Structure: Size, form and proportion.A historical review on the main criteria

for structural designo Theoretical andempirical studies on dead load

Thanks to progre ss made in analysis development, agreat success has been achieved in the field of

structural engineering.Nevertheless, the aspects regarding the design of

the preliminary schemes have been relegated, andeven valid approaches have been abandoned in all thisprocess. Our days, a key difference with regard topast times has been the introduction of computer-

based analysis.Traditionally, a common fact has conditioned the

design of Architecture and Ci vil Engineeringstructures, namely, the little attention paid, and thedifficulty, for getting industrial process. InArchitecture spans have often been designed on amodest scale, and in Civil Engineering, even in largerspans, the designing process has not changed

fundamentally over the last centuries. Moreparticularly, the designer draws up some schemes.

and then the structural type refinement is carried outslowly by combining analysis and practice.

In fact, the process works in financial terms, mainlydue to the fact that optimization of the total cost eitheris not always equivalent to the optimization of thestructure cost itself, or in case it is, it has beeninterpreted in the light of constructive -rather than

structural- parameters.This paper aims to pro vide a historical analysis on

the criteria adopted in the structural design process. Inthis regard, the design will be assessed in terms of thequantity of material employed. Thus, the history of

design process is in fact the dead load history. This

José Luis Fernández Cabo

paper will try to show that this has been the history of

a conflict between theory and practice, a debatebetween two conceptions, the constructor' s and the

mathematician' s.

HISTORICAL DEVELOPMENT

From the Andent Structures to Galileo.

It is now widely accepted that the theory of structuresfirst originated as a consequence of the ScientificRevolution. Galileo's Discorsi can be considered thefirst work in this field.

Architectural testimony from the previouscenturies has been revealed to us more often throughliving facts than through first-hand written materials,

which are in fact scanty.In this respect, there seems to be no doubt as to the

technical potential prior to the Scientific Revolution.However, there is no solid evidence as regards the

existence of a substantial theoretical background atthe time. Instead, those ancient projects might havebeen carried out following empirical knowledge.

Likewise, that empiricaJ knowledge is sure to haveadopted as a design instrument, explicitly or impJicitly,

the regulator aJignments as well as the proportion rules.The only factor common to all classicism stems

from the use of the c1assical orders, and not from theadoption of a unitary system of proportion, which

never existed. This fact was clear when the original art

Proceedings of the First International Congress on Construction History, Madrid, 20th-24th January 2003, ed. S. Huerta, Madrid: I. Juan de Herrera, SEdHC, ETSAM, A. E. Benvenuto, COAM, F. Dragados, 2003.

884 J. L. Fernández Cabo

works dating back to different periods were measuredin the 19th century (Ronde1et, 1834; Fauré, 1890).

Design empirical rules, most of them of proportionalcondition, have existed until the 17()¡century, with

traces which get up to the first half of the 20th century.The empirical methods are really efficient when it is aslight variation in the shape and size of the structure,being used both premises till the 19()¡century.

The architectural type and the order allowed acorrect and adequate structural designo That isencouraged by the confluence between structure andconstruction.

Galileo announced what we now know as cube-square law: given a body having any form and made

of any material, if a change in size (L) is introduced(with the same proportions), the dead load increases

in proportional to (U), while the resistant areaincreases in proportion to (U). Thus, we infer that:

a) geometric similitude does not imply, strictly

speaking, mechanical similitude.b) for any form and material there is a maximum

size where the structure is only capable ofwithstanding its dead loado

c) maintaining the same form, proportion and

material: stresses from the dead load «()dcadloa)increase in linear fashion as the size is increased(

O"dead loadoc L).

2000

:5 1500

z<[o..

'":>::J:>:x 1000<[:>:

500

27 B.C. PANTHEON oF ROME

Figure 1Drawing based on (Head 1988, p. 6) and enlarged by the author

This argument refutes the use of both thearchitectural types and the proportional designingrules. In other words, it undermines the validity of thegeometry as a design tool, and, in general, the face

value often attributed to the analogical methods.Nevertheless, the statement had no practical

consequences. As a matter of fact, it can now be

viewed as a fallacious argument, in so much as it doesnot have any effects on the intervals of size andmaterials widely employed in Architecture and CivilEngineering until the 19thcentury.

Regarding theory, the Scientific Revolution was

liable for the acknowledgement of size as a structuralproblem, bringing forward a future controversy

between Matter and Idea. For this reason, Panofskygave Galileo the category of «an art critic» (Panofsky

1954).

From Galileo to the 1850s

The ev01ution of «the new science» was slow andgradual. First, the Academies and then the

Technica1 Scho01s of Engineering started to gajnfoothold, but not much attention was paid to Gali1eoat the time. We wi11 argue that the few authors whoadopted and extended Galileo' s theories soon fell

into abeyance.

TIMBER o.ruj STONE.

\rrtROUGHT IRON

1Mn 17M 'ROn temo

Structure: Size, fonn and proportion 885

However, an unprecedented increase in thestructural spans took place at the turn of the 19thcentury. This process was to keep its upward trend

until the second half of the 20th Century. Over thenext one hundred years, the maximum sizes would bemultiplied by more than 30. This is even moresurprising now that we know the theoretical toolsemployed at the time.

The first big step ahead in spans -in the order of

6- took place in the first haft of the 19thcentury. Byestablishing the relation between the period and thesize of the structures, we can easily understand whythe 19th century has been regarded as a landmark inthe history of dead load (Figure 1). Likewise, datashow that this relation has grown exponentially sincethe first half of the 19th century.

For the first time, engineers were faced with deadload problems. Apart from an increase in size, theapplication of the new scientific methods resulted inhigher proportional tensions (a¡ / ama) if compared to

those considered in previous centuries.Some highly illustrative data from these historical

studies are worth mentioning now. In suspension brid-ges the range of spans was multiplied by five, and the

relation of dead load and live load (tu' deadload/ tu'liveload)stood around 1,5 and 3 according to size in the period1826-1883 (Steinman 1991). (See figure 4).1883 re-presents the construction of the Brooklyn bridge in

which the relation (tu' deadload/tu'li"load) = 3.2. These ex-cessive ratios, even for those spans, can only be un-derstood in the light of very simple analysis patterns.The data collected by former authors show higher rela-tionships (Rankine, 1863, p 583, Table VII).

However, for a long time Architecture remainedunaware of this problem. Even the largest roofs didnot exceed the limits of past construction based onmasonry. The most frequent uses in Architectureproceed at a very slow pace, between 4-7 m. In thisregard, any discussion on dead load runs the risk ofturning out absurdo This situation was to change in the

second half of the 20th century.Oead load appeared in the theoretical field as far

back as in the 18th century, but practical applicationdid not take place until one century later, at least ingreat works.

But Jet us now review some of those theoreticalworks.

One of the earliest theoretical works was that of the

American engineer, S. Wipple, who focused On the

dead load optimization problem by means ofdifferential calculus. He tried to gauge the optimalinclination of the truss diagonals so that the materialemployed is kept at a minimum. In this case, he used

a model of single load, achieving an optimumgeometry slenderness ratio (or just slenderness =spanlheight) up to six (Wipple, 1847). He was not

absolutely right, but he was close.

The most out standing figure in the first half of the19th century was Rankine, who reformulated the

cube-square law, and thence established an accurateand highly useful proportion. Expressing it in hisoriginal proportional notation, where (L) represents

the size and (tu') the load:[Lmax:L:(Lmax-L)::tu'total:

tu'deadload:tu'liveloadJ.To put in a different, and moresimplistic, way: [Lmax/ tu'ppJ=[(Lmax-L) / tu'extJ. (See

figure 2). (Safety factors have been omitted).

L (LwcL)

~~I Lwc / //1//I (fJ /(fJ /I ~IEAJIUWI / bLIVE L,9".

~pI (fJ / /I bTDTM.

/ /I / /I / /\ / /1//I / /I / /

1 //

I ///ItÍ~

Figure2

886 J. L. Fernández Cabo

The notation allowed him to calculate themaximum size of different structural types of bridgesfrom dead load data available. Now, we will take acloser look at one of his definitions of structural types

"Warren girder bridges, not continuous, with castiron struts, depth about 1-15th oUhe spall» (Rankine,1863). Gn defining Warren's type and slendemess in

the order of 15 he is defining geometry already, eventhough his statements are not so precise in other

cases. This structural type gradually reduced itsslenderness by half in a short time following a semi-empirical process. Gn a general basis, later authors

did not consider the slenderness criterion, as it wasimplicit in construction practice.

Rankine can be said to be one of the very fewtheorists of 19th century to be aware of the directrelation between slenderness (A==span/depth) (hewould always speak of the relation «depth to spall»)and the structure stiffness. As a matter of fact, in thecase of simple beams with constant section, heestablished a method of sizing stitlness by means ofthis parameter. This one has been proposed,independently, by Prof. Ricardo Aroca.

Additionally, Rankine introduced a variable that

was to be central to the dead load debate, namely, therelation (cr/p), that he termed «Moduli of Stiffnessand Strength.» (Rankine 1863, pp. 230, art. 154). Heidentified its physical sense too, the greatest size aprism of constant section may achieve (disregarding

the stability problems). This parameter appears whenthe greatest size is established by means of the

strength of a simple beam of rectangular sectionsubjected to his dead load.

Rankine's work was at once brilliant and isolated.Moreover, he enjoyed widespread recognition, but hisdead load and design works were not fullyunderstood, maybe because they might have been atodds with the time.

Despite the fact there was not a general theory ofdesign in the first half of the 19th century, and well

into the 20th century, the most outstanding progressmade in the design of structural types took place atthat time. For the first time, we could now affirm thatthe working of structures has been scientificlyunderstood.

The introduction of steel as a new material, thatengineers used far from any previous formalpreconception, would undoubtedly contribute to the

development of new structural types. The triangularstructure is bom at the same time as steel. Theprevious works in wood were limited and generaJlyhybrid. Perhaps, the only pure case is that of

Palladio's.Gn a general basis, in wood structures up to the 19th

century, the triangulation is an element employed to

stabiJize a general arch mechanism (see figure 3).The layout of simple triangulation, at least initially,

is closely linked to the necessity of designingdetermined structures. In fact, there are many examples

of steel and wood trusses dating back to the turo of the20th century most of which were not effectively. This

show the absence of the theory of designing. Slowly,

- -.

--

Figure 3Wood trusses from different periods, where structure variation ofinternal configuration can be observed. (Taken from James,1982).

Structure: Size, fonn and proportion 887

and when the problem has been progressivelyunderstood, and chietly due to a «selective natural»process, many of those structural types have fallen into

oblivion. By the mid 20th century, simple truss typesdid not exceed three or four.

From 18505 to 19505

Even though the 19th century witnessed theestablishment of some analytical bases in the field, afull-fledged theory on designing was neverdeveloped. The understanding of the structure was up

to the simple structural analysis and design, althoughlittle was known about how to improve the efficiencyof the structure geometry. Thus, there was not otherway but using a combination of ana10gical methods

and trial and error processes.We have previously referred to trusses as a

paradigmatic example of the changes taking place in

this periodo Waddell's book gathers 34 structuraltypes of simple truss bridges (Waddell 1916, ChapterXXIl). Among all these schemes, some of this are not

as effieient as one could expect, since they hadtriangulation patterns far from 45 °. Not only werethey poor, but they were virtually equivalent in terms

of the employment of materials. In view of the above,we can infer that the geometric variables allowingoptimization of trusses were generally ignored at the

time. By the end of the 191hcentury this situation wasto change; some studies from the beginning ofthe 20theentury already found the main eriteria to be applied

in truss designoFrom the mid 19thcentury, and once the importance

of size was fully recognized, a lot of theoretieal and,mostly, empirical work began to expand.

During this period spans continued growing. By

the mid 191h century, Bessemer converters allowedmass producing steel at a lower cost. «Prior to 1840,most of the evolution of bridge construction in theUnited States was along the lines of the wooden trussand the wooden arch». (Waddell, 1916: 1-19). In thissame period., the development of railways and theintroduction of the gas motor represented a greatcontribution to the process. The number of ears in theUnited Stated between 1900 and 1940 soared fromtwo million to thirty million. However, not only thegreater spans were still produced, but also smaller-

scope ones topped al! prior production. It is not

coincidental that most empirical data o[ the periodhave been collected in the USA. Given the highamount o[ structures built in this country, it has beenpossible to focus the problem of the dead load

determination from an empirical perspective.But the theoretical studies were inescapab1e at this

time. We will now proceed to outline some of those

studies before passing on to the empirical section.There was a large group intent on optimizing the

simple truss design, mostly the one employed inbridges. We could say they followed Wipple'sapproach. The main objective was to determine theoptimum depth.

In 1871, T. Willis Pratt threw some discussionsabout the economy of the sample truss. In 1877, EmilAdler set up a model for the determination of theoptimum depth, with wrought iron, and for a truss ofparallel chords: tJ chord, = tJ ,(mI>+ tJ

di""ooa!>cos(180--2a);

being (a) the angle formed by the cfiagonals with the

horizontal plane. This expression is not correct, but itis obvious that the optimal results are reached withang1es near 45°.

That same approach was adopted ten years later bylohn Lundie and Sherzer, who made the followingremarks: first, the formula does not consider theinfluence of the bar buckling, and second, theoptimum depth established for a simple panel cannot

be applied to the rest of the truss. At the turn of the20th century, Waling affirmed that in case this formula

was taken as valid, then it would demand a trial anderror test -case.

In 1877, Charles E. Emery developed another trialand error model in order to calculate proportions ofthe minimum load in parallel chord trusses. He basedhis work on big depths, except in the case of grids,twice as large as the ones previously in use. In fact,what W.E. Searles did in 1878 was using Emery' sconclusions successfully so as to restore a woodentruss of parallel chords.

In 1887, A.l. Dubois proposed some complexformulae on the eva]uation of bridge dead loads andeconomic slenderness of iron trusses with parallelchords. He is also known for deve10ped formulae formasonry arch sizing. The empirical formulae for archsizing had a long-standing tradition that would leave

an imprint in the most relevant technical manualsuntil the second half of the 20lh century.

As we have affirmed, these studies do not focus the

problem, since they do not offer mistaken results. As

888 J. L. Fernández Cabo

it is often the case with empirical research, practice isalways ahead of theory. If we observe the design of

the simple trusses, most of them show goodgeometrical desings: diagonal s with angles in theorder of 450 and slenderness between 6 and 8. Beingthese the two important variables. It seems clear that,in spite of the theoretical scarcity, some highlyinteresting projects were designed at the time.

The most important theoretical progress took placewith the new century, but recognition would comemuch later.

At the end of the century, Maxwell developed atheorem that was to be central to the establishment ofa design theory of structures. The new theorem wouldallow measuring the efficiency of geometry(Maxwell, 1890). Soon afterwards, Mitchell

supplemented Maxwell's work with two theorems

essential to understanding the optimal geometry(Mitchell, 1904). Mitchell's theorem based on

Maxwell's expression, estates that, given a loadsystem (N = axial force; L = bar length):

(LN,L)coMPREssIoN - (LN,L)TENSIoN =K; IIK remainsconstant. Michell proves that the structure involvingless quantity of material is also the most stiff, and alsothat in the case of structures with compression andtension groups, and for any optimum, its meetingtakes place at 900. In fact, this is tantamount toestablishing the differential equation of the optimalgeometry. Given the abstract nature of the concept,

engineers of the time might have been unable to graspits full implications.

Among the theoretical approaches there is afraction that applied the new theories of dimensionalanalysis to the structures field.

Most of these authors only provide conclusions toogeneral in scope, among them we can mentionArchibald Barr, James Thomson or A. G. Greenhill.

One of the most interesting works belongs to LordRayleigh (1915). Given similar structures, the

dimensional variables are: stress, size and forces. Thenon-dimensional variables gather in factor cp(), whichcomprises topology; proportion; sizing and therelative distribution of loads. The problem is definedwith only one non-dimensional monomial [o-U I P 1usually expressed by stating the normal stress:

a= p cp()IU. In the case of dead load where the load

is sort p=p (V); it is easy to obtain the relation ofstresses already stated by Galileo and Rankine:

app =kL where (k) remains constant.

In 1888, the Spanish engineer Joaquín Pan o Ruatapublished some articles on the prediction of dead load

and size limits. There is unanimous agreement in theliterature as to the quality of this work as unique inthe Spanish 19th century context. He set up amanageable dimensional study with the tools firstemployed by Galileo or Rankine . By re-elaborating

the formulae, we come to the same conclusion asRankine's: [Lma, Ippp] = [(Lma,-L) IPexJ The nextstep is also similar to Rankine's. Based on data fromstructures in existence, he reached the maximum sizesfor different types. Pano's formulation seems morecomprehensive than Rankine's. Moreover, thevariables used are not the same, so that a commontheoretical core is hard to maintain. In view of theabove, we could assume that none of them had any

influence among their contemporaries. Yet, it is evenmore surprising that, in Spain, Eugenio Ribera'sEncyclopaedia does not include any mention.

However, dimensional analysis could not go

further from Rayleigh's work, though itsconsequences may not have been really exploited. Atfirst, dimensional analysis could not establish thevariables of the problem, but it allowed to establish itsdimensional relation once the variables were given.Since the key problem was to know these variables,this procedure was not to be successful.

Additionally, Rayleigh chose a correct number of

dimensional variables in order to solve the problemaccurately with regard to dimensional analysis, yet

the variables of the problem of dead load were notdefined in any way. The shape factor cp() comprisedall the geometrical variables of the problem withoutdefining the parameters they depended on. Thisprocedure only succeeded with reduced samples.

At the end of the century, the first published critics

on the theoretical approaches for the deterrnination ofdead load began to emerge (Waddell 1896). Aspreviously referred, from the first half of the 19thcentury an exponential increase in al! known built

structural types took place; thus, the empiricalpractice could improve. This was without doubt apragmatic, brief solution. On the other hand,

technicians did not establish theories, but set boundsto problems with the known theories. Likewise, it isunderstandable why the development of the theory

was scarce.Waddell not only was a North American engineer

of great experience, but a firmo In his book of 1916

I Jl,/Fig.11.

"-

/'V I

V V~~~------

~~~.:::: l.->I--~-./ V ~.,.

S... 1.1off'~.....~~'"

Q~~tdr IO b4'H) K.~ ~OC) ~100

Structure: Size, fonu and proportion 889

CONSOLIDATED DIAGRAM (MEAN CURVES).

deO~lO1>:;..O

!:Jt~

Ir

r.AlO

~...O..J:!lO.

,., 1

s p'F.&

..... .A N

Figure 4

Relation between (ti dood'md/ ti

"'''"'''''''d)and the size for different steel bridges. (Thorpe principies of the 20th century).

about bridges construction we can find also the stateof art regarding bridge s designo (Waddell 1916, 1;Chapter XV, Principies of Designing). The title of thechapter cannot be more promising. Let us now have alook at some of its principies. «Principie 1: Simplicityis One of the Highest Attributes of Good Designing».»Principle II: The Easiest Way's the Best». «PrincipieV: There are No Bridge Specifications Yet Written,and there Probably Never Will be Any, which willEnable an Engineer to Make a Complete Design foran Important Bridge without Using His Judgment toSettle Many Points which the Specifications Do Notthoroughly Cover; or as Theodore Cooper Puts It:-

The most Perfect System of Rules to Insure SuccessMust be Interpreted upon the Broad Grounds ofProfessional Intelligence and Common Sense-»Principie XLIX: The Science of Bridge DesigningLies Mainly in the Detailing».

Waddell established 50 principies which showeddeep savoir faire in the subject. Though, theseprincipies have been implicitly used for centuries,they had little in common with a general theory of

designo This theory was not based on the scientific

knowledge, but on practice, something that already

existed before the Scientific Revolution.Due to the complexity ofthe problem, Waddell opted

for empirical approximations, though his works weretoo theoretical. He not only carried out a great amountof work on empirical formula of dead load, but he alsoestablished his proposals to modify those expressionswhen some of the variables changed. In order to do this,an understanding of variables was required. Both, thevariable of the material and its linear influence wereperfectly identified, but this was not same for the

geometrical variables. Waddle stated dimensionalanaIysis reasoning in order to quantify the influence of

the depth, in the case of trusses of parallel chords. It issomehow paradoxical that one of the greatest enemiesof the theoretical approach was not aware of the majoradvances he was giving in his effort to manipulate theempirical approach. The problem was that they did notknow how to propose a change in geometry in a moregeneral way. Thus, as this empirical work was toospecific, and other manipulations required of atheoretical knowledge which did not exist at that

moment; all this work fell into oblivion.

890 J. L. Fernández Cabo

One of the most complete compilations in steelbridge s, was that carried out by W.H. Thorpe. Itseems obvious that Waddell's work was more general

when trying to propose methods in order to modifythe empirical formula. From my point of view, he is

conscious of the great limitations of the empiricalapproach.

Let us look into one of Thorpe's graphs.In practical terms, at least temporarily, the problem

is sol ved by applying this method. Another key aspectof the problem is also shown, namely, the essentiallylinear variation between load and size recorded inpractice. However, there are still too many implicit

geometrical variables which do not contribute to theunderstanding of the problem. Likewise, these are themost outstanding geometrical variables regardingdesigno

New attempts to apply the dimensional analysisand combine both the theoretical and the practicalapproach were then carried out. In an effort to applythis method, Steinman (]91]) tried to sol ve in arational way the maximum sizes as well as theeconomic intervals of different structural types. Hecentered his work in cantilever and suspensionbridges, as they were the only types used in great

spans. More particularly, he worked on what he

named general semi-empirical formu]ae, in functionof constants (which comprise form and material)from reasoning of similar dimensional analysis to theones used by Galileo. In order to determine thosecoefficients he used theoretical calculus instead ofusing the available empirical data. Thus, his proposal

did not succeed, and Waddell disagreed about theexisting empirical data.

Shedd' s work was one of the most interesting onesregarding to design process. Like Steinman, he

combined the theoretical and the practical approach,giving formulae for the optimum depth of bridge

girders. He established a dead load empirical formu1a

for railway bridges: [fcIp/Ul =CL(fcI cjU)/CJ. Where

parameter C is a constant which remains almostinvariab]e respect to size; increasing in small spans in

order to correct the dimensioned excess. With regard

to trusses, he established a limitation of triangulationangles with the horizontal between 45 and 60°, theoptimum being between 50 and 55°. Though practice

had assumed these essential problems long time ago,they are not c1early shown nowadays.

It is obvious, that most of the graphics and

formulae were made for bridges. In the 1930s a greatnumber of formulations were settled. In USA therewere multip]e works as unified codes were notestablished till after the Second War World. M.

Ketchum's (1914, 192],1924), F. Dufour's & P.e.Schantz's (193]) or T. Shedd's (1934) manualsshowed a broad range of formulae and graphics. Thefirst ones are of type: (fcIpp / L) = Cl + C2L; beingC¡ = constants which depend on the shape, on the kind

of live load (in those years bridge load types weretypified) and on the material. The next step was the

introduction of the width bridge (h) as avariable:(fcIcpp / L) = CI + C2h + C3L + C4hL. Thelast step was to correct the smalllinearity detlectionwhich is produced with the size increase:(fcIpp / L) = CI + C2h + C3L + C4hL[1 + CsL]. Thedependent variable is the dead load for unit of length.This is right, as the live load for unit of length is aconstant datum in this problem, at least for big sizes.From the relation [Lma, / fcI pp] = [(Lma,-L) / fcI co,] it may

be observed that in built structures, the relation isbasically linear as empirical formulae indicate.

Empirical formulae also appeared in Architecturestructures field especially in roofs, even though in adecreasing degree. Robins Fleming gathered 13empirical expressions for the dead load ca1culus of

roof trusses (Fleming, 1919). After ana1yzing theseexpressions, he reached two successful conclusions.

His first conc1usion was that between suchformulae there were some times very greatdifferences. He marked out that the variables were notalways the same as they were not clarified. Such

formulae were ver y restrictive due to the chosenvariables and they were to be used cautiously.

With regard to his second conclusion, dead 10adhad an intluence not greater to 15%, due to analyzedstructures size with spans between 15 and 30 m.According to Fleming it was of no need to proceedany further.

At the beginning of the 20'h century, concrete wasused in construction works when structural typescreativity was not decreasing yet. In fact, workingwith concrete was parallel to shells development.Soon concrete will compete with steel in mostsamples. At this time, different empirical formulae

for bridges and roofs were also used.On the other hand, high-rise building s arose in

architecture between the turn of the 191hcentury andthe beginning of the 20[h in USA. Some of the most

Structure: Size, form and proportion 891

well-known being: the Monadnock building(1890-91) in Chicago having 16 stories, the

Woolworth building (1911-13) in New York with 50stories, The Empire State (1929-31) with a totalheight of 373m and an unfit structural design, Thanks

to Goldsmith and F. Khan this type of constructions isto be improved in the 60s and 70s,

From 1950s to the XXI century

There was a continuous decreasing of structural typesfrom mid 20th century, From the mechanical point ofview, despite the fact many more constructions were

carried out in this period than in previous times, thegreater structural types development arose basicallyin high-rise buildings, above all in the tension roofstructures field,

In that period, bridge s design proceeded with itseven slower improvement of semi-empirical kindinherited from the 20'h century. Comparing thesuspended bridge over the Mena, of Telford (1825),

which has a span of 177 m, and the Akashi Kaikyo(1996), with 1990m of span, there is only a notable

geometric difference, that is to say, slenderness goesfrom about 14 to 7. The topological configuration andthe method of the initial design proposition haschanged very little, and it certainly may be improved.

Meanwhile, the frequently empirical formulationnearly disappeared. Though, there were some

reminders, such as, the ACI that offered a generallinear formula to determine the total dead load forunit of surface of six different types of concretebridges (AC!, 1992, 343R-58). The interval size forevery type was offered but not its slenderness;namely, the same as was done in the beginning ofthe20th century formulae. Slenderness, as we have

previously said, is actually an implicit datum. We

must wonder here, the reason of the key parametersimplicitness.

However, the only group of experts who

considered empirical formulation essential, in the mid20th century, was started by Myron Goldsmith in the

lIT of Chicago (Goldsmith, 1953). Fazlur Khan wasto join it soon afterwards. Goldsmith monitoredseveral Ph. Doctorate research works in the 60s,among which we can mention David Sharpe's,Phyllis Lambert's and Peter Pran's. Those studies

including data from concrete and steel roofs are still

applicable. In most North American bibliographyproduced by this group of authors, there is not asingle reference to the empirical formulae for thedesign of bridges dating back to the beginning of thecentury. These formulae show the same conclusions

as the ones achieved in the case of bridges: the loadvariation for unit of surface with relation to size, isessentially linear; when this variation is not linear, thestructural type is not considered for this size and it

will be necessary to change the form, to change thetype.

Goldsmith was the first person to realize that theexisting structural types in high-rise buildings with

small spans gantries did not bear any relation to greatsizes. Instead, he proposed a very interesting high-rise building which laid the basis of Fazlur Khan'sfuture work.

Following Goldsmith work, Fazlur Khan was the

main thinking-mind behind the typological evolutionof high-rise buildings. Between the 60s and 70s high-rise buildings achieved appropriate structura] typesthanks to Khan. However, the new structural typesstemmed from an empirical, rather than a theoretical,process. The new methodology yielded excellentresults as previously in bridge designo Moreover,design efficient rules were also generated (Iyengar,1979), namely, reasonable size limit is defined by the

relationship: &ahorizontalload ~ $Olutalloads0,35.

In this period, which was to witness theestablishment of the optimization theory, authors asHemp, Prager, Cox and others resumed and enlarged

Maxwell's and Michell's work. Then, linearprogramming procedures began to be applied.Nowadays, nonlinear optimization methods are fullyconsolidated.

Until the present moment, the field of application

has been carried out on those works where anindustrialized production exists. However, itsapplication to Civil Engineering is much more recent.

As we have previously mentioned , without anadequate repetition, the variable which determinesfinancial optimization is not always the quantity ofmaterial.

In Architecture structures field, most tensionedstructures are mechanisms" thus the initial way theyshould be presented cannot be arbitrarily chosen. It iseasy to make a preliminary design which may

determine the structural type, but without establishing

a precise geometry. The exact geometry definition

892 J. L. Femández Cabo

requires sophisticated process, where for the first time

the structure geometry is to be the output. Actually,there has been no change in the design generalapproach. Previously, the form, and even the sizing, isbasically established thus, we cannot infer it is really

an «output».From my point of view Prof. Ricardo Aroca' s work

has been essential clarifying the fundamentalvariables of the dead load problem in the second halfof the 20th century. His approach is based on authorssuch as Rankine's, Mazwell's and Michell's, though

a great advance is to arise in the geometric variable.This work is to define the main variables of the deadload problem for the first time: size (L), geometry (K),proportion (A = span/depth) and the material (u/p).

Prof. Ricardo Aroca not only emphasizes the greatinfluence of geometry, but he also demonstrates thatthe essential parameter is slenderness (A).

Under these variables, dead load is defined by:

Pdead load =Protol L K (p/u)(l/2)(NAo + Ao/A); being(Ao) the optimum slenderness. For maximum size, thetotalload is only the dead load, thus maximum size isexplained only in terms of material (p/cr) , geometry

and proportion: Lmax= l/[K (p/u)(l/2)(NAo + Ao/A)].

This is a theoretical maximum. Real maximum sizes

are about 20% of the theoretical ones. Structurestiffness may be also expressed by means of thesevariabJes.

The understanding of the problem as well as theconsideration of its variables, allows predictingwhether a geometry is mechanically acceptable at afirst glance, which provides a first-rate designingtoo!. In fact, this approach demonstrates the facevalidity of the structural type as a designing too!.Basic geometry includes the main variables to controlmechanical efficiency. Thus, analogical methodssuccess is based on its application.

This relation between geometry and size is

assumed too soon in the engineering practice. But,usually , there has been a tendency to ignore theimportance of geometry in mechanical efficiency.

This may be influenced to the fact that geometry isalways part of the input in the usual analysis process.

Some ideas about the XXI century

Nowadays, optimization algorithms have achieved an

outstanding development. In highly defined

problems, geometry itself is the output. The drawback

of these methods is its numerical condition as it doesnot help in the understanding of the problem nature.

The customary practice has not taken intoconsideration these new approaches, and the workingmethod, referred to design process, has not been

modified for ages. The main unquestionable toolcontinues to be the structural type, and the analogicalis the method used. Likewise, the new tools blaze anunprecedented trail in the history of structures designo

On the other hand, the numerical algorithm works

out with very specific conditions and itsreprogramming can be very difficult. Practically, it is

not easy to establish which are the key parameters to

be optimized, even referred to cost. Besides, thestructure cost is usually a small part in the problem.As far as now, 1 agree with Waddell and Cooper thatthe best computer to face these questions is our mind.Structural types are valuable tools though their userequires a non verbal education and experience.

In structures of great size, or in those which will berepeated many times, traditional methods would notsurely be so efficiently. Every problem requires its

own different tools; and as there is no sense toestablish abstract comparisons, neither is to fix to

known procedures as a unique way of proceeding.On the other hand, all prior empírical and

theoretical advance of olden times on dead load andstructural design is still a great uncharted area. Surely,computer use has some say in the whole process; intruth, there is always the downside to everyinnovation.

This century should step ahead in the developmentof design tools, of which the computer is only oneinstrument among many more.

CÜNCLUSIONS

l. Design tools have not been up the samedevelopment as those applied to analysis. In turn,

most of the achievements in analysis have also beenparallel to lost of the already existing designs tools.

2. There is a great number of theoretical andempirical tools, though they are mostly scattered and

often unavailabJe.3. Structural types have been and still are the main

criterion for structures general designo Furthermore,they constitute the core of the analogical method, in

Structure: Size, fonn and proportion 893

so much as they go beyond the limits of geometry andmaterials.

4. The basic geometric scheme reveals importantinformation about the mechanical behavior ofstructures. Given a fixed material, the geometry is themain variable in design, being slenderness the keypoint. This fact backs up the use of this basicgeometry as a design too!.

5. There is now an increasing controversy aboutthe use of geometry as «input « for some of the designproblems outlined in this paper. In the short term,

software developments willlead to a new approach tothe structure design problem that should combineboth the traditional perspective premised on shapeand a more recent one in which form represents theresult instead of the onset datum. This fact stand s upin clear contrast to current trends in architecturaltraining, so that any progress in the field is bound to

overcome these monolithic practices.6. The absence of a general design theory has not

prevented the development and evolution of structuraltypes. This process has combined both logic and

analogical methods, sometimes unconsciously. In fact,the establishment of a general design theory is not anindispensable condition, yet it can put an sort-cut onthe design processes. Likewise, the non-lineariterative condition is peculiar to design itself. Thus,the evolution of the process seems more importantthan the onset data.

7. This historical research has done nothing butproving Thomas Khun's theory in that «Perhaps

science does not develop by the accumulation ofindividual discoveries and inventions.» (Kuhn, 1962:2). Maybe, we are now on the verge of witnessing the

revolution of structural design process.

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