Case Histories and the Study of Structural Failures

Case Histories and the Study of Structural FailuresHenry Petroski, Prof.Duke Univ.. Durham. North Carolina. USA

Construction.

Introduction

In what is generally considered theoldest book on engineering, the TenBooks on Architecture, Vitruvius dis-cusses a major embarrassment suf-fered by the contractor Paconius in at-tempting to move a large rectangularpiece of stone in a new way [1, 2]. Theproven method of Chersiphron formoving large circular cylindrical stonesfor use as columns had been to cut piv-ot cups into the flat ends of the stone,into which was fitted a wooden framethat extended forward as a yoke foroxen. This method obviated the needto lift the heavy stone onto a wagon.whose axle would be taxed by theweight and whose wheels would belikely to get bogged down in any softground that might be encountered onthe route. Rectangularly shaped archi-traves could not be moved by Cher-siphron's method, of course, and so hisson, Metagenes, modified it by build-ing wooden wheels around the ends ofthe stone before cutting pivot holesand fitting the yoke-like device for theoxen (Fig. la).When it came time to move a largerectangular piece of stone for use as areplacement pedestal for a statue ofApollo that stood in the middle of theancient Greek city of Selinus. theprocess of cutting pivot cups into theends of the stone was seen to introduceblemishes into faces that would not becovered by subsequent construction,and so a new scheme was developed bythe competing contractor Paconius.His idea was to eliminate the frameand yoke entirely. thus not only elimi-nating the need to deface the stone but

also narrowing the device and thusmaking it more suitable for movingthrough the narrow streets of the es-tablished city. Although he did nothave nearly the experience of Meta-genes. Paconius got the contract on thebasis of his novel procedure. whichpromised to be quicker and less expen-sive.

As Vitruvius tells the story. Paconiusproceeded with confident pride to con-struct a circular spool-like cage aroundthe rectangular stone, as shown inFig. lb. His idea was to wind a ropearound this spool and have oxen pull itfrom the quarry to the site of the stat-ue. When the time came to effect themove, however, Paconius found that itwas extremely difficult to keep thecontraption on a straight line, and theheavy cargo frequently veered off theroad. Each time this happened, consid-

erable effort was needed to return thestone to the middle of the road andmuch time was lost. In the end Paco-nius had to concede defeat and sufferbankruptcy.Vitruvius tells the story of Paconius asa case study of failure, and one thatshould be known not only literally butalso metaphorically by all who wouldengage in speculative designs that ap-pear to be improvements on the priorart. It is not that Vitruvius was againstprogress or the evolution of tech-niques and designs. it was rather thathe recognized that time and again theslightest deviation from past experi-ence produced an altered system thatwas potentially fraught with unfore-seen new modes of failure. In the twomillennia since Vitruvius repeated thestory of Paconius. thoughtful writersand thinkers about engineering designand construction have recorded andrepeated cases of failed schemes andstructures in order to help newer gen-erations understand how subtle and in-sidious the nature of error can be.

An Example from Galileo

Seventeen centuries after Vitruviushad written, Galileo opened his semi-nal work, Dialogues Concerning livoNew Sciences, with a recitation of em-

250 Lessons from Structural Failures Structural Engineering International 4/95

Summary

Case histories of failures have always been part of the engineering literature, buttheir lessons appear to have been least heeded during extended periods of greattechnological evolution, such as that associated with the progress in bridge build-ing that occurred between the 1840s and the 1930s. This period of ever increasinganalytical advances and great leaps in structural magnitude also witnessed someof the most significant bridge failures of all time. In the wake of the collapse ofthe Tacoma Narrows Bridge, especially, case histories of failures have come to berecognized as major sources of insight and judgement in structural design and

b)

Fig. 1: Two ancient schemes for moving large pieces of stone: a) that of Meta genes: b) that ofPaconius [16]

barrassments that had been sufferedby Renaissance engineers [2, 3]. It waswell known at the time that specialcare had to be taken when moving ex-tremely large structures like obelisksand ships. which had been confidentlyscaled up geometrically from smallersuccessful examples, lest they break.The structural failures that had oc-curred were inexplicable on the basisof geometry alone, and Galileo notedthat natural structures. as exemplifiedby the bones of small and large ani-mals, were not in strict geometric pro-portion. He took this to suggest thatnature understood a principle ofstrength that went beyond mere pro-portion.As if his examples of obelisk and shipfailures were not enough, Galileo alsorepeated a story of a curious failurethat occurred even though everyoneconcerned thought that they were tak-ing steps to prevent it. The situation in-volved a marble column that was instorage in a Venetian work yard. Ac-cording to Galileo, the heavy columnwas resting on two supports, in a man-ner that we would describe today as asimply supported beam, as shown inFig. 2. A workman, seeing this, and re-calling the propensity for largeohelisks and ships to crack and breakunder their own weight, suggestedthat a third support be added in themiddle to prevent a failure from occur-ring. Everyone consulted apparentlythought this a good idea, and a thirdsupport was added, as also shown inFig.2. With this precautionary step tak-en. little further attention was paid tothe piece of marble, now thought to besafely stored until needed in a remotecorner of the work yard.

A few months later, however, some-one walking in the vicinity of thestored column came upon it broken intwo! What had been feared, had hap-pened, as shown in Fig. 3, even though.precautionary steps had been taken toprevent it. Upon some reflection,Galileo explained, the design changeof adding an additional support. some-thing that had been thought to be animprovement, was in fact the verything that can be said to have causedthe damage. Indeed, according toGalileo, if the column had been left asoriginally supported, it would mostlikely not have failed at all.

Galileo analyzed the failure as follows:As originally supported. the columnmay indeed have been close to break-ing under its own weight, but that

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Fig. 2: Galileo's marble colu,nn: top, ivitli,nodified support; borto,n, as originally sup-ported

would not have happened unless addi-tional weight were added, such as inthe form of workmen sitting on thecolumn, or if it were moved suddenlyor carelessl Even if the supports wereto have settled unevenly into theground, the column would have beenrealigned but this would not necessari-ly have caused it to crack. However, byadding the third fresh support, the set-tlement of one or the other of the old-er two supports left the column-cum-beam balanced on the carefully locat-ed center support, with half its weightcantilevered to the left or the right,and it cracked in two. The column wasindeed close to breaking, and in timethe design change that was effectedmade the overload a certainty.

Nineteenth-Century Failures

While Galileo employed case studiesof failures very openly to establishthe inadequacy of contemporaryknowledge of structural mechanicsand thereby to motivate his famousanalysis of a cantilever beam, there ap-pears to have developed by the nine-teenth century a tendency to be lessforthright in employing failures to mo-tivate advances in structural analysis.This may have been due in part to therapid advance of analytical techniquesand the proliferation of design alterna-tives. That is not to say that failures

were not occurring, for they were, butrather than reflect openly upon thecauses of the failures and thereby bet-ter understand their implications forimproving design and analysis, theredeveloped a propensity among engi-neers to simply abandon technologiesin which failures would occur.In the case of suspension bridges, forexample, by the 1840s there had been asufficient number of structural andfunctional failures in the genre to leadBritish bridge building practice awayfrom the suspension bridge form forrailroad use. Such collapses as those ofthe decks of the Menai Strait andBrighton Pier suspension structures inhigh winds, coupled with the failure ofbridges on the Continent under therhythmic step of marching soldiers,produced a prejudice against employ-ing the form to support the consider-able weight and pounding action ofsteam locomotives.Rather than take the failure of suspen-sion bridges as a blanket indictment ofthe form. however, the American engi-neer John Roebling collected casestudies of such failures and analyzedthem for lessons to be learned. In a pa-per published in 1841, he explained hisdiscussion of failures to he motivatednot by any desire to bring discredit tothe form but rather to understand theforces that must be designed against tobuild a successful bridge [4]. Evidently.as indicated by the apologetic tone ofRoebling's article, there was some pro-fessional opposition at the time to say-ing anything more than was absolutelynecessary about engineering failures.The isolated paper, such as one hScott Russell [5], that explicitly pro-posed schemes designed to obviate theroot causes of failures appears to havereceived little contemporary attention.

Such an attitude about an open discus-sion of failures may have been a resultof the fact that an embarrassing num-ber of them were in fact occurring, es-pecially in the application of iron torailroad bridges of ever increasingscale. Robert Stephenson. for exam-ple. was no doubt embarrassed by the1847 failure of his Dee Bridge. atrussed girder design with a marginalfactor of safety, which led to a RoyalCommission charged with lookinginto the use of iron in railway bridges[see. e. g.. 2]. While some official doubtremained as to the exact cause of theDee Bridge failure. the incident cutshort further development of the de-sign and no doubt led Stephenson to

Structural Engineering International 4/95 Lessons from Structural Failures 251

Fig. 3: Galileo's illustration of failure modesfor the marble column: top, as occurred;bottom, as feared f3J

be even more cautious in the design ofhis Britannia tubular bridge then un-der construction.Stephenson saw the lessons of failuresas an important part of engineeringknowledge. In 1856. in writing to aneditor about a manuscript under re-view. Stephenson stated that [quotedin 6; see also: 2. 7]:"Nothing was so instructive to theyounger Members of the Profession, asrecords of accidents in large works.and of the means employed in repair-ing the damage. A faithful account ofthose accidents, and of the means bywhich the consequences were met, wasreally more valuable than a descrip-tion of the most successful works. Theolder Engineers derived their mostuseful store of experience from the ob-servations of those casualties whichhad occurred to their own and to otherworks, and it was most important thatthey should be faithfully recorded inthe archives of the Institution."There were plenty of failures of ironrailroad bridges, both in America andBritain. in the latter part of the nine-teenth century. of course, but discus-sions of failures like that of the DeeBridge. in which a number of liveswere lost tended to dominate profes-sional and public debate. The collapseof the Ashtabula Bridge in Ohio in1876 and that of the Tay Bridge inScotland in 1879 were also landmarkaccidents that led to prolonged in-quiries and that affected bridge build-ing tremendously. The collapse of theTa. for example. greatly influencedthe design and construction of the

great cantilever across the Firth ofForth. and the Forth Bridge in turngreatly influenced bridge buildingthroughout the world in the late nine-teenth and early twentieth century [8].

A Forum for FailuresIn 1887, the very influential trade jour-nal, Engineering News, then under theco-editorship of the American railwayengineer Arthur Mellen Wellington,carried an editorial headed, "TheTeaching of Failures" [9]. It began,"We could easily, if we had the facili-ties. publish the most interesting, themost instructive and the most valuedengineering journal in the world, bydevoting it only to one particular classof facts. the records of failures: of in-stances where engineering designsproved inadequate to the work thrownupon them; with such a full presenta-tion of facts as to enable it to be seenjust how and why they failed. For thewhole science of engineering, properlyso called, has been built up from suchrecords: and not only so. but there isno engineer who, if he will look backupon the past and be honest with him-self. will not find that his most valuableand most effective instruction hascome from his own failings."The editorial went on to note that"structures which fail are the only oneswhich are really instructive, for thosewhich stand do not in themselves easi-ly reveal whether they are well de-signed or so overly designed as to bewasteful of material and resources."Because Engineering .Vews recognizedthat the "natural impulse of those whoare in any way responsible for failureswhether from acts of commission oromission, is to keep the matter as quietas possible." something not difficult todo in cases where there is no great cat-astrophe or loss of life, the journalcalled upon its readers to "overcometheir natural reluctance to having thefacts as to failures for which they areresponsible made public." at leastanonymously. To facilitate the submis-sion of such information, the journalfurther pledged to reimburse contribu-tors for reasonable expenses. Pho-tographs and drawings, "especiallylarge-scale drawings of details." wereparticularly welcome.Perhaps the epitome of realization forWellington's vision of EngineeringVews as a journal of failure reportingcame in 1907 with the collapse of theQuebec Bridge. as shown in Fig. 4,

while under construction [2]. The de-scriptive copy and photographs of thetangled mass of steel were models offorensic documentation and specula-tion. Furthermore. the verbatim tran-scripts of testimony taken by the RoyalCommission from the consulting engi-neer and de facto chief engineer,Theodore Cooper, and others provid-ed insight into the design and construc-tion process that was to then unparal-leled. The detailed case history of theQuebec Bridge is one that is perhapsnot now known as well as it should bein part because the failure essentiallyended the design of record span can-tilever bridges that had so dominatedthe arena since the completion of theForth Bridge in 1890. To this day. the(redesigned) Quebec Bridge. with itsmain span of 550 m. stands as thelongest in the world.

Suspension BridgesUntil the collapse of the QuebecBridge. there was considerable compe-tition between cantilever and suspen-sion bridge designs for long span struc-tures for railroad traffic. Gustav Lin-denthal's late lX8Os proposal for a sus-pension bridge with a main span of theorder of 914 m designed to cross theHudson River at New York without amid-river pier met with opposition inpart because of the incontrovertiblestructural success of the Forth can-tilever and its demonstrated stiffnessunder railroad trains. Had economicfactors not argued against Lindenthal'sgrand scheme. the collapse of the Que-bec Bridge might have easily unbal-anced the scales toward the suspensionbridge design. As things developed.however, the alternative of tunnels un-der the Hudson River and the ascen-dancy of the automobile and truck asviable alternatives to the railroad ledto new bridge proposals. includingconsiderably less expensive suspensionbridge designs such as the bridge at179th Street that came to be called theGeorge Washington [10].Othmar Ammann. Lindenthal's assis-tant on the great Hell Gate archbridge, tried unsuccessfully to con-vince his aging mentor that a less am-bitious suspension bridge was appro-priate for the changing traffic patternsaround New York City. By designinghis structure for automobile, truck.and light rail traffic only. Ammann wasable to propose for an affordable sumwhat Lindenthal considered an unac-ceptable compromise. Furthermore.


Fig. 4: The collapsed Quebec Bridge [17]

the George Washington Bridge couldbe constructed in stages. with an up-per, vehicular roadway built first. Byinvoking favorable assumptions aboutthe nature of traffic on the bridge andabout how the lateral stiffness againstthe wind related to the dead weight ofits cables and deck structure alone, thebridge was designed and constructedoriginally with a single deck without aconventional stiffening truss, as shownin Fig 5. This made the structure akinto the early nineteenth century sus-pension bridges with unstiffeneddecks, such as the Menai Strait andBrighton Pier. The structural failuresof those decks were considered irrele-vant to the twentieth century. howev-er, because of the massiveness of themuch larger steel bridges like theGeorge Washington and the advancesin analysis that enabled design calcula-tions to he made with unprecedentedaccuracy.

Precedent of SuccessThe George Washington Bridge was,of course. a tremendous success. How-ever. as Wellington pointed out in hiseditorial in Engineering News, success-ful structures can be poor examples tofollow. In fact. such structures can bedownright misleading as to the princi-ples behind their structural evolution.Not heeding this fact. Ammann andhis contemporaries, such as DavidSteinnian and Leon Moisseiff, who de-veloped the displacement method ofanalysis that made possible structureslike the George Washington Bridge.went on to design lighter and moreslender suspension bridges throughoutthe late 1930s [8. 11]. Among the no-table ones were the Golden GateBridge. for which Moisseiff served asprincipal consulting engineer: theBronx-Whitestone. for which Am-mann was chief engineer: the Deer IsleBridge. for which Steinman was thedesigner; and the Tacoma NarrowsBridge. for which Moisseiff. again asconsultant, was principally responsi-ble.

The Golden Gate proved to be veryflexible in the wind, and to this day isnot considered structurally strongenough to accept the addition of lightrail traffic beneath its roadway. In thelate 1930s. the Bronx-Whitestone andDeer Isle bridges exhibited consider-able flexibility in the wind, and a van-clv of cable stays and other deviceswere debated over by Arnmann andSteinman to check what were consid-

ered psychologically troublesome butnot structurally dangerous movementsin the wind. Even the flexibility of theTacoma Narrows, while unexpected.was not considered threatening to thestructure when it first opened in mid-1940. However, when the bridge beganto exhibit the torsional oscillationsthat led to its catastrophic collapseonly three months later. the engineer-ing community began to realize that ithad been relying too heavily on mod-els of success.

Failure AnalysisThe collapse of the Tacoma NarrowsBridge. shown in Fig. 6, naturally ledto the appointment of a board of engi-neers charged with investigating thefailure and reporting on its cause. Theboard comprised Othmar Ammann,whose George Washington Bridge hadset the tone for suspension bridge de-sign and construction in America inthe 1930s: Glenn Woodruff, who hadbeen engineer of design for the SanFrancisco-Oakland Bay Bridge, com-pleted in 1936; and Theodore von Kr-man, then director of the GuggenheimAeronautical Laboratory at CaliforniaInstitute of Technology. While the me-chanical engineer and aerodvnamicistvon Krmn had, within days of theTacoma Narrows failure, publicly iden-tified aerodynamic instability as theprincipal cause of the collapse, he ap-pears to have deferred to the bridgeengineers when it came to drafting thereport and summarizing the conclu-sions of the investigatory board.The report on the failure of the Taco-ma Narrows Bridge [12] boldly de-

dared that the structure "was welldesigned and built to resist safely allstatic forces, including wind, usuallyconsidered in the design of similarstructures." while acknowledging thatthe failure resulted from "excessive os-cillations caused h wind action". Fur-thermore,"The excessive vertical and torsionaloscillations were made possible by theextraordinary degree of flexibility ofthe structure and of its relatively smallcapacitY to absorb dynamic forces. Itwas not realized that the aerodynamicforces which had proven disastrous inthe past to much lighter and shorterflexible suspension bridges would af-fect a structure of such magnitude asthe Tacoma Narrows Bridge. althoughits flexibility was greatly in excess ofthat of any other long span suspensionbridge."The report was in large part a defenseof the state of the art, which had


Fig. 5: The George Washington Bridge, as conipleted in 1931 with a single deck(courtesy ofspeciul Arc/jive. Trihorough Bridge and Tunnel .4uthori:v)

Fig. 6: The failed Tacoma Narroji's Bridge(Courtesy of University f Washington)

proven to be inadequate to deal withstructures of the extraordinary de-gree of flexibility" that the TacomaNarrows and its contemporaries haddemonstrated. The flexibility of thedesign of the Tacoma Narrows was dueprincipally to Moisseiffs confidence inhis deflection theory of analysis andhis use of plate girders rather than astiffening truss to achieve the then cur-rent aesthetic goal of an extrenielyslender deck profile. Ammann. whoowed so much to the design skills ofthe consultant Moisseiff for much ofhis own success as a chief engineer,was evidently reluctant to be too criti-cal of what he himself had subscribedto in his own bridges, such as theBronx-Whitestone, which had beenunder scrutiny since its opening in1939.

When Ammann had referred to histor-ical examples of suspension bridges.such as Telford's over the Nlenai Strait.he often invoked them solely as aes-thetic paradigms. omitting entirely amention of their self destructive be-havior in the wind. Rather than im-mortalize them as case studies of struc-tural failure, as Roebling had done,Ammann and his contemporaries evi-dently felt that the state of the art hadprogressed so far beyond the historicalcases that they expunged them fromthe canon. It was only when the Taco-ma Narrows took so much of the engi-neering community by apparent totalsurprise that the long history of the be-havior of suspension bridges in thewind began to appear once again to berelevant.Not long after the Tacoma NarrowsCollapse. J. Kip Finch published inEngineering \eii.r- Record a retrospec-tive article on the 'evolution and de-cay of the stiffening truss" [13]. inwhich he documented the troubleswith wind that had plagued suspensionbridges for over a century. In a letter tothe editor two weeks later, Finchsounded more like the authors of thefailure report as he reassured his read-ers that he meant no indictment of thebridge design community for not pay-ing attention to this history of failuresand thereby anticipating similar be-havior in the light modern structuresthat had been constructed in the 1930s.Indeed, he went so far as to deny ex-plicitly that he had suggested or in-tended the reader to infer "that themodern engineer should have knownthe details of these earlier disastersand should have anticipated the Taco-ma failure".

Yet this is precisely the value of his-toric case studies of the kind that Finchhad laid out in his article. Indeed, bothVitruvius and Galileo presented theircase studies of failure to help designersavoid similar failures in the future. Inparticular, ancient and Renaissanceengineers had been warned explicitlyabout the hidden dangers that can beencountered in scaling up structures.Concerns over the scale of the TacomaNarrows Bridge were, in fact, ex-pressed before its construction byTheodore Condron, a consulting engi-neer who had been retained by the Re-construction Finance Corporation toevaluate the plans during the loan ap-proval process [12, Appendix IV].Condron expressed great reservationover the extraordinarily small width-to-span ratio and recommendedstrongly that the width of the roadwaybe increased. This would, of course,have increased the torsional stiffnessof the bridge deck, and it may havemade the difference in the bridge'ssuccess or failure. In the end, however,it was the reputation of engineers likeMoisseiff. whose successful designs bythen included the George Washingtonand Golden Gate bridges, that pre-vailed over the misgivings of Condron.Yet Condron's cautionary report hadanticipated the findings of Sibly andWalker's later systematic study oflandmark bridge accidents [14, 15].Their work reveals that time and againfailures occurred in a climate of over-confidence in the state of the art and ina climate of ignorance of or the dis-missal of the relevance of historicalcase studies.

The Value of Case Studies

If World War Two had not interruptedthe design and construction of largesuspension bridges, the collapse of theTacoma Narrows certainly would have,for it forced a reevaluation of an ap-peal to the state of the art without ref-erence to historical case studies. Acontemporary phenomenon was theincreasing occurrence of brittle frac-ture in welded steel structures, includ-ing some Vierendeel truss bridges builtbefore the war. The surprising andspontaneous break-up of some weldedLiberty ships in calm water was re-markably reminiscent of unexpectedproblems with large wooden ships andmarble columns that Galileo had de-scribed three centuries earlier, and thestudy of such failures gave rise to thefield now known as fracture mechan-

ics, in which case studies play such animportant role in supporting and moti-vating theory and experiment.In the latter part of the twentieth cen-tury. case studies of failures have cometo be recognized as invaluable sourcesof insight and understanding for thedesign and construction of innovativestructures. While the next generationof bridges or ships may appear to havelittle resemblance to structures of thepast. and while the use of advanced an-alytical techniques such as are embod-ied in computers may appear to super-sede the pencil and paper methods ofthe past, in fact the design and erectionof the structures of today and tomor-row are subject to the same forces ofnature and sources of human error ashave been obelisks, ships, and suspen-sion bridges. The most advanced com-posite structural materials also aresubject ultimately to the same laws ofcohesion that Galileo studied in theseventeenth century. Thus, the caveatsthat were relevant ages ago can be noless relevant today. and it behooves en-gineers of all kinds of structures toknow their history lest they repeatwithout thinking some of the mistakesof the past. Those mistakes are record-ed in case studies of failures, and theyare among the most effective lessonsof history.

References

[1] VITRUVIUS, The Ten Books on Ar-chitecture. Translated h M.H. Morgan.Dover Publications, New York, 1960.[2] PETROSKI, H. Design Paradigms:Case Histories of Error and Judgement inEngineering. Cambridge University Press.New York. 1994.

[3] GALILEO. Dialogues Concerning TwoNew Sciences. Translated by H. Crew andA. de Salvio. Dover Publications, NewYork, 1954.

[4] ROEBLING, J.A. Remarks on Suspen-sion Bridges, and on the Comparative Mer-its of Cable and Chain Bridge.s AmericanRailroad Journal, and Mechanics Maga-zine 6 (n.s., 1841), pp. 193196.[5] RUSSELL. J. S. On the Vibration ofSuspension Bridges and Other Structures;and the Means of Preventing Injury fromthis Cause. Transactions, Royal Scottish So-ciety of Arts 1. pp. 304314.

[6] WHYTE. R. R., ed. Engineering Pro-gress through Trouble. Institution of Me-chanical Engineers, London. 1975.[7] PETROSKI. H. To Engineer Is Hu-man: The Role of Failure in Successful De-sign. St. Martin's Press, Ncs York. 1985.


[8] PETROSKI, H. Engineers of Dreams.Great Bridge Builders and the Spanningof America. Alfred A. Knopf, New York.1995.

[9] The Teaching of Failures. EngineeringNews, April 9, 1887, pp. 237238.

[101 DOIG. J. W.: BILLINGTON. D. P.A,nmann's First Bridge: A Study in En-gineering, Politics, and EntrepreneurialBehavior. Technology and Culture 35.pp. 537570.

[11] BILLINGTON, D. P. History and Aes-thetics in Suspension Bridges. Journal ofthe Structural Division: Proceedings of the

ASCE 103 (1977): 16551672. See also, dis-cussion. ibid., 104 (1978): various pages;and closure, ibid., 105: (1979): 671687.[12] AMMANN. 0. H.: VON KARMAN.T.; WOODRUFF. G. B. The Failure of theTacoma .Varrows Bridge. Federal WorksAgency, March 28, 1941.[13] FINCH. J.K. Wind Failures of Suspen-sion Bridges. Engineering News Record,March 13, 1941, pp. 7479. See also, March27. 1941. p. 43.

[14j SIBLY. P.O. The Prediction of Struc-tural Failure. Ph.D. Thesis. University ofLondon. 1977.

[15] SIBI.Y. P. G.: WALKER. A. C. Struc-tural Accidents and Their Causes. Proceed-ings of the Institution of Civil Engineers62. pp. 191208.

[16] COULTON, J. J. Ancient Greek Archi-tects at Work: Problems of Structure andDesign. Cornell University Press, Ithaca,NY. 1977.

[17] Government Board of Engineers. TheQuebec Bridge over the St. Lawrence Rivernear the Cit of Quebec on the Line of theCanadian National Railways. Dept of Rail-ways and Canals. Ottawa, Canada. 1918.

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