DISSERTATION REPORT
DISSERTATION REPORT
Session: 2013-14
Session: 2013-14
Space and Geometry
Space and Geometry
Undertaken by:
Undertaken by:
Neha Syal
Neha Syal
Enrollment No.:09EAAAR029
Enrollment No.:09EAAAR029
V Year B.Arch
V Year B.Arch
Prof.
Prof. Preethi
Preethi Agrawal
Agrawal
Prof.
Prof. Archana
Archana Singh
Singh
GUIDE
COORDINATOR
GUIDE
COORDINATOR
Aayojan School of Architecture
Aayojan School of Architecture
ISI-4, RIICO Institutional Block,
ISI-4, RIICO Institutional Block,
Sitapura, Jaipur-302022
Sitapura, Jaipur-302022
A-PDF Merger DEMO : Purchase from www.A-PDF.com to remove the watermark
APPROVAL
APPROVAL
The study titled
The study titled ““Space and GeometrySpace and Geometry”” is hereby approved as an original work ofis hereby approved as an original work of
Neha syal
Neha syal, enrolment no.:, enrolment no.: 09EAAAR02909EAAAR029 on the approved subject carried out and on the approved subject carried out and presented in manner satisfactory to warrant its acceptance as per the standard laid 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
down by the university. This report has been submitted in the partial fulfillm ent for theent for the award of
award of Bachelor of ArchitectureBachelor of Architecture degree from Rajasthan Technical University, degree from Rajasthan Technical University, Kota.
Kota.
It is to be understood that the undersigned does not necessarily endorse or approve 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 any statement made, any opinion expressed or conclusion drawn therein, but approves the study only for the
approves the study only for the purpose it has been submitted.purpose it has been submitted.
December 2013 December 2013 Jaipur
Jaipur
Prof. Preethi Agrawal Prof. Preethi Agrawal EXTERNAL EXAMINER
EXTERNAL EXAMINER GUIDEGUIDE
Prof.
Prof. ARCHANA ARCHANA SINGH SINGH Prof. Prof. K.S.MAHAJANIK.S.MAHAJANI CO-ORDINATOR
CO-ORDINATOR PRINCIPALPRINCIPAL
APPROVAL
APPROVAL
The study titled
The study titled ““Space and GeometrySpace and Geometry”” is hereby approved as an original work ofis hereby approved as an original work of
Neha syal
Neha syal, enrolment no.:, enrolment no.: 09EAAAR02909EAAAR029 on the approved subject carried out and on the approved subject carried out and presented in manner satisfactory to warrant its acceptance as per the standard laid 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
down by the university. This report has been submitted in the partial fulfillm ent for theent for the award of
award of Bachelor of ArchitectureBachelor of Architecture degree from Rajasthan Technical University, degree from Rajasthan Technical University, Kota.
Kota.
It is to be understood that the undersigned does not necessarily endorse or approve 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 any statement made, any opinion expressed or conclusion drawn therein, but approves the study only for the
approves the study only for the purpose it has been submitted.purpose it has been submitted.
December 2013 December 2013 Jaipur
Jaipur
Prof. Preethi Agrawal Prof. Preethi Agrawal EXTERNAL EXAMINER
EXTERNAL EXAMINER GUIDEGUIDE
Prof.
Prof. ARCHANA ARCHANA SINGH SINGH Prof. Prof. K.S.MAHAJANIK.S.MAHAJANI CO-ORDINATOR
CO-ORDINATOR PRINCIPALPRINCIPAL
DECLARATION
DECLARATION
I
I ,,Neha syalNeha syal, here by solemnly declare that the research work undertaken by me,, here by solemnly declare that the research work undertaken by me, titled
titled ‘‘Space and GeometrySpace and Geometry’’ is my original work and wherever I have incorporated is my original work and wherever I have incorporated
any information in the form of photographs, text, data, maps, drawings, etc. from any information in the form of photographs, text, data, maps, drawings, etc. from different sources, has been duly acknowledged in my report.
different sources, has been duly acknowledged in my report.
This dissertation has been completed under the supervision of the guide allotted to This dissertation has been completed under the supervision of the guide allotted to me by the school. me by the school. Neha syal Neha syal V Year B.Arch V Year B.Arch Aayojan School o
Aayojan School of Architecture, Jaipurf Architecture, Jaipur
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
CONTENTS
Page No.
Approval i Declaration ii Acknowledgement iii Contents iv-vCHAPTER 1: INTRODUCTION
7 - 13
1.1 Hypothesis 1.2 AIM1.3 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
CHAPTER 2: UNDERSTANDING SPACE
14 - 18
2.1 SPACES IN ARCHITECTURE
2.1.1 QUALITIES OF AN ARCHITECTURAL SPACE
CHAPTER 3: REALISATION OF FORM
19 - 26
(
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
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
27-36
4.1 REGULAR SHAPES 4.2 SHAPE 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
37
–40
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
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 vi-vii
LIST OF ILLUSTRATIONS GLOSSARY OF TERMS ANNEXURES
Neha Syal 5th Yr. B.Arch 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 office-Noida Pivotal serviced apartments-Gurgaon 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.
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 design (various perspectives)
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.
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
[rectangular-square, rectangle- curvilinear- circle polygonal- 5-sided polygon] are not covered.
AREA OF STUDY
1. Geometric shapes and forms- Regular .
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. Rectiliner Curvilinear
Geometric
Characteristics
Mathematical efficiency Role of building elements-[porch, chajja, staircase] in transformation of plan FORMTo study the term effectiveness and
derive its arameters.
To study the aesthetic aspect and analyze its parameters.
Optimum utilization Functionality. Data collection. Primary source Surveys Case studies Secondary Literature studies Books JOURNALS Analysis and Conclusion
1. INTRODUCTION
1| INTRODUCTION AND GLOSSARY OF TERMS
1. SPACE:
Space is a boundless 3-dimentional 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.
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.
HOW IS OPTIMUM UTILIZATION MEASURED?
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”.
The idea or c o n c e p t 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
1. INTRODUCTION
3| BRIEF UNDERSTANDING:
4| SPATIAL RELATIONSHIP:
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]SPACE
TRANSFORMATIONS SPACE EFFICIENCY
OPTIMUM UTILISATION USER SATISFACTION SHAPE FORM
SPACE
FUNCTION
SPACE
EFFICIENC
Y
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.
6|HOW 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
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.
2.
2. UNDERSTANDIN
UNDERSTANDING
G SPACE
SPACE
2.1 SPACES IN ARCHITECTURE 2.1 SPACES IN ARCHITECTURE
Physically space is shape, by what it is, that surrounds it and otherwise by objects Physically space is shape, by what it is, that surrounds it and otherwise by objects within it and is perceivable by us.
within it and is perceivable by us. A space is determined, meaning
A space is determined, meaning finite and fixed by its periphery and finite and fixed by its periphery and objects in it.objects in it.
It It is is meant meant for for something something andand
Offers Offers protection protection for for something.something. Spatiality is defined by : Spatiality is defined by : A A feelingfeeling A A sensationsensation Fig:1 Fig:1 A
A sense sense of of space space is is a a mental mental construct construct ,a ,a projection projection of of the the outside outside world world as as wewe experience it.
experience it.
As space begins to be
As space begins to be ‘captured’, ’enclosed’, ‘molded’, and ‘captured’, ’enclosed’, ‘molded’, and ‘organized’.‘organized’. By the elements of ‘Mass’ , Architecture comes into being
By the elements of ‘Mass’ , Architecture comes into being..
Fig:2 Fig:3
2.
2. UNDERSTANDIN
UNDERSTANDING
G SPACE
SPACE
Spatial Spatial economies, economies, different different activity activity roles roles will will derivederive different space allocation.
different space allocation.
A A designed designed space space is is expected expected to to support support the the activities- activities-functions-and human engagements about to take
functions-and human engagements about to take placeplace there.
there. 2.1.1
2.1.1 QUALITIES OF AN QUALITIES OF AN ARCHITECTURAARCHITECTURAL SPACEL SPACE
Fig:4 Fig:4 The qualities of an
The qualities of an architectural space, however are mucharchitectural space, however are much richer than what these diagrams are able to portray.
richer than what these diagrams are able to portray. Fig:5
Fig:5
BOUNDARY: BOUNDARY:
The most explicit quality of a space is its 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. 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
When we look at a space from the point of view of thethe Interior Interior Boundary Boundary Exterior Exterior We see that the
We see that the boundary is the only element which defines both iboundary is the only element which defines both interior andnterior and exterior space.
2.
2. UNDERSTANDIN
UNDERSTANDING
G SPACE
SPACE
PROPERTIES OF PROPERTIES OF ENCLOSERES ENCLOSERES QUALITIES OF SPACE QUALITIES OF SPACE SHAPE SHAPE Form Form SURFACE EDGES SURFACE EDGES Color Color Texture Texture Pattern Pattern DIMENSIONS DIMENSIONS Scale Scale P Prrooppoorrttiioonn CONFIGURATION CONFIGURATION Definition Definition OPENINGS OPENINGS
Degree Degree of of enclosuresenclosures Light Light View View Table 1 Table 1 The above table (
The above table (table1table1) indicates the various properties of ) indicates the various properties of enclosures andenclosures and lists out their qualities of space.
2. UNDERSTANDING SPACE
T h e t h e o r y o f e x p e r i e n c e i n A r c h i t e c t u r e i s t h e e x p e r i e n c e o f s p a c e .A
rchitecture is a solution in terms of practical purpose, material and techniques .The issue that matters the most is the design-the 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.
Machine-has a purpose Function to perform Building
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 ‘ acti 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 pace-def ining el ement (related to use)
• A sign (rel at ed t o arr ang ement , significance and effect)
3. REALISATION OF FORM
U
NDERSTANDING 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 anifestations-Matter 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. ( Reference : structure in nature –is a strategy for design)
Minimum path network in mud Fig-3.1
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.
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 fig-3.2) which has a minimum surface area to a given volume.
The spherical characteristics Fig-3.2
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 fig-3.3) or better understood that form is a diagram of forces (which supports the heading of this topic).
Form is a diagram of forces: Forces form-Form Fig-3.3
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 (fig-3.4).
The tetrahedral system Fig-3.4
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 (fig-3.5).
The cubic error Fig-3.5
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.
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 (fig-3.6a). 2) The lines form four right angles (fig-3.6b).
Non perpendicular intersection perpendicular intersection
Fig-3.6a Fig-3.6b
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 (fig-3.7 ).
The features of an acute angle Fig-3.7
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.
“ The ‘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 es .”
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 Fig-3.8
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 Fig-3.9
3. REALISATION OF FORM
Page 26 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!
Fig-3.9a Fig-3.9b
Usability factor of various shapes
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.
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
SHAPES-Refer 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. Fig-4
4. TRANSFORMATIONS IN SHAPE
4.2 SHAPE
S
hape is the characteristic outline or surface configuration of a particular form. It is the principal aspect by which we identify and categorizeforms-(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 right’ –
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 Fig-4.1a
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.
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 Fig-4.1b
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.
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
4. TRANSFORMATIONS IN SHAPE
4.4
1) DIMENTIONAL TRANSFORMATION
Dimensional transformation-shown in Form Fig-4.2a
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
Fig-4.2b
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/Robie-House-204473623
Fig-4.2c
Plan form type of Robbie house 4.5
2) SUBTRACTIVE TRANSFORMATION
Subtractive transformation-shown in 3 dimension Fig-4.3
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.
4. TRANSFORMATIONS IN SHAPE
BIANDA’S RESIDENCE
BUILDING BIANDA’S RESIDENCE
ARCHITECT MARIO BOTTA
LOCATION SWITZERLAND
Subtractive transformation-shown Fig-4.3a
4. TRANSFORMATIONS IN SHAPE
4.6
3) ADDITIVE TRANSFORMATION
Additive transformation-shown in 3 dimension Fig-4.4
Forms can be transformed by addition to its volume. Types of additive transformations:
Types of Additive transformations Fig-4.5
PLA CE DE STALINGARD
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.
5. EFFECTIVE SPACES
EFFECTIVE SPACES
PRELUDE
T
his chapter relates to the understanding and definition of effective spaces.‘’ Effectiveness of a space ’’, is a general concept reflecting an o utput from that 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
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
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.
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”.
The basic physical parameters of a
building shell will set rules for its
occupation by describing –‘How effectively’ a building can be planned.
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 two-thir ds, (7) two squares.
6. CASE STUDIES
6. CASE STUDIES
6.1 ARCHOHM ARCHITECTURE FIRM Architect: Ar Saurabh Gupta Location: NoidaE v o l u t i o n o f f o r m from basic geometric shapes:
PRIMARY FUNCTION: Architectural firm
PRIMARY GEOMETRY:
Regular solids-cylinder, 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
6. CASE STUDIES
Fig-6.1
The above floor plan shows the percentage circulation in the architectural firm.
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 fig-6.2) 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 Board room Cafe
To serve as a seminar hall To serve as a meeting area
Issues The functionality is not achieved in conjugation with its geometry
Functionality is achieved
Efficiency of a space
People/workstation: Will give us the
num erical data
P l a n n i n g / w o r k s t a t i o n : Give us subjective reasons to jus tify the
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 people present as per standard Area (Square M) 1 STUDIO 33 30 5 60 265 2 CABIN-1 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 B O A R D 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 designed Space designed for number of people Number people working at present Number people visiting on daily basis (approx) Number people present as per standard Area (Square M) 1 STUDIO 53 50 5 78 440 2 BEDROOMS 6 - - 6 93.8
6. CASE STUDIES
6.2 PIVOTAL
APARTMENTS-GURGAON ARCHITECT: Ar Anoj Tevatia
LOCATION: gurgaon PRIMARY FUNCTION: Serviced Apartments PRIMARY GEOMETRY:
Circular plan subjected to dimensional transformation changing into an oblong shape.
Typical plan of the serviced apartments.
6. CASE STUDIES
Fig-6.4
The above two typical plans shown in (fig-6.3 and fig-6.4) 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 .
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.
6. CASE STUDIES
6.3 RESIDENCE
RESIDENCE OF MR SYAL ARCHITECT: Er Murari Syal
LOCATION:Jaipur PRIMARY FUNCTION:
Residence
PRIMARY GEOMETRY:
Rectangular geometry-all 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
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 dr 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.
fig6.7
Fig 6.8 fig 6.9
Master bedroom Drawing room
22% 33% 18% 13% 14% Drawing room Master Bedroom kids bedroom Kitchen
Others and puja
6. CASE STUDIES
6.4 RESIDENCE
RESIDENCE OF AR ANOJ TEVATIA ARCHITECT: Ar Anoj Tevatia
LOCATION:New Delhi PRIMARY FUNCTION:
Residence
PRIMARY GEOMETRY:
Rectangular geometry-all rooms following the similar geometric pattern.
Fig 6.9a fig 6.9b
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 dr 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’’ )
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.
34% 25% 17% 13% 11% DRAWING ROOM MASER BEDROOM OTHER BEDROOM KITCHEN OTHERS AREA sq ft)
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”.
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……
“ H ow 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.
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
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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,
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Baker, H. G, D e s i g n S t r a t eg i e s in 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 in 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.
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 h it e c t u r e a n d D e s i g n , Van Nostrand Reinhold, New York, 1994.
Gargus, J, Ideas of Order. A F o r m a l A p p r o a c h t o A r c h i t e c t u r e , Kendall / Hunt Publishing Company, Iowa, 1994
Joedicke, J, Space a 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 the Past,
Karl Kramer Ver lag, Stuttgart, 1985
Jules, F, F o r m / Sp a c e a n d t h e L a n g u a g e o f A r c h i t e c t u r e , 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 in
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 in
A r c h i t e c 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.
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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.
