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Architecture is a ‘solution’ in terms of practical purpose, material and techniques.The issue that matters the most is the design-the discovered form. The moderndesigner therefore has to choose ‘optimum’ between ‘spatial’ quality and ‘efficiency’which depends on his perception of the problem. This leads us to believe what bestcan we do in an allotted space, which would then reflect in and eventually postulatethe 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 basisfor user satisfaction!
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DISSERTATION REPORT
Session: 2013-14
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
ISI-4, RIICO Institutional Block,
Sitapura, Jaipur-302022
A-PDF Merger DEMO : Purchase from www.A-PDF.com to remove the watermark
APPROVAL
The study titled “Space and Geometry” is hereby approved as an original work of
Neha syal, enrolment no.: 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 fulfillment for the
award of Bachelor of 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
CO-ORDINATOR PRINCIPAL
i
DECLARATION
I ,Neha 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 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
Passport Size
Photograph
CONTENTS
Page No.
Approval i
Declaration ii
Acknowledgement iii
Contents iv-v
CHAPTER 1: INTRODUCTION 7 - 13
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
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
iv
3.3 THE ORIGIN OF FORM
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
v
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 vi-vii
LIST OF ILLUSTRATIONS
GLOSSARY OF TERMS
ANNEXURES
vi
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 the design-the discovered form. 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. GUIDE: Prof. Preethi Agrawal.
1. INTRODUCTION
Page 7
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
Page 8
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 .
2. Interior, spaces in the chosen shape and Form.
1. INTRODUCTION
Page 9
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 types of forms
Rectiliner
Curvilinear
POLYGONA
L
Geometric
Characteristics
Mathematical efficiency
Role of building elements- [porch, chajja, staircase] in transformation of plan FORM
To study the term
effectiveness and
derive its
parameters.
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
Page 10
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
Page 11
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 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
1. INTRODUCTION
Page 12
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
EFFICIENCY
1. INTRODUCTION
Page 13
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
sensation within those spaces.
2. UNDERSTANDING SPACE
Page 14
UNDERSTANDING SPACE…..
PRELUDE
This 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. UNDERSTANDING SPACE
Page 15
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.
Fig:2 Fig:3
2. UNDERSTANDING SPACE
Page 16
Spatial economies, different activity roles will derive
different space allocation.
A designed space is expected to support the activities-
functions-and human engagements about to take place
there.
2.1.1 QUALITIES OF AN 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 interior and
exterior space.
2. UNDERSTANDING SPACE
Page 17
PROPERTIES OF
ENCLOSERES
QUALITIES OF SPACE
SHAPE Form
SURFACE EDGES Color
Texture
Pattern
DIMENSIONS Scale
Proportion
CONFIGURATION Definition
OPENINGS Degree of enclosures
Light
View
Table 1
The above table (table1) indicates the various properties of enclosures and
lists out their qualities of space.
2. UNDERSTANDING SPACE
Page 18
T
he
th
eo
ry o
f e
xpe
rie
nce
in
Arc
hite
ctu
re is th
e e
xp
erie
nce o
f sp
ace
.
Architecture 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 Le Corbusier:
The theory of experience in Architecture is the experience of space.
Machine-
has a
purpose
Function to
perform
Building
3. REALISATION OF FORM
Page 19
REALISATION OF FORM (study focuses on two dimensional aspect of Form)
PRELUDE
Form in Architecture is related to ‘space’ and the ‘activity occurring within this
space’. Apart from that, architectural form is also related to the elements
themselves;
Their arrangements, and combination with each other (syntax); the meaning
(semiotics); and the effects on people (pragmatics).
Form therefore cannot simply be reduced to a single of choice of elements and their
arrangement.
For that reason it is possible to appraise the architectural form within
the framework of:
• Space-defining element (related to use)
• A sign (related to arrangement, significance and effect)
• Structure (dependent on the laws of static and the strength of materials)
3. REALISATION OF FORM
Page 20
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 from ‘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 manifestations-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.
(Source: Peter Pearce-Structure in nature is a strategy for design-MIT Press-1978)
3. REALISATION OF FORM
Page 21
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
Page 22
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 tetrahedron geometry.
3. REALISATION OF FORM
Page 23
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
Page 24
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 optimum
utility of the spaces.”
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
Page 25
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 history of civilization!
Fig-3.9a Fig-3.9b
Usability factor of various shapes
Fig-3.9c Fig-3.9d
4. TRANSFORMATIONS IN SHAPE
Page 27
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
Page 28
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 geometry 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
Page 29
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-
(Francis Dk Ching).
According to ‘Frank Lloyd Wright’ –
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 twelve 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
4. TRANSFORMATIONS IN SHAPE
Page 30
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
Page 31
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
4. TRANSFORMATIONS IN SHAPE
Page 32
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.
ROBBIE HOUSE
Fig-4.2b
http://architecture.lego.com/en-us/products/architect/robie-house/story/
4. TRANSFORMATIONS IN SHAPE
Page 33
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
Page 34
BIANDA’S RESIDENCE
BUILDING BIANDA’S RESIDENCE
ARCHITECT MARIO BOTTA
LOCATION SWITZERLAND
Subtractive transformation-shown
Fig-4.3a
https://wiki.ucfilespace.uc.edu/groups/12u_20artn242001/wiki/b27fe/
4. TRANSFORMATIONS IN SHAPE
Page 35
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
PLACE DE STALINGARD
http://en.wikipedia.org/wiki/Place_de_la_Bataille-de-Stalingrad
4. TRANSFORMATIONS IN SHAPE
Page 36
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
Fig-4.6
5. EFFECTIVE SPACES
Page 37
EFFECTIVE SPACES
PRELUDE
This chapter relates to the understanding and definition of effective spaces.
‘’Effectiveness of a space’’, is a general concept reflecting an output 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
spatial experience.
5. EFFECTIVE SPACES
Page 38
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
5. EFFECTIVE SPACES
Page 39
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
Page 40
5.5 understanding efficiency through example.
Let us understand Efficiency by an example as stated by Palladio!
Andreas Palladio brings the theory of Renaissance proportioning to its most
sophisticated state. He turns the idea of subdividing a plan into harmonious parts
around by starting with rooms in harmonious ratios and joining them together to
produce the entire building.
Palladio’s seven sets of proportions in construction of rooms
Palladio supplies general rules for 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 room. He recommends seven shapes of rooms in the following
sequence:
(1) circular, (2) square, (3) the diagonal of the square for the length of the room, (4)
a square and a third, (5) a square and a half, (6) a square and two-thirds, (7) two
squares.
6. CASE STUDIES
Page 41
Case studies of Pivotal and Archohm
6. CASE STUDIES
Page 42
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 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
Page 43
Fig-6.1
The above floor plan shows the percentage circulation in the architectural firm.
Fig-6.2
6. CASE STUDIES
Page 44
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
numerical data
Planning/workstation:
Give us subjective
reasons to justify the
efficiency
6. CASE STUDIES
Page 45
6.1.2 CALCULATING area usage- “ people/workstation”
At upper ground floor level
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 CABIN -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”
At lower ground floor level
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
Page 46
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.
Fig-6.3
6. CASE STUDIES
Page 47
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
Page 48
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
Page 49
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
Analyzing the spaces in the house:
6. CASE STUDIES
Page 50
Ground floor consists of a Drawing room (12.6x16 feet)
Adjacent to a Kitchen (10.4X11 feet) and master bedroom (14x21 feet) and a
kids bedroom (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%
AREA(sq ft)
Drawing room
Master Bedroom
kids bedroom
Kitchen
Others and puja
6. CASE STUDIES
Page 51
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
Ground floor first floor
6. CASE STUDIES
Page 52
The second study conducted in order to analyze the efficiency of spaces is that of Ar
Anoj Tevatia.
Ground floor consists of a Drawing room (13’x18’-9’’)
Adjacent to a Kitchen (9’x13’-9’’) and master bedroom (16’-10’’x13’9’’)
kids bedroom and guest 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%
AREA(sq ft)
DRAWING ROOM
MASER BEDROOM
OTHER BEDROOM
KITCHEN
OTHERS
6. CASE STUDIES
Page 53
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 of spaces’, 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
Page 53
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.
Similarly, any space can be termed as a productive space, if the functionality
conjugates or resonates with the amount of people using the given space.
‘’The effectiveness will thus be, to calculate the output from that space.’’ This evokes
a question for us all to ponder upon……
“How 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.
8. REFERENCES
Page 54
Arnheim, R, The Dynamics of Architectural Form, University of California Press, London, 1977.
Blackwell, W, AlA, Geometry in Architecture, Key Cirriculum Press, Berkeley,California.
Baker, H. G, Design Strategies in Architecture (an Approach to the Analysis of Form), Van Nostrand Reinhold, New York, 1996
Percy E Nobbs, Treatise in the discovery of Form.
Ching, F, D.K, A Visual Dictionary of Architecture, Van Nostrand Reinhold, New York, 1995
Emde, H, Geometrical Fundamentals for Design and Visualization of Spatial Objects.CAAD Futures' 87. Eds. Tom Maver and Hanry Wagter, Amsterdam, Elsevier,1987.
Franck, K, A, Ordering Space: Types in Architecture and Design, Van Nostrand Reinhold, New York, 1994.
Gargus, J, Ideas of Order. A Formal Approach to Architecture, Kendall / Hunt Publishing Company, Iowa, 1994
Joedicke, J, Space and Form in Architecture. A Circumspect Approach to the Past, Karl Kramer Verlag, Stuttgart, 1985
Jules, F, Form/Space and the Language of Architecture, Publications m Architecture and Urban Planning, Wiscoin, 1974
Moore, C. and Allen, G, Dimensions: Space, Shape and Scale in Architecture, Architectural Record Books, New York, 1976
8. REFERENCES
Page 55
Perez, G, A, Introduction: The use of Geometry and Number in Architectural Theory: From symbols to Re-Conciliation to Instruments of Technological Domination, Diss. U.
Placzek, A, K, Palladio Andrea: The four Books of Architecture, Dover Publications Inc., New Yark, 1965
Scholfield, P.H, The Theory of Proportion in Architecture, Cambridge University Press, Cambridge, 1958
Schirm beck, E, Idea, Form, and Architecture, Design Principles in Contemporary Architectures, Van Nostrand Reinhold, New York, 1987
Steadman, P, Architectural Morphology: An Introduction to the Geometry of the Building, Pion, London, 1989.
Stevens, G, The Reasoning Architect, Mathematics and Science in Design, Mc-Graw-Hill Publishing Company, New York, 1976
Wilson, F, A Graphic Survey of Perception and Behavior for the Design Professions, Van Nostrand Reinhold, New York, 1984
Winters, N, B, Architecture Elementary. Visual Thinking Through Architectural Concepts, Gibbs, M, Smith, Salt Lake City, 1986
Wong, W, Principles of Two-Dimensional Form, Van Nostrand Reinhold, New York, 1988
9. GLOSSARY
Page 56
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.
9. GLOSSARY
Page 57
Grid: A framework of crossed lines; common architectural grids are four-square and
mne-square.
Morphology: Literally a branch of biology which examines the forms and structures
of plants and animals, used in architecture to discuss the study of form.
Order: A condition of logical, harmonious, or comprehensible arragement in which
each element of a group is properly disposed with reference to other elements and to
its purpose.
Proportion: The comparative relations between dimensions or sizes.
Radial: Disposed about a central point.
Shape: The outline or surface configuration of a particular form or figure.
Space: Space is a boundless 3-dimentional extent in which object and events have
relative position and direction.
Space Efficiency:
OPTIMUM UTILIZATION is defined as:
m sq / person.
m sq /workstation.
people / workstation.
Subtractive form: Shape which is understood to have been created by a process of
subtraction from a whole, i.e. by the removal of pieces or the carving out of a void
from a solid.
