Investigating the proportions of branching structures in architecture by larsen christian

Investigating the proportions of branching structures through form-finding process of tree-like structures in architecture.

Larsen Christian IU1443000006 2019

Investigating the proportions of branching structures through form-finding process of tree-like structures in architecture.

Presented to the Institute of Design, Environment and Architecture, Indus University

In partial fulfillment of the Requirement for the degree of Bachelors of Architecture

By: Larsen Christian

Thesis guides: Radhika Amin Mitalee Parikh

August 2019

Rancharda, Thaltej, Ahmedabad, Gujarat 382115

Approval of successful completion of B. Arch Thesis The following Bachelor of Architecture Thesis is hereby approved as credible work on the approved subject carried out and presented in a manner sufficiently satisfactorily to warrant its acceptance as a prerequisite to the Bachelor in Architecture for which it has been submitted. It is also to be understood that by this approval, the undersigned does not necessarily endorse and approve any statement made, opinion expressed or conclusion drawn therein, but approves the study only for the purpose for which it has been submitted and satisfies him to the requirement laid down by the thesis committee in July 2018.

Thesis Title: Investigating the proportions of branching structures through form-finding process of tree-like structures in architecture.

Name and Signature of Student:

Larsen Christian

Name and Signature of HOD:

Bhanupratap Sharma

Name and Signature of Thesis Guides:

Radhika Amin

Mitalee Parikh

Rancharda, Thaltej, Ahmedabad, Gujarat 382115

Rancharda,Thaltej, Ahmedabad, Gujarat 382115

Plagiarism Declaration Name of Student: Larsen Julius Christian Department: Architecture University: Indus University Guides: Radhika Amin, Mitalee Parikh Head of Department: Bhanu Pratap Sharma Title of Thesis: Investigating the proportions of branching structures through form-finding process of tree-like structures in architecture.

I affirm that I am aware of the Anti-Plagiarism Policy at Institute of Design Environment and Architecture (IDEA), Indus University. Plagiarism is using another personâ&#x20AC;&#x2122;s thoughts, words, results, judgements, ideas, images, drawings etc. and presenting them as your own. I declare that the conceptualisation, conduct of data collection, and ultimately the writing of the thesis report is my original work, except where duly acknowledged and referenced. I have identified and included the source of all facts, opinions, and viewpoints of others in the report. I have cited the source of all quotations, paraphrases, summaries of information, tables, diagrams, photographs, drawings, electronic media and other materials in which intellectual property rights may reside. I am solely responsibility for checking my work for plagiarism, and not my thesis guides or the thesis coordinator. I also declare that this report, or any part of it, has not been previously submitted by me or any other person for assessment in this Institute or any other Institute.

I understand that failure to comply with the Instituteâ&#x20AC;&#x2122;s regulations governing plagiarism constitutes a serious offence for which the Institute may impose severe penalties. A substantiated charge of plagiarism will result in a penalty being ordered, ranging from a mark of zero for the assessed work to expulsion from the Institute.

Signature of Student:

Rancharda, Thaltej, Ahmedabad, Gujarat 382115

ABSTRACT This research work illustrates the importance of proportions in three dimensional branching structure getting through the form-finding process with the manual calculations and rectifying it in 3d modeling software by structurally analyze the forms with available steel pipes for finding the most efficient structure. It is about an understanding the structural behavior and advantages of branching into the structure. Many architects have tried to achieve branching in architecture, some case studies showing the different ideology used as a structure with different materials and joints. Frei Otto has made a research model of branching structure with form-finding process in 1960 and tried to apply that structure in a proposal of Kocmmas government center, a branching column merging into dome shaped roof with the hexagonal grid, which was never built. The research model of branching structure made by Frei Otto has a relationship of proportions and these structures are mainly acting as a load bearing structure and only suffers from tension or compression and minimum or less bending moment, which comes under a category of lightweight structures. The research is done to find out the reason of finding the effect of multiple levels of branching on an actual structure with the existing proportion used by Frei Otto in his research model. By the using structural analytical software with the parameters affecting on structures like bending moment, slenderness ratio and displacement and the self-weight of structure, there is an outputs with the values proving the efficiency of the branching structure through different levels of proportions and fixed size of the roof area.

AKNOWLEDGEMENT This Thesis is an opportunity for me to dedicate myself towards architecture with the help of ‘nature’. The completion of my thesis would not have been possible without the following people, I would like to take this opportunity to thank them. First and foremost, I would like to thank my guides Radhika Amin and Mitalee Parikh for their time and guidance, to both the guides for understanding and resolving my doubts at all the phases throughout my thesis and kept me encouraged in a true direction. I would like to extend my gratitude to Kireet Patel, Mangesh Belsare, Sankalpa, Jitayu Purani, whose thought-provoking discussions provided a clearer insight into the inquiry of the research and providing a useful knowledge. I would also like to thank the idea faculty members Bhanu Pratap Sharma, Nitin Gurnani, Shreya Kaul, Manan Singhal, Pratik Zaveri, Atreya Bhattacharya and Tejendra Tank, Harsh Soni from the engineering department for their guidance and critics. I am grateful to my friend Keithy Gandhi for always being there to listen my problems and help me out in any circumstances throughout the journey, also would like to thank Parth Shah, Fenil Shah, Nilay Khatri, Purvang Gohel, Dixita Maniar, Priyanshi Pathak, Kajal Jani, Devarsh Patel, Shivam Oza and the whole batch of 2014 for their continuous support. I really appreciate the efforts from Fabiana R. Ortega F. to help me by providing enough informations. Special thanks to Dean D’Cruz and team Mozaic, I really appreciate the vigourous attempt, that made so much easier for me. Most importantly, I would like to thank my parents, my brother and sister-in-law for their enormous support and encouragement all along the way.

CHAPTERISATION Abstract Aknowledgement Co n t e n t s .................................................................... . . . . . . . . . . . 02

â&#x20AC;&#x2DC; W e a lwa y s b or r ow th e pri nci pl es f rom nat ure, Up on whi ch w e have bui l t our ow n w orl d .â&#x20AC;&#x2122;

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..........06 Aim/Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..........07 Research Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..........07 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...........08 Scope and Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...........08 Framework of Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..........09

CH A P T E R - 1 B ra nc hing S tru c tu re : Form vs Fu nc tion 1.1 Nature in to designing ......................................... . . . . . . . . . . 11-13 1.2 Design by Natural Systems and Principles................... . . . . . . . . . 14-16 1.3 Branching Structures 1.3.1 Introduction ............................................ . . . . . . . . . 17 1.3.2 Fractal Geometry in L-system.. .................... . . . . . . . . . . 18 1.3.3 Natural VS Branching Structure ................... . . . . . . . . . . 19 1.3.4 Mechanical Behaviour of tree .................... . . . . . . . . . . 20 1.3.5 Historical Evolution .................................... . . . . . . . . . 21-24 1.3.6 Branching in roofsurfaces........................... . . . . . . . . . 25 1.3.7 Secondary Case Studies ............................ . . . . . . . . . . a. Sagrada familia ................................. . . . . . . . . . . 27-28 b .Johnson Wax Office ............................ . . . . . . . . . . 29-30 c. Pallazzo Del Lavaro ............................ . . . . . . . . . . 31-32 d. Karwar Church .................................. . . . . . . . . . . 33-34 e.Tote Mumbai ..................................... . . . . . . . . . . 35-36 f. The Atelier ......................................... . . . . . . . . . 37-38

CH A P T E R - 2 Form -Find ing P roc e s s 2.1 Physical form-finding ......................................... . . . . . . . . . . . 43-46 2.2 Proportions in branching structures ......................... . . . . . . . . . . . 47-48 2.4 Forces applying on structures 2.4.2 Graphic Statics diagram ............................ . . . . . . . . . 49 2.3 Primary Case Study 2.3.1 Stuttgart Airport ....................... ............... . . . . . . . . . . 51-55

C H AP TE R - 3 S t ruct u r al An a l ysi s o n form-fi ndi ng p r oces s m od el s o f br an ch in g 3.1 Software for Analysis 3.1.1 Staad Pro Software.........................................................................57 3.1.2 Preparations for Analysis................................................................58-59 3.1.3 Graphical output of analysis.........................................................60 3.1.4 Memberâ&#x20AC;&#x2122;s Structural Property........................................................61 3.1.5 3D Diagram Setup for analysis.......................................................62 3.1.6 Material Selection...........................................................................63 3.2 Parameters for Structural Analysis............................................................... 64-65 3.3 Levels of Branching............................................................................66-107 C H AP TE R - 4 C o nclu sion .. . ................................. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 0 8 - 1 2 0 Li s t of Figu r es............................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2 4 - 1 2 5 I l l ust r at ion C r e d i ts......................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2 6 - 1 2 7 B i b liogr aph y

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INTRODUCTION

â&#x20AC;&#x153;Trees are organisms that stand by themselves, so their shape has an inherent structural rationality.â&#x20AC;? â&#x20AC;&#x201C;Toyo Ito

Fig. 1.1 Research models

In the building, structure only provides stability, and it cannot be the creator of architectural space. But, such an approach creates the border between structure and architecture. Due to lack of the structural limitation many buildings did not finish and in fact architecture had lost its identity and become a horizontal and vertical cover to the building structure. Structure and architecture are two significant components in shaping building creation. Interaction and conflict between the two components and the development of construction technologies has led to the creation of a new generation of buildings with advanced technological structure. Therefore the review of the history of the presence of structure in the building and its integration with architecture is necessary. Structures within natural systems effectively integrates the form and functions. Nature achieves maximum productivity with minimum efforts. The adaptation of natural systems and forms in architecture has been used for over decades for both form and constructional purposes. One of these natural form is the tree. For a long period of time architects like Antonio-gaudi and Frei-Otto have researched about these forms and trying to achieve principle of a tree into structures. The main issue about these structures is finding the most equitable form to solve the problem of the actual design. The process of form finding is helpful to get form through proportions and the symmetry of the branching structure with the help of manual calculations. Branching structures are mainly used to get more span with less materials, which comes under the category of lightweight structures. The Form-Finding methods have been changed due to the usage of computers but the research has done by physical form-finding process. If one has a requirement of getting more span with less material with minimum ground connections with appropriate proportions is the question and to answer this problem the availability of steel pipes as material with consideration of factors affecting on structures like weight of the structure, bending moment, axial forces, usable area,etc will help to set a guidelines for most efficient branching column as per different categories. The main concern is wider span and new challenging form, therefore, filling the gap will result in a better understanding of the way that changes in proportions of branching in structures.

AIM

HOW / METHODOLOGY

To investigate the structural behavior of branching structures by varying the relative proportions in order to develop an efficient system through a form - finding process and using available material by analyzing forms digitally with the factors affecting on the structure.

1. 2. 3. 4. 5. 6.

OBJECTIVES • • • • •

To study the adaptation of tree like structures in architecture. To understand the role of branching into structural system. To understand branching through case studies by role of materials and native of junctions in structural system as a tree-like column. To use Frei Otto’s form-finding technique to establish a geometric understanding of proportions in branching structure. To understand the proportions of branching affecting in structural strength and analyse efficiency of branching with different proportions through available material with limitations of structural members.

PRIMARY QUESTIONS •

Which form of proportion in three dimensional branching is the most efficient structure as a support for flat roof?

SECONDARY QUESTIONS • • • • • •

What are branching structures? What are the structural behavior and advan tages of branching structures? How different architects have tried to achieve branching in architecture? How the physical form finding process helps to achieve the proportions of branching struc tures? Which can be the most lightweight form of branching to support larger area with minimum material? How the changing in proportions with available material helps to get the most equitable form of branching.

Sequence of Study

Understanding the evolution of branching in to developing system for architectural application. Investigating proportions with the help of physical form-finding process of deriving branching in to structures. Manually Deriving dimensions from the physical form-finding process in modelling. Analyze how materials, joineries, and proportions affects the branching structures. Investigating the structure of different form of branching through structural analysis with availability of material. Looking forward to structural parameters like bending moment, ration of slenderness and displacement to analyze forms of branching.

SCOPE •

The study is restricted to analyze and understand branching structure with flat roof through physical form-finding process, manual calculations and structural analysis through software with the help of standard tata steel Structura hollow pipe sections as considering available material.

LIMITATIONS • •

The study is only limited to bilateral sym metrical geometry of branching pattern. The Structural analysis is only limited to some parameters aspects and not considering the function of the building in study. The Analysis is only for flat roof with fixed sizes available of material for all the forms.

FRAMEWORK OF ANALYSIS

• Bilateral symmetrical geometry • Pysical Form-Finding model scale: -1:100 • One of the case study with actual use of branching structurally is Stuttgart Airport Terminal-3, which has roof grid of 21m x 12m. 21m

12m

Fig. 1.2 Reference of a case study for an analysis 21m

21m

Fig. 1.3 Showing Decided Span for analysis

• Fixed roof grid – 21x21m, • Similar roof load for all the analysis. • Tata standard steel box section for roof members and hollow pipe sections for branching structural members. • Members length are not considered as of for the forms generated and analysis, after considered the design problem – as per tata standerd available member lenth

CHAPTER - 1 Bra nc hing S t ru ctur e : For m v s Fu nc t io n 1.1 Nature in to designing 1.2 Design by Natural Systems and Principles 1.3 Branching Structures 1.3.1 Introduction 1.3.2 Fractal Geometry in L-system 1.3.3 Natural VS Branching Structure 1.3.4 Mechanical Behaviour of tree 1.3.5 Historical Evolution 1.3.6 Branching in roofsurfaces 1.3.7 Secondary Case Studies a. Sagrada familia b .Johnson Wax Office c. Pallazzo Del Lavaro d. Karwar Church e.Tote Mumbai f. The Atelier

• Structural analysis by Staad Pro v8i software • The output of the analysis will be the values of bending moment, Slenderness Ration, displacement and self weight of the structure.

BENDING MOMENT DIAGRAM

ACCORDING TO THE BENDING MOMENT DIAGRAM THE COMPRESSION ON THE LONGER SPAN IS ABOVE AND ON THE SHORTER SPAN IS BELOW THUS THE ORIENTATION OF THE MEMBERS IN THE ARCH .

IDEOLOGY USED

COMPRESSION MEMBERS ARE ADDED BETWEEN TWO UNIT MODULES TO AVOIDE LATERAL BUCKLING

THE ARCH IS A THREE PINNED ARCH THAT MAKES THE SYSTEM DETERMINATE

STRUCTURE 7

THE DECKING IS ABOVE THE TECHNICAL MODULE COMPRESSION MEMBERS WHERE THA SPAN IS LONGER AND THE GLAZING ON THE SHORTER SPAN IS SUSPENDED FROM THE BELOW AS THE COMPRESSION MEMBER IS BELOW

GROUP

TECHNICAL MODULE

NO. 2

Waterloo station SCALE 1:250 Fig. 1.8 Its a railway station,when train comes the forces will try to pull roof which acts flixible.

BENDING MOMENT COMPONENTDIAGRAM MODEL SHOWING TWO UNIT MODULES

SCALE-1:50

Fig. 1.9 Steel trusses with different tubular sections and flexible hinge joints.

PLAN

STRUCTURAL ANALYSIS EXPANSION JOINTS ARE ADDED WHERE THE SHAPE AND THE DIRECTION OF THE BUILDING CHANGES

PINNED SYSTEM

Fig. 1.12 Steel exoskeleton is used as an efficient lateral bracing mechanism to hold the structure.

Fig. 1.13 Human body’s twisting principle taken as a concept. THE DECKING IS ABOVE THE COMPRESSION MEMBERS WHERE THA SPAN IS LONGER AND THE GLAZING ON THE SHORTER SPAN IS SUSPENDED FROM THE BELOW AS THE COMPRESSION MEMBER IS BELOW

priciple applied

UDL IS CONCIDERED ON LONG SPAN AS THE LOAD GIVEN BY SHORTER SPAN CAN BE TAKEN BY LONGER SPAN

BENDING MOMENT DIAGRAM

ACCORDING TO THE BENDING MOMENT DIAGRAM THE COMPRESSION ON THE LONGER SPAN IS ABOVE AND ON THE SHORTER SPAN IS BELOW THUS THE ORIENTATION OF THE MEMBERS IN THE ARCH .

“originality is returning to the origin.” - Antoni Gaudi

FORM MODEL SHOWING THE OVERALL BUILDING SCALE-1:200

STRUCTURE 7

Fig. 1.6 Structural elements used by Gaudi.

TECHNICAL MODULE TUBULAR SECTIONS ARE USED FOR THE COMPERSSION MEMBERS . THE SECTION SIZES ARE CONCIDERED ACCORDING TO THE BENDING MOMENT DIAGRAM ,AS WHERE THE MOMENT IS MAXIMUM THE SECTION SIZE IS MAXIMUM

COMPRESSION MEMBERS ARE ADDED BETWEEN TWO UNIT MODULES TO AVOIDE LATERAL BUCKLING

Eastgate Centre Fig. 1.14 No need of HVAC systemfor vantilation for whole building.

Afterwards, Frei otto was already preoccupied with the research fundamental questions of structures, How to achieve more with less. - To construct greater spans with less mate-rials and efforts. To understand and create these structures the behavior of natural forces has to be understood in a thorough manner. The structural efficiency is considered most essential. The process of imitating the natural structural principle into an actual building structure is still evolving and researching by lots of architects.

Fig. 1.10 Pangolin has a flixible armour skin, the concept the flexibility of it.SHOWING THE OVER ACCORDING TO THE is BENDING FORM MODEL

OVERALL PLAN OF THE WATERLOO TERMINAL STATION

Turning Torso THE ARCH IS A THREE ARCH with THAT MAKES THE Fig. 1.11 It is a residential building DETERMINATE 147 apartments are spread out across 54 floors, with a one-of-a-kind layout.

Fig. 1.15 The principle applied of the organisation in the building for the vantilation system.

Fig. 1.16 Termites mounds in Africa stay remarkably cool inside, even in blistering heat.

THE DECKING IS ABOVE THE COMPRESSION MEMBERS WHERE THA SPAN IS LONGER AND THE GLAZING ON THE SHORTER SPAN IS SUSPENDED FROM THE BELOW AS THE COMPRESSION MEMBER IS BELOW

STRUCTURE 7

TECHNICAL MODULE

GROUP NO. 2

DHRUTI PATEL MANYA JAIN RUTU PATEL AYUSHI SHAH

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Fig. 1.7 Soap Bubble experiment model by Frei Otto.

1 Peach, Joe. Gaudi’s Masterpiece Nature-Inspired Architecture. National Geographic magazine,2017.

The esplanade Fig. 1.17 This building has the two domes of skin with the glass panels for natural light.

Fig. 1.18 Extruded part of the skin, the sun is not directly heating up the glass and giving natural light.

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IU144000008 IU1443000020 IU1443000029 IU1443000034

COMPRESSION MEMBERS ARE ADDED BETWEEN TWO UNIT MODULES TO AVOIDE LATERAL BUCKLING

Scanned by CamScanner

Very first Gaudi drew inspiration from the natural world. Nowhere is this connection more clearly visible than in his masterpiece, Barcelona’s Sagrada Familia. The elements found in Gaudi’s nature-inspired work, which is referred to as biomimetic architecture, can be classified as ornamental or structural. Structural elements inspired by nature include: catenary arches, spiral stairways, conoid-shaped roofs, and a new type of tree-inspired column that uses hyperbolic paraboloids as its base.

DHRUTI PATEL MANYA JAIN RUTU PATEL AYUSHI SHAH

TUBULAR SECTIONS ARE USED FOR THE COMPERSSION MEMBERS . THE SECTION SIZES ARE CONCIDERED ACCORDING TO THE BENDING MOMENT DIAGRAM ,AS WHERE THE MOMENT IS MAXIMUM THE SECTION SIZE IS MAXIMUM

SECTION

Fig. 1.5 Idea of velcro used in many fields for different purposes

DHRUTI PATEL MANYA JAIN RUTU PATEL AYUSHI SHAH

MOMENT DIAGRAM THE COMPRESSION ON THE LONGER SPAN IS ABOVE AND ON THE SHORTER SPAN IS BELOW THUS THE ORIENTATION OF THE MEMBERS IN THE ARCH .

Fig. 1.4 Design Achieved from nature Neri Oxman and MIT have developed programmable water-based biocomposites for digital design and fabrication. Named Aguahoja, It uses natural ecosystems as inspiration for a material production process that produces no waste. “Derived from organic matter, printed by a robot, and shaped by water, this work points toward a future where the grown and the made unite.”

NO. 2

UDL IS CONCIDERED ON LONG SPAN AS THE LOAD GIVEN BY SHORTER SPAN CAN BE TAKEN BY LONGER SPAN

STRUCTURE 7

DRAWINGS OF WATERLOO TERMINAL STATION

GROUP

No priciple applied

THE DECKING IS ABOVE THE COMPRESSION MEMBERS WHERE THA SPAN IS LONGER AND THE GLAZING ON THE SHORTER SPAN IS SUSPENDED FROM THE BELOW AS THE COMPRESSION MEMBER IS BELOW

No priciple applied

Velcro was invented by Swiss engineer George de Mestral in 1941 after he removed burrs from his dog and decided to take a closer look at how they worked. The small hooks found at the end of the burr needles inspired him to create the now ubiquitous Velcro.

USED IN THE BUILDING

TUBULAR SECTIONS ARE USED FOR THE COMPERSSION MEMBERS . THE SECTION SIZES ARE CONCIDERED ACCORDING TO THE BENDING MOMENT DIAGRAM ,AS WHERE THE MOMENT IS MAXIMUM THE SECTION SIZE IS MAXIMUM

priciple applied

BUILDING

Many designers are inspired from nature which includes design analogies, metaphors, structural systems. Natural systems works efficiently.As an inspiration as a model, as a measure and as a mentor many researchers from many disciplines started to investigate natural forms,patterns and organisatons. From imitating the form to look like a nature itself, to extracting principles from natural systems and applying it to designs.

OVERALL PLAN OF THE WATERLOO TERMINAL STATION

Scanned by CamScanner

1 . 1 I m i t a t i n g N a t u r e i n t o designing

COMPRESSION MEMBERS ARE ADDED BETWEEN TWO UNIT MODULES TO AVOIDE LATERAL BUCKLING

TUBULAR SECTIONS ARE USED FOR THE COMPERSSION MEMBERS . THE SECTION SIZES ARE FORM MODEL SHOWING THE OVERALL BUILDING SCALE-1:200 CONCIDERED ACCORDING TO THE BENDING MOMENT DIAGRAM ,AS WHERE THE MOMENT IS MAXIMUM THE SECTION SIZE IS MAXIMUM

Fig. 1.19 durian fruit’s skin as geometry for roof.

1.2 Design by Natural Systems and Principles priciple applied

Bionics

Fig. 1.21 Surface of the building’s back catches the fog and roll down water into harvesting tank.

Fig. 1.22 Droplets form on the hydrophilic rough surface of the beetle’s back and roll down into mouth.

Biomimetic Otto Schmidt coined this term in 1950s. The abstraction of the principal extracted from the nature applied to design. The term itself is derived from bios, meaning life, and mimesis, meaning to imitate. This science represents the study and imitation of nature’s methods, designs, and processes. While some of its basic conﬁgurations and designs can be copied, many ideas from nature are best adapted when they serve as inspiration for human-made capabilities. By adapting mechanisms and capabilities from nature, scientiﬁc approaches have helped humans understand related phenomena and associated principles in order to engineer devices and improve their capabilities. “Question – Can the combination of the biological characteristics of life and the built environment offers new solutions for more appropriate, more sustainable architecture.”

priciple applied

Hydrological Centre Fig. 1.20 The concept of collecting water in desert from fog into usable water for a centre.

Biology + technics In 1958, Jack E. Steele introduced the term Bionics and he defined it as the science of natural systems or their analogues. The creation of products devices and process by using the materials and forces of nature.

Fig. 1.24 A plain paper and a folded paper,plain paper has less surface and folded paper has more inertia.

Fig. 1.25 Shells are always protected with the help of corrugation.

No priciple applied

Tagor Hall Fig. 1.23 This building has corrugation in roof and in the walls acting as a load bearing structure.

Biomimicry

Fig. 1.27 A bird’s wing movement has tried been tried to imitate for the outer skin with kinetic mechanism.

Fig. 1.28 A bird’s wing movement has taken as a approach for the designing moving skin.

priciple applied

Milwaukee Museum Fig. 1.26 This building has a sun shading automatic external ribs of wings which moves as per the sun’s directions.

bios to life and mimesis to imitate. Jenine Benyus used the term in her book;” Biomimicry: Innovation inspired by Nature” in 1997. The process of mimicking nature in to design, which can be translated as learning the opinions of nature by imitating them, started to be considered as a new science by designing the possible solutions and potential in nature’ “Nature as model.” imitates or takes inspirations from natural designs and processes to solve human problems.”

Munich Stadium Fig. 1.29 This building has the first tensite roof stadium designed by frei otto with membrane.

Fig. 1.30 Building model for the tensile structure with the help of tensile fabric.

Fig. 1.31 Soap bubbles are examples of the minimal surface with some amount of surface tension.

2 Benyus, Janine.M-BiomimicryInnovation Inspired by Nature, Harper Collins, New York,1998. 3 Gruber, Petra. Biomimetics in architecture, architecture of life and buildings, Springer Wien, New York,2011

“Nature as measure.” it has surviving since billion years and learned that what works and what lasts.” “Nature as mentor.” from what we can learn from it.

N a t u r e’ s P r in ci p l es A p p l i ed i n to d es i g ni ng

FRAMES/LINEAR

SURFACES

ORGANISATION

HUMAN BONE & MUSCLE

SPIDER WEB

TERMITE’S MOUND

Fig. 1.33 Femur Bone

Fig. 1.34 Spider’s web

The bone only has material where it is necessary to withstand the stresses and forces that are being applied to it - Porosity.

Membrane

Steel Trusses They are also very porous and only have steel where it needs to support the loads.

Fig. 1.36 Effile Tower

CATEGORISATION OF NATURAL SYSTEMS

TREE

‘SILK’ can be a structural member or a membrane.

Branching. Supply and Networks - Minimal pathways - Direct path system - System of minimised detour Structural Principles - Broad to narrow - One splits into two (mainly)

Fig. 1.38 East Gate Centre Fig. 1.39 CH2 city council 2

SOAP BUBBLES / FILMS

Nambian Beetle

These are extremely thin films of soapy water closing air that forms a hollow sphere with an iridescent Surface. Minimal surface Giving a certain Volume, They will always take the shape with the least surface.

Fig. 1.43 Palazzetto Del Lavoro Fig. 1.44 Stuttgard Airport

Fig. 1.32 Showing the axtracted principles from nature

For this vantilation system there is an organisation for each of the function

Fig. 1.37 The Federal Garden Exhibition

Fig. 1.41 Soap Bubble

Fig. 1.40 Tree’s Branching

Its Strength, Toughness, Elasticity and Robustness which originate from its heirarchical structures design to web architecture.

Fig. 1.35 Termite mound

Termite’s mound in Africa stay remarkably cool inside, even in blistring heat. No need of day ventilation systems. It has natural cooling system. Natural Ventilation System

Fig. 1.45 Olympic Stadium Munich

Fig. 1.42 Nambian Beetle

This beetle is capturing moisture however from the swift moving fog that moves over the desert by fiting its body into the wind. Droplets from on the hydropholic rough surface of the beetle’s back and wings and rolls down into its mouth. Water Generator Fog into usable water

Fig. 1.46 Hydrological Centre

1.3 Branching Structures

1.3.2 Fractal Geometry in L - System

1.3.1 Introduction

An L-system consists of an alphabet of symbols that can be used to make strings, a collection of production rules that expand each symbol into some larger string of symbols, an initial â&#x20AC;&#x153;axiomâ&#x20AC;? string from which to begin construction, and a mechanism for translating the generated strings into geometric structures. L systems have a set of production rules, which are repeated through a few generations. Each generation starts drawing a structure at a starting point, and draws lines at defined angles and lengths. Each subsequent generation draws a similar structure at new starting points. The simplest L-system is One where you take a point, and draw two lines, one at a positive vector angle, and one negative (the angle is a variable). The length of the line is proportionally reduced in each generation.

What is branching structures? A branching structure is established on the principle of a tree. Expanding from one point the structure branches out to multiple branches, expanding its extent. With a wider reach, a larger surface area can be supported. This is the major consideration as the main advantage of a branching structure. The structure can transfer the loads on a large surface to one single column or point with high structural efficiency. This division of members results in a shorter span for the roof members and therefore to smaller structural members. Also, the length of each member is decreased reducing the buckling length. Due to the dividing members a large span or area can be supported. This division of members results in an optimal load path system which helps in transferring loads to its minimum distance to the loading points.

Fig. 1.47 Branching as a structural system

Fig. 1.49 L-System Branching Method

One of the methods is Fractal geometry which is based on multiple mathematical or reproduction rules. A fractal is a non-regular geometric shape that has the same degree of non-regularity on all scales. By repeating these rules or functions, each repetition is called an iteration.

Iteration 1

Iteration 2

Iteration 3

Iteration 4

Fig. 1.48 Fractal branching Iterations

Iteration 5

Fig. 1.50 L-System Branching Exapmles 4 Joseph Claghorn, FRACTAL TREES BASIC L-SYSTEM, Generativelandscapes Wordpress,

1.3.4 Mechanical Behaviour of tree

1.3.3 Natural System VS Branching Structures

Fig. 1.51 Carrying Large Surface

Fig. 1.52 Carrying Large Surface

Fig. 1.61 Mechanical Behaviour of a tree

Fig. 1.53 Load transfer to a single Trunk

Fig. 1.54 Load transfer to a single Support

Fig. 1.55 Splitting in different directions

Fig. 1.56 Splitting can be manageable

Fig. 1.57 Material Distribution

Fig. 1.58 Material Distribution as per structural need

• The main principle of a natural tree is its capacity of carrying a large surface supported by a narrow element (trunk) trough fractal-like branching configuration. This is considered the advantage of a tree and is copied into a branching structure. • The structure is able to transfer the loads from a large surface to one single column or point in a both aesthetic as structural optimal form. • Branching structures, however, have a different structural behaviour compared to actual trees. • A tree is able to reduce the loading by deformations and stream-lining of branches, twigs, and leaves. a tree can absorb bending moments due to the big spreading roots and flexible trunk. Both trees as building structures suffer from the same loading types such as static, snow and wind loading. • The main problem with branching structures is to find the right proportions with the amount of levels. • By shaping the tree in an efficient way, it can reach high structural efficiency. This efficiency comes from the fact that spatial structures mainly suffer from tension or compression and no or bending moments. Therefore, the branches of tree structures should also be arranged properly. 5 lasef Md Rian, Mario Sassone.Tree inspired dendriforms and fractal-like branching structures in architecture: A brief historical review. Higher Education Press Limited Company, 2014. 6 Nerdinger, Winfried. Frei Otto, Complete Works: Lightweight Construction, Natural Design. Birkhäuser, Basel (2005).

Fig. 1.59 Static,snow and wind Loads

Fig. 1.60 Static,snow and wind Loads

1.3.5 Historical Evolution

Till medieval period, there were no such relatable examples that were directly inspired by the tree’s structure. The Basilica Cistern in Istanbul constructed in the 6th century is an ex-ample of pre-medieval dendriform structures. It was constructed by more than 9m high and 300 marble column, imitating a dense forest. It was designed for supporting the massive area of vault structures composed by semi-circular arches.

An imitation of the form and shape of a tree or plant is defined as Dendriform. The Greek word of the tree is ‘Dendron’. It is also known as ‘Dendron structure’. It Describes a mesh free branching structure. The origin of dendriforms in Architecture is not known. In architecture, many principles are inspired by natural phenomena. In the early stages, the sculptural shapes were represented by the natural shapes in construction. A well-known example, during the ancient civilized period of Egypt, the graceful papyrus cluster columns of Luxor Temple (1400 BC) built with sand-stone. Columns having the capitals that imitate the umbels of papyrus plant in bud (Figure 1).

The use of shapes of trees, plants and flowers as an ornamental feature is also seen in the Greek and Roman columns in Classical and Roman periods (500 BC to 400 AD). A well-known example is the Corinthian columns in the Roman period, these columns were decorated with floral decorations. Very few artisans were skillfull to make this kind of articulations.In post-Roman periods, we find other examples of mimicking trees and plant as ornamentation was designed using stone, masonry and stucco. After pre medieval periods, these decorations were also extensively seen in the Islamic architecture.

Fig. 1.62 Luxor Temple,Egypt

Fig. 1.63 Ajanta Caves

Fig. 1.64 Corinthian column

A few ages later the first example of a branching like structure are the Chinese Dougong Brackets, mainly found in Chinese temples and places. ‘Dou’ means wooden block or piece and ‘gong’ means wooden bracket. An interlocking assemblage of some ‘gongs’,bow-shaped brackets is a typical construction method. The dougong is a can-tilever structure, which carries the load of the beam and the overhang roof into the column. The dougong is a form of larger bracket as column capital replaced by interlocking self similar brackets to increase the stiffness as well as to transfer the roof and beam load sequentially to the column.

7 lasef Md Rian, Mario Sassone.Tree inspired dendriforms and fractal-like branching structures in architecture: A brief historical review.Higher Education Press Limited Company, 2014.

Fig. 1.65 Dougong Brackets

In the beginning of the medieval period, 12th century AD, The fan vaults - an important type of dendriform structure appeared in architecture. Sainte Chappelle in Paris constructed during 1242 AD to 1248 AD is one the earliest examples of fan vaults. The typical Gothic style in characteristics, these vaults were enclosed by stained glass, is supported by the columns, each of which is a bundle of thin columns that become ribs. Another example of fan vault was constructed in 1351 AD, designed by Thomas of Cam-bridge, in the Gothic period, a new structural approach towards constructing vaults known as fan vault where the pointed arch was used. A series of vaults were designed during that period to replicate the forest from inside. Between 1880 AD and 1920 AD, a style of structural dendriforms is found in the work of Antonio Gaudi, within his work, he was able to merge architectural form and structural efficiency by introducing the forms of trees. He often said “There is no better structure than the trunk of a tree or a human skeleton”. In the Sagrada Familia Cathedral in Barcelona, branching pattern of tree has a structural mechanism to hold the large tree crown, and this structural concept was adopted by Gaudi. He imagined this church as if it were the structure of a forest, with a set of treelike columns divided into different branches to support a structural of intertwined hyperboloid vaults. Gaudi’s structural dendriforms are one of the earliest and finest examples of making treelike concrete made branching structures inspired by nature.

Fig. 1.67 The basilica cistern

Fig. 1.68 Sainte Chapelle

Fig. 1.69 The Chapel of King’s College

Fig. 1.70 Sagrada Familia Cathedral

Fig. 1.66 Dougong Brackets branching

8 lasef Md Rian, Mario Sassone.Tree inspired dendriforms and fractal-like branching structures in architecture: A brief historical review.Higher Education Press Limited Company, 2014.

Fig. 1.71 Sagrada Familia Cathedral

Between 1930 AD to 1970 AD, Structural minimalism was one of the sophisticated techniques. The shape like mushroom’ or ‘umbrella’ were the abstract form of a tree’s overall shape. One of the earliest example of reinforced concrete mushroom structure having a shape of ‘mushroom’ or ‘umbrella’, is the Skovshoved Petrol Station in Denmark, which is designed by Arne Jacobsen in 1936. In the same time period, the sophistications of mushroom columns quickly reached their apex in the Johnson Wax Administration Building, constructed in 1939 and designed by F.L. Wright, became a landmark example of concrete mushroom structures. Herbert Johnson, the owner of the Building, Wright promised him to give a building in which a person could ‘feel as though he were among pine trees breathing fresh air and sunlight’.

Fig. 1.72 Skovshoved Petrol Station

Fig. 1.77 Frei Otto branching model of KOCOMMAS govenrment centre, Majilis al shura

Fig. 1.73 Johnson’s Wax Building

Two years later, Italian engineer Giorgio Baroni designed ‘ Baroni’s tree’ in 1938, having inverted mushroom umbrella structures. It was known as first inverted reinforced concrete umbrella structures. Palazzo Del Lavoro in Turin is one of the wellknown example constructed in 1961. The columns were cast in steel framework. Lined with narrow timber boards. These columns are cantilevered and splayed geometries structural efficiency by varying capacity with the bending moment distribution. The basic shape of column were ‘+’ and then it merges into circle at the top. In the early 1960’s another architect known for its experimenting with nature’s forms, began to work with branching structures. Frei Otto, German architect, professor and found-er of the Institute for Lightweight Structures. As a result, Otto started to design and investigate hanging models of branching systems as can be seen in figure 5. Different configu-rations and formations of architectural trees were developed and experimented with. In IL Publication 32 (1983). Otto describes that “Branching structures can transfer compression and bending forces with a low own mass. Otto started to design and investigate hanging models of branching systems 9 lasef Md Rian, Mario Sassone.Tree inspired dendriforms and fractal-like branching structures in architecture: A brief historical review.Higher Education Press Limited Company, 2014.

Fig. 1.74 Baroni’s tree

By using coputational method for form finding process stuttgart airport is one of the example showing the use of such kind of branching structures built in 1992 by Von Gerkan, Marg+Partners.In this structure four seperate steel members sprout from the base as a trunk and then each member turn into a seperate stem, and finally each branching stem further splits in to another four branches. The cross sectional diameter of the main trunk and each branching member are icrementally decresed upwards to achieve, the tapering feature of tree that can ensure a unifrom distribution.

Fig. 1.78 Stuttgart Airport Terminal-3

Tree-like column at the orient station, Lisbon constructed in 1998 designed by Santiago Calatrava is different compared to the columns of Stuttgart Airport. column has a steel members and branching outward like a palm leaf and creating a canopy.

Fig. 1.79 Orient Station, Lisbon

Fig. 1.75 Palazzo del Lavoro

Fig. 1.76 Frei Otto branching model

10 lasef Md Rian, Mario Sassone.Tree inspired dendriforms and fractal-like branching structures in architecture: A brief historical review.Higher Education Press Limited Company, 2014.

1.3.6 Branching with different roof surfaces Current development in architecture and building structure have resulted in more challenging forms and shape. Flat roofs are the simplest form of a canopy and to providing shelter to use that individual space beneath for appropriate functions. In a few built examples branching structures are used to support the flat roof or a free form surfaces which supports large area. Branching in Free form Surfaces

CASE STUDIES Fig. 1.80 Changsha South railway station

Multiple branching columns are supporting the whole free form roof which shelters the whole Changsha South railway station, China. In that case steel columns are placed with bundle of four with two leves of branching and a strategy to reduce the roof member size and getting more span with minimum ground junctions, which is working efficiently in a public building.

a. Sagrada familia b. Pallazzo Del Lavaro c. Karwar Church d. Johnson Wax Office e. The Atelier f. Tote Mumbai

Branching in flat Surfaces

Fig. 1.81 The national gallery museum extension in Singapore

The glass and metalwork continues onto the roof of the gallery and is supported by a series of tree-like structures made from steel. The filigreed roof and veil are supported by beams in three tree-like structures which were â&#x20AC;&#x2DC;the support solution as it was able to create maximum support for the new roof with minimum footprint.

Sagrada Familia

The outcome was obtained by the convergence of two helicoidal columns, one rotating clockwise and the other counterclockwise. At each intersection the number of edges increases with eight (in fact, it doubles), while the vertices reduce their size, so that the section is finally turned into something very near to a circle. Structural columns includes also transitional columns that in turn form the base for smaller columns, in number from 2 to 5, necessary to split the weight of the vault into separate forces. The vertical and partly inclined pillars are decorated with grooves. It creates the impression that the material organizing the pillars has been stretched. At the top the pillars branch out so that each can support multiple points of the ceiling. Whole segments of the roof are supported by such branched columns.

Architect :- Antoni GaudĂ Construction timeline (1882 - 2026) There are two substantial principles observed in Gaudiâ&#x20AC;&#x2122;s work: nature and geometry. Organic forms became essential structural elements in his architecture, along with the geometry.Gaudi translated the geometry of natural forms like tree trunks and branches into the design of cathedral.

Fig. 1.85 Columns holding ceiling

Fig. 1.83 Types of Column

Scale :- 1:1500 Fig. 1.82 Sagrada Familia Ground Floor Plan

The cathedral is characterized by four types of columns with less decorations and engraved with vertical striations, starting from star to end in a circle, and becoming thinner at top. The splitting in columns are transfering load of roof from four points to one primary point which helps to achieve more span and to reducing the amont of material at the top.

Fig. 1.86 Column Branching out

The columns are made of materials of different stiffness. The longest and heaviest columns are constructed of red porphyry, a very hard volcanic stone. The dark, somewhat smaller pillars are built of basalt, granite columns supporting the lighter and the outermost row of columns in the church building consist of a relatively soft rock. Fig. 1.84 Section with colums 11Jaume Serrallonga, The double twist columns: geometry, mechanics and symbolism.blog.sagradafamilia, Nov 21,2018.

Fig. 1.87 Column Geometrical order

Johnson Wax Office Building Architect :- Frank Lloyd Wright Construction timeline (1936 - 1939) Wright had promised Herbert Johnson to give him a beautiful building in which a person could feel as though he were among pine trees breathing fresh air and sunlight.He named the column ‘dendriform’- tree shaped and he borrowed from botany to name three of their four segments, stem, petal and calyx.

Each slab is circular, same diameter as the petal beneath it. The material of the column is reinforced concrete. They also tested the single column to know the strength and capacity of it. They started to test it with twelve tons and it was stable but wright, continued testing. After adding to the loads that column was carrying sixty tons, which is five times the load required by the state. Fig. 1.90 Load Testing Column

Fig. 1.91 Car Port Column

Fig. 1.88 Johnson Wax Building Ground Floor Plan

Scale :- 1:750 Fig. 1.93 Column Detailed Section

Scale :- 1:75 Fig. 1.92 Office Building

The base of each column is a seven inch high, three ribbed shoe, which he called a crow’s foot. On it rests the shaft, or stem, nine inches wide at the bottom and widening two and a half degrees from the vertical axis. The taller column are mostly hollow. Capping the stem is a wider hollow, which he called as a calyx. On the calyx sits a twelve and a half inch thick hollow pad wright called a petal. Two radial concrete rings and continuous concrete struts run through it. Both stem and calyx are reinforced with steel mesh, and a petal id reinforced with mesh and bars.

Fig. 1.89 Johnson Wax Building Section

Scale :- 1:750

12 Lipman Jonathan, Frank Lloyd Wright and the Johnson Wax Buildings.Dover Publications,INC,New York,1986.

Palazzo del Lavoro Architect :- Pier Luigi Nervi Construction timeline (1959-61)

A single steel framework, composed of six components bolted together which could be dismantled, with which to erect all sixteen columns; a huge machine. The concrete was to be poured in three different stages, each one every two components.

The building is 160×160 m×m in plan, and considering the architectural and functional constraints imposed on the design. The 40m-long free spans required between each vertical structural element. The solution devised by Nervi consisted in a mesh of sixteen reinforced concrete Wcolumns with variable section along the height (equal to 20 m to the base of the roof), each one supporting a steel mushroom-type roof panel with radial beams spanning from the centre of each column. The panels are mutually separated by a 2 m-wide joint covered by a glass skylight.

Fig. 1.96 Column Detailed Drawing

Fig. 1.94 Pallazzo Del Lavaro Plan

Scale :- 1:1500

The construction of the columns in exposed reinforced concrete presented various issues. it was crucial to have perfect vertical alignment of the columns, especially at the top where the steel capital was to be placed.

The six pieces in which the tall column was made, The complete cycle for the erection of one column was achieved in ten days. When a column was ﬁnished, the whole steel form was dismantled and its internal timber skin, formed by 12 cm wide timber strips, was taken out, polished and re-installed within the machine, ready for another cycle. This process, repeated for all columns, and steel canteliver members are having slenderness of each members where is also uses the less material.

Fig. 1.97 Column with roofing Fig. 1.95 Section

Scale :- 1:1500

Fig. 1.98 Column’s R.C.C Detail

13 S. Sorace & G. Terenzi, Structural and historical assessment of a modern heritage masterpiece:“Palazzo del Lavoro” in Turin,WIT Press 2011.

Cathedral of Our Lady of the Assumption at Karwar, Karnataka Architect :- Dean Dâ&#x20AC;&#x2122;Cruz Construction timeline (1959-61) This building attempts to create a protective sky supported by tree like structures (each tree representing an apostle) over a Roman amphitheathre like space (where early Christian gatherings actually started).The Sacraments in Christianity are also represented in the transition through the building, starting with the Baptismal Font close to the entrance - From Birth to Death and New Life.

Fig. 1.101 Front Elevation with levels

K A R W A R

B F LO O R P LAN

1. Altar Fig. 1.99 Karwar Cathedral Groung Floor Plan Scale : 1:500 2. Blessed Sacrament 3. Baptismal Font 4. Chapel The entrance draws one up to a vantage point where one can have a formal 5. Entrance overview of the building (from the inside). From here one can see the entire space where 6. Balcony 7. Music Room each space is positioned and detailed based on its religious significance, for eg., Seven 8. Central Hall 9. Vestry steps representing the Sacrements step down and up from a Baptismal Pond close to the

entrance (into Christianity). The twelve main internal columns represent the Apostles and S E C T I O NAL P LAN they support the roof of the Cathedral. 0m

10m

1. Sacristy 2. Blessed Sacrament 3. Altar 4. Baptismal Font

20m

Fig. 1.100 Karwar Cathedral Section AA

S E C T I O N A-A Scale : 1:500

C A T H E D R A L

The Church is located in karnataka, as their local available material is a stone, outer wall as a skin is from laterite stone and the twelve columns inside which is the actual structure holding the whole roof of steel rafters and mangalore tile with splitting into eight steel members

Fig. 1.102 Chapel with the natural Light

Fig. 1.103 Column holding the roof

D2 K A R W A R C A T

Fig. 1.104 Section BB

R.C.C columns are at the same level and the splitting junction is of mild steel plates, which is bolted to column.

The Tote Architect :- Serie Architects Construction timeline (1993) The site was covered with mature rain trees whose wide spread leaves shaded most of the spaces throughout the year, Inspired by these rain trees, a new structural system creates a stunning aesthetic that runs throughout the space. Designed as a steel truss, the challenge lay in working through the construction system compatible with local skills. Rather than looking at steel fabricators within the building construction sector, the architects sourced boiler fabricators for high precision work. they have explored two sectional profiles for the truss, a box section and an I-section for this truss system.

The design of this structure is been done by computational software to achieve tree like form structure not for purpose of full used as a structure but it more includes the asthetic use, to merge the surroundings into building with the beauty of branches holding the whole roof with some punctures with the natural light in ceiling, ceiling is covered with the gypsam board.

Fig. 1.105 Tote Ground Floor Plan

The platforms are roofed by a metal structure 25 meters high. This elegant solution consists of a series of slender pillars that split on the top and connect with each other to create a continuous folding structure. Consistent with the rest of Calatravaâ&#x20AC;&#x2122;s work the analogies from the natural world jump into peopleâ&#x20AC;&#x2122;s minds: The group of pillars resemble palm trees or lilies, and in a geometric sense. it is not far from the also floral fan vaults of the British perpendicular gothic. The structural elements are painted white and the nerves of these so-called palms spread out to hold a folding glass roof where geometry and organic shapes find a synthesis in abstraction.

Fig. 1.107 Column Branching Out

Fig. 1.106 Ideology for designing

The Idea behind the the design is to make the building which merges into the surrounding nature, why the building itself become like a tree structure, so the design has developed by the L-System, Mild Steel strips welded with each other to make each columns by the local workers.

Fig. 1.108 Column Detailed Section

Fig. 1.109 Columns holding ceiling

The column is fixed with tie rods to the r.c.c footing and there is also a roof members, which are welded to the mild steel branches with fixed joint.

The Atelier Architect :- Biome Environmental Solutions Construction timeline (2016) The school sits in a neighbourhood with constant construction activity and a godown is in its immediate vicinity. Creating a learning space for a young age group on such a site required that the school be an enclosed and protective space. The site factor played a key role in the design, along with the Reggio-Emilia education approach itself, on which the school is based.

Fig. 1.112 Column Details

Fig. 1.110 Atelier Mezzanine Floor Plan

Exploratory learning is encouraged through a permeable design of the interiors - walls of varying heights enclosing curvilinear classrooms and common spaces under a skylight-dotted roof. The roof is supported on eight columns, each in the form of a branching tree. This tree form, while being a structural element, allows the roof to be perceived from a height that children can relate to. It is also a reinterpretation of learning under a tree, a common sight in rural parts of the country.

Fig. 1.113 Column holding the roof

The columns are fixed with steel plate to the ground junction and from the primary member itself with intermediate distances it splits into four twice holding the steel roof members. The branching members are all three pinned, which makes them fixed, the eight colums holding the whole slopping roof of the building.

Fig. 1.114 Pinned Column Branches

Fig. 1.111 Atelier Section BB

STEEL

Materials Foundation

R.C.C & STEEL R.C.C

Fixed Joint

21000

Johnson wax R.C.C M.S column holder with fixed joint

Materials Foundation

Palazzo del lavaro

The Tote

R.C.C & STEEL

STEEL

R.C.C

Steel plate with fixed joint

7500

5500

38000

11000

5500

6000

12000

STEEL

Steel plate with fixd joint

38000

11000

The Atelier

7500

Karwar Church

Stuttgart Airport

Primary member

Secondary member

Tertiary member

Roof Grid

The process of finding the most reasonable shape is called form-finding.

CHAPTER - 2 Form-Finding Process of Branching 2.1 Physical form-finding 2.2 Proportions in branching structures 2.4 Forces applying on structures 2.4.2 Graphic Statics diagram 2.3 Primary Case Study 2.3.1 Stuttgart Airport

Hangign model of sagrada familia cathedral by Antoni Gaudi, 1889.

2.1 Physical form-finding Suspended Constructions A Chain suspended between two points takes on a specific form known as the catenary curve.In the given situations, the catenary curve represent an unequivocally ideal shape in which there is only tension and no compression or bending.Unlike load bearing structures in compression, there is no danger of buckling. Thus this system is suitable for very large spans and minimal cross-sections, The shapes of suspended construction are natural shapes in the sense that they are created according to the laws of nature.

Fig. 2.3 Hangign model of sagrada familia cathedral, barcelona

Fig. 2.1 Hanging Chain Principle

With the aim of finding the ideal structure for a certain load case, physical form finding is a dominant method. One way of making a structural approximation for a load case is the use of tension based hanging models. Like Gaudi’s well-known hanging model of the Sagrada Familia (figure 2.3) in Barcelona the model is hanged with small bags filled with sand. This sand represents the vertical loading on the building and shapes the network of strings. Because funicular models only suffer from tension, high structural efficiency is achieved. By reversing the model, all forces will be reversed and the most efficient structure for the compression load case is shaped.

Inverting the suspended shape

Fig. 2.2 Poleni’s drawing of Hooke’s analogy between an arch and a hanging chain, and (b) his analysis of the Dome of St.-Peter’s in Rome [1748]

The principle was first formulated in 1676 by Robert Hooke.There are sketches by Christopher Wren in which he uses thrust lines to develop the dome constructuion for St. Paul Cathedral in London. As Antoni Gaudi who finally used the principle of inversion as a true form-finding method in architecture.

14 Nerdinger, Winfried. Frei Otto, Complete Works: Lightweight Construction, Natural Design. Birkhäuser, Basel (2005).

Branching Structure modeled by Frei Otto,1960.

Frei Otto developed an early model of branching structures together with students at Yale in 1960. In a hanging model, a slab was attached to 64 threads which were gathered again and again at different heights until they had been collected into four bundles. The threads were stiffened and the model was subsequently inverted. In another study during 1970,the location of the nodes and hence the effective lengths, were perfected mathematically.

Fig. 2.4 Frei otto branching structure experimental model

These branching structures are usually referred to as tree-like columns. However, their action cannot be compared with that of a natural tree.While the branches of a tree are under bending stress, bending forces are systematically avoided in the technicaal tree-like column. The inner structure of the tree-like columns represents a type of framework that is unique in the constructuion industry. It is not a truss with the triangular structure which would stiffen the structure, allow articulated joints between the truss elements, and prevent bending even under alternating loads. In the tree-like column , therefore, the individual elements must be rigidly connected at the joints. A tree-like column is perticularly well suited for only the one main load scheme for which it is optimised. All other loading conditions will cause bending stress within the structure. The branching structure is particularly effective as a load-bearing structure when the constructional task involves relatively small loads which act separately on a larger area and must be transferred across a specific distance to individual points of support. Example of such loads include ceiling or roof loads which are transferred to individual foundations.

15 Nerdinger, Winfried. Frei Otto, Complete Works: Lightweight Construction, Natural Design. BirkhĂ¤user, Basel (2005).

Own Form-Finding Processes

2.2 Proportions in branching structures

X X

Fig. 2.5 Frei otto branching structure proportions

Observations through Model - The total length of each string changes by shifting the nodes. - The branching pattern can be changed in multiple ways by shifting the origin of primary member - The internal forces (tension) increase when the length is decreased. - There are infinite ways of making an equilibrium. - The force in each member differs. - As the angle increase all the nodes has to be rigid or it will fall. - As the levels increase the load transfer will occur through many points which avoids bending in structure. - The usble space will increase as angle increase.

Fig. 2.6 Own Form-Finding Models

2.3 Graphic Statics The creation of a force diagram from a form diagram (with its external applied forces) is called Graphic Statics. Graphic statics is a way to get understanding into the forces acting on a structure graphically. Using force directions and polygons by the equilibrium of a structural system is represented. To get a better understanding of the forces flowing through the branching structures. The graphic statics is also one of the useful method for designer to structurally solve the form with the forces into many ways. The process of Graphic Statics used to be a standard method of analysing trusses and can be applicable for the 2d branching structure.

Primary Case Study

Fig. 2.7 Cremona Diagram

If a branching structure is statically determined it can be represented with a Cremona diagram. A design study done by Allen and Zalewsky (2012) shows an example of a Cre-mona diagram for a branching structure. In this case, the structure is inclined and has a point load of 7.5 K on each branch. In the given illustration of the arch, each branching structure also has multiple explana-tions for equilibrium. If the force polygon or Cremona is closed, the structure is a stable system, and all the members are only suffering from normal forces.

2.3.1 Stuttgart Airport

Fig. 2.8 Stuttgart Airport Branching Column Details

Fig. 2.9 Stuttgart Airport Branching Details

The Stuttgart Airport has Tree-like branching Structures in the entry terminals to create an ascending open wider space. The entire roof is divided into twelve sections partitioned by skylights, erected as a two-way slabs. Each of these areas are supported by the steel tree-like structures. These columns transfer all the loads passing down through the branches which are translated into the trunk and then down to the foundation.

One single primary support contains four attached tubular poles (that form the trunk of the tree) and spread into three different levels (forms into the branches). They are distributed to carry the roof loads in compression with minimal bending moments. The branches direct the forces into smaller resultant points and then transfer into the four tubular poles that acts as one. Fig. 2.10 Stuttgart Airport

Fig. 2.13 Stuttgart Airport Column Holding Ceiling

Fig. 2.14 Stuttgart Airport Column Siingle line diagram Area :- 21.1 mX 12 m = 253.2 m2 Volume :- 10.55 mX 21.1 m X12 m = 2671.3

Column Details :Fig. 2.11 Stuttgart Airport Plan

Scale : 1:1000

Fig. 2.12 Stuttgart Airport Section

Scale : 1:1000

16 Rick Fairhurst, Stuttgart Airport Case Study,2017.

Fig. 2.15 Stuttgart Airport Column Details

Chapter - 3 Structural Analysis 3.1 Software for Analysis 3.1.1 Staad Pro Software 3.1.2 Preparations for Analysis 3.1.3 Graphical output of analysis 3.1.4 Memberâ&#x20AC;&#x2122;s Structural Property 3.1.5 3D Diagram Setup for analysis 3.1.6 Material Selection 3.2 Parameters for Structural Analysis 3.3 Levels of Branching

Fig. 2.16 Stuttgart Airport Column Details

3.1 Software for Structural Analysis

3.1.2 Preparations for Analysis

3.1.1 STAAD PRO V8i

STEP 1 : Intersecting all the members

STAAD. Pro is a structural analysis and design software developed by Research Engineers International in 1997. In late 2005, Research Engineers International was bought by Bentley Systems, which is widely used to analyze and design structures for bridges, towers, buildings, transportation, industrial and utility structures. It supports over 90 international steel, concrete, timber & aluminium design codes of different country

STEP 2 : Breaking beams at all the nodes

It can model structural steel shapes such as beams, columns, and braces, based on country specific steel tables or user-defined shapes. Complete steel design by modeling steel connections, either standard or custom, and automatically adjust based on the connecting members. Model comprehensive steel box sections, pipes and rods.

Fig. 2.17 Breaking beams in structure

STEP 3 : In General Tab, Assigning the sections with materials in properties menu

It is one of the most reliable software for architects and structural engineers to know about their designs, it will stand or not, or it fails then which member is failing because of which factor, it helps to check and solutions for designs.

Fig. 2.18 Assigning properties to members

STEP 4 : Adding fixed support showing transferring load to earth.

Fig. 2.19 Assigning Fixed Support

17 Bentley/en/products/product-line/structural-analysis-software/staadpro

STEP 5 : Adding Loads acting on the structures, with the amount of safety factor.

3.1.3 Graphical output of Analysis

Fig. 2.20 Assigning Load (Self Weight)

STEP 6 : Running Analysis with all the output needed.

Fig. 2.23 Axial Force

Fig. 2.24 Bending Moment in y direction

Fig. 2.21 Running Analysis

STEP 7 : In the design tab, selecting the IS Code according to the country Standerds.

Fig. 2.25 Bending Moment in z direction

Fig. 2.27 Displacement

Fig. 2.26 Bending Stress

Fig. 2.28 Torsion

Fig. 2.22 Applying Standerd Code

STEP 8 : Adding Yeild Steel amount, check code, take off commands for all the members from design tab.

3.1.4 Member’s Structural Property

3.1.5 3D Diagram Setup for an analysis

X = 3m Span = 21 X 21 m

Fig. 2.29 Selected members

Fig. 2.30 Selected members Geometry

Fig. 2.33 Branching Column Analysis Framework Fig. 2.31 Selected member’s Bending Max value

Fig. 2.32 Selected member’s Displacement Max value

Roof Members :- 21m X 21m Span, 7 grid of each square of 3m X 3m Maximum Standard Size available of box section in Tata Steel Structura YST 310 grade 300X200 6mm Thickness Vertical Proportion:- Maximum Proportion is 10(x)= 10(3)= 3m Minimum proportion is 3m for each levels. Horizontal Levels :- One level adding up to three level. 62

3.1.6 Material selection as per the availability

3.2 Parameters for Structural Analysis What is Slenderness Ratio ? Slenderness ratio is the ratio of the length of a column and the least radius of gyration of its cross section. Often denoted by lambda. It is used extensively for finding out the design load as well as in classifying various columns in short/intermediate/long. (Îť = kL/r) Slenderness ratio = effective length of column Radius of Gyration What is bending moment? A bending moment is the reaction induced in a structural element when an external force or moment is applied to the element causing the element to bend. The most common or simplest structural element subjected to bending moments is the beam.

Fig. 2.35 Bending Moment Diagram

What is bending Stress? Bending stress is the normal stress that is induced at a point in a body subjected to loads that cause it to bend. When a load is applied perpendicular to the length of a beam (with two supports on each end), bending moments are induced in the beam. ... The bottom fibers of the beam undergo a normal tensile stress.

What is Deflection? deflection is the degree to which a structural element is displaced under a load. It may refer to an angle or a distance. Displacement = Span 180 Fig. 2.34 Tata Steel Standerd Hollow Pipe section sizes

As per IS Code : 800 (2007)

One Level of Branching

Fig. 2.36 Terms of IS Code 800 : 2007

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Level - 2

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Two Level of Branching

OBSERVATION :As the branching level is increasing, the weight of the structure is also simultaneously increased but these branching structure are mainly because of the avoidance of the bending moment, as per the above analysis from one level of branching the amount of bending moment is more. More the angle, higher the bending moment and more the length, higher the slenderness ration of a particular member.

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Available material (Tata steel) Hightlighted one failing

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Three Level of Branching

OBSERVATION :As adding one more layer of branching members to modules, the weight of the structure is also comparatively increased but the amount of bending moment is lesser than the single branching modules. There are more feasibility for the braching with limited lengths, benefits in to slenderness ratio.

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Chapter - 4 Conclusion

OBSERVATION :To Commence with the idea of branching has multiple joints, one member is branching out in two and many more. This third proportion of branching structure has showed inevitable results by validation of the slenderness ration and with the properties of bending moment, which resulted into a actual use of the structure.

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A l l t h e Ex per ime nte d Branchi ng For m s

Fig. 4.1 All the modules, highlighted one failing 109

Fig. 4.1 All the modules, highlighted one failing 110

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Conclusion This research has done to find the efficient 3d branching structure through form finding process with the available standerd material and to understand the structural parameters and their behaviour. This analysis has begun from a question, Is the research model made by frei otto with the proportion of branching structure works in actual structure with understanding the importance of proportions into structure.The study has the transition of the one level of branching to the third level of branching, there is a principle which has been followed by frei otto in his research, one splits into four, at the top most third level of branching there are 64 members which is holding the roof surface, which affecting the parameters including bending moment and the total weight of the structure. There are some case studies in which branching principles has been applied and the material which is used is steel hollow pipes, which shows asthetically the branching as in the tree. Steel is available in all over the world and has availability of Y 310 grade steel, which has more strength than any other steel grade with the standerd sizes, one can use the same proportions of branching with the same material easily. The most important role in the structure is materialâ&#x20AC;&#x2122;s strength and length. With the help of manual slenderness ration with the length calculations, there are always limitations in hollow pipe section sizes with the appropriate lengths. These branching structure are acting as a load bearing structure and because of the amount of bending moment, it has to be less or minimum. As one can see that if the branching level is increasing the weight of the structure automatically increase but these branching structure are mainly because of the avoidance of the bending moment, as per the analysis from one level of branching the amount of bending moment is more in compare to sencond and third level of branching ,which shows the resistance of the structure in actual conditions. Some forms of branching in which the slenderness ration is appropriate for the selected hollow pipe sections with the lengths but because of bending moment there will be a bending stress acting on the members, each member has the limitations to take certain amount of stress, if the stress will increase beyond the limitation of the memberâ&#x20AC;&#x2122;s properties it will fail structurally, in that cases the cross section of hollow pipe has been increased for the analysis.

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Because of the bending moment there is always the displacement of the member which will moves, as the branching increasing the displacement ration is also decreasing. Through the analysis there will be never a failure because of angle if the material properties and the cross section which has been used id appropriate, even with the maximum angle it will never fail because of the material properties, it will certailnly fail because of the member length and strength, which includes material distribution.

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List Of Figures Fig. 1.1 Research models Fig. 1.2 Reference of a case study for an analysis Fig. 1.3 Showing Decided Span for analysis Fig. 1.4 Design Achieved from nature Fig. 1.5 Idea of velcro used in many fields for different purposes Fig. 1.6 Structural elements used by Gaudi. Fig. 1.7 Soap Bubble experiment model by Frei Otto. Fig. 1.8 Waterloo station building Fig. 1.9 Steel trusses with different tubular sections Fig. 1.10 Pangolin has a flixible armour skin Fig. 1.11 Turning Torso building Fig. 1.12 Steel exoskeleton is used as an efficient lateral bracing Fig. 1.13 Human body’s twisting principle taken as a concept Fig. 1.14 Eastgate Centre building Fig. 1.15 The principle applied of the organisation in the building Fig. 1.16 Termites mounds in Africa Fig. 1.17 The esplanade Fig. 1.18 Extruded part of the skin Fig. 1.19 durian fruit’s skin as geometry for roof. Fig. 1.20 Hydrological Centre building Fig. 1.21 Surface of the building’s back catches the fog Fig. 1.22 Droplets form on the hydrophilic rough surface of the beetle Fig. 1.23 Tagor Hall Building Fig. 1.24 A plain paper and a folded paper Fig. 1.25 Shells are always protected with the help of corrugation. Fig. 1.26 Milwaukee Museum building Fig. 1.27 A bird’s wing movement Fig. 1.28 A bird’s wing movement has taken as a approach Fig. 1.29 Munich Stadium building Fig. 1.30 Building model with the tensile structure Fig. 1.31 Soap bubbles are examples of the minimal surface Fig. 1.32 Showing the axtracted principles from nature Fig. 1.33 Femur Bone Fig. 1.34 Spider’s web Fig. 1.35 Termite mound Fig. 1.36 Effile Tower Fig. 1.37 The Federal Garden Exhibition Fig. 1.38 East Gate Centre Fig. 1.39 CH2 city council 2 Fig. 1.40 Tree’s Branching Fig. 1.41 Soap Bubble Fig. 1.42 Nambian Beetle Fig. 1.43 Palazzetto Del Lavoro Fig. 1.44 Stuttgard Airport Fig. 1.45 Olympic Stadium Munich Fig. 1.46 Hydrological Centre Fig. 1.47 Branching as a structural system Fig. 1.48 Fractal branching Iterations Fig. 1.49 L-System Branching Method Fig. 1.50 L-System Branching Exapmles Fig. 1.51 Carrying Large Surface Fig. 1.52 Carrying Large Surface Fig. 1.53 Load transfer to a single Trunk Fig. 1.54 Load transfer to a single Support Fig. 1.55 Splitting in different directions Fig. 1.56 Splitting can be manageable Fig. 1.57 Material Distribution Fig. 1.58 Material Distribution as per structural need Fig. 1.59 Static,snow and wind Loads Fig. 1.60 Static,snow and wind Loads Fig. 1.61 Mechanical Behaviour of a tree Fig. 1.62 Luxor Temple,Egypt Fig. 1.63 Ajanta Caves Fig. 1.64 Corinthian column Fig. 1.65 Dougong Brackets Fig. 1.66 Dougong Brackets branching Fig. 1.67 The basilica cistern Fig. 1.68 Sainte Chapelle Fig. 1.69 The Chapel of King’s College Fig. 1.70 Sagrada Familia Cathedral Fig. 1.71 Sagrada Familia Cathedral Fig. 1.72 Skovshoved Petrol Station Fig. 1.73 Johnson’s Wax Building Fig. 1.74 Baroni’s tree Fig. 1.75 Palazzo del Lavoro Fig. 1.76 Frei Otto branching model

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Fig. 1.77 Frei Otto branching model of KOCOMMAS govenrment centre, Majilis al shura Fig. 1.78 Stuttgart Airport Terminal-3 Fig. 1.79 Orient Station, Lisbon Fig. 1.80 Changsha South railway station Fig. 1.81 The national gallery museum extension in Singapore Fig. 1.82 Sagrada Familia Ground Floor Plan Fig. 1.83 Types of Column Fig. 1.84 Section with colums Fig. 1.85 Columns holding ceiling Fig. 1.86 Column Branching out Fig. 1.87 Column Geometrical order Fig. 1.88 Johnson Wax Building Ground Floor Plan Fig. 1.89 Johnson Wax Building Section Fig. 1.90 Load Testing Column Fig. 1.91 Car Port Column Fig. 1.92 Office Building Fig. 1.93 Column Detailed Section Fig. 1.94 Pallazzo Del Lavaro Plan Fig. 1.95 Pallazzo Del LavaroSection Fig. 1.96 Column Detailed Drawing Fig. 1.97 Column with roofing Fig. 1.98 Column’s R.C.C Detail Fig. 1.99 Karwar Cathedral Groung Floor Plan Fig. 1.100 Karwar Cathedral Section AA Fig. 1.101 Front Elevation with levels Fig. 1.102 Chapel with the natural Light Fig. 1.103 Column holding the roof Fig. 1.104 Section BB Fig. 1.105 Tote Ground Floor Plan Fig. 1.106 Ideology for designing Fig. 1.107 Column Branching Out Fig. 1.108 Column Detailed Section Fig. 1.109 Columns holding ceiling Fig. 1.110 Atelier Mezzanine Floor Plan Fig. 1.111 Atelier Section BB Fig. 1.112 Column Details Fig. 1.113 Column holding the roof Fig. 1.114 Pinned Column Branches Fig. 1.115 Casestudies with the branching diagrams of each members Fig. 2.1 Hanging Chain Principle Fig. 2.2 Poleni’s drawing of Hooke’s analogy between an arch and a hanging chain, and (b) his analysis of the Dome of St.-Peter’s in Rome [1748] Fig. 2.3 Hangign model of sagrada familia cathedral, barcelona Fig. 2.4 Frei otto branching structure experimental model Fig. 2.5 Frei otto branching structure proportions Fig. 2.6 Own Form-Finding Models Fig. 2.7 Cremona Diagram Fig. 2.8 Stuttgart Airport Branching Column Details Fig. 2.9 Stuttgart Airport Branching Details Fig. 2.10 Stuttgart Airport aesthetics of column Fig. 2.11 Stuttgart Airport Plan Fig. 2.12 Stuttgart Airport Section Fig. 2.13 Stuttgart Airport Column Holding Ceiling Fig. 2.14 Stuttgart Airport Column Siingle line diagram Fig. 2.15 Stuttgart Airport Primary Column Details Fig. 2.16 Stuttgart Airport Column Details Fig. 2.17 Breaking beams in structure Fig. 2.18 Assigning properties to members Fig. 2.19 Assigning Fixed Support Fig. 2.20 Assigning Load (Self Weight) Fig. 2.21 Running Analysis Fig. 2.22 Applying Standerd Code Fig. 2.23 Axial Force Fig. 2.24 Bending Moment in y direction Fig. 2.25 Bending Moment in z direction Fig. 2.26 Bending Stress Fig. 2.27 Displacement Fig. 2.28 Torsion Fig. 2.29 Selected members Fig. 2.30 Selected members Geometry Fig. 2.31 Selected member’s Bending Max value Fig. 2.32 Selected member’s Displacement Max value Fig. 2.33 Branching Column Analysis Framework Fig. 2.34 Tata Steel Standerd Hollow Pipe section sizes Fig. 2.35 Bending Moment Diagram Fig. 2.36 Terms of IS Code 800 : 2007 Fig. 4.1 All the modules, highlighted one failing

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ILLUSTRATIONS CREDITS Fig. 1.4 Fig. 1.5 Fig. 1.6 Fig. 1.7 Fig. 1.8 Fig. 1.10 Fig. 1.11 Fig. 1.13 Fig. 1.14 Fig. 1.15 Fig. 1.16 Fig. 1.17 Fig. 1.18 Fig. 1.19 Fig. 1.20 Fig. 1.21 Fig. 1.22 Fig. 1.23 Fig. 1.24 Fig. 1.25 Fig. 1.26 Fig. 1.27 Fig. 1.28 Fig. 1.29 Fig. 1.30 Fig. 1.31 Fig. 1.33 Fig. 1.34 Fig. 1.35 Fig. 1.36 Fig. 1.37 Fig. 1.38 Fig. 1.39 Fig. 1.40 Fig. 1.41 Fig. 1.42 Fig. 1.43 Fig. 1.44 Fig. 1.45 Fig. 1.46 Fig. 1.48 Fig. 1.49 Fig. 1.62 Fig. 1.63 Fig. 1.64 Fig. 1.65 Fig. 1.66 Fig. 1.67 Fig. 1.68 Fig. 1.69 Fig. 1.70 Fig. 1.71 Fig. 1.72 Fig. 1.73 Fig. 1.74 Fig. 1.75 Fig. 1.76 Fig. 1.78 Fig. 1.79 Fig. 1.80 Fig. 1.81 Fig. 1.82 Fig. 1.83 Fig. 1.84 Fig. 1.85 Fig. 1.86 Fig. 1.87 Fig. 1.88 Fig. 1.90

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