ENGINEER - Vol. XXXVIII, No. 03, pp. 45-61, 2005© The Institution of Engineers, Sri Lanka

Aesthetics in StructuresChandana Kulasuriya

Abstract: This paper describes the fact that 'aesthetics of structures' is related to various aestheticconcepts, styles, movements, theories and also with the technical considerations. Further, it also describesthat all the above-mentioned considerations have roots in the fundamental philosophical models ofaesthetics. It also discusses the application of geometric theories and structural theories in achievingaesthetics of structures.

1. Introduction

Normally architects are responsible for aestheticsof structures. However, structural systems andstructural components designed by the engineerplay a major role in the aesthetic appearance ofstructures. For example the visual appearance ofhigh-rise buildings mainly depends on thestructural system. Similarly, the roof structure isa prominent visual element of many structures.Therefore, the engineer has the challenge ofdesigning sub-structures like roof structure,supporting structure, etc., to achieve thearchitect's goal of aesthetics. In this exercise, ifthe engineer has the knowledge of basicaesthetics, he would be able to understand thearchitect's language easily and to designstructural components to satisfy the architect'srequirements. Further, if the engineer isaesthetically conscious, he would be able todevelop totally new structural forms and helparchitects to design innovative structures.

Although most of the buildings are designed byarchitects, there are certain structures designedby engineers themselves. For example, structures

like bridges, transmission towers, water towers,etc., are designed by engineers. Hence engineersshould be responsible for aesthetic aspects ofthese structures. This responsibility can befulfilled if the engineer has the knowledge ofaesthetics and design.

The above mentioned facts confirm that theknowledge of aesthetics would be very useful forengineers not only to help architects to achievetheir goals but also to design engineeringstructures such as bridges, towers, etc.

Within the discourse of 'aesthetics of structures',the 'structure' is considered as a threedimensional composition. Hence, before studyingaesthetics of structures, certain fundamentalconcepts about composition have to beunderstood. Hence the first few paragraphs of thispaper deal with that.

When 'aesthetics of structures' are concerned, itcannot be studied in isolation, as it has links withmany other areas such as art, architecture,philosophy, engineering, history, etc. Thereforethis discourse extends towards those areas as well.

2. Nature of Aesthetics

The word 'aesthetics' has been derived from theGreek word 'aesthesis'; meaning sensoryperception. It was regarded as a branch ofphilosophy concerned with the understanding ofbeauty and its manifestation in art and nature.3

However,, it is extremely difficult to give a precisedefinition for aesthetics. Aesthetic consciousnesscovers special sentiments, tastes, interests,concepts, ideals, views and theories.

Eng. Chandana Kulasuriya, BA-FineArts & Philosophy, MEng.-Struct.Eng., CEng., Chartered Civil Engineer, , MIE(SL), MCSA , Lecturer atOpen University of Sri Lanka

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It is generally recognised that aesthetics has twocomponents - 'emotional component' and the'intellectual component'. It is believed that theemotional component is very much subjectiveand the intellectual component is less subjective.The motional component is an indefinable,intuitive aspect of our personality and it providesus the ability to emotionally appreciate an object.On the other hand, the intellectual component isconsidered as a rational aspect, and hence, itprovides us the ability to rationally appreciate anobject, considering the function of the object,constraints, specifications, conditions, etc.

Nevertheless, some philosophers who doubt theexistence of 'so-called objectivity', question thevalidity of a 'so-called intellectual component'.According to them the 'so-called objectivity' ismerely an 'inter-subjective agreement', among aparticular group of people, based on certainviews, assumptions, ideas, theories, standards,values, etc. Hence according to this view, aestheticconsciousness is both an intra-sufy'ectiveand inter-subjective agreement.

3. Characteristics of A Composition

Primarily, structures can be considered as threedimensional compositions. Therefore, it would beuseful to study about compositions to understandthe aesthetics of structures.

A 'Composition' can be described as anarrangement of parts or elements into properrelation to produce a conceptual unified whole.There are a number of approaches to study'composition'20. However, the approach discussedin this paper is the 'principle of formal analysis'developed in the worlds of art and architecturewhich permit the description and investigationof our reactions to visual stimuli. The importanceof this analysis is that it can be related to scientificstudy of perception.

3.1 Fundamental characteristics of acomposition

Unity, balance, harmony, contrast, emphasis,movement, and rhythm are some of thefundamental characteristics of a composition.20

It seems unity, balance, harmony, rhythm, etc., areinnate needs of us. This is related to our desire tounderstand and control our environment, andmay be a part of our primitive survival skills. Itmay also be driven by basic emotions such asinsecurity and fear of the unknown.20 However,the pure, perfect form of these characteristics canresult in monotony or boredom. In view of thatunity with variety, occasional discontinuity ofrhythm, dramatic contrast can be used to makethe composition interesting.

Unity:

Unity is the quality of 'singleness effect' and the'completeness' of a composition. In a unified workof art, all the parts come together to form a'unified whole'; each part of a composition 'feels'like that it belongs with the rest. That is unitywhich refers to the visual linking of variouselements of the composition. A designer achievesunity by balancing all the aspects of thecomposition.

When the eye is attracted by two stimuli of equalimportance, the resolution of elements into a'unified whole' is prevented or disturbed. Thiseffect is known as 'duality'.

For example, when two objects which are spacedtoo far apart for the eye to see them as a unit, butnot far enough apart for them to be perceived ascompletely independent, 'duality' can beexperienced. However, this can be resolved byinserting a dominant central block between thetwo objects (Figure la).20

The same thing happens with bridges (Figurelb).33 A single-arch bridge shown in the figure,though simple, is visually satisfying. However,when there are exactly similar arches next to eachother, the eye finds it difficult to resolve it into aunified whole. Instead the eye looks at one spanand then at the other. The eye goes to arches andnot to the piers, and it will

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Duality

XX

Unity

(a)

i Duality [

*——L

.TK:~~\ ^~^Unify Unity

(b)

Unity

(c)

Duality

Fig. 1 - Unity & Duality

wobble from one centre-line to the other, so thatA feeling of restlessness is produced. However,this can be resolved by introducing a dominantcentral arch between the two arches. Here thecentre-line is not only the centre-line of the middlearch but also that of the bridge; and the eye is inno doubt at all to decide the line upon which toconcentrate. There is no question of it wobblingfrom one centre-line to another, and shows acomposition of complete restfulness.

Duality may also be experienced when the facadeof a building has equal horizontal and verticalemphasis (Figure lc).21

When the eye is attracted by multiple stimuli ofequal importance, a similar effect, which may betermed as 'multiplicity', can be experienced.

Normally 'Unity' is recognised as a basicrequirement of a good composition. Hence 'Lackof unity', duality, multiplicity may be consideredas a fault. However in certain periods people haveexhibited impatience with the concept of unityand duality was advocated as a means of relievingthe boredom of unity.

Balance

' Balance' can be described as a state of equilibriumbetween its elements. 21 Balance in design issimilar to balance in physics. Without it, thecomposition looks awkward and unstable.

The concept of balance is related to the 'visualcentre of gravity' of an object and 'visual weights'of elements. The eye expects a 'balance' about thevisual centre of gravity as though it were afulcrum and the various visual weights appliedwith various leverages. The 'visual weight' of anelement may be manipulated by delineation orvarying the play of light and shadow to hint atsolidity or hollowness.(Figure 2)

There are two types of balances, symmetrical andasymmetrical. Symmetrical balance is easier tounderstand. Symmetry is the balance of mirrorfigures about a point, line or plane. The usualemotional response to symmetrical balance is'stability' or 'satisfaction with the status quo'.Asymmetrical balance sometimes referred to asOccult balance, is much more subtle, but it usuallystimulates a dynamic and emotional response.Acceptable asymmetric balance depends largelyon the emotional qualities of aesthetics and thepersonality of the designer and the viewer.

Harmony

Harmony in a composition is the visuallysatisfying effect of combining similar, relatedelements. The designer can create harmonythrough elements such as shapes, colours,textures, etc. (e.g. - Adjacent colours on the colourwheel create a feeling of harmony)

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Fig. 2 - Symmetrical balance &Asymmetrical balance

There are two kinds of harmony with respect toany object present in the environment - internaland external. Internal harmony refers to therelation between parts of the object, where asexternal harmony refers to the relation of theobject to its surrounding environment.

Harmony gives a feeling of unity and coherencewith associated psychological reactions ofsecurity and relaxation.

Contrast

Contrast is an abrupt, unexpected change in avisual element. The designer can create contrastthrough the elements such as shapes, colours,textures, etc. For example, complementarycolours of colour wheel (red/green, yellow/purple, blue/orange) seem to create a feeling ofcontrast when they are placed together in acomposition.

Emphasis

As a composition develops a designer may decideto stress certain elements of the design over othersto create a 'focal point'. The eye of the viewer willfocus on the area of 'emphasis' or 'centre ofinterest' first, and then take in the rest of thecomposition. A designer uses emphasis to directand focus attention of the viewer on the mostimportant parts of a composition. A designercreates emphasis through size, colour, texture,and shape. A composition lacking emphasis willbe monotonous and uninspired.

Movement

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

Rhythm

Rhythm is the regular repetition of elements of acomposition to produce the look and feel ofmovement. A designer creates movement in acomposition by repeating elements such ascolours, shapes, lines, textures, etc. The repetitionof the elements invites the eye to jump rapidly orglide smoothly from one image to the next.Rhythm allows the designer to create a feeling oforganized movement. Elements placed at regularintervals create a calming rhythm. Suddenchanges in position and size create a livelyrhythm. Variety keeps rhythm exciting and active,moving the eye around the composition.

As the eye scans across a building it is affectedby the regularity or otherwise of elements suchas windows, mullions, columns, and arches whichmay give rise to an impression of 'rhythm'.Rhythms may be seen as slow and smooth whenthey are based on a few elements which arewidely spaced relative to the overall form, orrapid and staccato. Rhythms may be readvertically as well as horizontally.20

3.2 Other Qualities

In addition to fundamental characteristics suchas unity, balance, harmony, rhythm, etc.,structures, may be associated with features suchas identity, character, meaning, etc.20

Identity

Identity of a structure may be related to location,history, culture, society, etc. For example Pagodashave a Japanese Identity.

Character

Structures may have a character as in the case withhuman beings. For example a structure with astrong vertical emphasis may be seen as excudingpride, self-confidence.(Figure 3). Lighterconstructions (Figure 4) may have an air ofethereality.

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Fig. 3- Thomas Telf ord's Bridge :

Fig. 4 - Convention Centre, New York33

Meaning

A structure may express its' function. For examplethe appearance of a hospital may reflect its'function.

In addition to the above mentionedcharacteristics, qualities like sensuality, tension,excitement, humour etc., too can be integratedto structures to create an interest. This can be doneby the structure as a whole or by its' componentsin the form of 'innocent jokes', 'simple nonsense','pinch of insecurity', etc. For example an invertedpyramid-like structure may produce a sense ofinsecurity and a tension in the observer. Twistedshafts or hanging columns may produce a senseof humour in the observer.

Fig. 4 - Inverted Pyramid-like building

3.3 Elements of Composition

The above mentioned characteristics or qualitiesare acquired by a three dimensional compositionby some basic elements such as Size & Scale, Form& Shape, Proportion, Space, Texture, Colour, Light& Shade, Visual weight, Pattern, Ornamentationetc.

4. Aesthetic Concepts Related toStructures

There are various concepts behind aesthetics ofstructures. These concepts are integrated to thestructure not only by the designer but also by thecritics, conservators, users, observers, etc. This canhappen either at conscious or subconscious levelof the person concerned. Some of such conceptsthat are integrated with the structures are givenbelow.

"The structure should appear to spring naturally fromits surroundings'

"The structure should harmonise with surroundingcontext."

"The structure need not necessarily harmonise withthe existing surrounding context, the constructiveconflicts between the structure and the existingsurrounding context may create a new form ofprogressive aesthetics."

"The. structure should resemble or suggest forms foundin nature"

"The structural skeleton should be completely coveredwith a form giving skin (cladding), like in animals."

"The structure should be subjectively related with theconsumer or the user"

"The structure should express its' function"

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"The structure should be as simple as possible"

"Restructure should be like 'plug-in components' ofa printed electronic circuit board"

"Tlie structure should be truthful/rational/honestas possible"

These aesthetic concepts are reflected in manystructures. Clustered water tanks at Alencon,France, look like trees in nature. (Figure 6a) Thisreflects the concepts related to 'organic forms'.The Eiffel Tower in Paris contradicted with theenvironment and the contemporary society, whenit was first erected. However, later it was able tocreate new aesthetic values and became the'semiotic symbol' of France (Fig 6b). This mayreflect the concept of 'constructive conflicts'.Water Tower at Fisons Fertilizer Factory, UK, issubjectively related with the factory workers and

Fig. 6 - Reflections of aesthetic conceptsin structures

(a) (b)

Fig. 7 - George Washington Bridge

expresses the feeling of sharing the work (Figure6c). Verrazano Narrow's Bridge is a completelytruthful expression of a tensile material in theform of the 'funicular form' (Figure 6d) .Thisreflects the concept of 'truthful structures'.

The original design of the George WashingtonBridge, New York, is a steel structure with a stonecladding (Figure 7a). This reflects the concept of'form giving skin of animals'. However, after thestructural skeleton was erected, it was not cladby stones despite the opposition of a large part ofNew York intelligentsia and the design engineerhimself (Figure 7b). However, later, the aestheticsof the exposed structural skeleton has been widelyappreciated by all. Here, the naked steel structurereflects the concept of'honesty'. This indicates therapid changes of aesthetic appreciation and alsothe different reflections of aesthetic concepts.

5. Aesthetic Movements & StylesRelated to Structures

Aesthetics of structures cannot be understood inisolation. It has a historical narrative. Within thishistorical narrative aesthetics has evolvedthrough a number of movements. Thesemovements have influenced the aesthetics ofstructures directly or indirectly. Therefore,aesthetics of a particular structure has to beunderstood within that background.

Aesthetics of structures have been influenced bythe aesthetic movements. Rationalism, Arts andCrafts 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 aresome of such movements. Some of them arebriefly described below.8

Constructivism

A movement which originated in Moscow after1917, primarily in sculpture but with broadapplication to architecture. The expression ofconstruction was to be the basis for all buildingdesign. 8

FunctionalismA design movement that evolved from severalprevious movements in Europe in the early 20th

century, advocating the design of buildings,

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ImnJHhing, or the like as direct fulfilment of1 1 n it lional requirements, with the construction,materials, and purpose clearly expressed, andWith the aesthetic effect derived chiefly fromI MI portions and finished to the exclusion orsubordination of purely decorative effects.Puiu'tlonalists believe that when function isf u l f i l l e d , the form will follow automatically -I . ' i in lollows function'.8

iNpreislonism

I • |Mt?8Nionists rejected the hard, rectilinear andstandard boxes in favour of an

and romantic approach. Buildingsmeant to express or symbolise their use,

together form and content in a newI" I ' .onnl language. Symbols used were often

relating to speed and machines as well asof ten consciously or subconsciously

•PMIrtl"'

IniUllimI1u> term 'Hrutalism' was derived from the Frenchi ' M M ' I't'fuii briif which means rough concrete.Normally concrete is surfaced plaster, but theHi uMllnts thought that, in the interest of honesty

uil lu ' i i t ici ty, it should be exposed. Someli t i l l i l in^s which do not show rough exposedi mi. iHr luvr also been classified as Brutalist. In

, mi exposed steel frame is visible on the"•"

c architectural style

A movement of architectural design that emergedi M 1 1 in early 20"' century, asserting that a buildingilioiiUI have a structure and plan that fulfil itsf u m l i o n a l requirements, harmonize with itsn i i u i . i l environment, and form an intellectuallyin . hi, Integrated whole. The shapes or forms in»tn h rt work are often of irregular contour and»tH<m lo resemble or suggest forms found inti.ilure."

Mmli'rni.sm

A del ibera te philosophical and practical••iMiifiement from the past in the arts andl lU ' i r t tu re occurring in the course of the 20th

l i 'Mlnry and taking form in any of the variousInnovative movements and styles.8

Post-modernismA movement in architecture and the decorativearts that developed in the 1970's in reaction tothe principles and practices of modernism,especially, the influence of the International Style,encouraging the use of elements from historicalvernacular styles and often playful illusion,decoration, and complexity.8

Post-modern architects have continued to takeadvantage of the new materials available whileturning to different periods of the past for artisticinspiration. There has, for instance, been a revivalof the principles of classical architecture withemphasis on proportion and harmony. This haseven led to the design of supermarkets in the styleof palaces, and offices in the style of temples.8

High-techA style of design incorporating industrial,commercial, and institutional fixtures, equipment,materials, or other elements having the utilitarianappearance characteristic of industrial design.

One way of achieving this is by ensuring thatcertain essential services, which are normallyconcealed within the building, are clearly visiblefrom outside. Lifts travel up and down its frontor sides. Escalators are suspended from thestructure on to the exterior. Pipes for air-conditioning and water are not only visible butare designed as decorative features. Bright colourspredominate on the exterior. Pipe work may becolour-coded to indicate its various functions. Allthe structural parts may be in one distinctivecolour or clad in stainless steel.8

Deconstruction

A critical movement that started in the 1960's,especially, in the study of literature, questioningtraditional assumptions about the ability oflanguage to represent reality and emphasizingthat a text has no stable reference because wordsessentially refer only to other words. A readermust therefore approach a text by eliminating anyabstract reasoning or ethnocentric assumptionsthrough an active role of defining meaning,sometimes by a reliance on etymology and newword construction.8

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6. Aesthetics of Structures and RelatedTheories

Through the centuries, since the Greeks firstcodified their ideas on aesthetics, many theoriesabout preferences in the realms of art andarchitecture have been developed. These theoriescan be organised into four categories: geometric,rationalist, sculptural and structural.26

Geometric Theory (Proportioning Theories)

These theories are based on the idea that we findcertain things or experiences beautiful becausethey resonate with patterns built into ourcognitive systems. It is a common experience frommusic that certain combinations of sounds(chords) are generally judged to be beautiful,while others are considered dissonant, evenuncomfortable, such as the sound of fingernailson a blackboard. Perhaps the fingernail soundcauses our cells to vibrate in ways that disturbtheir functioning.26

Many of the classical theories of proportion traceback to this idea. Rectangles proportionedaccording to the 'Golden Ratio' (1:1.618) wereconsidered automatically superior because theysupposedly appealed to some inherent innersense of visual proportion. (See Appendix 1).26

Through the history, the golden proportion hasconsistently brought a sense of harmony todesign, not to mention a spiritual and even aphysical sense of well being. A number ofexamples could be cited, including Stonehengein England, in Egypt, classical temples of Greece,Gothic cathedrals and modern buildings.2 Someof these structures are presented in Appendix 2.

Rationalist Theories

This set of ideas states that we like objects whoseshape clearly reflect its function. For example, ateapot with a comfortable handle and efficientspout will be more attractive than a teapot shapedwithout regard to these functional necessities.26

This theory applies more easily to objects with asingle obvious function. Engineering structuressuch as bridges, water tanks, transmission towers,etc., fall clearly into this category. Buildingsaccommodating multiple functions are not aseasily approached this way.26

Sculptural TheoriesThe goal of sculpture is to produce three-dimensional objects which have the sole purposeof evoking emotions or reflecting ideas. Thesetheories state that we like certain objects becausetheir shapes evoke emotions or reflect ideas whichaccord with our needs or value systems.26

Structural TheoriesThese theories state that we like certain objectsbecause they clearly reflect their structuralbehaviour. The theory assumes that we all possessan inherent understanding of structure, based oneach person's struggle with gravity from the daywe begin to walk.26

The cantilever is an example of this idea whichapplies to bridges. To most people a cantilever ismore attractive if it is thicker at its support andtapers towards its free end. People find itattractive because it reflects the cantilevers theyare already familiar with: the shape of their ownarms and legs or the branch of a tree. From thisfamiliarity people develop an intuitiveunderstanding of what the engineer knows fromcalculation: that the stresses in a cantilever arelargest at the support, and therefore that's wheremost of the material should be.26

7. Philosophical Models of Aesthetics

All the above mentioned aesthetic concepts,styles, movements, theories etc., have their rootsat various philosophical models of aesthetics.These models are derived from fundamentalparadigms of philosophy. Although these modelsdo not directly reflect the philosophicalparadigms, which they were derived from, theyreflect certain characteristics of those paradigms.Naturalism, Objective Idealism, SubjectiveIdealism, and Materialism, are some of the majorhistorical philosophical models of aesthetics.1

Model of Naturalism:

Aesthetics is a natural property of nature. Objectsare perceived as aesthetic when they reflectproperties (proportion, form, shape, etc.) that arefound in nature. According to this modelaesthetics is considered as a natural form.

Model of Objective Idealism:Aesthetics is an objective quality, which isindependent of and external to human

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i i n i ' 1 , i M i i M H ' v . It is often associated with conceptsttml nr« 1'iinsidrrcd 'universal'. According to this

l rtWBthvtics is considered as an objectivei universal form; an absolute form; an

Hi m, i l l i m n , ,i t r u t h f u l form; a super-individuali. . in . i . In mi' form; etc.

Mi'.lt'l of Subjective Idealism:H I , 1 1. •. !•, , i Mibjivtive quality, whichis derived

..... i l n human consciousness, whichis primary.Ai i M i l l i n g to tliis model aesthetics is consideredUK • »til»|rt l i v r torin; an individual form.

of Materialism:

property of phenomena and objects' • . . i l ) , which is a result of their relations with

..... i k l l t i t Those relationships may beh m m i m l i i i i N , or conflicting (or dialectical).AM nul iM) ' , to this model aesthetics is consideredit i4 > . . .1. i M! Inrm; dialectical form; social form.

KfUttidiihlp with philosophical models withH! ltd uiMii'|>lN and theories

Ai ment ioned before, aesthetic concepts,MiWVi>itu<nlN or styles, theories mentioned in thei • • > Iniik paragraphs have their roots in various

i i n . , i l models of aesthetics. For example,«nlhi<lii t uiu'i'pts related to 'nature', 'organic• ft I ..... i i i t . i l style' , 'golden ratio' used in(jpMHiHi h tlu-ory, have their roots in the aesthetic

• Ir! n( naturalism'. Aesthetic concepts related' i t u t l i t i l l u l i i irlures', 'technical considerations'lit t l i iM hi ir t l theories, 'honesty' in the movement

i ul.ilum, are related to the 'model of objectiveilium' Afil l ictic concepts related to the 'user',> mil-lit nl lunctionalism, reflections of.. tloii' I I I rationalist theories are related to the.i|p| of subject ive idealism'. Concept of

. " i n t r i u l lv i - conflicts ' , 'expression of1 1 i n i H m' discussed in the movement ofi i n . i n r. i n , are related to the model of

Hi i l m.ilrrialisin.

Hi t i indi ' iManding of philosophical models offtM||n<tlr« would be helpful for any designer to

i I I J M (lie relevant aesthetic qualities to beiHli^iiiU'tl In the structure. Further, he would beili|i« In i n tmlruct new models of aesthetics. BasedHH llu'w mtulels new aesthetic concepts can be

' i i i i l n U ' i l .Hid these concepts can be applied in»4»«»lnntiip, •tlriu lures.

8. The Composition & The Context

A composition cannot be perceived in a vacuum.It has to be perceived with relation to thesurrounding context. Structures too areconsidered as compositions in the environment.Accordingly, structures too are perceived withrelation to the surrounding context. Therefore,aesthetic qualities of a structure too have to beappreciated within the surrounding context. Forexample, a particular bridge may harmonise withone environment but may conflict with anotherenvironment.

The designer's intention may be to make thestructure harmonise or conflict with thesurrounding context. Whatever it is, it could berealised only if the context is properly analysedand the structure is designed accordingly.Otherwise, the aesthetic outcome may be differentthan the expected one. Hence the word 'context'is very important.

APPENDIX 1 - Golden Proportion2

The 'golden proportion' is found when a line isdivided into two unequal lengths so that thelonger part relates to the shorter part as the wholelength relates to the longer part. The ratio isidentified by the Greek letter 0, and it translatesnumerically to a ratio of 1.618 :1.

i 1 1a b

a > b

Golden Rectangle and its Properties

A rectangle whose sides are proportionedaccording to the golden ratio is known as the'golden rectangle'. The golden rectangle issupposed to be the most visually satisfying of allrectangles.

A D

BCCD

Fig.37 - Golden Rectangle

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Properties of Golden Rectangle

If a square is constructed on the smaller side ofthe golden rectangle, the remaining portion of theoriginal rectangle would be a smaller but similargolden rectangle. This operation can be repeatedindefinitely to create a gradation of squares andgolden rectangles.

A E D

BBC CD DECD DE EF Y

Fig. 38- Gradation of Squares & Golden Rectangles

A series of arcs placed in the squares as shown inthe Figure 39, give rise to a special spiral knownas 'golden spiral'. This is also known as'equiangular spiral' or 'logarithmic spiral'. Thisis the only spiral that does not alter shape as itgrows. As shown in Figure 40, the curve of thespiral always intersects the outreaching radii at afixed angle.

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

Golden proportion in nature

The golden proportion appears in natureconstantly. Many of the proportions of the humanbody and some proportions of animals alsoconform to the golden ratio (Figure 41).

The golden spiral, which is derived from the goldenrectangle too, appears in nature. The shape of theshell of the chambered nautilus is a golden spiral(Figure 42). Golden spirals also occur in the curvesof elephants' tusks and in the horns of wild sheep.Similar, though less precise, spirals are formed bythe florets in the core of daisy blossoms (Figure 43).

Fig. 39 - Golden Spiral

Fig. 40 - Intersection of curve and radii

Vs= 1.618

L1Jm -V- 2

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

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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 structures1 - I , l « i i proport ion has been employed in

through the centuries. Some of thei ,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

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Fig, 46 -Golden Proportion of the Pylons of theVasco da Gama Bridge

Fig. 47- Golden Proportions of the Ting Kau Bridge

Fig. 48 - Golden Proportion of the Rama VIII Bridge

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aI

g Kau Bridge

Fig. 49- Proposed Chao Phraya Bridge

(Ufvrvncti

i * ulruni lyr t , f with Dias, WPS and Hettiarchchi

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