-
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
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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
.-'.-
_
(if IiLrr
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
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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.
252 Lessons from Structural Failures Structural Engineering
International 4/95
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
Structural Engineering International 4/95 Lessons from
Structural Failures 23
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.
254 Lessons from Structural Failures Structural Engineering
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[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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