ENGINEER - Vol. XXXVIII, No. 03, pp.

45-61, 2005
© The Institution of Engineers, Sri Lanka

Aesthetics in Structures
Chandana Kulasuriya
Abstract: This paper describes the fact that 'aesthetics of structures' is related to various aesthetic
concepts, styles, movements, theories and also with the technical considerations. Further, it also describes
that all the above-mentioned considerations have roots in the fundamental philosophical models of
aesthetics. It also discusses the application of geometric theories and structural theories in achieving
aesthetics of structures.

like bridges, transmission towers, water towers,

etc., are designed by engineers. Hence engineers
should be responsible for aesthetic aspects of
these structures. This responsibility can be
fulfilled if the engineer has the knowledge of
aesthetics and design.
The above mentioned facts confirm that the
knowledge of aesthetics would be very useful for
engineers not only to help architects to achieve
their goals but also to design engineering
structures such as bridges, towers, etc.
Within the discourse of 'aesthetics of structures',
the 'structure' is considered as a three
dimensional composition. Hence, before studying
aesthetics of structures, certain fundamental
concepts about composition have to be
1. Introduction understood. Hence the first few paragraphs of this
Normally architects are responsible for aesthetics paper deal with that.
of structures. However, structural systems and When 'aesthetics of structures' are concerned, it
structural components designed by the engineer cannot be studied in isolation, as it has links with
play a major role in the aesthetic appearance of many other areas such as art, architecture,
structures. For example the visual appearance of philosophy, engineering, history, etc. Therefore
high-rise buildings mainly depends on the this discourse extends towards those areas as well.
structural system. Similarly, the roof structure is
a prominent visual element of many structures.
2. Nature of Aesthetics
Therefore, the engineer has the challenge of
designing sub-structures like roof structure, The word 'aesthetics' has been derived from the
supporting structure, etc., to achieve the Greek word 'aesthesis'; meaning sensory
architect's goal of aesthetics. In this exercise, if perception. It was regarded as a branch of
the engineer has the knowledge of basic philosophy concerned with the understanding of
aesthetics, he would be able to understand the beauty and its manifestation in art and nature.3
architect's language easily and to design However,, it is extremely difficult to give a precise
structural components to satisfy the architect's definition for aesthetics. Aesthetic consciousness
requirements. Further, if the engineer is covers special sentiments, tastes, interests,
aesthetically conscious, he would be able to concepts, ideals, views and theories.
develop totally new structural forms and help
architects to design innovative structures.
Although most of the buildings are designed by
Eng. Chandana Kulasuriya, BA-FineArts & Philosophy, MEng.-Struct.
architects, there are certain structures designed Eng., CEng., Chartered Civil Engineer, , MIE(SL), MCSA , Lecturer at
by engineers themselves. For example, structures Open University of Sri Lanka

45 ENGINEER
It is generally recognised that aesthetics has two It seems unity, balance, harmony, rhythm, etc., are
components - 'emotional component' and the innate needs of us. This is related to our desire to
'intellectual component'. It is believed that the understand and control our environment, and
emotional component is very much subjective may be a part of our primitive survival skills. It
and the intellectual component is less subjective. may also be driven by basic emotions such as
The motional component is an indefinable, insecurity and fear of the unknown.20 However,
intuitive aspect of our personality and it provides the pure, perfect form of these characteristics can
us the ability to emotionally appreciate an object. result in monotony or boredom. In view of that
On the other hand, the intellectual component is unity with variety, occasional discontinuity of
considered as a rational aspect, and hence, it rhythm, dramatic contrast can be used to make
provides us the ability to rationally appreciate an the composition interesting.
object, considering the function of the object,
constraints, specifications, conditions, etc. Unity:
Unity is the quality of 'singleness effect' and the
Nevertheless, some philosophers who doubt the
'completeness' of a composition. In a unified work
existence of 'so-called objectivity', question the
of art, all the parts come together to form a
validity of a 'so-called intellectual component'.
'unified whole'; each part of a composition 'feels'
According to them the 'so-called objectivity' is
like that it belongs with the rest. That is unity
merely an 'inter-subjective agreement', among a
which refers to the visual linking of various
particular group of people, based on certain
elements of the composition. A designer achieves
views, assumptions, ideas, theories, standards,
unity by balancing all the aspects of the
values, etc. Hence according to this view, aesthetic
composition.
consciousness is both an intra-sufy'ectiveand inter-
subjective agreement. When the eye is attracted by two stimuli of equal
importance, the resolution of elements into a
3. Characteristics of A Composition 'unified whole' is prevented or disturbed. This
effect is known as 'duality'.
Primarily, structures can be considered as three
dimensional compositions. Therefore, it would be For example, when two objects which are spaced
useful to study about compositions to understand too far apart for the eye to see them as a unit, but
the aesthetics of structures. not far enough apart for them to be perceived as
completely independent, 'duality' can be
A 'Composition' can be described as an experienced. However, this can be resolved by
arrangement of parts or elements into proper inserting a dominant central block between the
relation to produce a conceptual unified whole.
two objects (Figure la).20
There are a number of approaches to study
'composition'20. However, the approach discussed The same thing happens with bridges (Figure
in this paper is the 'principle of formal analysis' lb).33 A single-arch bridge shown in the figure,
developed in the worlds of art and architecture though simple, is visually satisfying. However,
which permit the description and investigation when there are exactly similar arches next to each
of our reactions to visual stimuli. The importance other, the eye finds it difficult to resolve it into a
of this analysis is that it can be related to scientific unified whole. Instead the eye looks at one span
study of perception. and then at the other. The eye goes to arches and
not to the piers, and it will
3.1 Fundamental characteristics of a
composition

Unity, balance, harmony, contrast, emphasis,

movement, and rhythm are some of the
fundamental characteristics of a composition.20

ENGINEER 46
 Duality

i Duality [

XX
*
——L
~~\.TK:
^~^ Unity Unity Duality
Unity Unify

(a) (b) (c)

Fig. 1 - Unity & Duality

wobble from one centre-line to the other, so that The concept of balance is related to the 'visual
A feeling of restlessness is produced. However, centre of gravity' of an object and 'visual weights'
this can be resolved by introducing a dominant of elements. The eye expects a 'balance' about the
central arch between the two arches. Here the visual centre of gravity as though it were a
centre-line is not only the centre-line of the middle fulcrum and the various visual weights applied
arch but also that of the bridge; and the eye is in with various leverages. The 'visual weight' of an
no doubt at all to decide the line upon which to element may be manipulated by delineation or
concentrate. There is no question of it wobbling varying the play of light and shadow to hint at
from one centre-line to another, and shows a solidity or hollowness.(Figure 2)
composition of complete restfulness.
There are two types of balances, symmetrical and
Duality may also be experienced when the facade asymmetrical. Symmetrical balance is easier to
of a building has equal horizontal and vertical understand. Symmetry is the balance of mirror
emphasis (Figure lc).21 figures about a point, line or plane. The usual
emotional response to symmetrical balance is
When the eye is attracted by multiple stimuli of 'stability' or 'satisfaction with the status quo'.
equal importance, a similar effect, which may be Asymmetrical balance sometimes referred to as
termed as 'multiplicity', can be experienced. Occult balance, is much more subtle, but it usually
Normally 'Unity' is recognised as a basic stimulates a dynamic and emotional response.
requirement of a good composition. Hence 'Lack Acceptable asymmetric balance depends largely
of unity', duality, multiplicity may be considered on the emotional qualities of aesthetics and the
as a fault. However in certain periods people have personality of the designer and the viewer.
exhibited impatience with the concept of unity
and duality was advocated as a means of relieving Harmony
the boredom of unity. Harmony in a composition is the visually
satisfying effect of combining similar, related
Balance elements. The designer can create harmony
' Balance' can be described as a state of equilibrium through elements such as shapes, colours,
between its elements. 21 Balance in design is textures, etc. (e.g. - Adjacent colours on the colour
similar to balance in physics. Without it, the wheel create a feeling of harmony)
composition looks awkward and unstable.

47 ENGINEER
 Rhythm
Rhythm is the regular repetition of elements of a
composition to produce the look and feel of
movement. A designer creates movement in a
composition by repeating elements such as
colours, shapes, lines, textures, etc. The repetition
of the elements invites the eye to jump rapidly or
glide smoothly from one image to the next.
Fig. 2 - Symmetrical balance & Rhythm allows the designer to create a feeling of
Asymmetrical balance organized movement. Elements placed at regular
intervals create a calming rhythm. Sudden
There are two kinds of harmony with respect to changes in position and size create a lively
any object present in the environment - internal rhythm. Variety keeps rhythm exciting and active,
and external. Internal harmony refers to the moving the eye around the composition.
relation between parts of the object, where as
external harmony refers to the relation of the As the eye scans across a building it is affected
object to its surrounding environment. by the regularity or otherwise of elements such
as windows, mullions, columns, and arches which
Harmony gives a feeling of unity and coherence may give rise to an impression of 'rhythm'.
with associated psychological reactions of Rhythms may be seen as slow and smooth when
security and relaxation. they are based on a few elements which are
widely spaced relative to the overall form, or
Contrast rapid and staccato. Rhythms may be read
Contrast is an abrupt, unexpected change in a vertically as well as horizontally.20
visual element. The designer can create contrast
through the elements such as shapes, colours, 3.2 Other Qualities
textures, etc. For example, complementary
In addition to fundamental characteristics such
colours of colour wheel (red/green, yellow/
as unity, balance, harmony, rhythm, etc.,
purple, blue/orange) seem to create a feeling of
structures, may be associated with features such
contrast when they are placed together in a
as identity, character, meaning, etc.20
composition.
Identity
Emphasis
Identity of a structure may be related to location,
As a composition develops a designer may decide
history, culture, society, etc. For example Pagodas
to stress certain elements of the design over others
have a Japanese Identity.
to create a 'focal point'. The eye of the viewer will
focus on the area of 'emphasis' or 'centre of
Character
interest' first, and then take in the rest of the
composition. A designer uses emphasis to direct Structures may have a character as in the case with
and focus attention of the viewer on the most human beings. For example a structure with a
important parts of a composition. A designer strong vertical emphasis may be seen as excuding
creates emphasis through size, colour, texture, pride, self-confidence.(Figure 3). Lighter
and shape. A composition lacking emphasis will constructions (Figure 4) may have an air of
be monotonous and uninspired. ethereality.

Movement
Movement is the way the viewer moves his eye
around through the composition after seeing the
'focal point'. A designer arranges parts of a
composition to create a sense of motion by using
elements such as shapes, colours, textures, etc.

ENGINEER 48
 Fig. 4 - Inverted Pyramid-like building
:
Fig. 3- Thomas Telf ord's Bridge
3.3 Elements of Composition
The above mentioned characteristics or qualities
are acquired by a three dimensional composition
by some basic elements such as Size & Scale, Form
& Shape, Proportion, Space, Texture, Colour, Light
& Shade, Visual weight, Pattern, Ornamentation
etc.

4. Aesthetic Concepts Related to

Structures
There are various concepts behind aesthetics of
structures. These concepts are integrated to the
structure not only by the designer but also by the
critics, conservators, users, observers, etc. This can
happen either at conscious or subconscious level
of the person concerned. Some of such concepts
that are integrated with the structures are given
below.
Fig. 4 - Convention Centre, New York33
"The structure should appear to spring naturally from
Meaning its surroundings'
A structure may express its' function. For example "The structure should harmonise with surrounding
the appearance of a hospital may reflect its' context."
function.
"The structure need not necessarily harmonise with
In addition to the above mentioned the existing surrounding context, the constructive
characteristics, qualities like sensuality, tension, conflicts between the structure and the existing
excitement, humour etc., too can be integrated surrounding context may create a new form of
to structures to create an interest. This can be done progressive aesthetics."
by the structure as a whole or by its' components "The. structure should resemble or suggest forms found
in the form of 'innocent jokes', 'simple nonsense', in nature"
'pinch of insecurity', etc. For example an inverted
"The structural skeleton should be completely covered
pyramid-like structure may produce a sense of
with a form giving skin (cladding), like in animals."
insecurity and a tension in the observer. Twisted
shafts or hanging columns may produce a sense "The structure should be subjectively related with the
of humour in the observer. consumer or the user"
"The structure should express its' function"

49 ENGINEER
 expresses the feeling of sharing the work (Figure
"The structure should be as simple as possible"
6c). Verrazano Narrow's Bridge is a completely
"Restructure should be like 'plug-in components' of truthful expression of a tensile material in the
a printed electronic circuit board" form of the 'funicular form' (Figure 6d) .This
"Tlie structure should be truthful/rational/honest reflects the concept of 'truthful structures'.
as possible"
The original design of the George Washington
These aesthetic concepts are reflected in many Bridge, New York, is a steel structure with a stone
structures. Clustered water tanks at Alencon, cladding (Figure 7a). This reflects the concept of
France, look like trees in nature. (Figure 6a) This 'form giving skin of animals'. However, after the
reflects the concepts related to 'organic forms'. structural skeleton was erected, it was not clad
The Eiffel Tower in Paris contradicted with the by stones despite the opposition of a large part of
environment and the contemporary society, when New York intelligentsia and the design engineer
it was first erected. However, later it was able to himself (Figure 7b). However, later, the aesthetics
create new aesthetic values and became the of the exposed structural skeleton has been widely
'semiotic symbol' of France (Fig 6b). This may appreciated by all. Here, the naked steel structure
reflect the concept of 'constructive conflicts'. reflects the concept of'honesty'. This indicates the
Water Tower at Fisons Fertilizer Factory, UK, is rapid changes of aesthetic appreciation and also
subjectively related with the factory workers and the different reflections of aesthetic concepts.

5. Aesthetic Movements & Styles

Related to Structures
Aesthetics of structures cannot be understood in
isolation. It has a historical narrative. Within this
historical narrative aesthetics has evolved
through a number of movements. These
movements have influenced the aesthetics of
structures directly or indirectly. Therefore,
aesthetics of a particular structure has to be
understood within that background.
Aesthetics of structures have been influenced by
the aesthetic movements. Rationalism, Arts and
Crafts Movement, Art Nouveau, Cubism,
Chicago School, Constructivism, Functionalism,
Bauhaus, Expressionism, International Style,
Brutalism, Organic architectural style, Art Deco,
Vernacular Architecture, Modernism, Post-
modernism, High-tech and Deconstruction are
some of such movements. Some of them are
Fig. 6 - Reflections of aesthetic concepts briefly described below. 8
in structures
Constructivism
A movement which originated in Moscow after
1917, primarily in sculpture but with broad
application to architecture. The expression of
construction was to be the basis for all building
design. 8

(a) (b) Functionalism

Fig. 7 - George Washington Bridge A design movement that evolved from several
previous movements in Europe in the early 20th
century, advocating the design of buildings,

ENGINEER 50
ImnJHhing, or the like as direct fulfilment of Post-modernism
1 1 n it lional requirements, with the construction, A movement in architecture and the decorative
materials, and purpose clearly expressed, and arts that developed in the 1970's in reaction to
With the aesthetic effect derived chiefly from the principles and practices of modernism,
I MI portions and finished to the exclusion or especially, the influence of the International Style,
subordination of purely decorative effects. encouraging the use of elements from historical
Puiu'tlonalists believe that when function is vernacular styles and often playful illusion,
fulfilled, the form will follow automatically - decoration, and complexity.8
I . ' i in lollows function'. 8
Post-modern architects have continued to take
iNpreislonism advantage of the new materials available while
turning to different periods of the past for artistic
I • |Mt?8Nionists rejected the hard, rectilinear and
inspiration. There has, for instance, been a revival
standard boxes in favour of an
of the principles of classical architecture with
and romantic approach. Buildings
emphasis on proportion and harmony. This has
meant to express or symbolise their use,
even led to the design of supermarkets in the style
together form and content in a new
of palaces, and offices in the style of temples.8
I" I'.onnl language. Symbols used were often
relating to speed and machines as well as
o f t e n consciously or subconsciously High-tech
•PMIrtl"' A style of design incorporating industrial,
commercial, and institutional fixtures, equipment,
IniUllim materials, or other elements having the utilitarian
appearance characteristic of industrial design.
I1u> term 'Hrutalism' was derived from the French
i ' MM ' I't'fuii briif which means rough concrete. One way of achieving this is by ensuring that
Normally concrete is surfaced plaster, but the certain essential services, which are normally
Hi uMllnts thought that, in the interest of honesty concealed within the building, are clearly visible
uillu'iiticity, it should be exposed. Some from outside. Lifts travel up and down its front
litillilin^s which do not show rough exposed or sides. Escalators are suspended from the
i mi. iHr luvr also been classified as Brutalist. In structure on to the exterior. Pipes for air-
, mi exposed steel frame is visible on the conditioning and water are not only visible but
"•" are designed as decorative features. Bright colours
predominate on the exterior. Pipe work may be
c architectural style colour-coded to indicate its various functions. All
A movement of architectural design that emerged the structural parts may be in one distinctive
i M 1 1 in early 20"' century, asserting that a building colour or clad in stainless steel.8
ilioiiUI have a structure and plan that fulfil its
f u m l i o n a l requirements, harmonize with its Deconstruction
n i i u i . i l environment, and form an intellectually A critical movement that started in the 1960's,
in. hi, Integrated whole. The shapes or forms in especially, in the study of literature, questioning
»tn h rt work are often of irregular contour and traditional assumptions about the ability of
»tH<m lo resemble or suggest forms found in language to represent reality and emphasizing
ti.ilure." that a text has no stable reference because words
essentially refer only to other words. A reader
Mmli'rni.sm must therefore approach a text by eliminating any
A d e l i b e r a t e philosophical and practical abstract reasoning or ethnocentric assumptions
••iMiifiement from the past in the arts and through an active role of defining meaning,
llU'irtture occurring in the course of the 20th sometimes by a reliance on etymology and new
li'Mlnry and taking form in any of the various word construction.8
Innovative movements and styles.8

51 ENGINEER
6. Aesthetics of Structures and Related Sculptural Theories
Theories The goal of sculpture is to produce three-
dimensional objects which have the sole purpose
Through the centuries, since the Greeks first of evoking emotions or reflecting ideas. These
codified their ideas on aesthetics, many theories theories state that we like certain objects because
about preferences in the realms of art and their shapes evoke emotions or reflect ideas which
architecture have been developed. These theories accord with our needs or value systems.26
can be organised into four categories: geometric,
rationalist, sculptural and structural.26 Structural Theories
These theories state that we like certain objects
Geometric Theory (Proportioning Theories)
because they clearly reflect their structural
These theories are based on the idea that we find behaviour. The theory assumes that we all possess
certain things or experiences beautiful because an inherent understanding of structure, based on
they resonate with patterns built into our each person's struggle with gravity from the day
cognitive systems. It is a common experience from we begin to walk.26
music that certain combinations of sounds
(chords) are generally judged to be beautiful, The cantilever is an example of this idea which
while others are considered dissonant, even applies to bridges. To most people a cantilever is
uncomfortable, such as the sound of fingernails more attractive if it is thicker at its support and
on a blackboard. Perhaps the fingernail sound tapers towards its free end. People find it
causes our cells to vibrate in ways that disturb attractive because it reflects the cantilevers they
their functioning.26 are already familiar with: the shape of their own
arms and legs or the branch of a tree. From this
Many of the classical theories of proportion trace familiarity people develop an intuitive
back to this idea. Rectangles proportioned understanding of what the engineer knows from
according to the 'Golden Ratio' (1:1.618) were calculation: that the stresses in a cantilever are
considered automatically superior because they largest at the support, and therefore that's where
supposedly appealed to some inherent inner most of the material should be. 26
sense of visual proportion. (See Appendix 1).26
Through the history, the golden proportion has 7. Philosophical Models of Aesthetics
consistently brought a sense of harmony to
All the above mentioned aesthetic concepts,
design, not to mention a spiritual and even a
styles, movements, theories etc., have their roots
physical sense of well being. A number of
at various philosophical models of aesthetics.
examples could be cited, including Stonehenge
These models are derived from fundamental
in England, in Egypt, classical temples of Greece,
paradigms of philosophy. Although these models
Gothic cathedrals and modern buildings.2 Some
do not directly reflect the philosophical
of these structures are presented in Appendix 2.
paradigms, which they were derived from, they
reflect certain characteristics of those paradigms.
Rationalist Theories
Naturalism, Objective Idealism, Subjective
This set of ideas states that we like objects whose Idealism, and Materialism, are some of the major
shape clearly reflect its function. For example, a historical philosophical models of aesthetics.1
teapot with a comfortable handle and efficient
spout will be more attractive than a teapot shaped Model of Naturalism:
without regard to these functional necessities.26
Aesthetics is a natural property of nature. Objects
This theory applies more easily to objects with a are perceived as aesthetic when they reflect
single obvious function. Engineering structures properties (proportion, form, shape, etc.) that are
such as bridges, water tanks, transmission towers, found in nature. According to this model
etc., fall clearly into this category. Buildings aesthetics is considered as a natural form.
accommodating multiple functions are not as
easily approached this way.26 Model of Objective Idealism:
Aesthetics is an objective quality, which is
independent of and external to human

ENGINEER 52
iini'1, iMiiMH'v. It is often associated with concepts 8. The Composition & The Context
ttml nr« 1'iinsidrrcd 'universal'. According to this
l rtWBthvtics is considered as an objective A composition cannot be perceived in a vacuum.
i universal form; an absolute form; an It has to be perceived with relation to the
Hi m, il l i m n , ,i t r u t h f u l form; a super-individual surrounding context. Structures too are
i. .in. i .In mi' form; etc. considered as compositions in the environment.
Accordingly, structures too are perceived with
Mi'.lt'l of Subjective Idealism: relation to the surrounding context. Therefore,
aesthetic qualities of a structure too have to be
H I , 1 1. •. !•, , i Mibjivtive quality, whichis derived
appreciated within the surrounding context. For
..... i l n h u m a n consciousness, whichis primary.
example, a particular bridge may harmonise with
Ai i M i l l i n g to tliis model aesthetics is considered
one environment but may conflict with another
UK • »til»|rt l i v r torin; an individual form.
environment.
of Materialism: The designer's intention may be to make the
property of phenomena and objects structure harmonise or conflict with the
' • . . il), which is a result of their relations with surrounding context. Whatever it is, it could be
..... i k l l t i t Those relationships may be realised only if the context is properly analysed
h m m i m l i i i i N , or conflicting (or dialectical). and the structure is designed accordingly.
AM nuliM)', to this model aesthetics is considered Otherwise, the aesthetic outcome may be different
it i4 > . . .1. i M! Inrm; dialectical form; social form. than the expected one. Hence the word 'context'
is very important.
KfUttidiihlp with philosophical models with
H! ltd uiMii'|>lN and theories APPENDIX 1 - Golden Proportion2
Ai m e n t i o n e d before, aesthetic concepts, The 'golden proportion' is found when a line is
MiWVi>itu<nlN or styles, theories mentioned in the divided into two unequal lengths so that the
i • • > Iniik paragraphs have their roots in various longer part relates to the shorter part as the whole
i i n . , i l models of aesthetics. For example, length relates to the longer part. The ratio is
«nlhi<lii t uiu'i'pts related to 'nature', 'organic identified by the Greek letter 0, and it translates
• ft I ..... i i i t . i l style', 'golden ratio' used in numerically to a ratio of 1.618 :1.
(jpMHiHi h tlu-ory, have their roots in the aesthetic
• Ir! n( naturalism'. Aesthetic concepts related i 1 1
' i t u t lit ill uli i irlures', 'technical considerations' a b
lit tliiM hiirtl theories, 'honesty' in the movement a > b
i ul.ilum, are related to the 'model of objective
ilium' Afillictic concepts related to the 'user', Golden Rectangle and its Properties
> mil-lit nl lunctionalism, reflections of
A rectangle whose sides are proportioned
.. tloii' I I I rationalist theories are related to the
according to the golden ratio is known as the
.i|p| of subjective idealism'. Concept of
'golden rectangle'. The golden rectangle is
. " i n t r i u llvi- conflicts', 'expression of
supposed to be the most visually satisfying of all
1 1 in i H m' discussed in the movement of
rectangles.
i i n . i n r. i n , are related to the model of
Hi il m.ilrrialisin. A D
Hit iindi'iManding of philosophical models of
ftM||n<tlr« would be helpful for any designer to
i IIJM (lie relevant aesthetic qualities to be
BC
iHli^iiiU'tl In the structure. Further, he would be
CD
ili|i« In i ntmlruct new models of aesthetics. Based
HH llu'w mtulels new aesthetic concepts can be
'iiiilnU'il .Hid these concepts can be applied in
»4»«»lnntiip, •tlriu lures.
Fig.37 - Golden Rectangle

53 ENGINEER
Properties of Golden Rectangle Golden proportion in nature
If a square is constructed on the smaller side of The golden proportion appears in nature
the golden rectangle, the remaining portion of the constantly. Many of the proportions of the human
original rectangle would be a smaller but similar body and some proportions of animals also
golden rectangle. This operation can be repeated conform to the golden ratio (Figure 41).
indefinitely to create a gradation of squares and
golden rectangles. The golden spiral, which is derived from the golden
rectangle too, appears in nature. The shape of the
A E D shell of the chambered nautilus is a golden spiral
(Figure 42). Golden spirals also occur in the curves
of elephants' tusks and in the horns of wild sheep.
Similar, though less precise, spirals are formed by
the florets in the core of daisy blossoms (Figure 43).

B
BC CD DE
Y
CD DE EF
Fig. 38- Gradation of Squares & Golden Rectangles

A series of arcs placed in the squares as shown in

the Figure 39, give rise to a special spiral known Fig. 39 - Golden Spiral
as 'golden spiral'. This is also known as
'equiangular spiral' or 'logarithmic spiral'. This
is the only spiral that does not alter shape as it
grows. As shown in Figure 40, the curve of the
spiral always intersects the outreaching radii at a
fixed angle.

a /b = (a + b) / a
Let <j> = a /b
<|>2 - <j) -1 = 0
<)> = (1 + V5) /2 = 1.618

Fig. 40 - Intersection of curve and radii

Vs
= 1.618
L1J
m -V- 2

Fig. 41 - Golden proportions of the human body and of the animals

ENGINEER 54
 Fig. 42 - Golden spiral in Nautilus Shell

Fig. 43 - Golden spiral in daisy blossoms

A l ' l ' l N D I X 2 - Application of the

« i . i . i . i i Proportion in structures
1
- I , l « ii proportion has been employed in
through the centuries. Some of the
i ,m- presented here, where the
iHj»iM Imposed curves pick out golden
|, I . , p. .HI. in-,

44-Clreek Temple, Parthenon, Greece Fig. 45- Yakushi Temple Pagoda, Japan

55 ENGINEER
Fig, 46 -Golden Proportion of the Pylons of the
Vasco da Gama Bridge

Fig. 47- Golden Proportions of the Ting Kau Bridge

Fig. 48 - Golden Proportion of the Rama VIII Bridge

ENGINEER 56
 Fig. 49- Proposed Chao Phraya Bridge

a (Ufvrvncti
i * ulruni lyrt, f with Dias, WPS and Hettiarchchi 12. Nuttgens; Patrick : "The World's Great
M i l 4 I lu- Aesthetics of Proportion in Structural Architecture", The Hamlyn Publishing Group

I i Mthi H M - M n i r t u r n l Engineer, Journal of The

I n t l l l M l l o n of Structural Engineers, United
Limited, London, 1980.

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