space and geometry Dissertation
Short Description
Architecture is a ‘solution’ in terms of practical purpose, material and techniques. The issue that matters the most is...
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DISSERTATION REPORT Session: 201314
Space and Geometry
Undertaken by: Neha Syal Enrollment No.:09EAAAR029 V Year B.Arch
Prof. Preethi Agrawal
Prof. Archana Singh
GUIDE
COORDINATOR
Aayojan School of Architecture ISI4, RIICO Institutional Block, Sitapura, Jaipur302022
APPROVAL The study titled “Space and Geometry” is hereby approved as an original work of Neha syal, syal, enrolment no.: 09EAAAR029 09EAAAR029 on the approved subject carried out and presented in manner satisfactory to warrant its acceptance as per the standard laid down by the university. This report has been submitted in the partial fulfillm ent for the award of Bachelor of Architecture Architecture degree from Rajasthan Technical University, Kota.
It is to be understood that the undersigned does not necessarily endorse or approve any statement made, any opinion expressed or conclusion drawn therein, but approves the study only for the purpose it has been submitted.
December 2013 Jaipur
Prof. Preethi Agrawal EXTERNAL EXAMINER
GUIDE
Prof. ARCHANA SINGH
Prof. K.S.MAHAJANI
COORDINATOR
PRINCIPAL
i
APPROVAL The study titled “Space and Geometry” is hereby approved as an original work of Neha syal, syal, enrolment no.: 09EAAAR029 09EAAAR029 on the approved subject carried out and presented in manner satisfactory to warrant its acceptance as per the standard laid down by the university. This report has been submitted in the partial fulfillm ent for the award of Bachelor of Architecture Architecture degree from Rajasthan Technical University, Kota.
It is to be understood that the undersigned does not necessarily endorse or approve any statement made, any opinion expressed or conclusion drawn therein, but approves the study only for the purpose it has been submitted.
December 2013 Jaipur
Prof. Preethi Agrawal EXTERNAL EXAMINER
GUIDE
Prof. ARCHANA SINGH
Prof. K.S.MAHAJANI
COORDINATOR
PRINCIPAL
i
DECLARATION
I ,Neha syal, syal, here by solemnly declare that the research work undertaken by me, titled ‘Space and Geometry’ is my original work and wherever I have incorporated any information in the form of photographs, text, data, maps, drawings, etc. from different sources, has been duly acknowledged in my report.
This dissertation has been completed under the supervision of the guide allotted to me by the school.
Neha syal V Year B.Arch Aayojan School of of Architecture, Jaipur
ii
ACKNOWLEDGEMENT
This dissertation grew out of a series of dialogues with my Guide Professor Preethi Agrawal. My sincere thanks to my guide and only my Guide for invoking a critical thought in me regarding pursuing this research and eventually enabling me to grasp its rich complexity. Her comments on the chapter drafts have indeed been of utmost help. Ma’am has always been a great mentor in encouraging me all though the research. I thank my parents and my brother Anirudh Syal in always encouraging me while pursuing this study. Also I would like to thank my colleagues at office Ajay, Sana, Ali Sir in extending their support for initializing my dissertation topic. Not to forget my friends Anubhuti chandana, Shobhna singh, Rajat Sharma, Garima, Utkarsh Dalela, Eshank Rishi, and Snober Khan, in extending their support to me whenever needed!
Regards
Neha Syal 26.11.2013 V Year B.Arch Aayojan School of Architecture, Jaipur
iii
CONTENTS
Page No. Approval
i
Declaration
ii
Acknowledgement
iii
Contents
ivv
CHAPTER 1: INTRODUCTION 1.1
Hypothesis
1.2
AIM
1.3
Need of the study
1.4
Criteria of selection
1.5
Scope
1.6
Objectives
1.7
Scope & Limitation
1.8
Area of study
1.9
Methodology
1.10
Glossary of terms
1.11
Justification on topic
7  13
CHAPTER 2: UNDERSTANDING SPACE
14  18
2.1 SPACES IN ARCHITECTURE
2.1.1 QUALITIES OF AN ARCHITECTURAL SPACE
CHAPTER 3: REALISATION OF FORM (Study focuses on two dimensional aspect of Form)
3.1 THE FUNDAMENTALS
3.2 THE LAW OF MINIMUM
3.2.1 FORM AS A DIAGRAM OF FORCES
iv
3.3 THE ORIGIN OF FORM
19  26
3.3.1 THE ORTHO FACTOR
3.3.2 CIRCLE VS SQUARE
3.3.3 SINGLE ENVELOPE VS SEPARATE SYSTEM
3.4 AN INQUIRY INTO OUR PREFERENCES
CHAPTER 4: TRANSFORMATIONS IN SHAPE
4.1 REGULAR SHAPES
4.2 SHAPE
2736
4.2.1 CIRCLE 4.2.2 SQUARE 4.3.3 RECTANGLE 4.4.4 TRIANGLE
4.3 ROLE OF BUILDING ELEMENTS IN TRANSFORMATION OF A PLAN FORM
4.4 DIMENSIONAL TRANSFORMATION
4.5 SUBTRACTIVE TRANSFORMATION
4.6 ADDITIVE TRANSFORMATION
4.7 OTHER TRANSFORMATION
CHAPTER 5: EFFECTIVE SPACES
5.1 THE CONFIGURATION
5.2 DEPTH
5.3 PLANNING GRID
5.4 PRIMARY CIRCULATION AREAS
5.5 UNDERSTANDING EFFICIENCY THROUGH EXAMPLE.
CHAPTER 6: CASE STUDIES
41 – 52
6.1 ARCHOHM ARCHITECTURE FIRM 6.1.1 ANALYSING EFFICIENCY IN SPACES 6.1.2 CALCULATING LEVEL OF EFFICIENCY
v
37 – 40
6.2 PIVOTAL SERVICED APARTMENTS
6.3 RESIDENCE OF AR. ANOJ TEVATIA
6.4 RESIDENCE OF MR. SYAL.
CHAPTER 7: CONCLUSION
53
CHAPTER 8: REFERENCES
54  55
LIST OF TABLES
vivii
LIST OF ILLUSTRATIONS GLOSSARY OF TERMS ANNEXURES
vi
5th Yr. B.Arch
Neha Syal
Batch No. 11
TOPIC:
“Space and Geometry”.
HYPOTHESIS:
The effectiveness of a space and its optimum utilization is responsive to its geometric shape.
INTRODUCTION: Architecture is a ‘ solution’ in terms of practical purpose, material and techniques. The issue that matters the most is t h e d e s i g n  t h e d i s c o v e r e d f o r m . The modern designer therefore has to choose ‘optimum’ between ‘spatial’ quality and ‘efficiency’ which depends on his perception of the problem. This leads us to believe what best can we do in an allotted space, which would then reflect in and eventually postulate the balance of ‘usage’ in terms of ‘Spatial Economics’. ……………………..This evokes a question for us all to ponder upon………………….. “How productive is your space”? This therefore defines the, mathematical paradigm and helps us establish the basis for user satisfaction! OBJECTIVES: 1. To understand the term – space and determine its parameters. 2. To study types of forms and their geometric characteristics. To study the mathematical efficiency of a shape. To study role of building elements in transformation of a plan form. 3. To study the term effectiveness of a space and derive its parameters. Optimum utilization Functionally 4. To analyze the parameters and draw conclusion in order to establish a basis of its importance in terms of user satisfaction.
SCOPE: 1. Geometric shapes and forms Regular . 2. Interior, spaces in the chosen shape. Examples of building plan forms, demonstrating both the aspects and direction of our study.
CASE STUDIES: Archohm Architecture officeNoida Pivotal serviced apartmentsGurgaon Architect Anoj Tevatia’s residence Residence of Mr Syal.
PARAMETERS FOR ANALYSIS: Understanding and calculating efficiency. Mathematical parameter: People/workstation which will give us numerical data Subjective parameter : planning/workstation giving reasons to justify efficiency
RESULT OF STUDY: This study examines a given space primarily through its function and linking it to its geometry eventually evaluating the efficiency paradigm fulfilling the need of spaces to be user satisfying after all. GUIDE: Prof. Preethi Agrawal.
1. INTRODUCTION
INTRODUCTION TOPIC: SPACE AND GEOMETRY
HYPOTHESIS: Effectiveness of a space and its optimum utilization is responsive to its geometric shape.
AIM: To study effectiveness of a space, with response to its geometric characteristics and eventually understand its user perspective.
NEED FOR STUDY: Need to study and investigate development of spatial outcome. CRITICALLY EVALUATE
Spaces
Human environments Effectiveness of a perspectives)
design
(various
CRITERIA FOR STUDY: How spatial forms, reflect functional ends from the perspective of the ‘user’.
SCOPE THE STUDY SHALL COVER:
Understanding of space in architecture theory. Forms and their mathematical efficiency. Optimization in terms of effectiveness in architecture. Examples of building forms, demonstrating both the aspects and direction of our study.
Page 7
1. INTRODUCTION
OBJECTIVES 1. To understand the term – space and determine its parameters. 2. To study types of forms and their geometric characteristics. To study the mathematical efficiency of a shape. To study role of building elements in transformation of a plan form. 3. To study the term effectiveness of a space and derive its parameters. Optimum utilization Functionally 4. To define term the aesthetic paradigm and analyze its parameters in order to establish a basis of its importance in terms of user satisfaction. 5. To draw a conclusion based on the above 2 objectives.
LIMITATIONS
1. Restrictions will be at plan studies computer simulated forms, forms other than [rectangularsquare, rectangle curvilinear circle polygonal 5sided polygon] are not covered.
AREA OF STUDY 1. Geometric shapes and forms Regular . 2. Interior, spaces in the chosen shape and Form.
Page 8
1. INTRODUCTION
METHEDOLOGY
AIM: To study effectiveness of a space with response to its geometric characteristics and aesthetic aspect.
To study the term ‘space’ and determine its parameters.
To study the term effectiveness and derive its arameters.
Rectiliner Curvilinear
Geometric Characteristics
To study the aesthetic aspect and analyze its parameters.
Mathematical efficiency Role of building elements[porch, chajja, staircase] in transformation of plan FORM
Optimum utilization Functionality.
Data collection.
Secondary
Primary source
Literature studies Books JOURNALS
Surveys Case studies
Analysis and Conclusion
Page 9
1. INTRODUCTION
1 INTRODUCTION AND GLOSSARY OF TERMS
1. SPACE: Space is a boundless 3dimentional extent in which object and events have relative position and direction.
2. EFFECTIVNESS: Effectiveness of a space is a general concept reflecting an output from that space. SPACE EFFECTIVNESS IS MEASURED BY comparing: Space productivity Condition Flexibility Geometry
3. SPACE EFFICIENCY:
OPTIMUM UTILIZATION is defined as: m sq / person. m sq /workstation. people / workstation.
The manipulation of these ‘2’ ratios allows to secure the right level of utilization to meet the needs and reflect building characteristics.
Page 10
1. INTRODUCTION
2 JUSTIFICATION ON TOPIC
The qualities of space and how people experience interactions and sensations within the spaces will go to justify its optimum utilization to a certain extent not forgetting its mathematical efficiency after all. “Corbusier said”, “ Building is a machine taking into consideration then, every
machine has a purpose and therefore it has a certain function to fulfill………………………................................................
If we consider a space, then each space which is designed, has a certain thought behind it, and so, it has a function a purpose it has to perform. The
idea concept
or
of optimum utilization emerges from users and their spatial experience. The qualities of a space and how people experience interactions and sensation within those spaces
HOW IS MEASURED?
OPTIMUM
UTILIZATION
1. By justifying the effectiveness of that space using mathematical tools. 2. The second support or tool to justify space utilization, though subjective but holds certain importance, is user perception and their spatial experience, therefore, this study seeks to understand:
How do I introduce efficiency? is the measure – m sq / workability people / per workstation.
These 2 ratio will focus on level of space utilization better understood as “space efficiency”. Page 11
1. INTRODUCTION
3 BRIEF UNDERSTANDING: SPACE
SHAPE
FORM
TRANSFORMATIONS
SPACE EFFICIENCY
OPTIMUM UTILISATION
USER SATISFACTION
4 SPATIAL RELATIONSHIP:
SPACE
FUNCTION
SPACE EFFICIENC Y
5 SUMMARY OR OVERVIEW OF OUR STUDY
The framework proposed in this research is to examine a given space, primarily through its function, and linking it to its geometry.
[The geometries we have listed out in our study: are pure and regular geometries] Page 12
1. INTRODUCTION
Now on identifying the function of a space in relation to its geometry, we have tried to introduce and study of ‘effectiveness’, in this context.
6HOW DO WE PROVE OUR STUDY
This study: explores the various function in conjugation to their implicit geometries in analyzing efficiency of these spaces.
The given frame work of this study is built on: Mathematical transformations in “Shape”, establishing Effectiveness in space , function and there after its optimum utilization by the user.
The idea or concept of optimum utilization emerges from users and their spatial experience.
The qualities of a space and how people experience interactions and sensation within those spaces.
Page 13
2. UNDERSTANDING SPACE
UNDERSTANDING SPACE…..
PRELUDE
T his chapter relates to the understanding of Space and its parameters. What is a space in Architectural context, what are the various qualities of an architectural space and how do we as modern designers perceive and utilize a space to its optimum structure and functionality.
Page 14
2. UNDERSTANDING UNDERSTANDING SPACE
2.1 SPACES IN ARCHITECTURE Physically space is shape, by what it is, that surrounds it and otherwise by objects within it and is perceivable by us. A space is determined, meaning finite and fixed by its periphery and objects in it. It is meant for something and Offers protection for something. Spatiality is defined by : A feeling A sensation
Fig:1 A sense of space is a mental construct ,a projection of the outside world as we experience it. As space begins to be ‘captured’, ’enclosed’, ‘molded’, and ‘organized’. By the elements of ‘Mass’ , Architecture comes into being. being.
Fig:2
Fig:3 Page 15
2. UNDERSTANDING UNDERSTANDING SPACE
Spatial economies, different activity roles will derive different space allocation. A designed space is expected to support the activitiesfunctionsand human engagements about to take place there. 2.1.1 QUALITIES OF AN ARCHITECTURAL ARCHITECTURAL SPACE
Fig:4 The qualities of an architectural space, however are much richer than what these diagrams are able to portray. Fig:5
BOUNDARY: The most explicit quality of a space is its boundary. The physical boundaries of a space consists of its roof, ceiling and the wall. When we look at a space from the point of view of the Interior Boundary Exterior
We see that the boundary is the only element which defines both i nterior and exterior space.
Page 16
2. UNDERSTANDING UNDERSTANDING SPACE
PROPERTIES OF ENCLOSERES SHAPE
QUALITIES OF SPACE
Form
SURFACE EDGES
Color
Texture
Pattern
DIMENSIONS
Scale
Pr P roportion
CONFIGURATION
Definition
OPENINGS
Degree of enclosures
Light
View
Table 1 The above table (table1 (table1)) indicates the various properties of enclosures and lists out their qualities of space.
Page 17
2. UNDERSTANDING SPACE
. e c a p s f o e c n e i r e p x e e h t s i e r u t c e t i h c r A n i e c n e i r e p x e f o y r o e h t e h T
Architecture is a solution in terms of practical purpose, material and techniques .The issue that matters the most is the designthe discovered form. This is the subject of the artistic commentary in architectural treatment, so, when an Architect sets to work in 99.9 cases out of 100 he has a problem to solve. Therefore the modern designer has to choose the ‘optimum’ between ‘spatial’ quality and ‘efficiency’ which depends on his perception of the problem. This leads us to believe what best can we do in an allotted space, which would then reflect in and eventually postulate the balance of “usage” in terms of “Spatial Economics”. Thus understanding space in Architecture is the foremost, any designer needs to focus upon while beginning to design. It was well said by L e C o r b u s i e r : The theory of experience in Architecture is the experience of space.
Machinehas a purpose
Building
Function to perform
Page 18
3. REALISATION OF FORM
REALISATION OF FORM (study focuses on two dimensional aspect of Form)
PRELUDE
F orm in Architecture
is related to ‘ s p a c e ’ and the ‘ a cti v it y o c c u r r i n g w i t h i n t h i s
s p a c e ’ . Apart from that, architectural form is also rel ated to the elements
themselves; Their arrangements, and combination with each other ( synta x); t he meaning (semiotics); and the effects on people (pragmatics). Form ther ef ore c annot simply be reduced to a single of choice of elements and their arrang ement. For that reason i t is possibl e to appraise the architectural form within the framework of: • S pacedef ining el ement (related to use) • A sign (rel at ed t o arr ang ement , significance and effect) • St ruc ture ( dependent on t he laws of static and the strength of materials)
Page 19
3. REALISATION OF FORM
UNDERSTANDING THE BASIS AND ORIGIN OF ‘FORM’. Form refers to a shape or configuration or rather is a ‘product’ of space. Form is better understood as a special modification of matter under the agency of process. Let us try to establish the origin of form fr om ‘Nature’. 3.1 THE FUNDAMENTALS
At the very basis of all phenomenon in nature lies only one entity‘Energy’. It is, this energy that constitutes the universe through its two m anifestationsMatter and Force. The interaction of these two gives rise to a ‘tangible space’. Even the cracking of mud is not a random process it seems. The cracks appear in such a manner so that the affected area is covered in ‘minimum’ sized units using minimum crack lengths. ( R eference : structure in nature –is a strategy for design)
Minimum path network in mud Fig3.1 https://www.math.ucdavis.edu/~qlxia/mud.html
The tendency to find equilibrium governs all natural order. Therefore to hold itself in a particular ‘Form’, a structure has to spend the least amount of energy. Thus the basic aim of any natural system is to achieve a configuration that holds the minimum energy expenditure in stabilizing a structure. ( S o u r c e : Peter PearceStructure in nature is a strategy for designMIT Press1978)
Page 20
3. REALISATION OF FORM
3.2 THE LAW OF MINIMUM
All natural systems tend to structure themselves according to the law of minimum. All free bodies for example, tend to acquire a spherical shape (as shown in fig3.2) which has a minimum surface area to a given volume.
The spherical characteristics Fig3.2 3.2.1 FORM AS A DIAGRAM OF FORCES
An interacting system constituting matter and forces, tends to achieve minimum potential energy (stated earlier). A state where matter is positioned in space by the action of forces. Matter in a system is found at coordinates where forces meet to cancel out each other. Form or structure is the meeting point of forces (shown in fig3.3) or better understood that form is a diagram of forces (which supports the heading of this topic).
Form is a diagram of forces: Forces formForm Fig3.3 Page 21
3. REALISATION OF FORM
The idea of the energy expenditure can be made clear by the following comparison of the ‘tetrahedron’ and the ‘cube’. A tetrahedron is a very stable three dimensional entity. All stresses in the system are direct, ie: they are pure impression or tension along the lines of the tetrahedron. Any point in space can be stabilized using this configuration just like any point on a plane can be determined by triangulation (fig3.4).
The tetrahedral system Fig3.4 A cube on the other hand, needs extra energy apart from direct stresses. The joints or vertices of the cube need to be stabilized. In the absence of this extra stabilization, the cube tends to flatten out into a rhombic (fig3.5).
The cubic error Fig3.5 Thus a tetrahedron is more likely to be found in nature than a cube. In fact a large majority of all natural forms can be simplified to a tet rahedron geometry.
Page 22
3. REALISATION OF FORM
3.3 THE ORIGIN OF FORM
3.3.1 THE ORTHO FACTOR Man joins the linear elements instinctively at 90 degrees. Order has always been associated with right angles. When two lines intersect , they form a pair of opposite angles. Only two cases are possible: 1) The lines form the two acute and two obtuse angles (fig3.6a). 2) The lines form four right angles (fig3.6b).
Non perpendicular intersection
perpendicular intersection
Fig3.6a
Fig3.6b
Also the space bounded by an acute angle appears to be wasteful, since the size of the usable area approaches (zero) or diminishes rapidly as we approach the corner (fig3.7 ).
The features of an acute angle Fig3.7
Page 23
3. REALISATION OF FORM
3.3.2 CIRCLE VS SQUARE
It is interesting to note that while we are scribbling we generally make circles, ovals or abstract shapes for that matter. Yet when we are asked to sketch the plan of any room we immediately draw a rectangle or square. (result based on various opinions or research’s done ) Very seldom would you find a person drawing out a circular room when asked for a general room plan. ‘usability’ of a room is determined by how many usable furniture pieces it can accommodate in the least complex manner and therefore assures the o p t i m u m u t i l i t y o f t h e s p a c e s . ” “ The
According to the (fig 3.8) shown below, it is apparent that many small but regular shapes cannot fill a circle but a square can easily be divided into many shapes of varying sizes without any space wastage. A circle would have lot of strange and unusable areas left, especially at the circumference.
The usability factor Fig3.8
Page 24
3. REALISATION OF FORM
3.3.3 SINGLE ENVELOPE VS SEPARATE SYSTEM
Continuous surfaces have a limitation of being single floor structures in most cases. This limits the growth potential of a building and therefore single surface is not preferred. Flat roofs over straight walls can be used as floor of storey above. Therefore its more lucrative to the builder.
Single envelope v/s Separate system Fig3.9
Page 25
3. REALISATION OF FORM
3.4 AN INQUIRY INTO OUR PREFERENCES
Each of the varied properties do not find equal favor amongst human beings. However it can be said, within the limits of exception, that people appreciate right angle over others, the straight line over the curved ones, the vertical element over the tilted one, and the discontinuous element over the single surface or vice versa that is totally left upon the discretion of the user. The reasons behind these biases may lie in the psychology of man, the usability of a shape for human needs, or even for that matter from the hi story of civilization!
Fig3.9a Fig3.9b Usability factor of various shapes
Fig3.9c
Fig3.9d
Page 26
4. TRANSFORMATIONS IN SHAPE
TRANSFORMATIONS IN SHAPE
This chapter relates to the study of the types of shapes, their geometric characteristics and the Role of building elements in transformation of a plan form. ‘
TRANSFORMATIONS AS A WHOLE ’ ‘’ The process of change in the shape through a series of discrete permutations and manipulations in response to a specific context or set of conditions without a loss of identity or concept is the process of Transformation.’’ It is such a progression that changes the shape within the boundary of the object itself. The effects of these changes can be observed either in two or three dimensional form... In other words, in a transformational system, it is essential that a designer understands the fundamental nature and structure of the concept . Thus there is a prototypical architectural model which is transformed through a series of discrete manipulations in order to respond to specific conditions.
Page 27
4. TRANSFORMATIONS IN SHAPE
Form and its opposite space constitute primary elements of Architecture. Study of types of shapes and their geometric characteristics. 4.1 Regular shapes Are those shapes whose parts are related to one another in a consistent and orderly manner. They are generally stable in nature and symmetrical about one or more axis. In g e o m e t r y regular shapes are the circle, and the infinite series of regular polygons that can be inscribed within it Of these the most significant are the primary shapes: the circle, the triangle, the square and the rectangle. REGULAR SHAPESRefer to those whose parts are related to one another. They are generally stable and symmetrical about an axis.
SHAPES: can retain their regularity even when transformed dimensionally or by the addition and subtraction of elements. IRREGULAR SHAPES Are those whose parts are dissimilar in nature and related to one another in an inconsistent manner. Generally Asymmetrical and more dynamic than regular shapes. Regular and irregular shapes. Fig4
Page 28
4. TRANSFORMATIONS IN SHAPE
4.2 SHAPE
Shape is the characteristic outline or surface configuration of a particular form. It is the principal aspect by which we identify and categorize forms(F r a n c i s D k C h i n g ) .
According to ‘ F r an k L l o y d W r ight’ – 4.2.1 1) CIRCLE The simplest of the two dimensional shapes that are used is the circle. It is a centralized stable and self centering figure. Placing a circle at the centre of a field reinforces its inherent centrality.
Circle is placed at the centre Fig4.1a Circle can be subdivided into t w e l v e equal parts. This gives the circle great adaptability for architecture and allows the architects various ways to use the strength of the circle, while changing its appearance.
Compositions of circle and circular segments Page 29
4. TRANSFORMATIONS IN SHAPE
4.2.2 2) SQUARE The other primary shape is the square. It is probably the most used shape in architecture. It represents a pure and rational figure. It is static and neutral having no preferred direction. It becomes dynamic when resting on its corners.
Representations of squares Fig4.1b
Compositions of square and square segments 4.3.3 3) RECTANGLE Another very important shape is the rectangle. It has been used in most situations in architecture. Architects like it because it is easy to adapt for human needs. In building rectangles maybe used in windows, doors, rooms, etc. A rectangle depends on the right angles at the comers. The length and width depend on the eye of the architect. There is not one rectangle that will satisfy all architectural needs. Many rectangles can be said to be important in Architecture. Rectangles that are either off square or can be divided into even squares can be used in a variety of ways.
Page 30
4. TRANSFORMATIONS IN SHAPE
A rectangle building with the smallest perimeter surface is the most economical for the architects to build. The greater the length of the perimeter the more is the variety of shapes are available. 4.4.4 4) TRIANGLE Signifies stability, while resting on one of its sides, it is an extremely stable figure. When tipped to stand on one of its vertices, however it can either be balanced in equilibrium or be unstable and tend to fall over its sides. Because of the right triangles, corners of the buildings are square. Right triangles help to support buildings. All of the regular and irregular polygons, prisms, pyramids, and solids are dependent on right triangles
Compositions of triangle and triangular segments
4.3 Role of building elements in transformation of a plan form
Transformations of square in two dimensions Page 31
4. TRANSFORMATIONS IN SHAPE
4.4 1) DIMENTIONAL TRANSFORMATION
Dimensional transformationshown in Form Fig4.2a Form can be transformed by altering its dimensions and still retain its identity. A cube for example can be transformed by altering its height, width or length in its volumetric form and corresponding changes will be made in its ‘Planar form’ also.
ROBB IE HOUSE
Fig4.2b http://architecture.lego.com/enus/products/architect/robiehouse/story/
Page 32
4. TRANSFORMATIONS IN SHAPE
BUILDING
ROBBIE HOUSE
ARCHITECT
FRANK LLOYD WRIGHT
LOCATION
CHICAGO, ILLINOIS
ORIGINAL FORM
CUBE
TRANSFORMED FORM
CUBOID
http://towermax.deviantart.com/art/RobieHouse204473623
Fig4.2c Plan form type of Robbie house 4.5 2) SUBTRACTIVE TRANSFORMATION
Subtractive transformationshown in 3 dimension Fig4.3 Form can be transformed by subtracting a portion of its volume. Extent of subtractive process either helps to retain its identity or totally transformed to other. Subtracted space: volumetric void, negative spaces.
Page 33
4. TRANSFORMATIONS IN SHAPE
BIANDA’S RESIDENCE
BUILDING
BIANDA’S RESIDENCE
ARCHITECT
MARIO BOTTA
LOCATION
SWITZERLAND
Subtractive transformationshown Fig4.3a https://wiki.ucfilespace.uc.edu/groups/12u_20artn242001/wiki/b27fe/
Page 34
4. TRANSFORMATIONS IN SHAPE
4.6 3) ADDITIVE TRANSFORMATION
Additive transformationshown in 3 dimension Fig4.4 Forms can be transformed by addition to its volume. Types of additive transformations:
Types of Additive transformations Fig4.5
PLA CE DE STALINGARD
http://en.wikipedia.org/wiki/Place_de_la_BatailledeStalingrad
Page 35
4. TRANSFORMATIONS IN SHAPE
BUILDING
PLACE DE STALINGARD
ARCHITECT
HEUT BERNARD
LOCATION
PARIS
plan form of palace
4.7 4) OTHER TRANSFORMATIONS
Corners define the meeting of two planes. Corner condition introduces a distinct element that is independent of the surface it joins Opening is introduced to one side of its corner. One plane appears to bypass the other.
Various other transformations shown Fig4.6 Page 36
5. EFFECTIVE SPACES
EFFECTIVE SPACES
PRELUDE
T his chapter relates to the understanding and definition of effective spaces. ‘’ E f f ec t i v e n e s s o f a s p a c e ’’, i s a g e n e r a l c o n c e p t r e f l ec t i n g a n o u t p u t f r o m t h a t space.
Space effectiveness is what we call, space productivity is a general sense.
This study: explores the various functions in conjugation to their implicit geometries in analyzing efficiency of the spaces.
The idea or concept of optimum utilization emerges from users and their spatial experience.
Page 37
5. EFFECTIVE SPACES
5.
The basic physical parameters of a building shell will set rules for its occupation by describing –‘How effectively’ a building can be planned. 1) The CONFIGURATION Describes geometry of a typical floor within a building. Thus a square or an oblong plan with single/central core will be more efficient than a plan form which is irregular. A high floor plate efficiency is achieved by calculating the net to gross ratio of internal spaces. Note: configuration will also be affected by the number and distance of structural columns. 2) DEPTH Is a measurement across a floor window to window, window to core or atrium. 3) PLANNING GRID The planning grid describes the internal dimensions for structure finishes and services. These relate to structural columns and window spacing. Thus the planning grid will drive the ease with which internal rooms and partitions are introduced. 4) PRIMARY CIRCULATION AREAS Primary circulation Secondary circulation
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5. EFFECTIVE SPACES
The following parameters listed above help us to determine the amount of usable spaces and thereby its optimum utilization to what extent has been achieved. Thus the efficiency parameter is achieved by two ways: 1) By calculation people per workstation values 2) Planning per workstation The people per workstation will give us mathematical data regarding (for an office) The number of people for which the building is designed for No of people working at present No of clients visiting on a daily basis( approx) Also as per the architectural standards according to the given area how many people are working.
The basic physical parameters of a building shell will set rules for its occupation by describing –‘How effectively’ a building can be planned.
Also the planning per workstation will give us subjective reasons to justify the efficiency factor and calculate the net usable area. Subjective Understanding of the economics of a space ‘Economics’, here focuses on the mathematics based on the productivity of the analyzed space. This is the subject of the artistic commentary in architectural treatment, when an Architect sets to work, in 99.9 cases out of 100 he has a problem to solve. Therefore the modern designer has to choose the ‘optimum’ between ‘spatial’ quality and ‘efficiency’ which depends on his perception of the problem.
This eventually leads us to believe what best can we do in an allotted space, which would then reflect in and eventually postulate the balance of “usage” in terms of “Spatial Economics”.
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5. EFFECTIVE SPACES
5.5 understanding efficiency through example. Let us understand Efficiency by an example as stated by Palladio! Andreas Palladio brings the theor y of Renaissance pr opor tioning to its most sophisticated state. He tur ns the idea of subdividing a plan into harmonious par ts around by starting with r ooms in harmonious r atios and joining them together to pr oduce the entire building.
Palladio’s seven sets of proportions in construction of r ooms Palladio supplies general rules f or the proportions of the height of rooms to their width and length that is for the relationship of the three dimensions which constitutes the shape of a r oom. He recommends seven shapes of r ooms in the following sequence: (1) circular , (2) square, (3) the diagonal of the squar e f or the length of the room, (4) a squar e and a thir d, (5) a squar e and a half, (6) a square and twothir ds, (7) two squares.
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6. CASE STUDIES
Case studies of Pivotal and Archohm
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6. CASE STUDIES
6.1 ARCHOHM ARCHITECTURE FIRM Architect: Ar Saurabh Gupta Location: Noida Evolution of form from basic geometric shapes:
PRIMARY FUNCTION: Architectural firm
PRIMARY GEOMETRY: Regular solidscylinder, cuboids The basic physical parameters of a building shell sets the rules for its occupation by describing how a building can be planned.
Configuration Planning grid Circulation Depth
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6. CASE STUDIES
Fig6.1 The above floor plan shows the percentage circulation in the architectural firm.
Fig6.2 Page 43
6. CASE STUDIES
6.1.1 ANALYSIS AS PER: planning per workstation
The grid pattern followed across the plan typology is of 3.6m .(from fig6.2) According to the grid layout the planning is done without creating any negative spaces and unused areas in the office premises. Also according to the standard furniture layouts suggested by the standards the furniture is well in conjugation with the plan form and the grid followed through out the plan. Other important aspects to be noted down are the functionality of the board room and the café. Functionality
Issues
Board room
Cafe
To serve as a seminar hall
To serve as a meeting area
The functionality is not Functionality is achieved achieved in conjugation with its geometry
Efficiency of a space
People/workstation:
Planning/workstation:
Will give us the
Give us subjective
num erical data
reasons to jus tify the efficiency
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6. CASE STUDIES
6.1.2 CALCULATING area usage “ people/workstation” A t u p p e r g r o u n d f l o o r l e v el SNO.
The space designed
Space designed for number of people
Number people working at present
Number people visiting on daily basis (approx)
Number Area people (Square present M) as per standard
1
STUDIO
33
30
5
60
265
2
CABIN1
3
1
2
6
19
3
CAB IN 2
4
2
3
4
16
4
CABIN 4,5
4
2
3
4
11
5
MEETING ROOM
6


4
11
6
LOUNGE
6




7
BOARD ROOM
17

9
26
44
CALCULATING area usage “ people/workstation” A t lo w e r g r o u n d f l o o r le v el
SNO.
The space Space designed designed for number of people
Number people working at present
Number people visiting on daily basis (approx)
Number Area people (Square present M) as per standard
1
STUDIO
50
5
78
440
2
BEDROOMS 6


6
93.8
53
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6. CASE STUDIES
6.2 PIVOTAL APARTMENTSGURGAON ARCHITECT: Ar Anoj Tevatia LOCATION: gurgaon PRIMARY FUNCTION: Serviced Apartments PRIMARY GEOMETRY: Circular plan transformation shape.
subjected to dimensional changing into an oblong
Typical plan of the serviced apartments.
Fig6.3
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6. CASE STUDIES
Fig6.4 The above two typical plans shown in (fig6.3 and fig6.4) represent the floor plans the same building with changing the core of the building. Three typical plans were presented to the client in order to achieve maximum floor area in terms of area sellable .
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6. CASE STUDIES
fig6.5 The above three plans can be understood as under: The typical plan in fig6.5 shows a core at the centre of the building running right from the ground floor to the highest floor reaching upto a level of 28 floors. Therefore a maximum of 11 individual units are obtained from the plan in fig6.5. Similarly in order to achieve the maximum number of individual units per floor the designer decided to shift the core of the building from the centre to the two sides to optimize the floor area achieving more units as compared to the earlier plan in fig6.5 The area breakups of the above floor plans of the Pivotal serviced apartments is: Gross internal area: 12,0000 sq m Net internal area: 10.6700 sq m NUA: 81020 sq m. Therefore here the level of efficiency is achieved by calculating the increase in the number of individual units on each floor, increasing the number of units on each floor.
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6. CASE STUDIES
6.3 RESIDENCE RESIDENCE OF MR SYAL ARCHITECT: LOCATION:
Er Murari Syal
Jaipur
PRIMARY FUNCTION:
Residence PRIMARY GEOMETRY:
Rectangular geometryall rooms following the similar geometric pattern. Ground floor plan of residence The plan shown in fig6.5 is the plan of the residence being studied in this research. According to the study conducted for analyzing efficiency in this building we inspected the spaces. Specifications: 4 BHK house with a first floor consisting of 2bedrooms. There are two main entries and 1 backyard entry for the services. One entry is from the porch which opens up in the drawing room and the other entry is in the master bedroom which is rarely utilized.
fig6.6 Analyzing the spaces in the house: Page 49
6. CASE STUDIES
Ground floor consists of a Drawin g ro om (12.6x16 feet) Adjacent to a Ki tch en (10.4X11 feet) and m a s t e r b e d r o o m (14x21 feet) and a kid s bedro om (10.5x15 feet).
The graph below shows the area breakup of the various spaces of the residence of Mr Syal.
14%
22% Drawing room
13%
Master Bedroom kids bedroom
18% 33%
Kitchen Others and puja
fig6.7
Fig 6.8 Master bedroom
fig 6.9 Drawing room
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6. CASE STUDIES
6.4 RESIDENCE RESIDENCE OF AR ANOJ TEVATIA ARCHITECT: LOCATION:
Ar Anoj Tevatia
New Delhi
PRIMARY FUNCTION:
Residence PRIMARY GEOMETRY:
Rectangular geometryall rooms following the similar geometric pattern.
Fig 6.9a Ground floor
fig 6.9b first floor
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6. CASE STUDIES
The second study conducted in order to analyze the efficiency of spaces is that of Ar Anoj Tevatia. ) Ground floor consists of a D r a w i n g r o o m (13’x18’  9’’ ) ) Adjacent to a Kitchen (9’x13’  9’’ and m a s t e r b e d r o o m (1 6 ’ 10’’x13’9’’ k i d s b e d r o o m a n d g u e s t bedroom (13’x12’9’’ )
11% 34%
13%
DRAWING ROOM MASER BEDROOM
17%
OTHER BEDROOM KITCHEN
25%
OTHERS
fig6.9c On analyzing the spaces of the house we find that the maximum space is occupied by the drawing and dining area. The area breakup is as per the areas suggested by the standards. This gives us an overview that the areas divided in the house are as per the occupancy, its functionality and its usage, which will intern reflect the productivity of the spaces. It is understood that since the drawing room of a house is used at nearly all times in a day therefore its area allotment amongst all the rooms should be more. Rest of the allotment is as per requirement and their need.
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6. CASE STUDIES
On analyzing the spaces of the house of Mr Syal, we find that the maximum space is occupied by the Master bedroom. On the contrary as suggested by the standards, the area of the Drawing room should be if not maximum of all areas of the house but in this case should be larger than the area of Master bedroom. THE REASON behind this recommendation is: Let us come back to the issue of ‘functionality o f s p a c e s ’, which is explained in the earlier chapters of this book. Obviously the functionality of a Drawing room is to accommodate more people in a day rather than that in a master bedroom. Accordingly the area breakups change with the one major tool to win over from: that is: “Function”. Since a drawing room is a mass gathering space in a house, therefore the number of people visiting a drawing room in a day is ‘ more’, as compared to a master bedroom, whose occupancy as well as number of people visiting in per day is also comparably less. This analysis gives us a thought to kindle upon…………………………………………... Are spaces in OUR homes Efficient??? This efficiency analysis can be conducted by all of us with the simple tools mentioned in the above case studies. The very idea to conduct a study of a residential space was only to help us understand the concept of efficiency. Efficiency of spaces links to Productivity of spaces. Productivity establishes its connect to : the usage of a space. In order to understand this concept, let us frame a concrete idea of this thought. For any given space to be productive, its utilization should be optimum, only then will the space be efficient to us. This establishes a base to the Hypothesis of this research: which states that, “Effectiveness of a space and its optimum utilization is responsive to its geometric shape”.
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7. CONCLUSION
CONCLUSION
The study concludes itself with a view of keeping in mind the effective usage of space for the user. Effective spaces can be better understood as productive spaces. Any space can be effective or productive for which it defines to be fulfilling. Let us understand the level of productivity of a space with the help of an example of a restaurant. A restaurant can be termed productive only when its ‘prime functionality ’ to ‘ serve’ and its ‘popularity ’ reach at a certain appreciable level. Only then will the restaurant be productive. S i m i l a r l y , a n y s p a c e c a n b e t e r m e d a s a p r o d u c t i v e s p a c e , i f t h e fu n c t i o n a l i t y c o n j u g a t e s o r r e s o n a t es w i t h t h e a m o u n t o f p e o p l e u s i n g t h e g i v e n s p a c e.
‘’ The effectiveness will thus be, to calculate the output from that space.’’ This evokes a question for us all to ponder upon…… “ Ho w productive is your space”? The answer to the above thoughts and questions are already proved with the help of case studies conducted in the earlier chapters of this book. This study has therefore helped us to understand various spatial forms, studying their geometric characteristics, which help in optimizing a space and at the same time leaving the user satisfied with the levels of efficiency attained with the conducted spatial study. It therefore defines the mathematical paradigm and helps to establish a basis of user satisfaction. After all spaces are designed for people not forgetting the functionality of the space and by the people of this society. Therefore apart from the calculative aspects, spaces need to be user satisfying.
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8. REFERENCES
Arnheim, R T h e Dy n a m i c s o f A r c h i t e c t u r a l Fo r m , University of California Press, London, 1977. ,
Blackwell, W AlA, G e o m e t r y i n A r c h i t e c t u r e, Key Cirriculum Press, Berkeley,California. ,
Baker, H. G, D e s i g n S t r a t eg i e s i n A r c h i t e c t u r e (an Approach to the Analysis of Form), Van Nostrand Reinhold, New York, 1996
Percy E Nobbs, T r ea t i s e i n t h e d i s c o v e r y o f F o r m .
Ching, F, D.K, A V i s u a l Di c t i o n a r y o f A r c h i t e c t u r e, Van Nostrand Reinhold, New York, 1995
Emde, H, G e o m e t r i c a l F u n d a m e n t a l s f o r D e s i g n a n d V i s u a l i za t i o n o f S p a t i al O b j e c t s . CAAD Futures' 87. Eds. Tom Maver and Hanry Wagter, Amsterdam, Elsevier,1987.
h it e c t u r e a n d D esign Fr anck, K, A, O r d e r i n g S p a c e: T y p e s i n A r c , Van Nostrand Reinhold, New York, 1994.
c h t o A r c h i t e c t u r e Gargus, J, Ideas of Order. A F o r m a l A p p r o a , Kendall / Hunt Publishing Company, Iowa, 1994
n d F o r m i n A r c h i t e c t u r e . A Circumspect A ppr oach to Joedicke, J, Space a the Past, Karl Kramer Ver lag, Stuttgart, 1985 S p a c e a n d t h e L a n g u ag e o f A r c h i t e c t u r e Jules, F, F o r m / , Publications m Ar chitectur e and Urban Planning, Wiscoin, 1974
Moore, C. and Allen, G, Dimensions: Spac e, Sh a p e a n d S c a l e i n A r c h i t e c t u r e, Architectural Recor d Books, New Yor k, 1976
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8. REFERENCES
Per ez, G, A, Introduction: The u s e o f G e o m e t r y a n d N u m b e r i n Architec t u r a l T h e o r y : Fro m s y m b o ls to Re  C o n c i l i a t i o n t o I n s t r u m e n t s o f T e c h n o l o g i c a l D o m i n a t i o n , Diss. U.
Placzek, A, K, P alladio Andrea: T h e fo u r B o o k s o f A r c h i t ec t u r e , Dover Publications Inc., New Yar k, 1965
Scholf ield, P.H, The T h eo r y o f P r o p o r t i o n i n A r c h i t ec t u r e, Cambridge University Press, Cambridge, 1958
d ea, Form , a nd A rchitecture, Design Principles in Schirm beck, E, I Co n t e m p o r a r y A r c h i t e c t u r e s , Van Nostrand Reinhold, New York, 1987
Steadman, P, A r c h i t e c tu r a l M o r p h o l o g y : A n I n t r o d u c t i o n t o t h e G e o m e t r y o f t h e B u i l d i n g , Pion, London, 1989. Stevens, G, The R e as o n i n g A r c h i t e c t , M at h e m a t i c s a n d S c i e n c e i n Design , McGrawHill Publishing Company, New York, 1976 Wilson, F, A G r a p h i c S u r v e y o f P e r c ep t i o n a n d B e h a v i o r f o r t h e D es i g n P r o f e s s i o n s , Van Nostrand Reinhold, New York, 1984 Winters, N, B, A r c h i t e c t u r e E l em e n t a r y . V i s u a l T h i n k i n g T h r o u g h Arch itectural Concepts , Gibbs, M, Smith, Salt Lake City, 1986 Wong, W, P r i n c i p l e s o f T w o  D im e n s i o n a l F o r m , Van Nostrand Reinhold, New York, 1988
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9. GLOSSARY
Additive Forms: Characterized by a basic progress which involves adding simple solids together to make a more complex whole.
Balance: The pleasing or harmonious arrangement or proportion of parts or elements in a design or composition.
Cartesian Space: Based on th X, Y, Z coordinate system of Rene' Descartes, an infinitely expandeble and homogeneous space defined by a square grid.
Centralized Plan: A building plan which is organized around a central point.
Composition: The arranging of parts or elements into proper proportion or relation so as to form a unified whole.
Concept: A mental image or formulation of what something is or ought to be, esp. an idea generalized from particular characteristics or instances.
Effectiveness: Effectiveness of a space is a general concept reflecting an output from that space.
Form: The shape and structure of something as distinguished from its substance or material.
Geometry: The
mathematical
discipline
which
deals
with
measurements,
relationships and properties of points, lines, planes, angles, and figures in space.
Golden Rectangle: A rectangle whose proportions embody the relationships of the golden section. A golden Rectangle can be infinitely decomposed into a square and another golden rectangle.
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