project explores in the subsequent chapters. These include physical experimentation, digital simulation, physical and digital calibration, component analysis, structural system research, geometrical system research and system evaluation.

- Research Development commences physical and digital experimentation seeking to control and calibrate between work environments the parameters which affect the curvature of a timber element and also explores the lamination process through which pieces of veneer are glued together.

- Design Development analyses the properties of the laminated veneer component and its potentials for structural application as part of a material system. Defined through a geometric associative model many components are assembled as a system which displays different morphological states and structural adaptations for functional interpretation.

- Design Proposal applies the material system within the context of a timber residential tower. Parameters of the associative model are adapted to the context of the site and the generated geometry manipulated for variable spatial living conditions.

- Further Developments draws a close to the research and suggest how additional studies could explore more aspects of the material component, material system and application.

“The aim of the project is to create a holistic building system, the logic of which is built upon the associated relationships of material, structure and morphology.”

DOMAIN

Materiality is integral to the performance and organisation of all systems whether in nature or part of the built environment. Nature is very efficient at utilising the properties of its genetic structure in response to demands placed on the system. Unlike many current design approaches form generation in nature is driven by performance with the use of minimal resources and localised material variation in composition, thickness and scale. Whilst the integration of computational tools and innovative fabrication techniques have made complex geometries more accessible to design industries, a fundamental knowledge of material behaviour is being lost.

This chapter explores how wood as one of the oldest, naturally renewable and most commonly used construction materials may be reapplied as one of the most promising materials for new innovative designs. As the living, cellular and fibrous tissue of trees, wood embodies many versatile and performative characteristics. Recent scientific explorations have found a new understanding to explain the uneven and irregular behavioural trends that wood expresses. The findings explain some uncertainties as to why wood bends, warps and twists and may be applied as new opportunities for design exploration. With the notion that wood is natural, heterogeneous and curves by nature, construction and design industries may look to embrace these properties to produce non-rectilinear geometries that are more suited to containing lateral and torsion loads and can economise on material. Current built examples have only applied the manipulation of anisotropic and hygroscopic wood properties on precedents at the scale of the pavilion or façade.

With a greater understanding of how wood performs in fire and may be protected, there are an increasing number of plans for tall timber buildings and 2012 saw the world’s tallest residential timber building realised in London. The solid laminated lumber panel system employed reflects current timber construction methods for building tall and highlights the systems restriction

to create rectilinear geometries. The system also highlights the efforts the wood industry endures to engineer timber to minimise the inherent properties of wood that makes it naturally curve. Even with advances made in fabrication technologies construction and design industries still struggle to curve timber elements with material resourcefulness and structural efficiency. The chapter closes with the project ambition seeking to embed material information at the core of design computation and fabrication to drive a more integrated process where material, geometry and structure may negotiate collectively.

ARBOREAL FORMATIONS

FABRICATION

GEOMETRY

MATERIALITY

SCALE

STRUCTURE

SPACE

WOOD CURVE LAMINATION

HYGROSCOPY

ANISOTROPY

MID-RISE STACKING

BUILDING LATTICE FREE FLOW SHEET AGGREGATION

MIX THRESHOLDS

PIC.06 SERIES OF IMGES OF AGED LOG WALLS, WHERE DIMENTINAL INSTABILITY OF WOOD HAS CAUSED CRACKS AND SPLITINGS.

PIC.07 HYGROSCOPE, ACHIM MENGES AND STEFFAN REICHART AT THE CENTRE POMPIDOU IN PARIS, FRANCE.

PIC.08 HYGROSCOPE PANELS CLOSED, ACHIM MENGES AND STEFFAN REICHART AT THE CENTRE POMPIDOU IN PARIS, FRANCE.

PIC.09 HYGROSCOPE PANELS OPEN AS A REACTION TO AN INCREASE IN HUMIDITY, ACHIM MENGES AND STEFFAN REICHART AT THE CENTRE POMPIDOU IN PARIS, FRANCETO EXPOSURE TO MOISTURE.

MATERIAL DIMENSION INSTABILITIES

Throughout the life cycle of a product the dimensions of the material will fluctuate and respond to the environmental context in which it is situated. From the harvesting of raw commodities to the manufacturing and processing of the basic material to the environment in which the product is applied, the material will react to the temperature, humidity and localised pressures of its context. As the type and organisation of particles vary in different materials, the inherent behavioural qualities are also reflected through a very diverse range.

Many industries and designers understand the dimensional instability of materials to represent limitations. Whilst some systems are designed to accommodate expansion and shrinkage through joints and assembly methods, products have also been engineered to deliver stable and predictable solutions. For example plywood has developed as an alternative to solid wood because of its resistance to shrinkage, splitting, twisting, warping and improved strength. Through a cross lamination process veneers of wood are glued together with the grain of each layer alternating at right angles. The arrangement of the layers installs stability through the comprised panel with properties of the material consistent across both directions.

However through the work of material science and experimental research a more innovative approach may be envisaged for utilising dimension material limitations as design opportunities. Hygroscope, by Achim Menges in collaboration with Steffan Reichart at the Centre Pompidou in Paris PIC.07, PIC.08, PIC.09, exhibits how changing the humidity within a glass tank will influence the moisture content of wood components that morphologically respond to change shape by opening and closing. The work stands testiment to the convergence of computational design and material understanding. Uniting these two fields strives to create a more powerful medium through which material properties stand as the design generator in an integrated design process.

021

1 SOURCE:P419,

022 WOOD

From primitive dwellings to ten storey timber residential towers of today, wood has been widely utilised across the globe as a dependent and versatile building material. The availability of wood, accommodation for machining, structural stability and warm characteristics have been applied to many different functions and project applications. Although a wide knowledge of techniques for fabricating wooden elements have evolved over centuries, the introduction of industrial methods of production and trends for using isotropic materials, similar properties in all directions, has diluted the craft through which wood may be explored. However designers now more than ever have new opportunities to innovate. The science of wood technology is a relatively new field of research and offers a more detailed understanding of wood behaviour.

Wood is ‘an organic material made up of lignin and cellulose, obtained from the trunks of trees, and called timber when used in construction’1. As the fundamental material of a tree, wood must support the crown leaf canopy, conduct mineral solutions throughout the tree structure from roots to leaves and store food. These structural and functional roles are fulfilled by the anatomical organisation and behaviour of a trees cell structure. Therefore wood may more specifically defined as a living fibrous cellular tissue that displays material dimensional instability through hygroscopic behaviour and anisotropic characteristics. Hygroscopy refers to a substances ability to take moisture in from the atmosphere. Anisotropy denotes the directional dependency of a materials physical characteristics. These two defining principles form the research basis from which the thesis develops.

PIC.10 NORWEGIAN WILD REINDEER PAVILION BY SNØHETTA, DOVRE,NORWAY.

PIC.11 CELLULAR ARRANGEMENT IN A SCOTS PINE SOFTWOOD AND A EUROPEAN OAK HARDWOOD.

PIC.12 LENO BY METSÄ WOOD, CROSS LAMINATED TIMBER (CLT).

PIC.13 GLULAM BY METSÄ WOOD.

PIC.14 BIRCH PLYWOD BY METSÄ WOOD, CROSS LAMINATED VENEER (CLV).

EXPLORING WOOD

A strong demand has been made upon the building industry by designers and engineers for materials to be composed homogenously. Wood by nature however is heterogeneous with growth irregularities and anisotropic directionality. As a response to more uniform and isotropic materials such as concrete, steel and glass, many timber manufactures have focused their efforts to engineering timber based products that minimise or even eliminate the impact of hygroscopy and anisotropy such as cross laminated veneer (CLV) and cross laminated timber (CLT), PIC.12. This may seem very counter intuitive to how wood naturally behaves but as defects are evened out through the lamination of multiple layers the timber piece becomes more isotropic and properties such as its weight to strength ratio and structural performance increase.

This research questions the meaning of ‘engineered timber’ and if there is an alternative approach that embraces the hygroscopic and anisotropic natural behaviours of wood to create new types of component products for the manufacturing and construction sectors.

Timber has been heavily used in construction for its structural properties. The high tensile strength and slightly lower compressive strength properties inherent to wood make it a material well suited for many structural applications. Traditionally solid timber has been used in post and beam construction restricting the size of application achievable. Advances in CLT systems have however enabled the manufacture of larger scale building components. In both cases the timber members are well adapted to responding to a combination of tensile, compressive, shear and bending forces.

023

1 IGT REPORT PUBLISHED BY BIS - DEPARTMENT FOR BUSINESS INNOVATION & SKILLS, ESTIMATING THE AMOUNT OF CO2 EMISSIONS THAT THE CONSTRUCTION INDUSTRY CAN INFLUENCE, SUPPORTING MATERIAL FOR THE LOW CARBON CONSTRUCTION,

SUSTAINABLE RESOURCE

Forest covers about 30% of land worldwide with between 25,000 to 30,000 tree species. In Europe alone 190 hectares of forest cover 36% of the land area. About 600 tree species, both softwood and hardwood varieties, are traded for many different uses including building construction, furniture, paper and for fuel.

The building industry is a large contributor to global Carbon Dioxide (CO2) emissions. The UK Construction sector is responsible for almost 47% of total CO2 emissions from the UK.1 In order to minimise this footprint there are many different aspects of the building process that needs to be rethought. The processing and manufacturing of materials used in construction contributes heavily to the large carbon footprint generated by the industry. Therefore designers should be fully aware of how material choice and the means though which it was processed and will be fabricated could influence CO2 emissions.

Unlike other products that deplete the earth’s resources wood is the only major construction material that is sustainable and renewable. Trees are a growing biological tissue that converts solar energy captured by leaves into chemical energy. This process is called photosynthesis and it also uses CO2 and water releasing Oxygen as the waste product. This is a vital process that ensures other forms of life can survive. When forests are sustainably managed the impact on the environment is minimal in comparison to other materials. At the present time as the world is facing drastic climatic changes, which to large extent may have been triggered by human activity, wood appears as the material that designers and the construction industry should embrace more. Through new research and understandings of how wood can be widely applied the environment may have a more sustainable future.

DIAG.02 BUILDING WITH TIMBER AND FORESTING SUSTAINABLY MAY BE SEEN AS A CARBON OFFSETTING AGENT.

DIAG.03 FOREST AREA AS PERCENT OF TOTAL LAND AREA BY COUNTRY.

DIAG.04 LIFE CYCLE ASSESSMENT DOCUMENTING THE ENVIRONMENTAL IMPACT OF BUILDING MATERIALS, ASSEMBLIES AND WHOLE STRUCTURES FROM EXTRACTION OF THE RAW MATERIAL, THROUGH PROCESSING AND MANUFACTURE, ISTALLATION, OPERATION AND DISPOSAL. SOURCE:WWW.NATURALLYWOOD.COM/WHY-WOOD/ SUSTAINABLE-DESIGN

DIAG.05 EMBODIED ENERGY OF SELECTED BUILDING MATERIALS AND TOTALS IN A TYPICAL DWELLING. SOURCE:WWW.TECECO.COM/SUSTAINABILITY.EMBODIED_ ENERGY.PHP, PRODUCED BY CSIRO “THE EMBODIED ENERGY IN BUILDINGS” (WWW.DBCE.CSIRO.AU) USING DATA FROM TUCKER ET AL. (1999) AND TRELOAR (2000)

DIAG.06 STUDY APPLIED TO THREE SIMILAR FAMILY DWELLINGS CONSTRUCTED FROM DIFFERENT MATERIAL SYSTEMS TO ANALYSE THE EMBODIED AND OPERATION ENERGY USE OVER A SIXTY YEAR LIFE SPAN.

SOURCE:WWW.NATURALLYWOOD.COM/WHY-WOOD/ SUSTAINABLE-DESIGN/ENERGY

PIC.15 SUSTAINABLE FORESTING

ENVIRONMENTAL IMPACT

Life Cycle Assessments (LCA) are an internationally recognised approach to determining the environmental impacts of all building materials from individual components to complete structures through the course of their entire life. The life span of material may be considered from the harvest of the raw material through processing, transportation, installation, operation, maintenance and finally disposal or recycling. The sustainable and clean aspect of working with wood means it out performs Steel and Concrete in all LCA categories as shown in DIAG.04

Embodied energy of a material describes the total energy consumed from the acquisition of the natural resource to the final delivery of the product. The embodied energy per unit mass of material varies greatly, but this does not account for the actual quantities of material used in the construction of buildings. DIAG.05 shows that materials such as Stainless Steel and Copper have high energy contents but are used in small quantities, whereas concrete with almost the lowest embodied energy per tonne of material is consumed in large amounts.

The lower chart DIAG.06, documents part of a LCA study by the ATHENA Institute for the Canadian Wood Council. It is a comparative assessment of alternative material designs for an identical 220m2 family home. The research highlights that wood buildings do not only require less energy to construct but also to operate over time.

DIAG.07 CHART SHOWING THE RELATIONSHIP BETWEEN THE MOISTURE CONTENT OF WOOD AND THE TEMPERATURE AND RELATIVE HUMIDITY OF AIR.

SOURCE:P50, TIMBER:ITS NATURE AND BEHAVIOUR

DIAG.08 CHART SHOWING AVERAGE DESORPTION ISOTHERMS IN A GIVEN TEMPERATURE RANGE.

SOURCE: P57, TIMBER:ITS NATURE AND BEHAVIOUR

DIAG.09 MICROSCOPIC STUDIES OF CHANGES IN CELL SHAPES WITH MOISTURE CONTENT

DESORPTION. SOURCE:P29-37, SHRINKAGE OF TRACHEID CELLS WITH DESORPTION VISUALIZED BY CONFOCAL LASER SCANNING MICROSCOPY

DIAG.10 MAGNIFIED WOOD SECTION SOURCE:HTTP://WWW.SWST.ORG/TEACH/TEACH2/PROPERTIES2.PDF

PIC.16 SERIES OF IMAGES SHOWING TIMBER STORAGE YARDS.

PIC.17 MICRO-IMAGE OF THE CELLULAR STRUCTURE IN A PIECE OF WOOD.

PIC.18 MICROSCOPIC STUDIES OF CHANGES IN CELL SHAPES WITH MOISTURE CONTENT DESORPTION.

1 HYGROSCOPIC DEFINITION. SOURCE: P50, TIMBER:ITS NATURE AND BEHAVIOUR.

2+3 MOVEMENT IN TIMBER. SOURCE: CHAPTER 4, TIMBER:ITS NATURE AND BEHAVIOUR.

4 P29-37, SHRINKAGE OF TRACHEID CELLS WITH DESORPTION VISUALIZED BY CONFOCAL LASER SCANNING MICROSCOPY.

026 PRINCIPLES OF TIMBER BEHAVIOUR

The forest and timber industry take great care storing green and treated wood to minimise defects such as warping or splitting that may compromise the performance of the piece. When a piece of wood is sheltered from direct sun and rain, and depending upon the relative humidity and air temperature, the piece will attain a specific moisture content. Thus a piece of wood shrinks as it loses moisture and swells as it gains moisture. The industry goes to great lengths storing timber in a controlled manner and producing products such as plywood that alternate the direction of layers to control the warping of a panel. In reaction to this principle the thesis questions whether warping as a normally undesirable but natural behaviour of wood may be controlled to produce curved pieces of timber.

The way in which wood grows and displays complex behavioural patterns is founded upon the structural arrangement and functions that the cells of wood perform as the former living biological tissue of a tree. Hygroscopy and Anisotropy are two principles that have been increasingly researched to help explain how wood behaves.

Timber is Hygroscopic meaning it will gain moisture if dry or yield moisture if too saturated until the moisture content in the wood is in balance with the water pressure vapour of the surrounding atmosphere.1 The amount of water at this point of balance is called the equilibrium moisture content (EMC) and is always below 30% for a piece of seasoned timber. When a tree is freshly felled and is therefore un-seasoned or treated, its wood is called green wood and has a much higher MC ranging from 60 to 200%. The EMC that a piece of wood achieves depends on the relative humidity and temperature of the surrounding air. The relationship between moisture content, temperature and relative humidity is shown in DIAG.07. The chart for example documents that if a cut piece of wood is placed in an environment where the temperature is 50 0C and 55% relative humidity, it will either gain or lose water until it reaches approximately 8.75% moisture content.2

CHART SHOWING THE RELATIONSHIP BETWEEN THE MOISTURE CONTENT OF WOOD AND THE TEMPERATURE AND RELATIVE HUMIDITY OF THE SURROUNDING AIR. VALUES ARE BASED ON THE DRYING OUT OF GREEN WOOD. THE TREND IS FOR EMC TO INCREASE AS RELATIVE HUMIDITY INCREASES AND TEMPERATURE INCREASES.

CHART DOCUMENTING THE AVERAGE DESORPTION ISOTHERM FOR SIX DIFFERENT SPECIES. THE CURVE SHOWS THE AVERAGE BEHAVIOUR OF THE PIECES AT 40�C AND BLUE HIGHLIGHTED AREA THE CHANGE IN BEHAVIOUR BETWEEN 15�C AND 70�C.

THE AMOUNT OF WATER IN WOOD EXPRESSED AS A PERCENT OF THE DRY WEIGHT IS CALLED THE “MOISTURE CONTENT” MOISTURE CONTENT IS CALCULATED WITH THE FOLLOWING FORMULA:

WEIGHT OF WATER IN WOOD

MOISTURE CONTENT (%) = WEIGHT OF TOTALLY DRY WOOD

WOOD A LIVING CELLULAR TISSUE

Water is not only found in the cells of a tree but also in the cells’ cavity walls. As soon as a tree is felled and the processing of timber pieces starts, the wood begins to negotiate moisture equilibrium with the environment. Whether the wood is dried naturally or within a kiln the water will first leave the piece from the cell cavities. This is known as free water and is not held by any forces but is comparable to water in a pipe. Free water loss has no effect on the dimensional change or structural integrity of the wood. However the amount of free water lost is considerable and the moisture content of the whole piece drops to between 30% and 27% (first stage of timber seasoning). The remaining moisture is held within the walls of each cell bonded by forces between the water and cellulose molecules. This is called bound water and the cells are at ‘fibre saturation point’ as there is no free water and the cell walls are saturated with the maximum amount of water. Moisture Content loss from this point will only be from the bound water in the cell walls. As moisture is lost and the cell walls begin to shrink they also become stronger as the microfibrils comprising the walls contract closer together. Even after a process of drying is complete, wood will continue to shrink and swell as relative humidity varies and water either leaves or enters the cell walls. The rate at which absorption and desorption takes place differs but follows an s-shaped relationship as shown in DIAG.08.3 Research undertaken in DIAG.09 highlights that the cell walls all react at uneven and irregular rates but it is the changes at the micro-cellular scale that inevitably cause timber to be dimensionally unstable.

The closely packed fibrous composition of cells in wood defines the anisotropic characteristics which informs different directional behaviours of the material depending upon the grain orientation. The strength of wood is highest and most resistant to bending when the forces are oriented parallel to the grain direction. The images show that the length of cells, the thickness of the cell walls, type of cells (early and late wood types) are all contributing factors to distinct patterns of variation which determines the directional deformations that occur in a piece of wood.

VARIABLE MOISTURE CONTENT BY CLIMATE

Values for temperature and relative humidity vary depending upon the climatic conditions for different geographical locations on the Earth. DIAG.14 to the right, documents the variation between three different locations and localised changes in climate for the different months of the year. The Köppen climate classification has five different categories of classifying climates.1 London is a temperate oceanic climate, Sao Paulo a humid subtropical climate, and New York a humid continental climate. These different classifications have very different conditions and the diagram shows that moisture content will fluctuate constantly as it is directly associated to temperature and relative humidity changes throughout the month and of each day of the year.

JOHANNESBURG

SYDNEY

MOSKOW

BERLIN

ROME

INSTAMBUL

BEIJING

STOCKHOLM

VIENNA

LOS ANGELES TOKYO

SANTIAGO

BANGLADESH

SAO PAULO

MEXICO CITY

LONDON

MADRID

PARIS

JOHANNESBURG

SYDNEY

MOSKOW BERLIN

SANTIAGO

BANGLADESH

SAO PAULO

MEXICO CITY

LONDON

MADRID

PARIS

JOHANNESBURG

SYDNEY

MOSKOW

BERLIN

ROME

INSTAMBUL

BEIJING

STOCKHOLM

VIENNA

LOS ANGELES

TOKYO

DIAG.14 LOCATION SPECIFIC TEMPERATURE, HUMIDITY AND MOISTURE CONTENT VARIATION. SOURCE: WWW.WOODCHANGES.COM

DIAG.15 WOOD RELATIVE DIMENSIONAL CHANGE DEPENDENT ON TYPE OF SHRINKAGE FACTOR, WEATHER CONDITIONS(IN THIS CASE LOCATION) AND ANNUAL PERIOD. SOURCE: WWW.WOODCHANGES.COM

BANGLADESH

SAO PAULO MEXICO CITY

MADRID PARIS

JOHANNESBURG SYDNEY

STOCKHOLM

VIENNA

LOS ANGELES

TOKYO

SANTIAGO

BANGLADESH

SAO PAULO

MEXICO CITY

LONDON

MADRID

JOHANNESBURG

LOS ANGELES

TOKYO

NEW YORK

SANTIAGO

BANGLADESH

SAO

LONDON

MADRID

JOHANNESBURG

1 KÖPPEN–GEIGER CLIMATE CLASSIFICATION SOURCE: PEEL, M. C. AND FINLAYSON, B. L. AND MCMAHON, T. A. UPDATED WORLD MAP OF THE KÖPPEN–GEIGER CLIMATE CLASSIFICATION.

TIMBER DIMENSIONS BY LOCAL ENVIRONMENT

With the understanding that moisture content varies by climate and geographical location, if the same piece of timber is placed in different environments around the world the dimensions of the piece will change due to hygroscopic action. DIAG.15 displays the range of dimensional change as maximum swelling and minimum shrinkage for a spruce species piece of wood throughout the months of the year for London, Sao Paulo and New York. Relative to the changing temperature, humidity and moisture content by location, the dimensions of the wood will change by differing degrees of motion within the tangential and radial directions. This again suggests the importance of understanding that the way in which the tree log is cut and processed will have an impact upon the behaviour of the timber piece.

planed

032

PROCESSING OF TREES TO TIMBER

In recent times the harvesting and processing of trees to timber has been driven by the sustainable need to maximise the use of a wooden log and minimise wastage. There are many different techniques and cut methods for creating the wide range of solid timber products now available. Striving to create the most efficient use of a tree, the industry is increasingly moving away from cutting large solid wood sections which is difficult to attain without some wastage. Modern production methods include using compound sections that constitute individual segments fixed together as elements, or glulam products which glue multiple thinner solid sections of wood together.

ARCHITECT

YEAR OF COMPLETION LOCATION

BUILDING TYPE

DESIGN STRUCTURE

JÜRGEN MAYER-HERMANN

2011

SEVILLE, SPAIN

A MIXED USE STRUCTURE CREATES AN ELEVATED PLAZA

ROOF CANOPY APPROXIMATELY 26 M HIGH BONDED TIMBER CONSTRUCTION WITH POLYURETHANE COATING, 3000 CONNECTIONS

ARCHITECT

YEAR OF COMPLETION LOCATION

BUILDING TYPE

DESIGN STRUCTURE

AA’S INTERMEDIATE UNIT 2, LED BY TUTORS CHARLES WALKER AND MARTIN SELF

2007

LONDON, UNITED KINGDOM

SUMMER PAVILION FOR SOCIAL GATHERING DOME LIKE PAVILION REACHING 4.3 M HIGH

A COLLECTION OF FREE FROM SOLID STRANDS OF LAMINATED TIMBER SHEETS WHICH ARE STAIGHT, SINGLE CURVED OR DOUBLE CURVED

ARCHITECT

YEAR OF COMPLETION LOCATION

BUILDING TYPE

DESIGN STRUCTURE

KYEONGSIK YOON (KACI INTERNATIONAL) & SHIGERU BAN ARCHITECTS

2008

YEOJU, SOUTH KOREA

A CANOPY THAT CARRIES THE ROOF OF THE FACILITY

BUILDING FOR THE GOLF CLUB

ROOF CANOPY REACHING 14 M HIGH, 21 SLENDER COLUMNS SUPPORT 32 ROOF ELEMENTS, MADE OF WOVEN TIMBER GLUELAM GIRDERS

LAMINATED TIMBER SHEETS WITH CNC CUT PROFILES LAMINATED TIMBER SHEETS WITHIN A CUSTOMISABLE JIG

SOLID TIMBER SECTION MILLED TO SHAPE

METROPOL PARASOL IS FORMED THROUGH THE CREATION OF A COMPLEX SURFACE THAT IS SECTIONED AT INTERVALS IN PERPENDICULAR CROSS DIRECTIONS. THIS GENERATES PLANAR PANELS, WHICH WHEN CNC CUT CAN BE INTERLOCKED.

BAD HAIR PAVILION ADAPTS THE LAMINATION PROCESS AS USED IN FURNITURE MANUFACTURING TO CREATE BUILDING SCALE ELEMENTS. INDIVIDUAL DOUBLY CURVED BEAMS ARE MANUFACTURED USING CUSTOM MADE JIGS AND STRAP APPLIED PRESSURE TO ENSURE COMPACT LAMINATION.

NINE BRIDGE CLUB HOUSE IS A DOUBLY CURVED SURFACE THAT IS PRECISELY DESCRIBED BY AN INTERLOCKING DOUBLY CURVED GRID SHELL. EACH BEAM IN THE GRID IS OF A DOUBLY CURVED FORM CNCMILLED FROM SOLID GLULAM BLOCKS OF TIMBER.

DIFFERENT FABRICATION METHODS FOR EACH OF THE CHOSEN KEYSTUDIES.

PIC.22 METROPOL PARASOL

BAD HAIR PAVILION

NINE BRIDGE CLUB HOUSE

DOWNLAND GRIDSHELL

ARCHITECT

YEAR OF COMPLETION

LOCATION

BUILDING TYPE

DESIGN STRUCTURE

EDWARD CULLINAN ARCHITECTS AND BURO HAPPOLD ENGINEEERS

2002

WEALD & DOWNLAND MUSEUM, UNITED KINGDOM MUESUM AND WORKSHOP SPACES

6M HIGH TRIPLE BULB LATTICE A DOUBLE LAYERED GRIDSHELL OF OAK LATHS INITIALLY FORMED FLAT AND GRADUALLY BENT INTO SHAPE THROUGH A SYSTEM OF NODES

IN-SITU BENDING OF OAK LATHS

THE DOWNLAND GRIDSHELL UTILISES THE BENDING PROPERTIES OF GREEN OAK TO CREATE A TRIPLE BULB DOUBLY CURVED FORM. A LAYERED LATTICE OF OAK LATHS ARE INITIALLY LAID FLAT AND ELEVATED TO THE FINISHED STRUCTURE HEIGHT. UTILISING A PROP SYSTEM THE INTERLOCKING OAK STRIPS ARE GRADUALLY BENT INTO SHAPE THROUGH A NETWORK OF LOCKING NODES.

FABRICATING LARGE COMPLEX GEOMETRIES

There are relatively few examples of large scale complex geometrical structures manufactured in timber. These four examples, DIAG.18 documents some of the most expressive curving wood structures currently built. They also reveal the limitations of different wood fabrication methods by either the geometrical form created or the fabrication process used.

Metropol Parasol approximates a complex geometrical form through the employment of flat interlocking panels. None of the timber panels actually curve to create the structure. The Bad Hair Pavilion utilises some of the anisotropic properties of wood to aid the bending and twisting of individual laminate layers. However the technique is extremely labour intensive and time consuming as hot or cold presses cannot be used to clamp and apply pressure to the form. Whilst the CNC milling method used for creating the doubly curve beams in Nine Bridge Club House formulates the appearance of doubly curving wood, the manufacturing process generates much waste material and neglects the behavioural properties of wood to twist and bend. The form could have equally been created from an alternative material. The Downland Gridshell is a good example of combining wood properties and fabrication techniques. Employing the hygroscopic properties of green oak, freshly felled and containing moisture content close to 30%, the wood laths are more pliable to bending. This aids the process for pulling the lattice down into place before the moisture content of the oak equalises with the surrounding environment. Whilst holding the potential to create different doubly curved surfaces the lattice is restricted to defining single surfaces which have gradual curvature change as the solid green oak laths have bending limitations.

PIC.26 FORTUNE COOKIE STOOL, DESIGNED BY PO SHUN, 2008.          PIC.27 CHURCH OF CHRIST THE WORKER BY ELADIO DIESTE, ATLANTIDA, URUGUAY, 1958-60.

PIC.28 NAUTILUS SEA SHELL SECTION.          PIC.29 “A MATTER OF TIME” BY RICHARD SERRA, OPENED JUNE 8 AT THE GUGGENHEIM MUSEUM IN BILBAO. THIS MEGA-INSTALLATION OF EIGHT BENT STEEL SCULPTURES IS CONSIDERED THE LARGEST INSTALLATION TO EVER BE HOUSED IN A MUSEUM GALLERY.

GEOMETRY

Research technologies have aided the progress of fabrication industries in recent years to make the manufacturing of complex geometries more accessible. Design trends and designers needs to explore geometrical organisations, other than those orthogonal, have created a demand for the manufacture of curved building elements. The more precise level of control achieved through digital means of fabrication has instigated the manufacture of more ergonomic, compact and detailed products and furniture. At the building scale geometry plays a vital role in determining the performance of a buildings operation functionally, structurally and environmentally. Embracing complex geometries may reveal a more responsive and exploratory framework for creating spatial models of variation and interest. A change of formulating space from rectilinear ideals towards curved geometry potentially leads to new categories of space and use.

STRUCTURAL PERFORMANCE

Geometry has a profound effect on the structural performance of all forms found in nature or manmade. Whether it is a seashell that needs to protect its occupant from the attack of predators, a chair that has to support a person sitting on it, or a wall in a building that supports not only it’s self weight but also prevents the rest of the building from collapsing, geometry plays a vital performance role.

The potential for geometrical variation within design systems may improve the structural performance and efficient use of material. Nature very rarely deploys homogenous materiality in form or composition to deliver function and performance. The building industry repeatedly increases the thickness of material in rectilinear formations to attain structural stability. However the introduction of even the smallest curved geometries would allow for more efficient structures to be built in terms of material use and performance. For example in the case of the Fortune Cookie Stool, PIC.26, inducing a curvature into the backrest helps to overcome bending moments when the load of a person is applied. Similarly, the expressive curved walls in the Church of Christ The Worker, PIC.27, integrate a geometry which is more resistant to shear forces and buckling within a relatively small structural thickness of bricks. Whilst traditionally the building industry has been opposed to more expressive geometries for reasons of cost and complexity, the advances made in geometrical exploration, material understanding and fabrication research may now make this very achievable.

IN SITU WOOD BENDING

THIS TECHNIQUE INVOLVES DELIVERING STRAIGHT PIECES OF PLYWOOD, CUT WITH SLITS TO AID BENDING, TO A BUILDING SITE WHERE WATER IS APPLIED TO THEM. THE APPLICATION OF MOISTURE MAKES THE SHEETS MORE PLIABLE FOR INDUCING CURVATURE WHEN FORCE IS PHYSICALLY APPLIED AND THE GEOMETRY IS THEN LOCKED INTO PLACE.

STEAM WOOD BENDING

IN THIS METHOD STRIPS OF WOOD ARE PLACED IN A STEAM BOX, WHERE HEAT AND MOISTURE INFILTRATES THE WOOD. THIS MAKES THE WOOD MORE PLIABLE AND ALLOWS THE TIMBER STRIPS TO BE EASILY BENT AROUND A MOULD. STEAM BENDING IS LIMITED BY THE DEGREE OF CURVATURE THAT TIMBER ELEMENTS CAN ACHIEVE AND IS MAINLY USED IN BOAT BUILDING, FURNITURE AND MUSICAL INSTRUMENT MANUFACTURE.

LAMINATION & PRESS BENDING

PRESSURE APPLIED LAMINATION IS A VERY COMMON TECHNIQUE FOR FABRICATING FURNITURE. THE TECHNIQUE UTILISES MULTIPLE LAYERS OF THIN VENEER LEAVES WHICH ARE LAYERED TOGETHER WITH GLUE. WHILST THE LAMINATE IS STILL WET IT IS PLACED OVER A FORMING MOULD AND AN INDUSTRIAL PRESS IS APPLIED SO THE WOOD ASSUMES THE MOULDS SHAPE. THIS TECHNIQUE IS A VERY EFFICIENT METHOD OF FABRICATION WHEN MULTIPLE COPIES OF THE SAME ITEM NEED TO BE MANUFACTURED. A HIGH NUMBER OF IDENTICAL ITEMS IS REQUIRED AS THE PRICE OF THE MOULDS AND FABRICATION SET UP CAN BE VERY HIGH.

LAMINATION & VACUUM PRESSURE BENDING

VACUUM PRESSURE BENDING IS SIMILAR TO THE LAMINATION PROCESS THAT USES AN INDUSTRIAL PRESS, BUT UTILISES A VACUUM SEAL TO APPLY THE PRESSURE. VENEERS ARE PLACED IN A SEALED BAG TOGETHER WITH THE FORM MOULD. AIR IS THEN REMOVED FROM THE BAG WHICH INDUCES A FORCE BIG ENOUGH TO BEND THE VENEERS AROUND THE MOULD. THIS TECHNIQUE IS ESPECIALLY USEFUL WHEN VERY LARGE PIECES NEED TO BE LAMINATED. EXAMPLES OF 35 METER LONG FIBRE GLASS PROPELLERS ARE KNOWN TO BE LAMINATED USING THIS TECHNIQUE.

COMPOSITE MATERIAL CONSTRUCTION

UPM GRADA IS A COMPOSITE PLYWOOD MATERIAL WHICH ALLOWS CURVATURE TO BE INDUCED INTO A WOOD PANEL WITH THE APPLICATION OF HEAT AND PRESSURE. A THERMOPLASTIC FOIL IS PLACED BETWEEN CROSS BONDED ROTARY CUT BIRCH VENEER LAYERS WHEN THEY ARE MANUFACTURED AS FLAT PANELS OF PLYWOOD. TO APPLY CURVATURE TO A PANEL IT IS FIRST HEATED UP TO 130 °C. AT THIS TEMPERATURE THE FOIL MELTS ALLOWING THE VENEERS TO SLIDE. THE HOT PANEL IS THEN PLACED INTO A PRESSURE MOULD AND LEFT TO COOL DOWN.

BENDING WOOD TECHNIQUES

Wood is a material which by nature expands, shrinks and bends. Focusing on the use of veneers, there are several fabrication methods used by different industries that make use of woods hygroscopic and anisotropic properties in order to manufacture curved elements. Each method has limitations and application restrictions. Lamination is currently the most common method for fabricating single and doubly curved geometries out of timber. Whilst in-situ bending and steam bending apply post curvature to pieces or flat sheets of cross laminated veneer such as plywood, the direct lamination of veneers around a mould, allows for a much greater control of material and geometrical form. To bridge the gap between these two methods new composite plywood sheets are being developed to achieve tighter and more complex curvatures without the need for applying wet glue.

DIAG.19 ASSEMBLY LOGIC OF THE CHAISE LOUNGE.

DIAG.20 LAMINATION ELEMENTS AND FIBRE ORIENTATION OF COMPONENTS COMPRISED IN THE ASSEMBLY OF THE CHAISE LOUNGE.

PIC.35 SERIES OF VIEWS OF THE 1:5 CHAISE LOUNGE PROTOTYPE.

PIC.36 SIDE VIEWS OF THE 1:1 CHAISE LOUNGE PROTOTYPE. LAMINATED PLYWOOD.

PIC.37 CHAISE LOUNGE CONCEPT VISUALISATION.

KEYSTUDY : CHAISE LOUNGE

Our first experience researching and working with wood fabrication techniques was for the seating of a Pop-Up Cinema project in Gillett Square, Dalston, London. A chaise lounge wave design concept was developed to provide the user with a comfortable and embracing form on which to sit and enjoy the film. Whilst the curve of the top piece undulates to hold the user, an interlocked system of three waves distributes the users load to the ground, DIAG.19.

The chair utilised 3mm thick layers of plywood which were laminated together in different numbers of layers for the three wave components and bracing seat deck. In order to induce the required curvature into the components, three individual jigs were built. Strips of plywood were then laminated in the jigs and notches cut for the pieces to slide together. Individually each component of the system was flexible, but once the pieces were connected together, the components interlocked as one system, providing the assembly with enough strength and stiffness to assume the weight of the user.

Grain orientation of the wood played a crucial part in the fabrication process, DIAG.20. Bending strips of plywood parallel to the grain direction allowed for tighter curvatures to be achieved, but reduced the stiffness of each piece. Whilst the magnitude of the curvatures in the three wave strips was too tight to introduce alternating plywood pieces with perpendicular grain direction, the deck combined a cross lamination assembly to increase the stiffness of the plate.

041

PIC.38 JIG OF THE CHAISE LOUNGE’S UPPER PART.

PIC.39 UPPER PART REMOVED FROM THE JIGS.

PIC.40 MIDDLE WAVE OF THE CHAISE LOUNGE IS REMOVED FROM THE JIG.

PIC.41 FINAL SIDE WAVE IS LAMINATED.

PIC.42 LAMINATION PROCEDURE

DETAILING: CLAMPING THE POSITIVE AND NEGATIVE JIG.

PIC.43 LAMINATION PROCEDURE

DETAILING: LOCAL DELAMINATION.

PIC.44 FINAL PRODUCED PARTS FOR THE CHAISE LOUNGE AND POSITIVE PART OF JIGS FOR THE WAVES.

PIC.45 BOTH PARTS OF EACH OF THE TWO JIGS NEEDED FOR THE LAMINATION OF THE WAVES.

PIC.46 REAL SCALE PROTOTYPE TESTING ON LOADING.

FABRICATION OBSERVATIONS

Working with wood through a hands on approach to build the chair, exposed some vital findings. Whilst we found the fabrication process to be very labour intensive and time consuming, it was easy to envisage the same procedure being adapted to the industrial scale for the manufacture of multiple copies. However the process also highlighted the difficulties in thinking this manufacturing process could be applied to large curving timber components at the building scale. The quantity of material and size of formwork required in the process combined with the power required to physically bend larger sheets of plywood would inevitably lead to an increase in costs and time. The work required to create three formworks emphasised that every time a different curvature was required another formwork would need to be machined and assembled. This was seen as a large restriction regardless of the applications scale and could only be overcome with the use of an adjustable formwork jig or exploring an alternative way of inducing curvature in laminated timber elements.

045

FURNITURE SCALE

PAVILLION SCALE

DWELLING SCALE

MULTI-DWELLING SCALE

TIMBER APPLICATIONS SCALE

The use of laminated timber is apparent at many different scales of design. In the furniture industry there are many elegant and original solutions for bending and curving wood to make chairs and tables. There are also several examples showcasing the innovative use of laminated timber for pavilions or at the scale of a single house. The properties of wood are used here as a means to create novel morphologies and spatial conditions. Above this scale however there are very few examples of buildings that assemble to reveal different but exciting spatial conditions within the same system. Whilst there are many examples of large spanning roofs that cover single spaces there are few which accomodate different functions and uses. The tallest timber building is located in London in the borough of Hackney. This 9 storey apartment block is built from Cross Laminated Timber panels, PIC.54, organised to define apartments and rooms. There are several planned projects that aim to surpass the current record height, such as The Centre for Cultural and Innovative Interchange Between Russia and Norway in Kirkenes, Norway, PIC.55 and PIC.56, which will stand at 17 stories high. However built or planned none of these buildings explore the anisotropical properties and potentials of wood, limiting their application to standard engineered timbers and orthogonal geometries.

MULTI-FUNCTIONAL

PIC.47 LOUNGE CHAIR DESIGNED BY GRETE JALK IN 1963, BEND PLYWOOD, BACK DETAIL.

PIC.48 LOUNGE CHAIR DESIGNED BY GRETE JALK IN 1963, BEND PLYWOOD.

PIC.49 TEMPORARY RESEARCH PAVILION (STUTTGART, GERMANY), DESIGNED AND FABRICATED BY INSTITUTE FOR COMPUTATIONAL DESIGN (ICD) AND THE INSTITUTE OF BUILDING STRUCTURES AND STRUCTURAL DESIGN (ITKE), TIMBER PAVILION USING 6.5 MM THIN BIRCH PLYWOOD SHEETS.

PIC.50 TEMPORARY RESEARCH PAVILION (STUTTGART, GERMANY), DESIGNED AND FABRICATED BY INSTITUTE FOR COMPUTATIONAL DESIGN (ICD) AND THE INSTITUTE OF BUILDING STRUCTURES AND STRUCTURAL DESIGN (ITKE), INTERIOR SPATIAL CONDITIONS.

PIC.51 FABLAB HOUSE (CAMPO DEL MORO ,MADRID, SPAIN), DESIGNED AND FABRICATED BY INSTITUTE FOR ADVANCED ARCHITECTURE OF CATALONIA, THE CENTRE FOR BITS AND ATOMS AT MIT AND THE GLOBAL FAB LAB NETWORK, SELF SUFFICIENT SMALL SCALE DWELLINGMADE OF 2.5M X 12M LVL (LAMINATED VENEER LUMBER) PANELS + CURVABLE PLYWOOD.

PIC.52 FABLAB HOUSE (CAMPO DEL MORO ,MADRID, SPAIN), DESIGNED AND FABRICATED BY INSTITUTE FOR ADVANCED ARCHITECTURE OF CATALONIA, THE CENTRE FOR BITS AND ATOMS AT MIT AND THE GLOBAL FAB LAB NETWORK, SMALL SCALE STRUCTURAL PROTOTYPE.

PIC.53 THE STADTHAUS (LONDON, UK), DESIGNED BY WAUGH THISTLETON ARCHITECTS ,RESIDENTIAL NINE STOREY TIMBER STRUCTURE USING CROSS-LAMINATED TIMBER PANEL SYSTEM.

PIC.54 THE STADTHAUS (LONDON, UK), DESIGNED BY WAUGH THISTLETON ARCHITECTS, INTERIOR SPACE DURING CONSTRUCTION.

PIC.55 CENTRE FOR CULTURAL AND INNOVATIVE INTERCHANGE BETWEEN RUSSIA AND NORWAY (KIRKENES, NORWAY), DESIGNED BY REIULF RAMSTAD ARCHITECTS, 16-17 STOREY BUILDING, UNMATERIALIZED.

PIC.56 CENTRE FOR CULTURAL AND INNOVATIVE INTERCHANGE BETWEEN RUSSIA AND NORWAY (KIRKENES, NORWAY), DESIGNED BY REIULF RAMSTAD ARCHITECTS, 16-17 STOREY BUILDING, UNMATERIALIZED.

PROJECT SCALE AMBITION

The complexities of a residential programme create an ideal test bed to explore new models of inhabitation in morphologically complex environments. Our project aims to double the height of the Hackney Stadhaus. A building of 20 stories will be designed as a test model for a material system which exploits the inherent anisotropic properties of wood to curve, and depart away from orthogonal geometries. With the intent for achieving efficient structural performance and exciting spatial arrangements a building system will be created on the foundations of material component research.

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DIAG.22 MULTIPLE LAYERS OF DIFFERENT ORIENTATION ARE LAMINATED TOGETHER SHAPING THE AEREAL PROPELLAR.

PIC.57 DETAIL DRAWINGS BY M.N.NUNK, 1949.

MATERIAL SYSTEM AMBITION

In 1949 Max Munk applied his design for a new wooden propeller blade to the United States Patent Office in order to protect it. The design sought to improve the performance of the propeller and alleviate some of the stresses which flowed through other designs where the layers were laminated perpendicular to each other. He was aware that wood being a fibrous material had a greater stiffness in the direction of the fibres and the angle through which layers of wood are laminated together would affect the performance of the propeller. Through laminating twelve layers of wood with alternating layers rotated diagonally rather than at right angles to each other, a more elastic behaviour could be achieved. Thus as the thrust of the engine increased and the propeller spun faster, the organisation of the wooden layers would accommodate for a small elastic twist and allow the propeller to spin more efficiently.

The ambition of our project is to investigate a material defined architecture in which structure, spatial organisation, physical performance and fabrication are conceived as an integrated system. In a similar manner to the propellar, combining material knowledge with design application and development, the work seeks to explore how the microscopic behavioural traits of wood and fabrication methods may combine to create new curved building components.

METHODS

Very few materials have homogenous properties that can be applied to any form and function. The methodology for the thesis research aims to utilise the dimensional instability behavioural properties of wood to program a material component that displays variation and adaption for application within the material system of a twenty story timber residential tower. The project seeks to unite the knowledge of physical material studies as a driver for computational design and performance exploration. This chapter documents the methods and steps taken to develop such an approach through seven interrelated methods of research.

- Physical Experimentation forms the basis of the project and aims to understand the behavioural trends of wood and parameters that may program a conceptual material component.

- Digital Simulation draws upon the parameters found in initial physical research as inputs for a computational simulation method that can efficiently test many different experiments.

- Physical-Digital Calibration seeks to establish and calibrate the key parameters that define the material component both as physically fabricated pieces and computationally simulated pieces.

- Component Analysis aims to quantify the mechanical and physical properties of the material component and scale limitations for application.

- Structural System Research examines the context of the design application and the suitability of the material component to act as part of a structural system to meet the performance led demands.

- Geometrical System Research explores the computational development of a material and structural system that displays variant morphological expressions that are adaptable to different requirements of space and function.

- System Evaluation applies the material component and system within the context of a test case project to understand the adaptability, emerging potentials and constraints of the system and how this may influence an iterated design.

METHODS

PHYSICAL EXPERIMENTS

• UNDERSTANDING BEHAVIOUR OF WOOD

• UNDERSTANDING PARAMETER OF TIMBER COMPONENTS

RESEARCH DEVELOPMENT

DIGITAL SIMULATION

• CONTROLING PARAMETERS OF TIMBER COMPONENTS

PHYSICAL - DIGITAL CALIBRATION

• SYNCHRONISATION OF PARAMETERS THAT DESCRIBES THE MATERIAL BEHAVIOUR OF THE COMPONENT IN BOTH ENVIRONMENTS

• UNDERSTANDING MECHANICAL PROPERTIES OF THE COMPONENT

• UNDERSTANDING PHYSICAL PROPERTIES OF THE COMPONENT

• UNDERSTANDING SCALE CONSTRAINTS

DESIGN DEVELOPMENT

STRUCTURAL SYSTEM RESEARCH

• POTENTIALS OF COMPONENTS TO ACT AS PART OF STRUCTURAL SYSTEM

• EXISTING TIMBER STRUCTURES

• EXISTING STRUCTURAL SYSTEMS IN RESIDENTIAL STRUCTURES

• MORPHOLOGICAL EXPRESSION UPON THE CONSTRAINTS OF THE MATERIAL AND STRUCTURAL SYSTEM, SPATIAL ORGANISATION AND FUNCTION

DESIGN PROPOSAL

• EMERGING POTENTIALS AND CONSTRAINTS OF THE SYSTEM

• POSSIBLE APPLICATIONS OF THE SYSTEM IN THE CONTEXT OF SPECIFIC FUNCTIONS AND PERFORMANCE DEMANDS

• ADAPTATION OF GEOMETRICAL SYSTEM TO MEET TECHICAL REQUREMENTS

METHODS FLOWCHART

METHODS

PHYSICAL EXPERIMENTS

Embracing the hygroscopic and anisotropic properties of wood a series of physical experiments may be undertaken to understand how moisture content, grain direction and fabrication techniques may programe laminated pieces of veneer to curve and twist. From the conception and development of different material components it is vital that the parameters used to define the pieces are quantifiable and have the potential for creating a range of results.

Commencing the research with the physical testing of wood and lamination fabrication methods seeks to prioritise these disciplines as the generative context for a more integrated design process.

DIGITAL SIMULATION

Limited by time, material and scale of physical testing, digital simulation offers a technique for efficiently pursing the experimentation of virtual timber components founded on the parameters discovered by physical experimentation.

Finite Element Analysis (FEA) software is used within the construction industry for the structural analysis and performance testing of designs. Traditionally FEA software is employed to check for the deflection of structural members when loaded and test for areas of structural failure. In the case of this research FEA is explored as a tool for simulating the behavioural nature of hygroscopic and anisotropic characteristics in pieces of laminated veneers. The objective for the exercise is to gain a closer understanding as to which parameters not only influence the curvature of laminated veneer components but may also be programmed.

PHYSICAL - DIGITAL CALIBRATION

Combining physical tests and digital simulations may focus a common set of rules from which a material component may be manufactured.

Physical testing is the only real means through which a material component can be proven in manufacture and operation. The computation of parameters which describes the design and manufacture of a material component will open a broader information resource through which different applications are able to be explored. If physical and digital experiments are successfully calibrated then a very powerful tool may be developed that is ensured to create the same material component results in both workspace environments.

RESEARCH DEVELOPMENT

This chapter documents the many experimental procedures that were undertaken with the aim to comprehend the complex behaviour of wood when exposed to moisture. Initial physical experiments revealed that curved strips could be created through a process of differentially soaking layers of veneer to achieve differing moisture contents, gluing and then laminating the pieces together with an elasticised clamping method.

Research Development attempts to understand which of many different parameters would affect the curvature of a veneered piece, the material component. A series of experiments were undertaken trying to explore the numerous parameters that could potentially program a component and utilise those that were quantifable to bring control over the fabrication process. The method for quantifying material information data combined parallel experiments undertaken with physical material testing and digital simulations. Successful calibration between these two fields could then be employed to form a matrix of relationships between the key influencing parameters.

STRIP OF ASH VENEER IS CUT TO A RECTANGULAR SHAPE OF 100 BY 100 MM AND THE MEASUREMENTS WERE RECORDED TO SEE HOW MUCH THE PIECE EXPANDS IN EACH AXIS.

THE SAMPLE IS TAKEN WITH A PREDOMINENT GRAIN DIRECTION PARALLEL TO ONE SIDE AND LITTLE VARIATION OF THE GRAIN DENSITY ALONG THE ENTIRE PIECE.

IT IS 1.4 MM THICK AND COMES OUT OF A FLAT CUT STRIP, WHICH IS IN A DRY STATE, MEANING ITS MOISTURE CONTENT IS AROUND 8% - 14% FOR THE INDOOR TEST ENVIROMENT.

THE SAMPLE PIECE IS SUBMERGED IN WATER FOR TEN MINUTES AND REMOVED.

OVER EXPOSING THE WOOD FIBRES TO MOISTURE ENSURES THE CELLS WILL REACH THEIR SATURATION LEVEL, SINCE THE PIECE WILL ABSORB AS MUCH WATER AS POSSIBLE (APPROXIMATELY 28% MOISTURE CONTENT).

AS ALREADY MENTIONED IN THE DOMAIN CHAPTER, THE WOOD EXPERIENCES NO DIMENSIONAL CHANGE BEYOND THE SATURATION LEVEL, SINCE THE REDUNDANT WATER IS KEPT IN THE CELL CAVITIES WITHOUT CAUSING FURTHER FIBRE SWELLING.

ON WITHDRAWING THE SAMPLE SHEET, MEASUREMENTS ACROSS BOTH AXIS ARE TAKEN AND RECORDED.

THE PIECE NOW MEASURES 100MM BY 105.5MM, EXPANDING MINIMALLY IN THE DIRECTION OF THE GRAIN BUT 5.50% ACROSS THE GRAIN.

AS EXPECTED, DUE TO THE ANISOTROPY OF WOOD, THE PIECE PERFORMS DIFFERENTLY IN THE TWO AXIS. AT THE SAME TIME, THE EXPANSION OF THE PIECE IS NEITHER THE RADIAL (4.90%) NOR THE TANGENTIAL AMOUNT (7.8%), AS INDICATED IN DIAG.21 FOR ASH. INSTEAD THE 5.5% VALUE ATTAINED FROM THE EXPERIMENTS WAS A BLEND OF THOSE TWO VALUES. THIS RESULT REMAINED CONSTANT FOR 3 REPEATED EXPERIMENTS BASED ON THE SAME SETUP.

BEECH SPRUCE SCOTS PINE WESTERN RED CEDAR

OAK

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BEECH SPRUCE SCOTS PINE WESTERN RED CEDAR

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BEECH SPRUCE SCOTS PINE WESTERN RED CEDAR

OAK

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BEECH SPRUCE SCOTS PINE WESTERN RED CEDAR

OAK

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BEECH SPRUCE SCOTS PINE WESTERN RED CEDAR

OAK

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BEECH SPRUCE SCOTS PINE WESTERN RED CEDAR

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DIAG.23 BASIC PRINCIPLE OF PHYSICAL MATERIAL EXPERIMENTS.          DIAG.24 EXPANSION FACTORS FOR DIFFERENT SPECIES OF WOOD SOURCE : HTTP://WWW. WOODBIN.COM.

RELATIVE DIMENSION CHANGES FOR DIFFERENT TYPES OF WOOD PLACED IN THE ENVIRONMENT OF NEW YORK SOURCE : HTTP://WWW.WOODCHANGES.COM/

BASIC MATERIAL BEHAVIOUR PRINCIPLE

The basic principle of the physical experimentation is based on two main properties of wood : anisotropy and hygroscopy. As explained in DIAG.23, the dry ash veneer has a moisture content of around 8% - 19% when moisture equilibrium is reached with its surrounding environment.

When moisture is applied to the dry piece, it starts expanding, according to the moisture absorbed. The limit for the expansion is set at the fibre saturation point, which is around 28% moisture content. This indicates that 28% of wood’s weight is the weight of the water captured in the piece and only within the cell walls of its fibres. Therefore, if the moisture applied exceeds this amount, no further expansion is noticed, since the additional water, free water, is kept in cavities between the cells.

The micro change at the cellular level, shrinking and swelling, cause noticeable dimensional changes at the global component scale. This basic principle was found to be independent of the size of the piece and same behaviour occurred for pieces of different lengths when fully saturated.

The constant shrinkage factor is also referred to as expansion factor in the context of this project, the reciprocal action of swelling. DIAG.24 documents the constant factor through which wood shrinks tangentially and radially for different species of wood. The experiment also supports the notion explained in the domain that if the veneer cut from the trunk can reflect tangential or radial shrinkage, its degree of expansion may consistently be predicted. In the physical experiments a flat cut ash veneer was unfortunately used displaying a blend of those two values.

Equally important to the cut type of the veneers is the type of wood. As shown in DIAG.25, for the given environment of New York City showing specific temperature and relative humidity variations throughout the year, different species of wood have different relative dimensional changes.

INITIAL STATE : TWO STRAIGHT LAYERS OF VENEER

TWO STRIPS OF ASH VENEER ARE CUT WITH THE GRAIN PERPENDICULAR TO THE LONG AXIS. BOTH PIECES HAVE SAME WIDTH (60MM) BUT ONE OF THEM IS CUT SHORTER THAN THE OTHER (300MM AND 283MM).

STEP.01 : MOISTURE APPLIED TO ONE LAYER

WATER IS APPLIED TO THE SHORTER PIECE AND LEFT FOR THE WOOD CELLS TO ABSORB THE MOISTURE.

GRADUALLY THE PIECE EXPANDS TO REACH ITS SATURATION POINT. EXPANSION ACROSS THE GRAIN IS MINIMAL BUT BY 5.5% PERPENDICULAR TO THE GRAIN (FOR FLAT CUT ASH VENEER).

STEP.02 : WET LAYER EXPANDS

ONCE THE WET PIECE IS OF THE SAME LENGTH TO THE DRY PIECE (CALCULATED TO REACH ITS SATURATION POINT AT THAT LENGTH), PVA GLUE IS APPLIED TO THE DRY LAYER IN ORDER FOR THE TWO LAYERS TO BE LAMINATED.

STEP.03 : TWO LAYERS ARE LAMINATED TOGETHER

THE TWO PIECES ARE CLAMPED TOGETHER FOR 20 MINUTES, UNTIL PARTLY GLUED, AND THEN SET FREE TO DRY FURTHER.

STEP.04 : INNER LAYER CONTRACTS

AS THE PIECE BEGINS TO DRY, THE CELLS IN THE INNER WET LAYER LOSE MOISTURE, CAUSING IT TO SHRINK AND PULL THE OUTER LAYER INWARDS. AS A RESULT, THE PIECE BEGINS TO CURVE ALONG THE LONG AXIS.

FINAL STATE : PIECE IS CURVED

THE PIECE CONTINUES TO CURL UNTIL THE MOISTURE IN BOTH LAYERS EQUALISES WITH THE MOISTURE WITHIN ITS ENVIRONMENTAL CONTEXT.

FABRICATION PRINCIPLE          DIAG.26 GENERAL PRINCIPLE OF THE LAMINATION PROCEDURE BETWEEN TWO PIECES OF VENEER WITH DIFFERENT MOISTURE CONTENT.          PIC.61 CURVED MATERIAL COMPONENT OF TWO LAMINATED LAYERS OF ASH, 0.6MM THICKNESS EACH.

A Bi-Metallic Strip is comprised of two fused metal layers that when heated expand at different rates. The properties of the two layers are independent but when joined together exert influence upon each other. The metal with the lower coefficient of thermal expansion is overcome by the metal with the higher coefficient and is thus on the inside as it bends.

Inspired by the Bi-Metallic Strip logic this initial experiment, DIAG.26, explores the potential of applying moisture to one layer of veneer, causing it to swell and change length, and leaving the other one dry. When the two layers are laminated together and left to dry, the layer which has been subject to the added moisture content gradually dries out, causing the wood cells to shrink. Bonded together, the drying layer contracts pulling the drier piece into curvature. In the case of the two laminated veneers, the layer that pulls the piece to curve is the one situated on the inner side of the curve rather than the outer, as in the case of the Bi-Metallic Strip.

Whilst the initial experiments showcased a promising basic fabrication principle, multiple aspects needed to be addressed in order to gain control over the overall process and the produced pieces. Effects of de-lamination could clearly be seen suggesting methods for fabrication would need great improvement. Observations for development included controlling the required moisture to reach the desired length for each layer of veneer, trialling different types of glue and advancing the quality of lamination bonding. The experiment also raised questions of what potential application could be suitable for a curved wood component.

VENEER TYPE GRAIN ORIENTATION LAMINATION LAYERS

WALNUT BLACK G.O. 900

WALNUT BLACK G.O. 900

WALNUT BLACK G.O. 00

WALNUT BLACK G.O. 900

[L.01] 60.0 X 300.0 X 0.6 MM

[L.01] 60.0 X 310.6 X 0.6MM

[L.02] 60.0 X 300.0 X 0.6 MM

WALNUT BLACK G.O. 450

WALNUT BLACK G.O. 450

[L.01] 60.0 X 300.0 X 0.6 MM

[L.01] 60.0 X 300.9 X 0.6MM

[L.02] 60.0 X 300.0 X 0.6 MM

[L.01] 60.0 X 300.0 X 0.6 MM

[L.01] 60.0 X 300.6 X 0.6MM

[L.02] 60.0 X 300.0 X 0.6 MM

x y z x y z x y z x y z x y z x y z x y z x y z x y z x y z x y z x y z x y z x y z x y z x y z x y z x y z

STRAIGHT LAMINATION

CROSS LAMINATION

ANGLED LAMINATION 450

DIAG.27 USING THE SAME FABRICATION PROCESS (LAMINATION) MANIPULATING THE GRAIN ORIENTATION MAY PRODUCE DIFFERENT GEOMETRIES.

PIC.62 THREE MATERIAL COMPONENTS PRODUCED THE GRAIN ORIENTATIONS OF DIFFERENT VENEER LAYERS ( 0°, 45°, 90°)

PIC.63 SERIES OF COMPONENTS PRODUCED OUT OF THE SAME PROCESS. IN ALL CASES, GEOMETRIES WITH SIMPLE CURVATURES CAN BE PRODUCED.

GRAIN DIRECTIONALITY

The anisotropic properties of wood deduce that the grain directionality of the wood will affect how the piece may perform, in terms of deformation, bending and twisting, and structural performance. Three experiments were undertaken to document the effects of changing the orientation of the grain for two layers of Black Walnut veneer, 0.6mm thick, 300mm long and 60mm wide.

The first experiment, straight lamination, was created with the grain of both layers perpendicular to the long axis. When dried, the strip curves to complete more than a full radius. The component shows high compressive strength along its y axis, and low strength in bending on the x and z axis.

The second experiment, cross lamination, orients the grain of one layer parallel to the long axis and the other perpendicular. This caused the strip to curve less than the first one, but with a noticeable improvement in its ability of resisting bending along the x axis, whereas its loading capacity in compression along its y axis is slightly decreased.

The final experiment, angled lamination, oriented both layers through 450 degrees to the long axis and caused the strip to both bend and twist. In this case, the strip shows similar behaviour to the first experiment, though its compression strength is significantly decreased.

All the laminated pieces transformed to single curvature geometries, the first two displayed single curvature radial motion and the third twisted like a coil around a cylinder in a radial ruled surface motion. The results of manipulating grain direction within the three experiments displayed very different results and potentials for development. With the ambition to gain control over the component a decision was taken to progress the project’s research using the first experiment technique where all the veneer layers were laminated with the same grain orientation. This would allow the grain orientation variable to remain constant and the behaviour of other parameters to be studied in more detail.

Tmax

DIAG.29 CURVATURE AND VENEER LAYER CALCULATIONS FOR THE PHYSICAL EXPERIMENTS.

PIC.64 FABRICATION PROCEDURE : EXPANDING, CLAMPING, CONTRACTING, DRYING.          PIC.65 (NEXT PAGE) TIME FRAMES OF THE MATERIAL COMPONENT DURING THE DRYING PERIOD AS IT REACHES MOISTURE EQUILIBRIUM WITH THE ENVIRONMENT.

L - length of the inner layer

L o - length of the outer layer

R - radius of the inner arc

R o - radius of the outer arc

α - angle of the arc (in radians)

T max - maximum thicknes of the laminate

L o Li

L = R *α

L o = R o *α

L = Lo/Fexp

T max = R o - R

R = L /α

R o = L o/α

R = L o/(α*Fexp)

T max = L o/α - Lo/(α*Fexp) = = (1/α - 1/(α*Fexp)) =

= L o((α*Fexp - α)/(α2*Fexp)) =

= Lo((α*(Fexp-1))/(α2*Fexp))

T max = Lo((Fexp-1)/(α*Fexp))

L - length of the inner layer

L o - length of the outer layer

R - radius of the inner arc

R o - radius of the outer arc

α - angle of the arc (in radians)

T max - maximum thicknes of the laminate

L = R *α

L o = R o *α

L = Lo/Fexp

T max = R o - R R = L /α

R o = L o/α

R = L o/(α*Fexp)

L - length of the inner layer

T max = L o/α - Lo/(α*Fexp) = = (1/α - 1/(α*Fexp)) =

L o - length of the outer layer

R - radius of the inner arc

R o - radius of the outer arc

= L o((α*Fexp - α)/(α2*Fexp)) =

= Lo((α*(Fexp-1))/(α2*Fexp))

T max = Lo((Fexp-1)/(α*Fexp))

α - angle of the arc (in radians)

T max - maximum thicknes of the laminate

L = R *α

L o = R o *α

L = Lo/Fexp

T max = R o - R

R = L /α

R o = L o/α

R = L o/(α*Fexp)

T max = L o/α - Lo/(α*Fexp) = = (1/α - 1/(α*Fexp)) =

= L o((α*Fexp - α)/(α2*Fexp)) =

= Lo((α*(Fexp-1))/(α2*Fexp))

T max = Lo((Fexp-1)/(α*Fexp))

LAMINATION PROCEDURE

As detailed in the fabrication methodology, each physical experiment requires a number of layers, each of different length. In order to calculate and program the length of each individual veneer, a geometrical method was investigated, based on the principle that each species of wood has a known and constant tangential shrinkage Fexp. The required radius was set for the outer dry layer, which had a length Lo and then the length Li of the inner wet layer was calculated, to the maximum tangential shrinkage factor, indicating the maximum feasible expansion of the veneer strip along its long axis, where grain is oriented vertically. Based on those two limits, intermediate layers could be computed as a range between the inner and outer lengths. Additionally, through the mathematical type as indicated in DIAG.29, we could calculate the maximum thickness of the laminate piece, for a given curvature.

The results of the calculation presented a curving wood strip but with a different radius than expected. This validated that a method for geometrically setting a radius and trying to calculate the length of the inner layers could not be used, although the fabrication methodology was correct. Thus a series of experiments would need to be undertaken to search for a relationship between different parameters that affect the curvature of the laminate component.

065

5

MATERIAL COMPONENT

PHYSICAL EXPERIMENTS

• UNDERSTANDING BEHAVIOUR OF WOOD

• UNDERSTANDING PARAMETER OF TIMBER COMPONENTS

DIGITAL SIMULATION

• CONTROLING PARAMETERS OF TIMBER COMPONENTS

PHYSICAL - DIGITAL CALIBRATION

• SYNCHRONISATION OF PARAMETERS THAT DESCRIBES THE MATERIAL

BEHAVIOUR OF THE COMPONENT IN BOTH ENVIRONMENTS

FROM PHYSICAL TO DIGITAL EXPERIMENTS

The research development intended to present a series of experiments, conducted in both physical and digital environments with the ambition for creating a controlled and quantified material component. The steps below summarise three stages of exploration.

As detailed in the methods chapter, physical material experimentation was first initiated to set the groundwork for comprehending the behaviour of wood and how through a fabrication process curved pieces of timber may be produced.

Findings from the physical experiments could then be utilised as an input for the digital simulation of the components material behaviour. In this manner, a deeper understanding and identification of specific curvature influencing parameters could be explored.

The Final stage of this parallel exploration between physical and digital workspaces is the process of calibration. With a notion that the computation workspace would allow more complex application strategies to be undertaken uniting the two working methods would ensure that computed digital components could then be physically fabricated.

GRAIN ORIENTATION OF VENEER

THICKNESS OF VENEERS

NUMBER

PHYSICAL EXPERIMENT PARAMETERS

With the aim of understanding which parameters would affect the curvature of a wood strip, PIC.67, a series of physical experiments were initiated. The setup of these experiments was built on the described fabrication methodology and the failure to produce desired curvatures through a solely geometrical method for calculating the length of veneers. An alternative method was therefore required to progress the project and focused on the parameters which we thought affected the curvature of the component.

Physically working with different wood species, ash and walnut veneer, of different thicknesses, 0.6mm and 1.4mm, made us aware that both the species and thickness of each layer of veneer affected the curvature created. As anticipated the expansion factor of each layer controlled fundamentally in the fabrication process by its moisture content, also caused the component to curve in different ways. The grain orientation played a significant role in forming the produced geometry and was identified as the first influential parameter in the system but locked to ensure only single curved radial pieces were fabricated. Other variables that could affect the fabrication of the component were also assumed as variables and were thought to be related to the scale and basic dimensions, length, width and overall thickness or number of layers in the composition.

These seven outlined parameters, wood species, grain orientation, thickness of veneers, number of layers, expansion factor (shrinkage factor) of layers, length and width of component, concluded our initial physical observations and would need to be quantified and catalogued by further physical experiment investigations.

The following pages document a series of experiments investigating the affect of each individual parameter on the curvature of a laminated piece with the aim of gaining a holistic and complete apprehension of the material component’s behaviour.

PRE - ANALYSIS

COMPONENT OF

-3.875464X10¯³ [PT:96,ND:390]

[pt:324,nd:1149]

= - 0.7039 0C

POST - ANALYSIS

DIGITAL

OAK VENEERS

DIGITAL COMPONENT

MAHOGANY VENEERS

0.0175 0.0075 LAY_03 0.0350 0.0150

LAY_04 0.0525 0.0225

LAY_05 0.0700 0.0300

LAY_06 0.0875 0.0375

LAY_07 0.1050 0.0450

LENGTH

INPUT DATA FOR THE FINITE ELEMENT ANALYSIS, INDICATING THE DIFFERENT PARAMETERS.

INPUT

DIGITAL SIMULATION METHOD

Digital simulation apart from simulating the material behaviour of the physical experiment, also allowed the work to continue performing experiments when sourcing the proper material or proper size was not feasible, due to time, cost, logistic etc. Additionally, when the computational set up for the digital experiment was attained, multiple experiments could be processed, saving time and material, while delivering more accurate results.

The data from the physical component tests was fed into the Finite Element Analysis (FEA) software, for both the multiple layers of veneer, example in DIAG.32, and the bonding PVA glue, DIAG.33. Next, a ΔΤ of -0.7039 0C was applied to the laminated digital component, equal to reaching equilibrium within an indoor space, simulating the physical difference in moisture content. The results as shown in the example for different wood species in DIAG.31, display the component curved and successfully simulating concurrent behaviour with that of the physical experiment. At the back of the book is an appendix in which the raw material data from all the digital FEA experiments is documented.          DIAG.31 FINITE ELEMENT ANALYSIS ON TWO MATERIAL COMPONENTS OF DIFFERENT WOOD SPECIES.

DIGITAL EXPERIMENT

PLATE CURVATURE:XX (/MM)

-7.660491X10

PHYSICAL EXPERIMENT

CROWN ASH VENEER

LAYERS OF 1.4MM

SHRINKAGE FACTOR : 5.50%

DIGITAL COMPONENT SIMULATION FINITE

SHRINKAGE RADIAL — RADIAL SHRINKAGE IS SHRINKAGE IN THE DIRECTION FROM THE CENTER OF THE TREE TO THE PERIMETER OF THE TRUNK.

SHRINKAGE TANGENTIAL — TANGENTIAL SHRINKAGE IS SHRINKAGE DIRECTLY PERPENDICULAR TO RADIAL, PARALLEL TO GROWTH RINGS AND ROUGHLY DOUBLE IN MAGNITUDE.

COMPRESSIVE STRENGTH PARALLEL TO GRAIN—MAXIMUM STRESS SUSTAINED BY A COMPRESSION PARALLEL-TO-GRAIN SPECIMEN HAVING A RATIO OF LENGTH TO LEAST DIMENSION OF LESS THAN 11.

COMPRESSIVE STRENGTH PERPENDICULAR TO GRAIN—REPORTED AS STRESS AT PROPORTIONAL LIMIT. THERE IS NO CLEARLY DEFINED ULTIMATE STRESS FOR THIS PROPERTY.

SHEAR STRENGTH PARALLEL TO GRAIN—ABILITY TO RESIST INTERNAL SLIPPING OF ONE PART UPON ANOTHER ALONG THE GRAIN. VALUES PRESENTED ARE AVERAGE STRENGTH IN RADIAL AND TANGENTIAL SHEAR PLANES.

TENSILE STRENGTH PERPENDICULAR TO GRAIN—RESISTANCE OF WOOD TO FORCES ACTING ACROSS THE GRAIN THAT TEND TO SPLIT A MEMBER. VALUES PRESENTED ARE THE AVERAGE OF RADIAL AND TANGENTIAL OBSERVATIONS.

SOURCE : HTTP://WWW.WOODBIN.COM/CALCS/SHRINKULATOR.HTM

DIAG.36 DATA FOR PROPERTIES OF DIFFERENT WOOD SPECIES, SOURCE : HTTP://WWW.WOODBIN. COM/CALCS/SHRINKULATOR.HTM

DIAG.37 DIGITALLY PRODUCED CURVATURE FOR EACH WOOD SPECIES.

DIAG.38 CURVATURE AS FUNCTION OF COMPONENT WOOD SPECIES.

DIAG.39 FINE ELEMENT ANALYSIS FOR COMPONENTS OF DIFFERENT WOOD SPECIES.

PIC.69 DIFFERENT WOOD SPECIES OF VENEER.

01 WOOD SPECIES OF VENEER

AIM :

How do different wood species influence the produced curvature of the material component?

PROCEDURE :

Sourcing different veneer types was proved to be a difficult process, and since the initial physical experiments revealed a relation between that parameter and the produced curvature, it was decided proceeding only with the digital simulation for this experiment, trying to understand the material behaviour of different wood species.

Eight components of different wood species were digitally simulated with the use of FEA. Each set of experiments consisted of seven layers of 1.4mm thickness and different physical properties as indicated in DIAG.36, while every digital component was programmed to reach its maximum tangential shrinkage factor on the inner of the layers.

A ΔΤ = -0.7039 is then applied to the laminated pieces and after the simulation is run, the components curve differently, as shown in DIAG.39.

OUTCOME :

Each wood species has a different tangential shrinkage factor and therefore each strip displays a different radial curvature. Consequently, the selection of wood species determines the permissible range of curvatures of the material component.

For the proceeding digital experiments, white ash was picked, as one of the most easily sourced veneer types of 1.4mm thickness, displaying at the same time high tangential shrinkage factor, allowing the fabrication of tight curvatures.

X THICKNESS OF

DIAG.40 CALLIBRATION BETWEEN PRODUCED CURVATURES OF PHYSICAL AND DIGITAL EXPERIMENTS.

DIAG.41 CURVATURE AS FUNCTION OF COMPONENT’S LAYER THICKNESS.

DIAG.42 FINE ELEMENT ANALYSIS FOR COMPONENTS OF DIFFERENT LAYER THICKNESS.

AIM :

How do different thicknesses of individual veneers influence the produced curvature of the material component?

PROCEDURE :

As in the case of the previous parameter, sourcing veneers of white ash but of different thicknesses was not feasible, and therefore, the only physical experiment conducted was limited to the thickness of 1.4mm for 10 layers of veneer.

The same setup but within the digital environment, DIAG.42, was carried out for five components of ten layers each, but of different thicknesses, 0.50mm, 1.00mm, 1.40mm (most commonly used within the building industry and called constructional veneer), 2.00mm and 2.50mm. A ΔΤ = -0.7039 is applied to the laminated pieces and after the simulation is run, the components curve differently with a function described in DIAG.41.

OUTCOME :

The thickness of the white ash veneers within the laminate influence the curvature achieved. This suggests that the thinner the individual layers are, the tighter the produced radii for a given number of layers. However an observation from physical experiments suggests difficulties in precisely controlling moisture levels in veneer under 0.6mm thick.

04 NUMBER OF LAYERS DIGITAL COMPONENT SIMULATION FINITE ELEMENT ANALYSIS

DIAG.43 CALLIBRATION BETWEEN PRODUCED CURVATURES ON PHYSICAL AND DIGITAL EXPERIMENTS.

DIAG.44 CURVATURE AS FUNCTION OF COMPONENT’S NUMBER OF LAYERS.

DIAG.45 FINITE ELEMENT ANALYSIS FOR COMPONENTS OF DIFFERENT NUMBER OF LAYERS.

X THICKNESS OF LAMINATE(MM)

PIC.70 SERIES OF PHYSICAL MATERIAL COMPONENTS OF DIFFERENT NUMBER OF LAYERS, AFTER EQUILIBRIUM IS REACHED.

PIC.71 MULTIPLE COMPONENTS WITH DIFFERENT NUMBER OF LAYERS.

AIM :

How does varying the number of layers of the component influence the produced curvature?

PROCEDURE :

Three physical experiments were carried out, for two, six and ten layers of white ash veneer of 1.4mm thickness, PIC.70. The inner layer of each component was calculated with the maximum moisture content, using the shrinkage expansion factor of 5.50% obtained from the initial experiments. The pieces after laminated and clamped were set free to reach equilibrium and showed similar curvatures.

The experiment was simulated using FEA but for a range of numbers of layers from two to ten. Those nine experiments were run for ΔΤ = -0.7039 applied on the components and revealed a linear relationship between curvature and the number of layers, DIAG.44.

OUTCOME :

When the number of the laminated layers increases, the component forms wider curvatures. Although the physical and the digital results shown in DIAG.43 did not much and the full calibration was not achievable, the physically produced curvatures are the same with the digital ones, scaled by a factor of 120%, allowing us to draw reliable conclusions on the behaviour of the piece in relation to the number of layers.

AIM :

DIAG.46 CALLIBRATION BETWEEN PRODUCED CURVATURES ON PHYSICAL AND DIGITAL EXPERIMENTS.

DIAG.47 CURVATURE AS FUNCTION OF COMPONENT’S LENGTH.

DIAG.48 FINITE ELEMENT ANALYSIS FOR COMPONENTS OF DIFFERENT LENGTH.

PIC.72 SERIES OF PHYSICAL MATERIAL COMPONENTS OF DIFFERENT LENGTHS, AFTER EQUILIBRIUM IS REACHED.

PIC.73 MULTIPLE COMPONENTS WITH DIFFERENT LENGTHS. 47

How does the length of the material component influence the produced curvature?

PROCEDURE :

Five physical experiments were carried out, with five layers of white ash veneer of 1.4mm thickness each. The components have fixed widths of 60mm but different lengths, ranging from 180mm to 420mm, PIC.72. The dried pieces show similar curvatures, apart from the piece of 380mm which curved to a tighter radii, indicating probably a mistake in the fabrication process.

In order for the physical experiments to be verified and draw conclusions regarding the influence of this parameter, the same five experiments were simulated with FEA. The data for all laminates are the same and when ΔΤ = -0.7039 is applied, the digital components curve with the exact same radii, DIAG.48.

OUTCOME :

The physical and digital experiments showcase similar material behaviours, as shown in DIAG.46, where curvatures of both procedures are overlaid and differ by a factor of 140%. Although the calibration is not achieved by matching the results, it is evident that the parameter does not influence the curvature.

07 WIDTH OF COMPONENT DIGITAL COMPONENT SIMULATION FINITE ELEMENT ANALYSIS

DIAG.49 CALLIBRATION BETWEEN PRODUCED CURVATURES ON PHYSICAL AND DIGITAL EXPERIMENTS.

DIAG.50 CURVATURE AS FUNCTION OF COMPONENT’S WIDTH.

DIAG.51 FINE ELEMENT ANALYSIS FOR COMPONENTS OF DIFFERENT WIDTH.

PIC.74 SERIES OF PHYSICAL MATERIAL COMPONENTS OF DIFFERENT WIDTHS, AFTER EQUILIBRIUM IS REACHED.

PIC.75 MULTIPLE COMPONENTS WITH DIFFERENT WIDTHS.

AIM :

How does the width of the material component influence the produced curvature?

PROCEDURE :

X THICKNESS OF LAMINATE(MM)

Five physical experiments were carried out, with five layers of white ash veneer of 1.4mm thickness each. The components have fixed length of 300mm but different widths, ranging from 30mm to 300mm, PIC.74. The four dried pieces, 30mm, 60mm, 150mm and 300mm wide show similar curvatures, whereas the 100mm wide piece curved in wider radii, indicating probably a mistake in the fabrication process.

In order for the physical experiments to be verified and draw conclusions regarding the influence of this parameter, the same five experiments were simulated with FEA. The data for all laminates are the same and when ΔΤ = -0.7039 is applied, the digital components curve with the exact same radii, DIAG.51.

OUTCOME :

The physical and digital experiments showcase a similar material behaviour, as shown in DIAG.49, where curvatures of both procedures are overlaid and differ by a factor of 140%. Although the calibration is not achieved by matching the results, it is evident that the parameter does not influence the curvature.

0.010.020.030.040.050.060.070.080.090.1

FACTOR (%)

SUMMARY OF THE MATERIAL COMPONENT INFLUENCING AND NON INFLUENCIAL PARAMETERS.

PIC.76 MATERIAL COMPONENT OUT OF BIRCH VENEER, 10 LAYERS OF 1.4MM THICKNESS, SHRINKAGE FACTOR : 5.50%

INFLUENCIAL STRAIGHT LAMINATION 900

INFLUENCIAL CONSTANT VARIABLE YELLOW BIRCH THICKNESS OF VENEERS

GRAIN ORIENTATION OF VENEER

INFLUENCIAL CONSTANT VARIABLE 1.4 MM

NUMBER OF LAYERS

INFLUENCIAL VARIABLE

INFLUENCE OF PARAMETERS

The results of the five sets of experiments defined which parameters controlled the curvature of a strip and could be considered as constant or variable inputs of the material system for its further exploration.

EXPANSION FACTOR OF LAYERS

INFLUENCIAL VARIABLE

WOOD SPECIES OF VENEER LENGTH OF COMPONENT

NON INFLUENTIAL SIZE VARIABLE

The dimensions of the material component, width and length were found not to affect the curvature. Thus the width of potential pieces is only restricted by the size of the tree log. The length is restricted by the length of veneer which could be peeled from a log and therefore fairly long strips could potentially be fabricated. Focused to defining the lamination process influencing parameters, the expansion factor and the thickness of each individual layer, as well as the number of layers were proved to be influential parameters of the material components behaviour. Ultimately, the selection of wood species has very different effects on the range of curvatures produced and always operates in relation to the type of function the component will be applied to.

Width and length were defined to be size variables. The thickness and species of wood were defined to be constant variables that are function specific. The expansion factor and number of layers were defined to be curvature influencing parameters.

NON INFLUENTIAL SIZE VARIABLE

The experiments concluded that a further set of tests should be undertaken over a larger sample range exclusively within the digital environment, since the material behaviour in both workspaces was found to be true. The aim of the next set of experiments would be to test a variety of shrinkage factors for a number of strips fabricated with a different number of layers.

DIAG.53 FINITE ELEMENT ANALYSIS FOR COMPONENTS OF DIFFERENT NUMBER OF LAYERS AND DIFFERENT EXPANSION FACTORS PER SERIES, REVEALING THE MATERIAL BEHAVIOUR IN RELATION TO THOSE TWO INFLUENCIAL VARIABLES.

DIAG.54 COMPUTATIONAL DATA INDICATING THE DIGITAL COMPONENT’S CURVATURE IN RELATION TO EXPANSION FACTOR AND NUMBER OF LAYERS.

DIAG.55 CURVATURE AS A FUNCTION OF EXPANSION FACTOR OR NUMBER OF LAYERS.

EXTENDING COMPUTATIONAL DATA

For this set of digital experiments the size dependent and constant variables were fixed, allowing a more controlled investigation into the relationship between the expansion factor and number of layers affecting the curvature of the material component.

The digital component’s dimensions were set to 60 x 300mm, since curvature was found not to be influence by the width and length of the component. For the constant variables a yellow birch species of a 1.40mm thickness was picked as one of the most commonly used species of constructional veneer within the building industry and displaying at the same time a high tangential shrinkage factor which would potentially allow the pieces to achieve tighter curvatures.

Nine sets of digital simulations each undertaking nineteen independent shrinkage factor experiments were run measuring the produced curvature for a set of inputs, DIAG.53. With a tangential shrinkage of 9.5% a limit was set through which the wood could bend. Taken at 0.5% intervals nineteen shrinkage factors were explored through nine different thicknesses ranging from 5.6mm (four layers of 1.4mm veneer) to 28mm (twenty layers of 1.4mm veneer). As a result, a wide catalogue of computed curvatures was created, DIAG.54, enabling a more precise comprehension of the relations between tangential shrinkage factor or number of layers and radii. Curvature as a function of tangential expansion factor, showed an exponential relation, whereas curvature as function of number of layers showed a linear relation, DIAG.55.

NUMBER

X=TANGENTIAL SHRINKAGE (%)

Y=THICKNESS (NO OF LAYERS)

Z= CURVATURE RADIUS (MM)

Z(X) = A1*X-1

Z(Y) = A2*Y+B

Z(X,Y) = ((1.9398*Y) - 2.3189)*X

Z= 36.544 X-1

Z= 32.625 X-1

Z= 28.711 X-1

Z= 24.803 X-1

Z= 20.902 X-1

Z= 17.015 X-1

Z= 13.149 X-1

Z= 9.3225 X-1

Z= 5.5553 X-1

COEFFICIENT= 1.9387*X - 2.3025

DIAG.56 PLOTTED RESULTS FOR CURVATURE AS A FUNCTION OF TANGENTIAL SHRINKAGE FACTOR AND CURVATURE AS FUNCTION OF NUMBER OF LAYERS, COMPOSING A 3D DATABASE.

DIAG.57 EXTENDED 3D GRAPH OF THE INFLUENCIAL PARAMETERS FOR COMPUTING THE MATERIAL COMPONENT’S CURVATURE.

DIAG.58 CHANGE OF COEFFICIENT VALUES AS A FUNCTION OF THICKNESS.

MATERIAL COMPUTATION MATRIX

Curvature against thickness and curvature against tangential shrinkage factor were measured and plotted to understand the relationship between results and compiled in a three dimensional matrix.

Since curvature is a function both of thickness and expansion factor, a general equation could have been derived. The series of data describing linear relation of curvature as a function of thickness is given by the general equation z(y) = a2*y+b, where difference of coefficient a2 is exponential between consecutive series of data. Series of data describing the exponential relation of curvature as a function of tangential shrinkage is given by the general equation z(x) = a1*x-1, where difference of coefficient a1 is linear between consecutive series of data. A linear change of coefficient a1 defining the relation between curvature and tangential shrinkage for a given thickness is shown in DIAG.58. These interrelations allowed for generalising the thickness (as the number of layers) against curvature and tangential shrinkage against curvature equations into one, plotted as the threedimensional matrix in DIAG.57. The formula allows for extending the matrix and plotting data for any input parameters without the need for testing results through experimentation. This formulated an incredibly powerful tool for programming a timber component to achieve a specific curvature from picking a thickness and using the correlative tangential shrinkage factors.

RADIUS 17,000.00 MM

RADIUS 5,000.00 MM

RADIUS 1,000.00 MM

A02

R01

R02

R03

B01

B02

C01

C02

CATOLOGUE OF MATERIAL COMPONENTS

The catalogue documents 500 sample components of different thicknesses and tangential expansion factors that produce variable curvatures based on the material information matrix. All the components are 60mm wide and 300mm long of yellow birch veneer, 1.40mm thick. Among the multiple pieces, in the bottom left corner, the thinnest components show notably tighter curvatures, compared to the bottom right corner where pieces reach thicknesses of 140mm and really wide curvature revealing the bilateral restriction of curvature against thickness.

FABRICATION DEVELOPMENT

The material and digital experiments suggest that very long and thick panels may be manufactured. As the moisture content in the panels changes at the cellular scale, the individual micro material changes induce the curvature in a panel. This means that the force required to bring about curvature in the panel occurs cell by cell and does not have to overcome the force throughout the panel. Therefore it is feasible to think that the process initially explored on a 100mm x 100mm test piece of veneer could be scaled to work for much larger applications.

The length of veneer peeled from a log limits the size of panel that may be fabricated. To realise the potential of very long panels the fabrication method needs to change. One problem with using elastic straps to retain the lamination during drying is a small force in the straps needs to be overcome and affects the curvature potentially achievable.

An alternative method is to place the strip after the veneers are of the required length and glued into a vacuum sealed case, DIAG.59. Whilst the individual layers retain their moisture, removing air from the case applies pressure upon the piece and can be left for lamination to occur between the layers until glue is properly dried. Once the laminated component is removed from the case, the flat panel will begin to curve as the moisture content in the layers is lost. This approach is commonly utilised at a larger scale in the propeller and boat industries for creating laminated wind turbine blades up to 32m long and the hulls of sailing boats.

DESIGN DEVELOPMENT

Findings within the domain and material research show that the curvature of laminated timber components can be controlled in order to fabricate pieces of desired curvature and their scale is only limited by the maximum dimensions of veneer leaves from a log. This chapter of the thesis aims to apply the generation of a material system which is structurally coherent and utilises properties of the material component to further express its geometrical potentials at the architectural scale of a twenty-storey tower and use curvilinear geometry to develop new models of functional living space.

Based on early key studies of mathematical minimal surfaces preceding the main research, an interest of the thesis lies in developing systems that describe geometrical complexity through rule sets associating simple components. Geometrical complexity is not merely an aim in itself, but a mean of developing a system of integrated structural logic and dynamic architectural space of continuity and mixed thresholds, resulting in variable morphological responses. As displayed through an example of a Costa’s minimal surface, the same geometry can be described for fabrication in various ways. The photo on the top of the opposite page shows the surface approximated through interlocking planar components in opposing U and V directions. Although the resulting geometry depicts Costa’s minimal surface, logic of its fabrication does not derive from the mathematical logic given by the equation of a surface. The second photo shows the same surface, but fabrication is based on its integral geometrical logic. Interlocking UV lines are a direct physical translation of lines that describe this geometry in mathematical space. Therefore fabrication and materiality of surface is integral to its geometrical logic. The thesis takes on this path of research, focusing on developing rule sets that originate from the internal logic of a material system, to invent a formula which describes a resultant geometry.

The understanding of material system component properties is crucial to that route of investigation, thus components are analysed based on their structural and geometric capacities. These findings are then utilised to inform the structural principle for a building system. This combined with spatial ambitions for the project is employed to develop a parametric model, which associates structural logic with geometry and functional requirements. The aim is to develop a design system integrating all the project ambitions to deliver building morphologies, which in the next step of the research could be evaluated to context specific criteria.

PIC.78 WOOD-CUT PRINT OF A WILLOW TREE BY BRYAN NASH GILL, 2011

PIC.79

COSTA’S MINIMAL SURFACE, MODEL FABRICATED OUT OF PLANAR INTERSECTING COMPONENTS.

PIC.80

COSTA’S MINIMAL SURFACE, MODEL FABRICATED BASED ON UV CURVES DEFINED BY THE MATHEMATICAL FORMULA OF A SURFACE.

PIC.81 EXTERIOR AND INTERIOR VIEWS OF THE OKURAYAMA APARTMENTS IN TOKYO, ARCHITECT: KAZUYO SEJIMA & ASSOCIATES.

FLOOR PLANS OF THE THREE LEVELS OF THE APARTMENT BUILDING.

KEY STUDY INTRO

Potentials of the material system to describe geometries at a building scale were first tested on an existing building morphology. An apartment block in Okurayama designed by Kazuyo Sejima & Associates was chosen for two reasons.

First, its geometry is based on complex planar spline curvatures, which were then extruded to the height of two to three storeys. The extruded geometry creates walls displaying single curvature. Secondly, a residential function was chosen in order to learn how space based on these geometries can provide novel models of inhabitation that remain functional, as opposed to conventional residential spaces based on orthogonal plans or overly complex plans displaying chaos.

The aim of this exercise was to test the potential of the proposed timber material system that is based on radial arcs to describe more complex curved geometries.

1.68M

01B02

3.31M

3.37M

01B03

THICKNESS:

01C02

3.77M

THICKNESS: 0.179M SR.FACTOR: 0.050%

02A23 RADIUS: 1.57M

THICKNESS: 0.084M SR.FACTOR: 0.949%

THICKNESS: 0.106M SR.FACTOR: 0.925%

DIAG.69 ANALYSIS OF THE PERIMETRIC WALLS OF THE APARTMENT BUILDING AND THROUGH THE USE OF A GENETIC ALGORITHM APPROXIMATION OF THE CURVATURES WITH ARCS.

DIAG.70 CLASSIFICATION OF THE COMPONENTS THAT CONSIST EACH FLOOR PLAN. FIRST ATTEMPT TO APPLY THE MATERIAL COMPONENT MATRIX.

THICKNESS: 0.112M SR.FACTOR: 0.946%

THICKNESS: 0.115M SR.FACTOR: 0.933%

02A24 RADIUS: 1.76M

02C01 RADIUS: 1.76M

02A08 RADIUS: 1.97M 02A09 RADIUS: 1.86M

THICKNESS: 0.120M SR.FACTOR: 0.935%

THICKNESS: 0.120M SR.FACTOR: 0.935%

THICKNESS: 0.129M SR.FACTOR: 0.945%

THICKNESS: 0.134M SR.FACTOR: 0.932%

THICKNESS: 0.137M SR.FACTOR: 0.939%

THICKNESS: 0.151M SR.FACTOR: 0.942%

02B04 RADIUS: 2.38M 02B05 RADIUS: 2.38M

02B08 RADIUS: 2.42M 02C05 RADIUS: 2.50M

02A20 RADIUS: 2.73M

02B03 RADIUS: 3.31M

02A10 RADIUS: 3.37M

THICKNESS: 0.162M SR.FACTOR:

THICKNESS: 0.165M SR.FACTOR: 0.934%

THICKNESS: 0.171M SR.FACTOR: 0.937%

THICKNESS: 0.179M SR.FACTOR: 0.900%

THICKNESS: 0.179M SR.FACTOR: 0.742%

THICKNESS: 0.179M SR.FACTOR: 0.728%

THICKNESS: 0.179M SR.FACTOR: 0.729%

THICKNESS: 0.179M SR.FACTOR: 0.692%

THICKNESS: 0.179M SR.FACTOR: 0.654%

THICKNESS: 0.179M SR.FACTOR: 0.644%

02A19 RADIUS: 3.82M

02B01

THICKNESS: 0.179M SR.FACTOR: 0.645%

02A11 RADIUS: 3.84M

02C04 RADIUS: 4.75M

RADIUS: 4.80M

02A07 RADIUS: 5.00M

THICKNESS: 0.179M SR.FACTOR: 0.642%

THICKNESS: 0.179M SR.FACTOR: 0.518%

THICKNESS: 0.179M SR.FACTOR: 0.516%

THICKNESS: 0.179M SR.FACTOR: 0.510%

THICKNESS: 0.179M SR.FACTOR: 0.289%

THICKNESS: 0.179M SR.FACTOR: 0.472%

CURVATURE

02C03 RADIUS: 1.20M 02C02 RADIUS: 6.28M

1.86M

1.97M

02A12 RADIUS: 5.59M 02A26 RADIUS: 5.26M

THICKNESS: 0.179M SR.FACTOR: 0.466%

02B06 RADIUS: 5.56M

02B07 RADIUS: 5.84M

02A18 RADIUS: 2.00M 02A17 RADIUS: 2.20M 02A16 RADIUS: 5.20M 02A15 RADIUS: 3.82M 02A14 RADIUS: 5.96M

02A25 RADIUS: 7.27M

02A22 RADIUS: 13.26M 02A21 RADIUS: 1.61M

02A13 RADIUS: 43.74M 02A05 RADIUS: 3.37M 02A04 RADIUS: 1.68M 02A03 RADIUS: 3.77M 02A02 RADIUS: 3.55M 02A01 RADIUS: 4.73M 02B02 RADIUS: 48.21M

THICKNESS: 0.179M SR.FACTOR: 0.443%

THICKNESS: 0.179M SR.FACTOR: 0.423%

THICKNESS: 0.179M SR.FACTOR: 0.394%

THICKNESS: 0.179M SR.FACTOR: 0.338%

02A06 RADIUS: 7.81M

THICKNESS: 0.179M SR.FACTOR: 0.314%

THICKNESS: 0.179M SR.FACTOR: 0.184%

THICKNESS: 0.179M SR.FACTOR: 0.052%

THICKNESS: 0.179M SR.FACTOR: 0.050%

THICKNESS

2.38M

2.73M

3.31M

3.37M

3.77M

3.82M

KEY STUDY ANALYSIS

4.80M

5.56M

5.96M 03A10

13.46M 03C01

1.61M 03C02

In order to approximate the freeform geometry of the floor plans with the radial arcs, the spline geometry was subdivided into segments. Curvature of these segments was then evaluated through a genetic algorithm, based on its proximity to radii of radial arcs from the material system matrix. Each segment of a spline was assigned an arc, that most closely approximates its curvature, and has the biggest thickness for a given radius, DIAG.69. This process resulted in generating a catalogue of curved laminated timber wall segments shown on DIAG.70, which could be used to recreate the morphology of the Okurayama project.

7.81M

The case study demonstrated that although the geometry of the building in Okurayama delivers a novel model of spatial arrangements for residential functions and an interesting interplay between interior and exterior, there is no strong logic to how this geometry performs as an integral part of a structural system. Therefore, instead of generating an arbitrary morphology and approximating its geometry with the material system, further research focuses on using the limitations of the material system as a guideline to develop a building system based on radial geometry. This geometry should correlate with the structural logic of a building system.

DIAG.71 SECTION AND STRUCTURAL STACKING LOGIC OF THE STADHUS, THE TALLEST RESIDENTIAL TIMBER BUILDING IN THE WORLD LOCATED IN LONDON BOROUGH OF HACKNEY.          PIC.83 INTERIOR VIEW OF THE STADHUS          PIC.84 EXTERIOR VIEW OF THE STADHUS

ARCHITECT: WAUGH THISTLETON ARCHITECTS

DATE OF COMPLETION: 2008

LOCATION: 24 MURRAY GROVE, HACKNEY, LONDON

BUILDING TYPE: RESIDENTIAL

DESIGN: NINE STOREY TIMBER TOWER STRUCTURE: KLH CROSS-LAMINATED TIMBER PANEL SYSTEM

1 ALL INFORMATION ABOUT CLT HAS BEEN TAKEN FROM THE ONLINE PUBLICATION: WWW.SLIDESHARE.NET/JEFFRANSON/ STADTHAUS-MURRAY-GROVE-CASE-STUDY-PRESENTATION

2 FIRE REGULATIONS. SOURCE: P124, APPROVED DOCUMENT B

TIMBER IN MODERN RESIDENTIAL STRUCTURES

Recent trends in delivering sustainable solutions in construction have drawn an increased interest on the use of timber for larger building applications. The tallest residential building at present is located in London in the borough of Hackney. Large scale crosslaminated timber panels developed by KLH were used to build a structural system of stacking walls and floors. Although the CLT (Cross-Laminated Timber)1 is of a similar scale to components and their compressive strength in the material system developed through this thesis, geometries that can be produced by CLT are always limited to rectilinear solutions. Geometrical limitations of CLT result in a structural logic similar to a honeycomb, where load-bearing walls are oriented in opposite directions leading to compartmentalisation of internal space. The use of curvilinear laminated wall components is seen as a potential for moving away from conventional space based orthogonal floor plan layouts, towards space drawn upon curvilinear geometry, characterised by mixed thresholds and continuity.

When designing a timber structure aspects of safety need to be addressed. The most critical one is fire resistance, understanding that timber buildings are prone to failure due to fire. Although solid timber is not easily ignited, it is combustible. Its combustibility can be modified through retarding chemicals. However, while exposed timber surface burns vigorously at the beginning, it soon builds up a layer of insulating charcoal. CLT has sufficient resistance to fire. For example 128 mm thick panel provides 72 minutes of fire resistance with two vertical load bearing layers remaining. The aim of this design research is to design a timber apartment building of 20 floor. A building of that function and height requires 120 minutes period of fire resistance and use of sprinkler system.2 Therefore the period of fire resistance of timber panels can be extended trough a sprinkling system and other means of fire protection. In case of fire, no damaging thermal expansions of timber structures should be credited as an advantage of this method of construction.

107

BUILDING SYSTEM STUDIES

Building upon findings from the key study of Okurayama apartments project and structural stacking logic of the Hackney residential tower the research focused on developing a structural strategy informed by geometrical and material properties of the curvilinear timber components. Several studies were undertaken with key principles as guidelines for the system:

- potential of fabricating large-scale components

- take advantage of the compressive strength of wall components

- utilise radial geometry of components as a mean for improving structural performance of a system

- introduce subdivision of space suitable for residential function

- exhibit the potential of fabricating range of curvatures from straight panels to components with tight radii

- explore variable thickness of components to function as structural, partition and furniture elements of design

- employ curved geometry to inform a novel way of approaching functional living

The set of geometrical exercises shown in DIAG.72 were undertaken and each experiment was evaluated based on criteria listed above. Several issues were common for most of the experiments. Developed systems were either too restrictive or displayed insufficient order in the geometries created. Most of the systems could potentially function within individual floors, but didn’t give notions of how these floors could be aggregated into vertical arrangements and exhibit a change of curvature ranges between floors. All the systems displayed too high level of complexity at the starting position, resulting in problems such as obscure joinery details, when multiple components met in a single node, or difficulty in gaining control of the whole system. The many problems that were encountered led to the conclusion, that existing construction systems should be analysed and complexity should emerge upon a simpler structural strategy.

STRAIGHT WALL SYSTEM REQUIRES SHEAR WALL

WALL SYSTEM REQUIRES SHEAR WALL

WALL SYSTEM REQUIRES SHEAR WALL

WALL SYSTEM REQUIRES SHEAR WALL

WALL SYSTEM REQUIRES SHEAR WALL

WALL SYSTEM REQUIRES SHEAR WALL

WALL SYSTEM REQUIRES SHEAR WALL

WALL SYSTEM REQUIRES SHEAR WALL

STRAIGHT

STRAIGHT

STRAIGHT

STRAIGHT

STRAIGHT

STRAIGHT

STRAIGHT

TIMBER WALL, BALOON SYSTEM.

SOLID PLANAR CROSSLAMINATED TIMBER WALL PANEL.          DIAG.75 SOLID CURVILINEAR LAMINATED TIMBER WALL PANEL.

SHEAR WALL IN CONVENTIONAL STRUCTURAL SYSTEM AND SYSTEM BASED ON CURVILINEAR GEOMETRY WITHOUT SHEAR WALL.

STRUCTURAL SYSTEMS

Lateral forces within structural systems are always an issue that needs to be addressed by individual components in the system.

An example of the balloon system on DIAG.73 shows how the make-up of a wall component helps to overcome lateral forces in horizontal directions parallel to the surface of a wall. The inner frame of a wall needs to be stabilised with an external sheet of plywood to prevent the wall from shearing.

Flat solid walls, such as solid timber laminated panel walls, are stable in horizontal directions parallel to their surface, but are not supported at all in the horizontal direction perpendicular to the surface of a wall as shown on DIAG.74.

Curved wall components of our material system are able to overcome lateral forces in either horizontal directions both through their solid make-up and curvilinear geometry (DIAG.75).

This principle allows us to move away from the conventional structural system of walls and beams based on orthogonal geometry. As shown in DIAG.76 this system requires the introduction of shear walls (indicated with red colour) in the perpendicular direction to main structural walls, in order to ensure stability of a structure. The introduction of curvilinear walls eliminates the need for shear walls, which potentially allows the shape and subdivision of internal space to be more free and continuous whilst at the same time maintaining the robustness of a coherent structural logic.

DIAG.77 BASIC GEOMETRICAL STATES OF A STRUCTURAL SYSTEM EXHIBITING CURVATURE RANGE OF THE MATERIAL SYSTEM.

DIAG.78 SMOOTH TRANSITION OF GEOMETRY BETWEEN TWO BASIC GEOMETRICAL STATES.

ORTHOGONAL SYSTEM ORTHOGONAL SYSTEM

BASIC GEOMETRY EXPLORATION

113

Upon the logic of intersecting walls and beams and the range of curvatures that are available in material system matrix, a geometry of walls and beams is described by two basic states as illustrated in DIAG.77:

- orthogonal system where walls are oriented in one direction and beams in the perpendicular direction

- radial system where walls form concentric circles and beams are oriented radially to them.

DIAG.78 shows how an orthogonal system may be smoothly manipulated through morphed distortion into a radial system. This fluent transition is important for our application, as it exhibits the full potential of the material system to produce a range of curvatures, which would find their expression in different geometrical configurations of individual floors within the building

SMOOTH TRANSITION OF GEOMETRICAL STATES WITHIN THE STRUCTURAL SYSTEM .

ORTHOGONAL SYSTEM          DIAG.79 KEY GEOMETRICAL STATES OF A STRUCTURAL MODEL BASED ON THE BASIC PRINCIPLE

DEVELOPED GEOMETRY EXPLORATION

The simple logic of distortion from one geometrical state into another as introduced in DIAG.78 and may be used in order to develop more complex geometrical arrangements. A Sequence of transitional states in DIAG.80 takes the same principle of distortion and the departure state of an orthogonal system to develop a more advanced geometrical system. By warping the orthogonal state inwards the system reaches its lower extreme state (shown on the left side of chart in DIAG.80), geometry of which can be enclosed in a circle. By warping the orthogonal state outwards the system reaches it upper extreme (right side of the same chart), which is essentially described by two interconnected radial entities. Therefore in this transitional geometry system there are three key states as shown in DIAG.79.

However it needs to be mentioned that the orthogonal system is taken only as a departure point for developing a transitional geometry model and never actually exists in its pure orthogonal form. As described previously, an orthogonal structural system cannot functionally perform without the support of a shear wall. Since the aim is to design a system which uses curved geometry of main structural components to eliminate the need for shear walls, it is ensured within system that the geometrical state which is closest to the orthogonal state has always a minimum curvature induced to provide the lateral stability which is integral to the structural system.

TWO RADIAL ARCS DEFINE THE SYSTEM. THESE ARCS DEPICT OUTERMOST WALLS.

TWO VECTORS ARE DRAWN AT THE ENDS OF BOTH ARCS, PERPENDICULAR TO ARCS’ CURVATURE AT THESE POINTS.

ARCS CONNECTING TWO INITIAL ARCS ARE DRAWN AT EACH END WITH A TANGENT DEFINED BY THE VECTORS IN STAGE 02.

DISTANCE BETWEEN MIDPOINTS OF THE ARCS IS SUBDIVIDED INTO EQUAL SEGMENTS OF 150 CM.

ASSOCIATIVE MODEL

A transitional geometry system has been developed further into an associative model, that establishes interrelations between walls and beams, as the system changes from one geometrical state into another. The associative model was created through digital tools such as python scripting language and parametric modelling software.

The initial configuration of walls and beams is based on constant moduli.

Modulus for walls is 1.5 meters and delimits the maximum distance between adjacent walls. This modulus provides sufficient flexibility to the system, to be adapted for various programmatic needs required by residential functions.

Modulus for beams is 1 meter and limits the maximum distance between neighbouring beams.

The logic of the geometrical system within the associative model is based on two opposing walls that might curve inwards or outwards. From each end of both walls a new curve is constructed, going in a perpendicular direction from the wall to connect with the opposing one. This new arc describes the most outer beam. New walls are introduced between the two initial walls. Spacing between them is based on a 1.5 m modulus. Whenever distance between walls curving in opposite directions becomes more than 1.5 meters, new wall segments ate introduced. If the spacing between beams exceeds 1 meter, new beams are introduced between already existing ones. Once this phase of the scrip executes, segments of beams that are redundant are deleted. Beam segment becomes redundant whenever the distance to its neighbouring beams becomes less than 1 meter. Upon this detailed rule set, a class based scripting approach enable the geometry to be manipulated in real time.

08

ARCS ARE DRAWN THROUGH DIVIDING POINTS FROM STAGE 06 AND TANGENT TO VECTORS FROM STAGE 07. THESE ARCS DEPICT BEAMS.

09

DISTANCE BETWEEN ADJACENT BEAMS IS SUBDIVIDED WHENEVER IT EXCEEDS 100 CM. DISTANCE IS SUBDIVIDED INTO SEGMENTS OF 100 CM.

10

ADDITIONAL ARCS ARE INTRODUCED THROUGH THE POINTS FROM STAGE 09. THESE ARCS DEPICT ADDITIONAL BEAMS.

11

WHENEVER DISTANCE BETWEEN ARCS DEPICTING WALLS BECOMES GREATER THAN 150 CM, ADDITIONAL WALLS ARCS ARE INTRODUCED. WALLS DESCRIBED THROUGH THEM PROVIDE EXTRA SUPPORT FOR BEAMS.

12

WHENEVER DISTANCE BETWEEN ARCS DEPICTING BEAMS BECOMES LESS THEN 100 CM, REDUNDANT SEGMENTS ARE REMOVED.

(NEXT PAGE) SEQUENTIAL STEPS OF THE ASSOCIATIVE MODEL’S DIARTHROSIS.

GENERATIVE PARAMETERS 2D

The associative model is driven by a set of parameters controlling the geometry in each state. Floor plans described through these geometrical modifications can potentially respond to various programmatic and morphological requirements. The alteration of parameters might result in changes of floor area of each floor plan, number of walls or orientation.

FOLLOWING PAGE:

The matrix shows the domain of geometrical transitions within the associative model. Curvature of the walls is the only parameter displayed in its full range. The other three parameters are constant.          DIAG.83 PARAMETERS OF THE ASSOCIATIVE MODEL.

STACKING OF GEOMETRICAL STATES

Consecutive geometrical states defined by the associative model inform the sequence of stacked floors. Aggregation of these morphologically independent storeys defines the holistic morphology of the building. Small geometrical differences between succesive floors assures that walls and beams on one floor correlate with the walls and beams on the floor above and below it.

SAMPLE FLOOR PLANS

Each geometrical state informs different floor plan layouts. Sample floor plans on DIAG.88 and DIAG.87 show how different configurations created with an associative model generate different models of inhabitation.

In these examples a base geometry from the associative model was taken and modified to respond to specific functional needs. This is clearly shown in DIAG.87, where the base geometry from the upper range of the matrix generated by the associative model is significantly modified, in order to shallow the floor plan and assure proper insulation of each apartment. Different geometrical states of the associative model give only a framework for creating floorplans. They inform floorplans, but can’t be directly translated into them.

DIAG.87 shows how these base geometrical states can be modified according to needs. Apartments on the left hand side of the floor plan are more enclosed and organised around quasi-courtyards, whilst the apartments on the right hand side are open towards surroundings.

Some geometrical states are more susceptible to modifications than others. As mentioned above the geometry used to generate the floor plan on DIAG.87 provides many potentials for adaptation, whereas the base geometry of the floor plan on DIAG.88 is rather restricted and is denoted by clear bidirectional orientation.

Considering the potentials and restrictions of each geometrical state as a different floor plan layout offers a greater awareness as to how the shape and global morphology of the building may respond to context specific conditions.          DIAG.87

127

GENERATIVE PARAMETERS 3D

DIAG.89 demonstrates how parameters described in DIAG.83 vary throughout the floors of a building. Slight modifications of parameters from floor to floor results in significant changes to the global morphology. In the examples shown in DIAG.89 only one parameter is modified at a time.

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0.03

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MORPHOLOGY 03

MORPHOLOGICAL VARIATIONS

Through the slight modifications of parameters affecting simultaneously all the flooplates in the height of a building, a model was generated to display different global morphologies, based on a gradient of smooth transitions between the geometries of each floor. Depending on how the parameters are changed within a range, the resulting morphologies can vary significantly. If a parameters’ range of change is not big or they are constant as displayed through example shown on DIAG.90, the resulting geometry of a building might be simple and moderate. Changing parameters to the limits of their range results in the creation of more complex geometries. The example shown in DIAG.91 embodies a linear change of parameters within the full range.

The most extreme morphologies are achieved by the nonlinear modification of parameters within full range of their domain. DIAG.92 demonstrates an example when parameters change nonlinearly throughout the range from the lower boundary of the range to the upper boundary of the domain and back to the middle range of the domain. More extreme generated morphologies result in more iconic and dynamic expressions.

DEFORMATION OF STRUCTURE

Due to the hygroscopic and fibrous nature of timber, cells within its tissue continually change their dimensions in relation to humidity. This leads to the deformation of timber elements and internal stresses within the structure. DIAG.93 demonstrates how fabricated wall components in axis V03 and V04 of sample floor plan in DIAG.87 deform due to humidity change. Unrestricted wall components were analysed in the range of maximum humidity change between 11.2% MC and 15.9% MC in sample location in New York for a month September (DIAG.14). Displacement of a wall component was determined at 700 mm for V03 component (length:800 cm) and 150 mm for V04 component (length:400 cm). External walls are prone to biggest deformation as they are exposed to humid external environment on one side and drier internal environment on the other side. In the analysis it is assumed that walls are not weather proof and moisture can penetrate down to 20% of a wall thickness.

Deformations indicated through the analysis convey the need of restraining wall components from deformations. The bottom edge of the wall needs to be restricted by connecting it with a floor and top edge of a wall needs to be braced by beams. Both anchorages result in increased internal stresses within the structure, which need to be considered during the design process.

V03

V04

POTENTIALS AND LIMITATIONS

Resulting building morphologies feature some emerging potentials and constraints that could not be resolved directly within the associative model. As shown on DIAG.96 these emerging qualities derive from transitions within a morphology. As the form steps back, emergent external spaces may be utilised as balconies(DIAG.95). As the form steps out, geometry of the building needs to be adapted in order to ensure continuity of the structure. DIAG.94 demonstrates how walls stepping out towards the top of the building cause discontinuity in the structure, that requires the adjustment of structural components. In order to provide structural support for disjointed walls, beams and floorplates of a floor below need to be extended to these walls.

These two examples demonstrate limitations of the associative model in resolving emergent properties of the system. The associative model needs to be seen merely as a design tool and a mean of establishing interrelations between consecutive floors, creating a framework for the further development of a system.

CONCLUSIONS

The same evaluation process applied previously for the residential project in Okurayama described in DIAG.70 was repeated for the designed building system. Wall components were analysed for their curvature as displayed in DIAG.97. To each wall component a maximum thickness for a given curvature was assigned and all components were catalogued and divided into hierarchical groups (DIAG.98).

Thickest components displaying the largest radii are mostly indicated with blue and are utilised as structural elements. Thinner wall elements within the yellow range of smaller radii are used as partition walls. Thinnest components of small radii can be used to design furniture.

The analysis demonstrates the potential of the materials system to deliver a complete building solution at each hierarchical level: from structural elements down to the furniture scale. What is more, the analysed building elements have constant curvature throughout their full length, which exploits the potential of components to be manufactured as single prefabricated elements, which could then be assembled on a site.

DESIGN PROPOSAL

Previous chapter discussed logic and development of the design system. This system based on the associative model can generate various morphologies upon material system logic, structural strategy and functional conditionings.

This chapter investigates how outcomes produced by the system could be evaluated based on context specific parameters.

The competition site in New York was chosen as a test field for the system. Competition calls for an innovative mid-rise timber building in Red Hook, Brooklyn with mixed use. Basic site conditions were analysed in scope of their potential to drive morphology of a building generated within the design system. Produced geometry was then modified to meet requirement for specific programmatic needs such as floor area or size of a site. Resulting building was examined in scope of reaching research aims and ambitions.

REQUIREMENTS

MID-RISE

MIXED-USE BUILDING

HOUSING UNITS

JOB TRAINING + EDUCATIONAL FACILITY

CENTRE OF WOOD TECHNOLOGY

DISTRIBUTION CENTRE

PROJECT CONTEXT

Red Hook is the neighbourhood that is geographically cut off from much of Brooklyn, yet becomes increasingly vibrant. Project site is located at the edge of Coffey Park on the south. This provides an opportunity to create apartments oriented towards the park on the lower floors. Proximity to Manhattan on the north gives the potential of creating apartments on the top floors of the building that make use of stunning views on the panorama of the island. The site area is 2400 m2, its dimensions defined by rectangle 60 x 40 meters. Design brief draw programmatic requirements for housing units and commercial functions.

PARAMETERS DRIVING THE MORPHOLOGY

MORPHOLOGICAL RESPONSE

Site specific conditions inform parameters of the associative model. Parameters are manipulated throughout the height as shown in DIAG.100 in order to generate smooth transition of geometrical states between floors. Shift from southern orientation towards the park on the lower floors, to northern orientation towards Manhattan on the top floors was obtained by manipulating rotation parameter. Transition from large floor plans utilised for commercial functions on bottom floors to small floor plans for residential functions on top floors was manipulated through curvature and spacing between edge arcs parameters. Openness towards park, increased exposure of facade to south to ensure proper internal lighting conditions and minimised exposure on the north to reduce heat loss, were achieved by modifying arc 01 and arc 02 length parameters. Resulting morphology shown at the bottom of DIAG.99 had to be then trimmed down to meet site restrictions of the site and requirements for floor plans. Top of DIAG.99 displays final modified building geometry.          DIAG.99 GEOMETRY GENERATED THROUGH ASSOCIATIVE MODEL AFTER AND BEFORE MODIFICATION

141

CATALOG OF FLOORPLANS, THEIR PROGRAMMATIC DIFFERENTIATION AND SUBDIVISION INTO APARMENTS

PROGRAMMATIC DIFFERENTIATION OF THE DESIGNED TOWER BLOCK

RESIDENTIAL USES

PROGRAMMATIC STRATEGY

DIAG.101 demonstrates how sequential geometrical states generated with associative model were modified in order to meet functional requirements. of the brief. Base geometry on the ground level was trimmed down to create passage providing access to commercial functions. Diagrams of residential floor plans illustrate sample subdivisions into individual apartments.

DIAG.102 conveys how deep floor plates in the base of the building are used for mixed-use program, that does not require direct sunlight. Shallow floor plate provide access to daylight, thus are suitable for residential uses.

CONCLUSIONS

Through the study of wood and its inherit properties, we managed to understand and control its behaviour, exploring at the same time the widely used fabrication technique of lamination combined with wood’s dimensional change due to moisture exchange. A material component could then be shaped based on simple principles, by controlling the variable parameters and at the same time its behaviour was simulated with the use of computational means. The potentials and the limitations deriving from our material component guided the geometrical explorations towards complex geometries with prominent biaxial orientation. Consequently the structural logic of our system was coupled with this idea of interlocking U and V lines in space that allow structural and at the same time spatial performance. The chosen design proposal consists an experiment for applying our building system on an environment with imposed limitations which deteriorate the multiple configurations that the system can generate. At the same time evaluation criteria, based on the specific environment, justify our design decisions, leading to a set of adequate morphologies.

FURTHER DEVELOPMENTS

The research presented in Arboreal Formations documents an approach to generating design solutions through investigating and understanding the inherent properties of wood. With the aim of creating a generative process for a twenty storey timber residential building system, a methodology was implemented to prioritise materiality and enhance the performance relationship between material, structure and geometry.

The project conveys the potential for creating a new and exciting timber component for both industrial design and construction industries. However this research only documents the conceptual idea and initial explorations undertaken in a five month period. If further developments were to be pursued, the work may focus on three interrelated fields of the thesis work; material component, material system and application.

Limited by time and unsuccessfully sourcing rotary cut veneers the scale of physical material experiments was restricted. The largest scale test undertaken in Finite Element Analysis (FEA) simulated the successful bending behaviour of a component 140mm thick. The thesis would therefore be further supported by trialling the findings of the FEA on a full scale laminated piece. The test may also provide the opportunity to advance the technique of laminating the veneers together using vacuum pressure and with alternative types of glue. Live loading and pressure test could also be applied to the physical experiment to further understand the performance properties of the piece such as its strength and stiffness.

The early material investigations highlighted the potential for orienting the grain in different directions. It is a well documented fact that alternating layers perpendicular to each other will improve the strength and stability of the piece. Initial thesis findings from diagonally orientating layers suggested that the twisting forms produced was of a ruled surface nature. These tests could be further investigated both physically and digitally to understand more thoroughly the relationship and parameterisation of curvature and grain direction simultaneously. Whilst the notion of double curved timber pieces is an exciting prospect, none of our experiments suggested this may be attainable. An idea to be explored in the hope of achieving this may stitch different orientations of veneer grains together within the same layer.

MATERIAL COMPONENT

COLLECTION OF PHYSICAL MATERIAL EXPERIMENTS

MATERIAL SYSTEM APPLICATION

The associative model employed to organise the material system offers many potentials for development. At present the model does not allocate true structural thicknesses to the elements and assumptions are made to the spacing and distance between structural members. Information data about the material components only transcribes the relationship between a specified curvature and thickness for which it may be fabricated. Introducing the structural performance of the elements in relation to thickness and curvature would help to enforce the structural potentials and limitations of the holistic material system. This work would require both the physical and computational structural testing (using FEA) of individual and aggregated assemblies of components. Gaining a more detailed understanding and quantification of the systems structural performance, the spacing between walls and beams could be further optimised to ensure the timber components are employed with efficiency and resourcefulness. The additional research may also lead to the adjustment of the geometric aggregation method as a structural hierarchy between components and the stacking of floor plates would be initiated. Applying this new associated model to a functional context would deliver a greater degree of clarity in the design solution and may also present emergent qualities of space.

The architectural application is currently used to inform the parameters of the associative model that order and define the material system. The output of this model is a pure smooth geometry which displays various states of different geometric instances and sizes. The system would benefit from the active integration of the proposed building programme to help assign building and space functionality as part of the various morphological states. This work would help define kill strategies to remove elements of the structural system with a greater notion of the desired spatial conditions and influence the overall building composition.

Buildings comprise three main elements of design; function, structure and environment. The project unites the first two of these fields but did not focus on the integration of environmental factors. Building physics and the consideration of local climatic conditions offers an opportunity to enhance a buildings performance and operation. For example the associated model might also adapt to ensure a certain amount of solar radiation or light is received on each floor plate. Building physics also encompasses the way in which building structures are sealed for reasons of moisture and thermal control. Aware that the inherent properties of wood may cause the component to move and react to moisture and thermal changes this would be a interesting lines of investigation. Although the project is very much a conceptual idea developing facade and threshold details between the juxtaposed floor plates would also deliver a greater degree of credibility for the buildings realisation.

Developed in the thesis is a material system designed for the specific functional use of a residential mid-rise tower block. Applied to other functions the material component may be employed to perform in a different manner and thus the organisation and strategy for forming the material system would change too. The range of curvatures and thickness of elements that the fabrication method may produce is a fantastic opportunity for the exploration of other design applications.

BIBLIOGRAPHY

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APPENDICIES

PHYSICAL EXPERIMENTS

MULTIPLE MATERIAL COMPONENTS

CHAISE LOUNGE CHAIR

FINITE ELEMENT ANALYSIS

JIG SHEETS

DIGITAL SIMULATIONS (FEA)

BASIC PARAMETERS

3D MATRIX DATA

COSTA SURFACE

FABRICATION METHOD 01

FABRICATION METHOD 02

ASSOCIATIVE GEOMETRICAL MODEL PYTHON CODE

APPENDICIES

PHYSICAL EXPERIMENTS

MULTIPLE MATERIAL COMPONENTS

CHAISE LOUNGE CHAIR

FINITE ELEMENT ANALYSIS

CHAISE LOUNGE CHAIR JIG SHEETS

DIGITAL SIMULATIONS (FEA) BASIC PARAMETERS

WOOD SPECIES OF VENEERS

LAYER THICKNESS OF VENEERS

NUMBER

WIDTH

DIGITAL SIMULATIONS (FEA)

COSTA SURFACE FABRICATION METHOD 01 FABRICATION METHOD 02

ASSOCIATIVE GEOMETRICAL MODEL PYTHON CODE

166 import math import rhinoscriptsyntax as rs import sys import scriptcontext import Rhino import System

#creates defining node arcs def arc(arclen,topt,rot,check,curvature,centpt,rotG,arclen2): arclenLt=[arclen,arclen2]

UVC.Rotation=rotG arcs=[]

UVC.state=check for in range(2):

if check ==1:

angle=(360-(360*(curvature*2)))+1 rad=(arclenLt[i]/(angle/360))/(2*math.pi)

elif check ==0:

# Figure out how ‘wide’ each range is if curvature==0.5: curvature=0.501 initialrange = 1 - 0.5 angle=((360-(360*((1-curvature)*2)))/2) radmin=(arclenLt[i]/(angle/360))/(2*math.pi)

mappedrange = (arclenLt[i]/2) - radmin

# Convert the left range into a 0-1 range (float) valueScaled = float(curvature - 0.5) / float(initialrange) # Convert the 0-1 range into a value in the right range. rad= (radmin + (valueScaled * mappedrange)) d=arclenLt[i]/rad angle=(d*360)/(2*math.pi)

arc=rs.AddArc(centpt,rad,angle)

arc=rs.RotateObject(arc,centpt,((-angle/2)+rot/2)+rotG) arcmidPt=rs.DivideCurve(arc,2) vectmove=rs.VectorCreate(topt,arcmidPt[1]) rs.MoveObject(arc,vectmove) if i==0: arcs.append(arc)

vect=rs.VectorCreate(topt,centpt) vectrot=rs.VectorRotate(vect,90,(0,0,1)) if i==1: arc1=rs.MirrorObject(arc,centpt,vectrot,True) arcs.append(arc1)

UVC.tmpLt2.append(arcs) UVC.Arcs=arcs

return arcs

#subdivides node arcs and creates UV curves def arcU(arcs,arclen,check): pts=[] crvsU=[] div=arclen/1

arcCent1=rs.ArcCenterPoint(arcs[0]) arcCent2=rs.ArcCenterPoint(arcs[1]) vectCheck=rs.VectorCreate(arcCent1,arcCent2) lineCent=rs.AddLine(arcCent1,arcCent2) lineMid=rs.CurveMidPoint(lineCent) if check ==1:

arcCentPt=[] arcRad=[] for in arcs:

arcRad.append(rs.ArcRadius(i)) pts.append(rs.DivideCurve(i,div)) arcCentPt.append(rs.ArcCenterPoint(i))

arcMidLt=[] meanCrvc=[] tmpLt=[] tangLt1=[] tangLt2=[] arcAddLt=[] para1=[] para2=[] for in range (len(pts[0])): tang=rs.PlaneFromPoints(pts[0][i],arcCentPt[0],((pts[0][i][0]),(pts[0][i] [1]),((pts[0][i][2])+1))) tangLt1.append(tang) UVC.tmpLt2.append(tang)

tang2=rs.PlaneFromPoints(pts[1][i],arcCentPt[1],((pts[1][i][0]),(pts[1][i] [1]),((pts[1][i][2])+1))) tangLt2.append(tang2) vectang=rs.VectorAngle(vectCheck,tang[1])

if vectang>-0.00001 and vectang<0.00001:

arcNe=rs.AddLine(pts[0][i],pts[1][i]) arcMid=rs.CurveMidPoint(arcNe) arcMidLt.append(arcMid) tmpLt.append(arcNe) crvsU.append(arcNe)

else:

arcNe=rs.AddArcPtTanPt(pts[0][i],-tang[1],pts[1][i]) arcMid=rs.ArcMidPoint(arcNe) arcMidLt.append(arcMid) tmpLt.append(arcNe) crvsU.append(arcNe)

LtlenCh=len(pts[0]) if i>0:

arcL=rs.AddArcPtTanPt(pts[0][i-1],tangLt1[i-1][3],pts[0][i]) arcR=rs.AddArcPtTanPt(pts[1][i-1],-tangLt2[i-1][3],pts[1][i])

lineM=rs.AddLine(arcMidLt[i-1],arcMid) dist=rs.Distance(arcMid,arcMidLt[i-1]) noWall=int(dist/1)

arcLdiv=rs.DivideCurve(arcL,noWall) arcLdiv.pop() arcRdiv=rs.DivideCurve(arcR,noWall) arcRdiv.pop() arcMdiv=rs.DivideCurve(lineM,noWall) arcMdiv.pop() ltlen=len(arcLdiv)

for j in range(1,ltlen): vectN=rs.VectorCreate(arcLdiv[j],arcMdiv[j]) vectang=rs.VectorAngle(vectCheck,vectN) if vectang>-0.00001 and vectang<0.00001: stwall=rs.AddLine(arcLdiv[j],arcRdiv[j]) UVC.straightwall=stwall continue

else:

arcInt=rs.AddArc3Pt(arcLdiv[j],arcRdiv[j],arcMdiv[j]) crvsU.append(arcInt)

elif check == 0: arcCentPt=[] for in arcs: pts.append(rs.DivideCurve(i,div)) arcCentPt.append(rs.ArcCenterPoint(i)) for in range (len(pts[0])): tang=rs.PlaneFromPoints(pts[0][i],arcCentPt[0],((pts[0][i][0]),(pts[0][i] [1]),((pts[0][i][2])+1))) vectN=tang[1] vectang=rs.VectorAngle(vectCheck,vectN) if (vectang>179.99 and vectang<180.01) or (vectang>-0.01 and vectang<0.01): stwall=rs.AddLine(pts[0][i],pts[1][i]) UVC.straightwall=stwall else:

crvsU.append(rs.AddArcPtTanPt(pts[0][i],tang[1],pts[1][i]))

midlist=int(len(crvsU)/2) cnt=-1 crvsU1=[] crvsU2=[]

for i in crvsU: cnt=cnt+1 if cnt<midlist: crvsU1.append(i)

else: crvsU2.append(i) distLt=[] for j in crvsU1: testpt=rs.CurveMidPoint(j)

dist=rs.Distance(testpt,lineMid) distLt.append(dist)

distLt,crvsU1 = zip(*sorted(zip(distLt,crvsU1)))

distLt1=[] for j in crvsU2: testpt=rs.CurveMidPoint(j) dist=rs.Distance(testpt,lineMid) distLt1.append(dist)

distLt,crvsU2 = zip(*sorted(zip(distLt1,crvsU2)))

crvsU=[]

crvsU.append(crvsU1) crvsU.append(crvsU2) UVC.Ucurves=crvsU

return crvsU

def arcV(arcU,arcs,rot,check,rotG):

distofwalls=1.5 arcCentLt=[] for i in arcs: arcCent=rs.ArcMidPoint(i) arcCentLt.append(arcCent) cnt=0 crvs=[] arcsV=[] tmpArcLt=[] for j in arcs: # if curvature is less than 0.5 if check ==1: cnt=cnt+1 crvsV=[] arcsRad=rs.ArcRadius(j) arcMid=rs.ArcMidPoint(j) dist=rs.Distance(arcMid,centpt) noWalls=math.floor(dist/distofwalls) vect=rs.VectorCreate(centpt,arcMid) vect=rs.VectorUnitize(vect) for k in range (1,(int(noWalls)+2)): if k==1: nradius=arcsRad else: nradius=(arcsRad*((k)**1.2)) circ=rs.AddCircle(arcMid,nradius) if cnt ==1 and rot ==0: circ=rs.RotateObject(circ,arcMid,180+rotG) elif cnt==2 and rot ==0: circ=rs.RotateObject(circ,arcMid,0+rotG) elif cnt==1 and rot ==-90: circ=rs.RotateObject(circ,arcMid,90+rotG) elif cnt==2 and rot ==-90: circ=rs.RotateObject(circ,arcMid,-90+rotG) raddiv=rs.DivideCurve(circ,4) vectM=rs.VectorCreate(arcMid,raddiv[2]) circ=rs.MoveObject(circ,vectM) scaleWall=distofwalls*(k-1) vectSc=rs.VectorScale(vect,scaleWall) circ=rs.MoveObject(circ,vectSc) crvsV.append(circ) # if curvature is more than 0.5 elif check ==0: crvsV=[] crvsV1=[] cnt=cnt+1 arcsRad=rs.ArcRadius(j) arcMid=rs.ArcMidPoint(j) dist=rs.Distance(arcMid,centpt) noWalls=math.ceil(dist/distofwalls) vect=rs.VectorCreate(centpt,arcMid) vect=rs.VectorUnitize(vect) ltlen=int(noWalls)+1 for k in range (1,ltlen):

if k==1 or k==ltlen-1: radius=arcsRad*(k**0.4) circ=rs.AddCircle(arcMid,radius) if cnt==1 and rot ==360: circ=rs.RotateObject(circ,arcMid,0+rotG)

elif cnt==2 and rot ==360: circ=rs.RotateObject(circ,arcMid,180+rotG)

raddiv=rs.DivideCurve(circ,4) vectM=rs.VectorCreate(arcMid,raddiv[2]) circ=rs.MoveObject(circ,vectM) scaleWall=distofwalls*(k-1)

vectSc=rs.VectorScale(vect,scaleWall) circ=rs.MoveObject(circ,vectSc) crvsV.append(circ)

ltlen0=len(arcU[0]) ltlen1=len(arcU[1])

intStLt=[] intStTanLt=[] intEnLt=[] intEnTanLt=[]

for i in crvsV: divpts=rs.DivideCurve(i,4) arc=rs.AddArc3Pt(divpts[3],divpts[1],divpts[2]) intSt=rs.CurveCurveIntersection(arc,arcU[0][(ltlen0)-1]) intParaSt=rs.CurveClosestPoint(arcU[0][(ltlen0)-1],intSt[0][1]) intTanSt=rs.CurveTangent(arcU[0][(ltlen0)-1],intParaSt)

intStLt.append(intSt[0][1]) intStTanLt.append(intTanSt) intEn=rs.CurveCurveIntersection(arc,arcU[1][(ltlen1)-1]) intParaEn=rs.CurveClosestPoint(arcU[1][(ltlen0)-1],intEn[0][1])

intTanEn=rs.CurveTangent(arcU[1][(ltlen0)-1],intParaEn) intEnLt.append(intEn[0][1]) intEnTanLt.append(intTanEn) intPtOn=rs.CurveCurveIntersection(arc,arcU[0][0])

segs=ltlen-2

if cnt==1:

Arc1=rs.AddArcPtTanPt(intStLt[0],intStTanLt[0],intStLt[1]) Arc2=rs.AddArcPtTanPt(intEnLt[0],intEnTanLt[0],intEnLt[1]) StLine=rs.AddLine(rs.CurveMidPoint(crvsV[0]),rs.CurveMidPoint(crvsV[1]))

elif cnt==2:

Arc1=rs.AddArcPtTanPt(intStLt[0],-intStTanLt[0],intStLt[1]) Arc2=rs.AddArcPtTanPt(intEnLt[0],-intEnTanLt[0],intEnLt[1]) StLine=rs.AddLine(rs.CurveMidPoint(crvsV[0]),rs.CurveMidPoint(crvsV[1]))

Arc1Div=rs.DivideCurve(Arc1,segs)

Arc2Div=rs.DivideCurve(Arc2,segs) StLineDiv=rs.DivideCurve(StLine,segs) for i in range (segs): crvsV1.append(rs.AddArc3Pt(Arc1Div[i],Arc2Div[i],StLineDiv[i]))

distLt=[]

if check==0: for i in crvsV1:

testpt=rs.CurveMidPoint(i) dist=rs.Distance(testpt,arcCentLt[0]) distLt.append(dist) distLt,crvsV1 = zip(*sorted(zip(distLt,crvsV1))) for i in crvsV1: arcsV.append(i) crvs.append(crvsV1)

if check==1: for i in crvsV:

testpt=rs.CurveMidPoint(i) dist=rs.Distance(testpt,arcCentLt[0]) distLt.append(dist) distLt,crvsV = zip(*sorted(zip(distLt,crvsV))) ltlen0=len(arcU[0]) ltlen1=len(arcU[1]) for i in crvsV: intSt=rs.CurveCurveIntersection(i,arcU[0][(ltlen0)-1]) intEn=rs.CurveCurveIntersection(i,arcU[1][(ltlen1)-1]) intPtOn=rs.CurveCurveIntersection(i,arcU[0][0]) arcsV.append(rs.AddArc3Pt(intSt[0][1],intEn[0][1],intPtOn[0][1])) crvs.append(arcsV)

UVC.Vcurves=arcsV[:] UVC.Vcircles=arcsV[:] return crvs

#class to store UV curve for splitting and additional UV curves class UVCurves(): def __init__(self):

self.Arcs=[] self.ArcsRad=[] self.ArcsCent=[] self.Rotation=[] self.Vcurves=[] self.UcurvesCopy=[] self.Vcircles=[] self.VcrvRad=[] self.VcrvCent=[] self.Ucurves=[] self.UarcsSplit=[] self.UarcsSplitDead=[] self.UarcsReverse=[] self.ArcsPt=[] self.Vcrvpts=[] self.ExtraWalls=[] self.tmpLt=[] self.tmpLt2=[] self.straightwall=[] self.state=[] self.StLine=None self.CircVect=None def setCentLine(self): self.StLine=rs.AddLine(self.ArcsCent[0],self.ArcsCent[1]) self.CircVect=rs.VectorCreate(self.ArcsCent[1],self.ArcsCent[0]) def getArcRad(self): for i in self.Arcs: self.ArcsRad.append(rs.ArcRadius(i)) self.ArcsCent.append(rs.ArcCenterPoint(i)) def getVcrvRad(self): for i in self.Vcircles: self.VcrvRad.append(rs.ArcRadius(i)) self.VcrvCent.append(rs.ArcCenterPoint(i)) def intersectcurves(self): for i in self.Ucurves: tmLt1=[] UcurveLt=[] for j in i:

stpt=rs.CurveStartPoint(j) enpt=rs.CurveEndPoint(j) midpt=rs.CurveMidPoint(j)

vectcheck=rs.VectorCreate(enpt,stpt) vectang=rs.VectorAngle(vectcheck,self.CircVect) if vectang>-0.00001 and vectang<0.00001: UcurveLt.append(rs.AddLine(enpt,stpt)) else: UcurveLt.append(rs.AddArc3Pt(stpt,enpt,midpt)) tmLt2=[] divPts=[]

VcrvLen=len(self.Vcurves) for k in range(1,(VcrvLen)-1): intPt=rs.CurveCurveIntersection(j,self.Vcurves[k]) para=rs.CurveClosestPoint(j,intPt[0][1]) divPts.append(para) tmLt2=rs.SplitCurve(j,divPts) tmLt1.append(tmLt2) self.UcurvesCopy.append(UcurveLt) self.UarcsSplit.append(tmLt1) def addwalls(self): if self.state==1: rang= len(self.UarcsSplit[0]) rang2=len(self.UarcsSplit[0][0]) cnt1=-1

#cycle through the lists e1=[] Lt1=[] Lt2=[]

for i in self.UarcsSplit: cnt1=cnt1+1 cnt2=-1

Ltlen=(len(i))-1 check=-1 pc=-1 KillCounter=-1 for j in i: check=check+1

if check == Ltlen: continue else:

cnt2=cnt2+1

cnt3=-1

mid=len(j) mid=int(math.floor(mid/2))

for k in j:

#check to see the length of a split beam

tmpextwalls=[] tmpchlt=[]

cnt3=cnt3+1

if cnt3==mid: arcLen=rs.CurveLength(k)

ce=-1 if KillCounter<4: #if beam is longer than set length then create two new walls if arcLen>4.5 and cnt2!=rang: KillCounter=KillCounter+1

if self.UarcsSplit[cnt1][cnt2] == None: continue

LtlenSp=len(self.UarcsSplit[cnt1][cnt2]) SpPos=int(math.floor(LtlenSp/2))

#VLtlenSp=len(self.Vcircles) #VSpPos=int(math.floor(VLtlenSp/2))

if cnt1==0: pc=pc+1 if pc ==0: e=int(math.ceil(len(self.Vcircles)/2)) else: e=e+1 e1.append(e) if cnt1==1: pc=pc+1 e=e1[pc]

LeCircRad=self.ArcsRad[0]*((e+1)**1.2) LeCirc=rs.AddCircle(self.ArcsCent[0],LeCircRad) LeCirc=rs.RotateObject(LeCirc,(0,0,0),self.Rotation) LeCircDiv=rs.DivideCurve(LeCirc,2) LeCircVectM=rs.VectorCreate(self.ArcsCent[0],LeCircDiv[0]) LeCirc=rs.MoveObject(LeCirc,LeCircVectM) LeCircVectC=rs.VectorCreate(self.ArcsCent[1],self.ArcsCent[0]) Sca=self.ArcsRad[0]+(e*1.5)

LeCircVectU=rs.VectorUnitize(LeCircVectC) LeCircVectS=rs.VectorScale(LeCircVectU,Sca) LeCircVectM=rs.VectorCreate(LeCircVectS,self.ArcsCent[0]) LeCirc=rs.MoveObject(LeCirc,LeCircVectM) LeCircVect=rs.VectorCreate((0,0,0),self.ArcsCent[0]) LeCirc=rs.MoveObject(LeCirc,-LeCircVect) tmpextwalls.append(LeCirc) if cnt1==1: self.Vcircles.insert(SpPos,LeCirc) ch=0 tmpchlt.append(ch) self.tmpLt.append(LeCirc)

RiPos=SpPos+1 Lt1.append(RiPos)

RiCircRad=self.ArcsRad[1]*((e+1)**1.2)

RiCirc=rs.AddCircle(self.ArcsCent[1],RiCircRad) RiCirc=rs.RotateObject(RiCirc,(0,0,0),self.Rotation) RiCircDiv=rs.DivideCurve(RiCirc,2) RiCircVectM=rs.VectorCreate(self.ArcsCent[1],RiCircDiv[1]) RiCirc=rs.MoveObject(RiCirc,RiCircVectM) RiCircVectC=rs.VectorCreate(self.ArcsCent[0],self.ArcsCent[1]) Sca=self.ArcsRad[1]+(e*1.5) RiCircVectU=rs.VectorUnitize(RiCircVectC) RiCircVectS=rs.VectorScale(RiCircVectU,Sca) RiCircVectM=rs.VectorCreate(RiCircVectS,self.ArcsCent[1]) RiCirc=rs.MoveObject(RiCirc,RiCircVectM) RiCircVect=rs.VectorCreate((0,0,0),self.ArcsCent[1]) RiCirc=rs.MoveObject(RiCirc,-RiCircVect) Lt2.append(RiCirc) self.tmpLt.append(RiCirc) tmpextwalls.append(RiCirc) ch=1 tmpchlt.append(ch) if cnt1==0: self.Vcircles.insert(RiPos,RiCirc)

Ltlen=(len(tmpextwalls))-1 cnt=-1

ptArcLt=[]

#for each circle wall cycle through beams to make arcs for i in tmpextwalls:

LtLen= len(self.UarcsSplit[cnt1]) cnt=cnt+1

outline=rs.JoinCurves(self.UarcsSplit[cnt1][LtLen-1])

ccint1=rs.CurveCurveIntersection(k,i) para=rs.CurveClosestPoint(i,ccint1[0][1]) tang=rs.CurveTangent(i,para)

UcCoLen=len(self.UcurvesCopy[cnt1])

#need the last line from each list ccint2=rs.CurveCurveIntersection(outline,i)

if ccint1==None or ccint2==None: continue

if ccint1[0][1]==ccint2[0][1]: break if round(ccint1[0][1][0],4)==round(ccint2[0][1][0],4): break

else: if cnt1==0 and tmpchlt[cnt]==0: tang=-tang elif cnt1==1 and tmpchlt[cnt]==0: tang=tang elif cnt1==0 and tmpchlt[cnt]==1: tang=tang elif cnt1==1 and tmpchlt[cnt]==1: tang=-tang

ptArc=rs.AddArcPtTanPt(ccint1[0][1],tang,ccint2[0][1]) ptArcLt.append(ptArc) self.ExtraWalls.append(ptArc)

#split beams to arcs and pass back into the original list if len(ptArcLt)>1: for m in range (cnt3,LtLen):

EvalPtLt=[] DivPt=[]

intPt1=rs.CurveCurveIntersection(self.UarcsSplit[cnt1][m] [SpPos],ptArcLt[0])

intPt2=rs.CurveCurveIntersection(self.UarcsSplit[cnt1][m] [SpPos],ptArcLt[1])

if intPt1==None or intPt2==None: continue else:

stpt=rs.CurveStartPoint(self.UarcsSplit[cnt1][m][SpPos]) mdpt=rs.CurveMidPoint(self.UarcsSplit[cnt1][m][SpPos]) enpt=rs.CurveEndPoint(self.UarcsSplit[cnt1][m][SpPos]) arc=rs.AddArc3Pt(stpt,enpt,mdpt)

EvalPtLt.append(rs.CurveClosestPoint(arc,intPt1[0][1]))

EvalPtLt.append(rs.CurveClosestPoint(arc,intPt2[0][1])) SpCrv=rs.SplitCurve(arc,EvalPtLt) SpCrv.reverse() self.UarcsSplit[cnt1][m].pop(SpPos) for i in SpCrv: self UarcsSplit[cnt1][m].insert(SpPos,i) def killbeams(self): #cycle through beams and kill any which are less than 1m apart cnt=-1

#cycle two list if self.state==1: for i in self.UarcsSplit:

Len1=len(self.UarcsSplit[0][0]) SpPos=int(math.floor(Len1/2))

cnt=cnt+1

#cycle through U lists avoiding the middle tempCnt=[] tempCntMid=[] for j in i: cnt2=-1

len2=len(j)-SpPos templt=[] templt2=[] for k in j:

cnt2=cnt2+1 if SpPos>cnt2 or cnt2>len2-1: templt.append(cnt2) else:

templt2.append(cnt2)

tempCntMid.append(templt2)

tempCnt.append(templt)

cntt=-1

Lt=len(tempCnt)

Lt1=len(tempCnt[0]) for j in range (Lt1):

if j==(Lt1): continue

else: for k in range(Lt): ind=tempCnt[k][j] if ind==Lt: continue

else: arc=self.UarcsSplit[cnt][k][ind] if arc== None: continue

else: arcMid=rs.CurveMidPoint(arc)

#check against rest of list for m in range(k,Lt): ind1=tempCnt[m][j]

archeck=self.UarcsSplit[cnt][m][ind1] if archeck == None: continue

else:

archeckMid=rs.CurveMidPoint(archeck) dist=rs.Distance(archeckMid,arcMid)

if dist== 0 or m == Lt-1: continue if dist<1:

#self.UarcsSplitDead.append(archeck) self.UarcsSplit[cnt][m][ind1]=None else: continue

Lt= len(tempCntMid) for j in range (Lt): if j==Lt: continue else:

Lt2=len(tempCntMid[j]) for k in range (Lt2): ind= tempCntMid[j][k] arc=self.UarcsSplit[cnt][j][ind] if arc ==None: continue else: arcLen=rs.CurveLength(arc) arcMid=rs.CurveMidPoint(arc) if arcLen>1.1:

for m in range (j,Lt-1): Lt3=len(tempCntMid[m]) for n in range (Lt3): ind1= tempCntMid[m][n] archeck=self.UarcsSplit[cnt][m][ind1]

if archeck ==None: continue else: archeckMid=rs.CurveMidPoint(archeck) dist=rs.Distance(arcMid,archeckMid) if dist ==0 : continue elif dist<1: self.UarcsSplit[cnt][m][ind1]=None else: continue if self.state==0: for i in self.UarcsSplit: cnt=cnt+1 #cycle through U lists avoiding the middle tempCnt=[] tempCntMid=[] Lt1=len(i) for j in range (Lt1): if j==(Lt1): continue else: Lt2=len(i[j]) for k in range(Lt2): if k==Lt2: continue else: arc=self.UarcsSplit[cnt][j][k] if arc== None: continue

else: arcMid=rs.CurveMidPoint(arc) #check against rest of list

for m in range(j,Lt1): archeck=self.UarcsSplit[cnt][m][k] if archeck == None: continue else: archeckMid=rs.CurveMidPoint(archeck) dist=rs.Distance(archeckMid,arcMid)

if dist== 0 or m == Lt1-1: continue if dist<1: self.UarcsSplit[cnt][m][k]=None else: continue

#initiate main class list UVCLT=[] for i in range (0,int(noFloors)): UVC=UVCurves() z=i*3

centpt=0,0,z #creates four nodes manipulated by footprint defCircle=rs.AddCircle(centpt,radius[i]) defCircle=rs.RotateObject(defCircle,centpt,rotG[i]) divCircles=rs.DivideCurve(defCircle,4) b=divCircles[2] #conditional statement to flip the node about the xy axis and create base geometry if curvature[i] >= 0.5: #greater than check=0 rot=360 a=arc(arclen1[i],divCircles[2],rot,check,curvature[i],centpt,rotG[i],arclen2[i]) b=arcU(a,arclen1[i],check) c=arcV(b,a,rot,check,rotG[i]) elif curvature[i] < 0.5: #smaller than check=1 rot=0 a=arc(arclen1[i],divCircles[2],rot,check,curvature[i],centpt,rotG[i],arclen2[i]) b=arcU(a,arclen1[i],check) c=arcV(b,a,rot,check,rotG[i])

UVC.getArcRad() UVC.getVcrvRad() UVC.setCentLine() UVC.intersectcurves() UVC.addwalls() #UVC.killbeams() UVCLT.append(UVC)

p=noFloors-1 b=[] c=[] d=[] e=[] f=[] for p in range(noFloors): for i in UVCLT[p].Ucurves: for j in i: b.append(j) for i in UVCLT[p].Vcurves: c.append(i)

d.append (UVCLT[p].straightwall) for i in UVCLT[p].UarcsSplit: for j in i: for k in j: d.append(k) for i in UVCLT[p].ExtraWalls: e.append(i)

for i in UVCLT[p].tmpLt2: f.append(i)