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Failure By Design (Two Case Studies of Bridge Design Failure) by Granger Meador Physics Teacher, Bartlesville High School Bartlesville, OK failurebydesign.info

Failure by Design Hyatt Regency

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Page 1: Failure by Design Hyatt Regency

Failure By Design(Two Case Studies of Bridge Design Failure)

byGranger Meador

Physics Teacher,Bartlesville High School Bartlesville, OK

failurebydesign.info

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FAILURE BY DESIGN(Two Case Studies of Bridge Design Failure)

by Granger Meador

Published by the Author

Version 2.0

Contact information:

Granger MeadorPhysics InstructorBartlesville High School1700 SE Hillcrest DriveBartlesville, OK 74003-72991-918-336-3311FAX 1-918-337-6226Email: [email protected] or [email protected]: http://failurebydesign.info

This work is licensed under the Creative Commons Attribution-Noncommercial-ShareAlike 3.0 United States License. To view a copy of this license, visithttp://creativecommons.org/licenses/by-nc-sa/3.0/us/ or send a letter to CreativeCommons, 171 Second Street, Suite 300, San Francisco, California, 94105, USA.

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PURPOSE

Disasters are inherently intriguing to students, and can motivate them to engage inhigh levels of analysis. My goals in having my own 11-12th grade physics studentsanalyze the Hyatt Regency hotel walkways collapse and the failure of the TacomaNarrows bridge include:

• develop students’ analytical and deductive skills in determining the possible andactual failure modes of a structure

• illustrate for students how engineers and architects must utilize physics indesigning safe structures

• have students use their knowledge of force loading and vectors to explain theflaw in the design change of the Hyatt walkways

• introduce concepts of wave motion and aerodynamics to explain the vibrationsand failure of the Tacoma Narrows bridge

I have attempted to include enough information in this document to allow otherteachers to deal with each disaster at varying levels of sophistication. Teachers’ owninstructional goals and knowledge of their students’ level of conceptual andmathematical development will dictate how much time and effort they wish to devoteto these topics.

The Hyatt disaster is introduced as a puzzle to be solved, to increase student interestand motivation. Evidence is presented for students to debate and analyze in smallgroups or as a class. Students can use the evidence to develop and evaluatespeculative conceptual solutions, which are then judged against additional evidencegathered after the accident. I have also included any additional data I could find foroptional quantitative analysis. Students are asked to suggest possible designimprovements, and the societal aspects of the design failure and the repercussions ofthe accidents are also presented.

The Tacoma disaster is too complex to expect most introductory physics students toanalyze its failure. Instead, a qualitative description of its behavior is used to illustratesome aspects of wave motion and point out how a large structure’s aerodynamicbehavior cannot be safely neglected. Students are again asked to suggest possibledesign improvements which are compared to the changes made when the bridgewas reconstructed.

Many physics texts identify resonance as a reason for the Tacoma disaster; in recentyears some engineers have argued that resonance was not involved, but morecomplex modes of self-excitation. The reader is referred to the technical discussionson the CD-ROM for more information.

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ONLINE PRESENTATION

In addition to this handout, there is online presentation at http://failurebydesign.infowith graphical images, animations, and movies. The online presentation is adaptedfrom a PowerPoint presentation, and you can progress through it in your web browser.

TACOMA NARROWS VIDEOTAPEThe public domain and online clips of the Tacoma Narrows disaster are of limitedquality and duration. For the greatest dramatic effect, teachers are urged to considerpurchasing a high-quality color video from a respected source.

The American Association of Physics Teachers offers a videotape with three segments:Tacoma Narrows Bridge Collapse by Franklin Miller, Jr. (1963), The Puzzle of theTacoma Narrows Bridge Collapse by R.G. Fuller, D.A. Zollman, & T.C. Campbell (1982),and the combined footage (1998). As of March 2008 the videotape andaccompanying user’s guide was available for $48.95 for AAPT members, $37.00 forstudent members, and $61.00 for non-members. The user’s guide includes a numberof suggested activities where students analyze the videotape to obtain quantitativedata.

Catalog Number: VT-20Description: Twin Views of the Tacoma Narrows Bridge Collapse

American Association of Physics Teacherswww.aapt.orgOne Physics EllipseCollege Park, MD 20740-3845PHONE 301-209-3311

The incredible footage of the Tacoma disaster used in the above videotape was shotby a Tacoma camera store owner. His shop is now run by his son-in-law, who also hasa videotape and DVD for sale. As of March 2008 the DVD price was $65.00 and thevideotape price was $49.00 from:http://www.camerashoptacoma.com

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THE COLLAPSE OF THE HYATT REGENCY HOTEL WALKWAYS IN KANSAS CITY

Hallmark Cards, Inc. is headquartered in Kansas City,Missouri. By 1968, the area surrounding its headquarterssouth of downtown suffered from urban blight, and thecompany began the massive “Crown Center” 85-acreredevelopment project. As part of the project, a HyattRegency Hotel was designed and constructed from 1976 to1980. Unfortunately, the hotel had design and constructionproblems which led to a horrific disaster one year after itopened.

The hotel has three main sections: a 40-story tower, afunction block, and a connecting atrium area. The atrium’sdimensions are 145 ft (44.2 m) by 117 ft (35.7 m), and 50 ft(15.2 m) high. For guest convenience, three walkways wereconstructed along the width of the atrium to connect thetower and function block on the second, third, and fourthfloors of the structure. The walkways were suspended fromthe ceiling so that the main floor would not be obstructed bysupport columns. The third floor walkway, which connectedto a ballroom, was wider than the others and suspendedfrom the roof on its own set of rods. The fourth floor walkway,which led to the health club and sports area, was alsosuspended from the roof by rods. The second floor walkwaywas suspended by rods from the fourth floor walkway, asseen in the architectural rendering at right.

The Disaster:

On July 17, 1981 the hotel had been open for a year and alocal radio station was holding a dance competition. By 7 pm the atrium wascrowded with between 1500 and 2000 people, with many spectators observing fromthe walkways. At 7:05 pm a loud crack echoed through the building and the secondand fourth floor walkways collapsed, killing 114 people and injuring over 200 others.

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Hyatt Puzzle

What part(s) of the walkways failed? Given the overall design asconstructed, what parts of the support structure could have failed tocause both the second and fourth-floor walkways to collapse? Whatevidence would you look for to decide which part actually failed?

The fourth-floor walkway wassuspended from the roof bythree sets of hanger rods. Therods passed throughlongitudinally welded box beamsand were capped with washersand nuts which held up thewalkway by pressing on theunderside of the box beams.

The second-floor walkway wassuspended from the fourth-floorwalkway by another set ofhanger rods. These rods wereheld up by washers and nutspressing on the top surface ofthe 4th-floor box beams. The rodspassed through box beams forthe second-floor walkway andwere again capped with washersand nuts pressing against theunderside of the 2nd-floor boxbeams.

Long I-beams running down thesides of each walkway weresuspended from the box beams byangle brackets. At right is a close-up view of the construction of the4th-floor walkway and itsconnections to the hanger rods.

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Hyatt Structural Details

Walkway length: 117 feet (35.7 m)Walkway width: approx. 18 feet (5.49 m); 4th and 2nd-floor walkways were

15.6 in (0.397 m) narrower than separate 3rd-floor walkwayHanger rod diameter: 1.26 in (32 mm)Hanger rod length: as built, each approx. 20-23 ft (6-7 m); 4th-floor connection

was 6.1 m below roofInset for 2nd-floor rods: 4 in (102 mm) inward along axis of box beamI-beams: 16-inch (40.6 cm) deep (W16x26 steel: wide flange steel

beam of 16-in depth, weighing 26 pounds per foot)Box beams: two 8-in (20.3 cm) deep rectangular channels welded toe-

to-toe (MC8x8.5: flanged channel steel beams of 8-indepth, weighing 8.5 pounds per foot); Jensen (2000)assumed capacity of 115 kips or 115,000 pounds of force

Walkway floor: concrete, 3.25 in (8.26 cm) thick, approx. 150 lb/ft3

Hyatt Possible Conceptual Solutions/Failure Modes

These are presented to assist you in leading a student discussion.

Likely failure modes:

1) The hanger rods from the roof to the fourth-floor walkway snapped or the roofconnection failed.Examination of the accident scene would show the upper rods broken off, most likelynear the roof where the load in each rod would be maximized.

2) The nuts under the fourth-floor box beams stripped free.The accident scene should reveal nuts stripped from the hanger rods, but few if anypunctures of the nuts through the fourth-floor box beams.

3) The fourth-floor box beams gave way at the ends, allowing the washers and nutsunderneath them to punch through.The accident scene should reveal washers and nuts still on the rods hanging from theroof, with punctures through the box beams.

4) A combination of the above failure modes occurred.One would expect a mix of the above physical evidence in the debris.

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Unlikely failure modes:

5) The fourth-floor box beams gave way, but not at the ends, allowing the washersand nuts above them to punch through.The physics of the situation makes this highly unlikely: the washer/nuts under the beamcarry a much greater load than the washer/nuts above the beam. This would,however, be able to cause the full failure of the fourth-floor walkway if the puncturedbox beams separated sufficiently along the welds to allow the washers and nuts underthe beam to escape.

6) The nuts above the fourth-floor box beams stripped free.This scenario suffers from the same defect as the one above.

7) The nuts below the second-floor box beams stripped free.8) The washers and nuts below the second-floor box beams pulled through those

beams.9) The hanger rods for the second-floor walkway snapped.

Each of the above three scenarios would likely only lead to the failure of the second-floor walkway, rather than both the second and fourth-floor walkways. However, if oneside of the second-floor walkway failed, sufficient stress or torque could be placed onthe upper walkway to make it collapse.

10) The I-beams or angle brackets on one of the walkways failed.This would have allowed one section of a walkway to collapse, but the remainingsections would likely have survived.

Evaluation of these possibilities:

Possible failure modes 1, 2, and 3 will likely be the ones most frequently raised indiscussion. There is no direct evidence given of the relative load-bearing strength ofthe hanger rods, nuts, or box beams. The actual solution must be ascertained from anexamination of the accident scene. There is, however, an important clue we have notyet revealed: a design change in the fourth-floor connection. This change wouldmake the placement of the washers and nuts above and below the welded seams onthe box beams the culprit.

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Original design

As-built

Hyatt Clue: The Design Change

To help one pick from the alternatives, a valuable clue isa design change that occurred. The originalconceptual design did not have one set of hanger rodsgoing to the fourth-floor walkway and then another setfrom it to the second-floor walkway. Instead, originallythere were to be long hanger rods attached to the roofand passing through the box beams under the fourth-floor walkway and continuing down through the boxbeams under the second-floor walkway. The schematicat right shows the original design for the connectionbetween the hanger rod and the fourth-floor walkway.

This original design called for extremely long hangerrods, which were difficult to manufacture and install. Another problem was that the design did not use sleevenuts, but somehow threads for a nut had to appear6.1 m along each rod. This would have either requireda specially manufactured rod with extruding threads atthat location, or a rod with threading 6.1 m down itslength from one end.

The steel company subcontracted for the hanger workproposed a simple design change which wasapproved by the structural engineers for the project. The change consisted of replacing each single longhanger rod with a pair of rods offset on the fourth-floorwalkway’s box beams, as seen earlier and shown againat right. This allowed for easy installation of a nut andwasher below the beam to support the fourth-floorwalkway, and another nut and washer above the beamsupporting a hanger rod for the second-floor walkway. This greatly reduced the expense and complexity of theconstruction.

The size of the washers and nuts and the design of thebox beam were NOT changed when this change in the4th-floor connection was made.

Now which part(s) do you think most likely failed?

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Fourth-floor hanger rods intact,with nuts and washers in place

Close-up of intact nut andwasher on upper hanger rod

Close-up of fourth-floor box beam, showing how upperhanger rod pulled completely through (hanger rod fromfourth to second floor is still in place)

Hyatt Conceptual Solution

What actually happened was that the washers and nutsbelow the fourth-floor box beams punctured those beams,as shown by the photographs on this page (and the finalparts of the video animations on the accompanying CD-ROM).

The design change was conceptually flawed, as itdoubled the load on the upper box beam. A usefulanalogy is that of two monkeys hanging from a rope:the design change is equivalent to tying one monkey ontothe other with a second rope, making the first monkey’sgrip on the rope treacherous.

The actual failure began with the centerrod connection on one side of the 4th-floor walkway, and then all of that side’sconnections failed. (The top west rods atthe accident scene were bent west whilethe east rods were not distorted.)

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Hyatt Quantitative Solution

A common misconception is that the design change halved the number of peoplethe walkways could support. In fact, the change had a much more dramatic impacton the number of people that could be supported. Knowing that the walkways as builtcould barely support themselves and with some data from the National Bureau ofStandards, we can calculate the probable impact of the design change:

An investigation by the National Bureau of Standards reported:

• The Kansas City Building Code required a minimum support value of 151,000 newtons for eachhanger rod/box beam connection in the original design.

• A test showed that each connection could, on average, support only 90,000 newtons. This wasonly 60% of the required minimum for the original design.

• The design change doubled the load on the fourth floor box beam, so the code would havecalled for a support value of 302,000 newtons at the fourth floor connections, yet as-built thoseconnections could still only support 90,000 newtons.

Q: Assume that the two walkways themselves each weighed 220,000 N. Each of the six 4th-floorhanger rod/box beam connections could support 90,000 N, as could the six 2nd-floorconnections. How many 150 lb (667 N) people could the walkway connections supporta) as built? b) as originally designed? c) if built with the original design, but meeting code?

A. a) AS-BUILT:(6 * 90,000 N) – (2 * 220,000 N) = 100,000 N remaining capacity(we have to subtract the weight of BOTH walkways from ONLY the 4th floor totalconnection strength, since as-built those connections carried both walkways)100,000 N / 667 N = 150 total people on both walkways(video at time of collapse showed about 80 people on the 4th-floor walkway)

b) AS ORIGINALLY DESIGNED:(6 * 90,000 N) + (6 * 90,000 N) – (2 * 220,000 N) = 640,000 N remaining capacity(as designed the 2nd and 4th-floor connections were independent of each other)640,000 N / 667 N = 960 total people on both walkways(which is over SIX TIMES more than the as-built design)

c) IF BUILT TO ORIGINAL DESIGN, BUT MEETING CODE:(6 * 151,000 N) + (6 * 151,000 N) – (2 * 220,000 N) = 1,372,000 N remaining capacity1, 372,000 N / 667 N = 2057 total people on both walkways(which is almost FOURTEEN TIMES more than the as-built design)

Thus one can see that if the design change had not been made, the walkways would likely still be intactto this day, giving no indication that they did not meet the conservative building code.

It also turned out that the hanger rods did not meet specifications: the preliminary design sketches forthe walkways called for hanger rods with a strength of 413 megapascals. This was omitted from the finalstructural drawings and the contractor specified rods with a strength of only 248 megapascals. However, their weakness played no role in the catastrophe.

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Hyatt Quick Demonstration

The doubling of the load on the fourth-floor box beams due to the design change canbe illustrated with some very simple equipment:

3 spring scales2 equal weightssupport

One spring scale will represent the load at the roof connection for a hanger rod. Theother scales represent the load on the second and fourth-floor box beams.

Original design analogy:

Hang the first scale from the support. Hang both of the remaining scalesfrom the first scale. Hang the weights from those scales. The two “boxbeam” scales will read identical amounts, while the “roof connection”scale will read approximately twice what the other scales read.

As-built analogy:

Now shift one of the lower scales so that it hangs from the other lowerscale. Now the lower “box beam” scale reads the same amount asbefore, but the upper “box beam” scale reads twice that, almost asmuch as the top “roof connection” scale.

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Hyatt Consequences

There were a number of warnings during its construction that the Hyatt hotel projectwas troubled. The atrium roof collapsed during construction, fortunately during aweekend so that no one was injured. After the walkways were up, there were reportsthat construction workers found them unsteady under heavy wheelbarrows, but theconstruction traffic was merely rerouted and the walkway design not subjected tointense scrutiny.

After the terrible tragedy, the Kansas City Star newspaper hired consulting engineers toreview the evidence and identify the cause of the accident. Within four days of thefailure, the front page of the Star showed drawings pinpointing the cause. Theinvestigative reporting of the accident won a Pulitzer Prize that year.

Within days of the tragedy, the remaining walkway for the third floor was dismantledand removed in the middle of the night, despite protests from the city mayor. Thehotel owners argued it was a hazard, but attorneys for the victims objected. Engineersstudying the tragedy were disappointed they did not have the chance to use theremaining walkway to test theories that the tempo of dancers on the walkways mayhave contributed to the collapse (similar to the vibration problems of the TacomaNarrows Bridge).

After a twenty-month investigation, the U.S. attorney and county prosecutorannounced they had no evidence of a federal or state crime in connection with thecollapse. But two months later the state attorney general charged the designengineers with “gross negligence” and the U.S. Department of Commerce eventuallyconcluded that the steel fabrication contractor (Havens Steel Company) was not atfault. The design engineers had approved the original design that did not meet codeas well as the design change that weakened the structure. During a 26-weekadministrative trial the detailer, architect, fabricator, and technician on the project alltestified that during construction they had contacted the project engineer regardingthe structural integrity of the connection detail. Each time he assured them that theconnection was sound, claiming to have checked the detail when in reality he hadnever performed any calculations for this design at all. The Missouri Board of Architects,Professional Engineers, and Land Surveyors eventually convicted engineer of recordJack D. Gillum and project engineer Daniel M. Duncan of gross negligence,misconduct, and unprofessional conduct in the practice of engineering. Their Missouri(and later Texas) professional engineering licenses were revoked, and their company(Gillum-Colaco or G.C.E. Inc.) lost its certificate of authority as an engineering firm. Asof September, 2000 Gillum was an Adjunct Professor of Civil Engineering at WashingtonUniversity in St. Louis, Missouri.

The tragedy eventually led to what has been reported as over $140 million in damagesawarded in civil cases brought by the victims and their families. These amountsdwarfed the half million dollar cost of the building.

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Hyatt Prevention

This accident could have been prevented by a better design, better designprocedures, and ethical engineer behavior.

Better Design:There are a bewildering number of design details in a massive project like the HyattRegency, and it is too easy when one presented with the accident as a puzzle to thinkthat the problems in the design were obvious. But there were some severedeficiencies in the walkway design. The original design, with its extremely long hangerrods and awkward nut threading, was difficult to implement, and it did not meetbuilding codes.

Engineers have suggested possible improvements:• add additional hanger rods and box beams to

reduce the load on each connection• use larger washers to lower the pressure on each

box beam’s welded face• keep the toe-to-toe channels in the box beams,

but add bearing crossplates to transfer part of theload to the sides of the box beam (see upperdiagram)

• rework the box beams to have back-to-backchannels with web stiffeners to prevent buckling(see lower diagrams)

• add support pillars from the floor as an alternateload path

So how was the Hyatt atrium rebuilt? Noted engineeringauthor Henry Petroski reported, “Today the Hyatt Regencylobby in Kansas City is spanned by a single walkwayresting on stout columns sitting on the solid floor (1985, p.93).”

Better design procedures:In this disaster, the firms involved did not have clear procedures for approval of designchanges. Procedures should ensure that the engineers recalculate loads and safetyfactors when a support structure is redesigned. In this case, there was also aprocedural failure when the shop detail specifying the required rod strength was notincluded in the final drawings.

Ethical engineers:Martin (1999a) criticized the project engineer: “Neglecting to check the safety andload capacity of a crucial hanger even once shows his complete disregard for thepublic welfare.”

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ACTIVITY: Balsa Bridge Building courtesy of Pitsco (www.pitsco.com)

Objective:Design and engineer a bridge using 1/8 inch x 1/8 inch balsa wood to hold as muchmass as possible over a 12-inch span.

Construction:1. The overall width of the bridge may not exceed 3 inches.2. The overall length of the bridge may not exceed 15 inches.3. The bridge shall allow a 1-inch wide x 3/4-inch thick board to pass through it over

the roadbed.4. The bridge shall have no structures below the abutments that support the bridge.5. The bridge shall allow a 3/8-inch bolt to pass through the center of the bottom of

the bridge unobstructed (for testing).6. The bridge shall be constructed entirely of 1/8-inch x 1/8-inch balsa wood.7. Any common adhesive may be used at the joints of the wood members.8. Adhesives may be used only at joints.9. Wood joints may be notched if desired.10. The mass of the bridge may not exceed 40 grams.

Competition:1. The mass of the bridge will be determined before testing.2. All bridges will use the same test device.3. The bridge will be tested using a 1-1/2-inch wide x 10-inch long x 3/4-inch thick

wood block with a hole in its center for the testing mechanism.4. The bridge is placed on the bridge tester, with the span set at 12 inches.5. The teacher will attach the testing mechanism to the bridge.6. When the testing mechanism is ready, the student will begin to add sand to the

bucket at the rate he or she chooses.7. There will be a 10-minute time limit on adding sand to the bucket.8. The student will continue to add sand to the bucket until the bridge collapses, and

the bucket falls.9. The mass of the sand will be measured.10. The bridge supporting the greatest load is the winner.11. In the event that the bucket is completely filled without breaking for more than one

bridge, then, of those bridges, the one that has the least mass wins.

Variations:• Vary the length of the span of the bridge from 8 inches to 24 inches.• Assign dollar amounts to supplies (wood and glue), and judge the bridges on cost

efficiency (cost per pound of load held).

Products for this competitive event can be found in the Pitsco Competitive Events Theme Catalog.

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ACTIVITY: Toothpick Bridge Building courtesy of Pitsco (www.pitsco.com)

Objective:Design and engineer a bridge using toothpicks (or Blunt End Structure Sticks) to hold asmuch mass as possible over a span of 6 inches.

Construction:1. The overall width of the bridge may not exceed 3 inches.2. The overall length of the bridge may not exceed 9 inches.3. The bridge shall allow a 1-inch wide x 3/4-inch thick board to pass through it over

the roadbed.4. The bridge shall have no structures below the abutments that support the bridge.5. The bridge shall allow a 3/8-inch bolt to pass through the center of the bottom of

the bridge unobstructed (for testing).6. The bridge shall be constructed entirely of toothpicks (or Blunt End Structure Sticks).7. Any common adhesive may be used at the joints of the wood members.8. Adhesives may be used only at joints.9. The mass of the bridge may not exceed 20 grams.

Competition:1. The mass of the bridge will be determined before testing.2. The bridge will be tested using a 1-1/2-inch wide x 4-inch long x 3/4-inch thick

wood block with a hole in its center for the testing mechanism.3. The bridge will be placed on the bridge tester, with the span set at 6 inches.4. The teacher will attach the testing mechanism to the bridge.5. When the testing mechanism is ready, the student will begin to add sand to the

bucket at the rate he or she chooses.6. There will be a 5-minute time limit on adding sand to the bucket.7. The student will continue to add sand to the bucket until the bridge collapses and

the bucket falls.8. The mass of the sand will be measured.9. The bridge supporting the greatest load is the winner.

Variations:• Vary the length of the span of the bridge.• Assign dollar amounts to supplies (toothpicks and glue) and judge the bridges on

cost efficiency (cost per pound of load held).• Model the bridge after a local or famous bridge.

Products for this competitive event can be found in the Pitsco Competitive Events Theme Catalog.

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THE COLLAPSE OF THE TACOMA NARROWS BRIDGE

A costly yet less tragic accident than the Hyattwalkway collapse was the dramatic demise of theTacoma Narrows Bridge in 1940. The collapse iswell remembered, thanks to color film footageshot by a local camera store owner. The generaldesign problems of the bridge were identified longago, but the precise technical explanation for itscollapse is still a subject of debate.

The first suspension bridge toconnect the Olympic Peninsulawith the mainland of WashingtonState, the bridge linked Seattle toTacoma with the nearby PugetSound Navy Yard. The WashingtonState Toll Bridge Authority spentover $6 million on the project. Construction began on November23, 1938 and concluded on July1, 1940. The bridge wouldcollapse four months later, onNovember 7.

Koughan (1996) notes, “Suspension bridges workon essentially the same principle as a clothesline. This type of bridge fundamentally consists ofcables anchored to the earth at their ends andsupported by towers at intermediate points. Fromthese cables a floor or ‘deck’ is suspended.” Thesebridges are inherently more flexible than otherdesigns, and require bracing to reduce verticaland torsional motions. The inadequate design ofthe Tacoma Narrows bridge would subject it tovertical and torsional motions of incredible anddestructive magnitudes.

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Open trusses under thedeck of the reconstructedTacoma Narrows Bridge

Overhead, side, and cross-sectional views of the bridge and its deck bracing

Bridge deck underconstruction; note solid I-beams along sides

Bridge Deck Design

One cause for the inadequate design was cost-cuttingimposed when one of the funding sources, the FederalPublic Works Administration, balked at the $11 million designfrom the state’s Toll Bridge Authority. A $7 million budget waseventually secured and a radically narrow, shallow-deckdesign was put forward by the respected bridge designerLeon S. Moisseiff. This aesthetically pleasing designsubstituted the usual deep open trusses with 8-foot tall steel I-beams along the sides of the deck. The bridge was thethird-longest in the world at the time, with a 2800 foot centerspan, but was only 39 feet wide with two lanes of traffic andtwo sidewalks.

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Center cable stays

Attempts to Reduce Vibration

The bridge began exhibiting unusually large vertical oscillations (transverse waves)during construction. Consulting engineer F.B. Farquharson of the Department of CivilEngineering at the University of Washington was brought in to study the bridge’sbehavior and recommend solutions. An accurate scale model of the bridge wasconstructed and tested in a wind tunnel for $20,000. This led to several attempts tocorrect the bridge’s behavior:

1. After proving successful on the model, 1 9/16 -in. steel cables attached a point oneach side span to 50-yd concrete anchors in the ground. Unfortunately thesecables snapped a few weeks later, proving to be an ineffective solution, althoughthey were reinstalled in a matter of days.

2. In addition to these cables, center stays and inclinedcables, which connected the main cables to thestiffening girder at the middle of the bridge, wereinstalled.

3. Finally, untuned dynamic dampers, similar to onethat had helped curtail torsional vibrations ofMoisseiff’s Bronx-Whitestone Bridge in New York, failedimmediately after their installation in the TacomaNarrows Bridge. It was discovered that the leatherused in the devices was destroyed during thesandblasting of the steel girders before they werepainted, rendering them useless.

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The road deck tilted alarmingly by torsionalvibrations; note the center stripe which served as anodal line of little vibration

Galloping Gertie

Prior to the day of its collapse, the bridge only exhibited vertical oscillations. Thetransverse modes of vibration had nodes at the main towers, with from 0 to 8 nodesbetween the towers. The maximum double amplitude (crest to trough) was about 5 ftin a mode with 2 nodes between the towers, with a frequency of 12 vibrations/min. Thismode would startle motorists as cars ahead of them would disappear from view andthen reappear later. The bridge bounce led a wit to call it “Galloping Girdie” for itsmotion and its side girders. This was corrupted into the sobriquet “Galloping Gertie.” Some motorists would drive across the bridge and even stop midway to enjoy thebouncing sensation, while others made long detours to avoid it.

The most frequently observed vibration was one with no nodes between the towers, adouble amplitude of up to 2 feet, and a frequency of 8 vibrations/min. Measurementsmade before the bridge failed indicated that higher wind speeds correlated to higher-frequency vibration modes. But there was no significant correlation between windspeed and vibration amplitude: winds of 3 or 4 mph could create motions of severalfeet, while at other times the bridge remained motionless in winds as high as 35 mph.

The Collapse

A midnight storm on November 7, 1940 probably weakened the K-bracing under thebridge deck, since a lone observer reported the bridge’s amplitude of vertical vibrationincreased. By early morning the wind speed was 40 to 45 mph, and the bridge wasundergoing large vertical oscillations. By 9:30 am the span was vibrating in 8 or 9segments at a frequency of 36 vibrations/min and a double amplitude of about 3 feet.

Traffic was shut down, but two cars with three passengers were trapped on the bridgewhen it suddenly began to vibrate torsionally (twist) around 10 am. The passengers,gripping the concrete curbs, crawled tosafety. Unfortunately a frightened dog inone car refused to budge and had tobe left behind. Farquharson was on thescene studying the bridge. At one point,he walked along the torsional nodal linealong the center of the roadway to studythe center stays and, incidentally,unsuccessfully attempt to retrieve thedog, which perished in the collapse.

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Frayed north cable

Sagging side spanBuckling of one tower after collapse

The twisting vibration was in 2 segmentsbetween the towers with a frequency of14 vibrations/min, later changing to12 vibrations/min. The amplitude of torsionalvibration built up to an amazing 35E eachdirection from horizontal, amid sounds ofcracking concrete. This vibration occurredwhen the north bridge cable loosened in itscollar, which was tied to the deck girder bydiagonal stays. One stay broke and theother’s cable clamp slipped, allowing thecable to slip back and forth. This allowedthe destructive torsional vibration to build upuncontrollably.

By 11 am, the vibration was simply toomuch and the center span broke apart,crashing into the water below. The sidespans remained intact, although theysagged about 45 ft. The two towers eachsagged shoreward 25 ft at their tops,buckling them. The main cables wereintact, except for a 42-inch section in thecenter of the north cable where the collarscraped; 500 of the 6308 strands of No. 6galvanized cold-drawn steel wire wereruptured.

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Tacoma Puzzles:

Why did this bridge oscillate so much?

The Tacoma Narrows bridge was a victim of poor aerodynamics. The long, narrow,and shallow deck with its solid I-beam sides was too flexible to survive the winds of thecanyon in which it was situated. Most suspension bridges used deep, open trusseswhich allowed wind to flow through relatively unimpeded. Designers were used tomaking sure that a bridge could handle static loads, but the dynamic forces of windswere seldom considered at the time of this bridge’s construction. In fact, subsequentto this failure large bridges and buildings were routinely checked for aerodynamicstability, often incorporating wind tunnel testing of scale models.

The Federal Works Agency investigated the failure after the collapse, and included onits commission Theodore von Karman, a noted aeronautical engineer. The reviewstressed that the bridge had met accepted engineering criteria of the time, havingbeen built to accepted safety factors for static loading. It did not cast blame on LeonMoisseiff, but accepted that the bridge failure was the result of design limits beingstretched into previously unexplored areas.

The commission focused on three possible sources for the destructive dynamics of thebridge: aerodynamic instability producing self-induced vibrations, periodic eddyformations, and random turbulence. Many textbooks today attribute the collapse toresonance. Resonance is when a system begins to oscillate with a large amplitude asit is acted upon by periodic impulses of a frequency approximately equal to one ofthe natural frequencies of oscillation of that system. However, an analysis by Billah andScanlan (1991) showed that the bridge’s behavior was not due to simple resonance. Mathematical models of its motion are better explained by more complex self-excitation mechanisms.

Commission member von Karman had proposed that the wind blowing across thebridge deck created turbulent vortices. This process of “vortex shedding” would havecreated alternating high and low pressure regions on the lee side of the bridge,causing it to oscillate.

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Billah and Scanlan agree that von Karman’sexplanation is suitable for the vertical or transverseoscillations the bridge exhibited until the day offailure. But they argue that the twisting or torsionaloscillations cannot be attributed to resonance orvon Karman’s vortices. Instead, they argue that thenorth cable slipped back and forth, changing theangle of the bridge deck in the wind. This changein the “angle of attack” would have interacted withthe wind: the wind supplying power and thetorsional oscillation itself and the resulting changesin deck angle tapping into that power.

Why did this bridge fail when other, longer bridges didn’t?

The extreme flexibility of the Tacoma Narrows bridge arose from its shallow deck andnarrow width in comparison to its long span. A comparison to other bridges of the timeis revealing:

Bridge(Location; Designer; Year Opened)

Deck Depth /Span Length

Ratio ofDepth to

Span

Deck Width /Span Length

Ratio ofWidth to

Span

Tacoma Narrows(Puget Sound, WA; Moisseiff; 1940)

8 ft / 2800 ft 1 : 350 39 ft / 2800 ft 1 : 72

Bronx-Whitestone(Long Island Sound, NY; Moisseiff; 1939)

11 ft / 2300 ft 1 : 209 74 ft / 2300 ft 1 : 31

Golden Gate(San Francisco, CA; Strauss; 1937)

25 ft / 2400 ft 1 : 168 89 ft / 2400 ft 1 : 47

George Washington(New York; Ammann; 1931)

36 ft / 3500 ft 1 : 97 106 ft / 3500 ft 1 : 33

The lower depth-to-span and width-to-span ratios of the other bridges made themmuch less vulnerable to both vertical and torsional deflections, as shown by the graphson the following page.

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Comparative torsional deflections (in %tilt of floor) of the five-longestsuspension bridges in 1940

Comparative vertical deflections (in feet) ofthe five-longest suspension bridges in 1940,with data showing the slight improvement made in the Bronx-Whitestone Bridge whencenter stays were added

What design changes might have prevented this failure?

Martin (1999) identified a number of design changes that could have saved theoriginal Tacoma Narrows Bridge:

• Use open stiffening trusses which would allow the wind free passage through thebridge

• Increase the width to span ratio • Increase the weight of the bridge • Use an untuned dynamic damper to limit the motions of the bridge (the dampers

on the bridge did not work)• Increase the stiffness and depth of the trusses or girders • Streamline the deck of the bridge

The concept of deep stiffening trusses was applied in retrofitting several other bridges. Moisseiff’s Bronx-Whitestone bridge had a truss added above its side I-beams in 1946. The famous Golden Gate Bridge in San Francisco had a $3.5 million retrofit to stiffen itas well.

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1950 bridge deck design1940 bridge deck design

Several design changes were made when a new Tacoma Narrows Bridge wasconstructed, using the original bridge’s piers. Scale models of the new $18 millionbridge were tested in wind tunnels at the University of Washington during its design, andit was a four-lane structure with a 60-ft wide deck and 25-ft deep stiffening opentrusses. It has been a successful design for over 50 years.

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Analysis of the specifications on this page reveals that the new bridge had adepth/span ratio of 1:112, versus the 1:350 ratio of the failed design. The new designalso boasted a width/span ratio of 1:47, versus the 1:72 ratio of Galloping Gertie.

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The Latest Tacoma Narrows Bridge

In 2007 another suspension bridge opened at Tacoma Narrow, adjacent to the 1950structure. There had been hours of daily congestion on the 1950 bridge, leading tothoughts of building another bridge.

After seven years in early development, the political arena and the courts, andanother five years in design and construction, the new Narrows bridge openedto traffic on July 16, 2007. It was built parallel to and south of the 1950Narrows Bridge, and carries four 11-foot-wide lanes of eastbound traffic towardTacoma. The left lane is a high-occupancy-vehicle (HOV) lane, the two centerlanes are general purpose lanes open to all traffic, and the right lane is an"add/drop" lane that extends across the bridge to the Jackson Avenueeastbound exit. In addition, the bridge has a 10-foot right shoulder for disabledvehicles, and a 10-foot barrier-separated bicycle/pedestrian lane.

-Washington State Department of Transportation

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Wave Demonstrations

Slinky Wave DemosSimple but effective demonstrations of wave motioncan be performed with a Slinky, two people, and ashort length of string. While a regular metal or plasticSlinky will work, you will obtain better results using anextra-long Slinky, such as the one shown in thephotograph. You can obtain such springs fromscience education supply houses.

Transverse Waves:A transverse wave vibrates perpendicularly(at right angles) to the wave travel (water wavesare a good example). To demonstrate, havetwo students each take one end of a Slinky andstretch it out along the floor (the waves will bemore apparent this way). Have one student move his or her end of a plastic or metalSlinky back and forth (left and right, like a snake crawling), perpendicular to its stretchedlength. The other student must hold his or her end of the Slinky still. A series oftransverse waves will be generated.

Transverse Wave Reflection:A wave striking the boundary of a more dense medium will partially reflect, and thereflection will be inverted. This is seen in the above demonstration, where one end ofthe Slinky is held by a student, whose grip creates a more dense medium for the waveenergy. However, a wave striking the boundary of a less dense medium will have anerect reflection. This can be demonstrated by tying some string onto one end of theSlinky and having the student hold the string rather than the Slinky. The string is a lessdense medium for wave travel, so waves sent toward the student holding the string willreflect right-side-up.

Standing Waves:When a series of wave pulses are reflected off amore dense medium, standing waves can begenerated. These distinctive waveforms have placeswhere the medium does not vibrate at all, callednodes, and other places where the medium vibratesthe most, called antinodes. When the students aredemonstrating transverse waves (without using astring), standing waves with varying numbers of nodesand antinodes can be generated by having thestudent moving the Slinky vary the rate at which he orshe continually moves it back and forth.

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Longitudinal Waves:A longitudinal wave vibrates parallel to (in thesame direction of) wave travel (sound wavesare a good example). This kind of wave wasNOT exhibited in the movies of the Tacoma Narrows Bridge. To demonstrate, have onestudent grasp and draw toward himself or herself several coils of a stretched metalSlinky and then release the coils. The other student must hold his or her end of theSlinky still. A longitudinal wave pulse will be generated and travel down the length ofthe Slinky.

Longitudinal Compressions and Rarefactions:Longitudinal waves can be composed of compressions, where the parts of themedium (coils of the Slinky) are closer together than normal, or rarefactions, where theparts of the medium are farther apart than normal. In the above demonstration, thestudents created compressional longitudinal waves. A rarefactional longitudinal wavecan be produced by stretching a segment of the Slinky and then releasing it. Thestretched area (rarefaction) will then travel along the length of the Slinky.

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The Wave Machine (from Ronald Edge’s String and Sticky Tape Experiments)

A fancy Shive wave machine like theone in the photograph will exhibittorsional waves. But you can buildyour own cheap “wave machine” withstraws and sticky tape, as describedbelow.

You will need about half a meter of stickytape, and twenty or so straws. Turn each endof the tape over about one centimeter, andstick them on the desk, or other flat surfaceas shown in the upper figure. Now place thestraws about 1 cm apart crosswise with theircentres on the tape as shown in the lowerfigure. Pick up the ends of the tape, and attach oneend to the lintel of a door, or other suitably high placewhere the chain of straws is free to oscillate. Nowsharply tap the bottom straw, and a torsional pulse willtravel up the machine and be reflected at the top. Since the top is fixed, the pulse will be of oppositesign on reflection, descending. This device can beused to display almost all the properties of onedimensional transverse traveling and stationary waves. For example, increasing the tension by hanging aweight at the bottom will speed up the waves,loading the ends of the bottom half of the straws(which can easily be done by inserting paper clipsinto each end of a straw) will be like a "densemedium"- with a lower velocity and reflection at theinterface with the light straws. Moving the bottomstraw to and fro with the correct period will producestanding waves.

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IMAGE CREDITS for this documentused for non-profit educational purposes in accordance with the “fair use” provisions of copyright law

Page Description Source (see reference list for details)

1 Hyatt walkway collapse L. Lowery, 1999, online image: 11th.gif1 Tacoma Narrows bridge Institute for Structural Analysis, 1997, extracted image from

online movie:http://www.cis.tugraz.at/ifb/img/others/tacoma/tacoma1.mov

2 Author photo G. Meador, photo by Ken Dolezal, ISD 30, Bartlesville, OK4 CD-ROM clipart Corel WordPerfect Clipart Collection5 Hyatt hotel exterior Crown Center, Inc., http://www.crowncenter.com/crown-

hyatt.html, online image: big_hyatt.jpg5 Architect’s walkway

renderingH. Petroski, 1994, book illustration: p. 59

5 Crowd in Hyatt atrium Exponent, Inc., extracted image from online movie:hyatt_lg.mov

5 Overhead view of collapse R. Martin, 1999a, online image: hyatt1.gif5 Floor-level view of collapse L. Lowery, 1999a, online image: 10th.gif6 Schematic of both walkways G. Meador, original to this document6 Close-up of 4th floor

connectionH. Petroski, 1994, book illustration: p. 61,as modified by G. Meador for this document

9 Schematics of original andas-built designs

H. Petroski, 1994, book illustration: p. 61

9 Lower schematiccomparing the designs

C.E. Harris & M.J. Rabins, 1992, p. 157

10 Close-up of 4th floor beam L. Lowery, 1999, online image: 5th.gif10 4th floor hanger rods L. Lowery, 1999, online image: 13th.gif10 Close-up of hanger rod L. Lowery, 1999, online image: 4tha.gif10 Monkey analogy G. Meador, original to this document12 Demo diagrams G. Meador, original to this document14 I beam diagrams R. Martin, 1999a: online images: hyatt7.gif & hyatt8.gif14 Web stiffener Hanley-Wood LLC, 2000: online image: squash2.gif as

modified by G. Meador for this document17 Bridge shot from shore B. Lou, undated, online image: new.jpg17 Map of Washington state Expedia, 2000, online map as modified by G. Meador for this

document17 Aeriel photo USGS, 18 Old bridge deck R. Andradne, 2000, online image: img10.gif18 New bridge trusses K. Rogers, 199718 Old deck design J. Koughan, 1996, online image: figB2_jk.gif, as modified by G.

Meador for this document 18 Bridge schematics J. Koughan, 1996, online image: figB2_jk.gif19 Old bridge view J. Koughan, 1996, online image: figB2_jk.gif, as modified by G.

Meador for this document19 Center cable stays D. Smith, 1974, online image: tac12.gif, as modified by

G. Meador for this document20 Titled bridge deck D. Smith, 1974, online image: tac07.gif

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IMAGE CREDITS (continued)

Page Description Source (see reference list for details)

21 Twisting bridge D. Smith, 1974, online image: tac06.gif21 Bridge collapse D. Smith, 1974, online image: tac09.gif21 Sagging side span D. Smith, 1974, online image: tac10.gif21 Frayed cable D. Smith, 1974, online image: tac12.gif, as modified by

G. Meador for this document21 Buckled tower D. Smith, 1974, online image: tac14.gif, as modified by

G. Meador for this document22 Vortex shedding diagram B. Tan, et al., 1998, online image: diagram.gif, as modified by

G. Meador for this document23 Vortices from bridge tilt K. Billah & R. Scanlan, 1991, Fig. 6. Vortex pattern over rotating

deck section.24 Vertical deflection graph J. Koughan, 1996, online image: fig1_jk.gif24 Torsional deflection graph J. Koughan, 1996, online image: fig2_jk.gif25 Old bridge side view D. Smith, 1974, online image: tac08.gif25 New bridge side view S. Scott, undated, online image: narrows.jpg25 Old deck design Underwater Atmospheric Systems, undated, online image:

bridge71.jpg25 New deck design Underwater Atmospheric Systems, undated, online image:

bridge72.jpg25 Buckled old deck D. Smith, 1974, online image: tac13.gif, as modified by

G. Meador for this document25 New bridge trusses K. Rogers, 1997, online image: tnb27pic.gif26 Old bridge shot from shore B. Lou, undated, online image: new.jpg26 New bridge M. Ketchum, undated, online image: Tacoma-320x500.JPG26 Bridge specifications R. Andradne, online image: img31.gif27 Two bridges, profile view Washington State Dept. of Transportation, online image

(2007a)27 Two bridges, top view Washington State Dept. of Transportation, online image

(2007b)28 Slinky on lecture table P. Groutt, 1996, online image from:

http://jedlik.phy.bme.hu/~hartlein/physics.umd.edu/deptinfo/facilities/lecdem/g3-24.htm

28 Transverse waves G. Meador, 1997, online image: transver.gif28 Nodes and antinodes G. Meador, 1997, online image: nodes.gif29 Longitudinal waves G. Meador, 1997, online image: longit.gif30 Shive wave machine P. Groutt, 1996, online image from:

http://jedlik.phy.bme.hu/~hartlein/physics.umd.edu/deptinfo/facilities/lecdem/g3-01.htm

30 Wave machine, upperdiagram

R. Edge, 1998, online image: Image101.gif

30 Wave machine, lowerdiagram

R. Edge, 1998, online image: Image102.gif

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REFERENCE LISTused for non-profit educational purposes in accordance with the “fair use” provisions of copyright law

Andradne, R. (2000). Gertie’s last gallop [Online]. Available: http://www.gateline.com/gertie/index.htm orhttp://www.gateline.com/gertie/Galloping%20Gertie.zip [2001, January 27].

Billah, K.Y., & Scanlan, R.H. (1991, February). Resonance, Tacoma Narrows bridge failure, andundergraduate physics textbooks. American Journal of Physics, 59(2), 118-124. Available:http://www.ketchum.org/billah/Billah-Scanlan.pdf [2001, January 27].

Edge, R. (1998). String and sticky tape - and other fun experiments [Online]. Proceedings of the Handson - Experiments in Physics Education International Conference. Duisburg, Germany. Available:http://ubntint.uni-duisburg.de/hands-on/files/autoren/edge/edge.htm [February 8, 2001].

Elliot, E. (undated). Tacoma Narrows bridge video [Online]. Available:http://www.camerashoptacoma.com/narrows.asp [2001, February 4].

Expedia, Inc. (2000). Tacoma, Washington [Online map]. Available:http://maps.expedia.com/pub/agent.dll [2001, February 10].

Exponent, Inc. (undated). Hyatt walkway collapse [QuickTime Video; Online]. Available:http://www.exponent.com/multimedia/cases/hyatt.html [2001, January 27].The author thanks the Exponent engineering company and its webmaster for agreeing to providethe extra-large MPEG animation of the Hyatt Regency walkway collapse.

Fuller, R.G., Lang, C.R., & Lang, R.H. (2000). Twin views of the Tacoma Narrows bridge collapse. CollegePark, MD: American Association of Physics Teachers. [http://www.aapt.org]

Gies, J. (1963). Bridges and men. Garden City, NY: Doubleday.

Groutt, P. (1996). University of Maryland physics lecture-demonstration facility [Online]. Available:http://jedlik.phy.bme.hu/~hartlein/physics.umd.edu/deptinfo/facilities/lecdem/lecdem.htm#hp[2001, February 8].

Hanley-Wood LLC. (2000). Q&A: squash blocks and web stiffeners [Online]. Available:http://www.jlconline.com/jlc/qana/framing/squash_blocks/ [2001, February 10].

Harris, C.E. & Rabins, M.J. (1992). Engineering ethics: The Kansas City Hyatt Regency walkways collapse(NSF Grant Number DIR-9012252) [original version of Lowery (1999) online document]. CollegeStation, TX: Texas A&M University, Department of Philosophy and Department of MechanicalEngineering.

Institute for Structural Analysis. (1997). Tacoma Narrows Bridge (1940) failure [Online]. Available:http://www.cis.tugraz.at/ifb/img/others/tacoma/tacoma.htm [2001, January 28].

James, M.N. (undated). Failure as a design criterion [Online]. Available:http://www.tech.plym.ac.uk/sme/FailureCases/Failure.htm [2001, February 5].

Jensen, J.N. (2000). Civil engineering case study [Online]. Available:http://www.acsu.buffalo.edu/~jjensen/cie.htm [2001, February 17].

Ketchum, M. (undated). Mark Ketchum’s bridge engineering page [Online]. Available:http://www.ketchum.org/bridges.html [2001, February 8].

Koughan, J. (1996). The collapse of the Tacoma Narrows bridge, evaluation of competing theories of itsdemise, and the effects of the disaster on succeeding bridge designs [Online]. Available:http://www.me.utexas.edu/~uer/papers/paper_jk.html [2001, January 27].

Lank, S., Robinson, M., Sevigny, S., Steger, M., & Tsai, J. (1997). Smash and crash: The Kansas City HyattRegency walkway collapse [Online]. Available:http://www.people.virginia.edu/~jtt3e/hyatt/paper.htm [2001, February 17].

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REFERENCE LIST (continued)

Lou, B. (undated). Bridge and resonance [Online]. Available:http://instruction.ferris.edu/loub/media/BRIDGE/Bridge.htm [2001, February 4].

Lowery, L. (1999). Engineering ethics: The Kansas City Hyatt Regency walkways collapse [Online]. Available: http://lowery.tamu.edu/ethics/ethics/hyatt/hyatt1.htm andhttp://lowery.tamu.edu/ethics/ethics/hyatt/hyatt2.htm [2001, January 28].

Martin, R. (1999a). Hyatt Regency walkway collapse [Online]. Available:http://www.eng.uab.edu/cee/REU_NSF99/hyatt.htm [2001, January 28].

Martin, R. (1999b). Tacoma Narrows bridge collapse [Online]. Available:http://www.eng.uab.edu/cee/REU_NSF99/tacoma.htm [2001, January 28].

Meador, G. (1997). Activity #2: Slinky waves [Online]. Available:http://www.teachingtools.com/SlinkyShindig/activ2.html [2001, February 8].

Moore, K.S. (1999). Large amplitude torsional oscillations in a nonlinearly suspended beam: Atheoretical and numerical investigation [Online]. Available:http://www.math.lsa.umich.edu/~ksmoore/ [2001, February 4].

Neyman, P. (undated). Torsion wave representation [Online]. Available:http://sps1.phys.vt.edu/~pat-man/LiNC/movies/torsion.mov [2001, February 5].

Petroski, H. (1985). To engineer is human: The role of failure in successful design. New York: St. Martin’sPress. Available for purchase at: http://www.amazon.com/exec/obidos/ASIN/0679734163

Petroski, H. (1994). Design paradigms: Case histories of error and judgment in engineering. New York:Cambridge University Press. Available for purchase at:http://www.amazon.com/exec/obidos/ASIN/0521466490

Pitsco. (undated). Bridge building competition [Online]. Available:http://www.pitsco.com/p/CCbridges.htm and http://www.pitsco.com/p/rulesdoc.pdf [2001, February13].

Rogers, K. (1997). The Tacoma Narrows bridge disaster [Online]. Available:http://137.142.19.40/seconded/second/Kent/Kent.html [February 8, 2001].

Russell, D. (2000). Vibration and wave animations [Online]. Available:http://www.kettering.edu/~drussell/Demos.html [2001, February 4].

Scott, S. (undated). Tacoma Narrows bridge [Online]. Available:http://people.mn.mediaone.net/sscott2/Text_Files/gertie.html [2001, February 8].

Smith, D. (1974, March 29). A case study and analysis of the Tacoma Narrows Bridge failure [Online].Unpublished manuscript, Carleton University, Department of Mechanical Engineering, Ottawa,Canada. Available: http://www.civeng.carleton.ca/Exhibits/Tacoma_Narrows/DSmith/photos.html[2001, February 7].

Tan, B.T., Thompson, M.C., & Hourigan, K. (1998). Simulated Flow around Long Rectangular Plates underCross Flow Perturbations [Online]. International Journal of Fluid Dynamics, 2(1). Available:http://sibley.mae.cornell.edu/IJFD/1998_vol2/paper1/paper1.html [2001, February 8].

Underwater Atmospheric Systems. (undated). Tacoma Narrows bridge [Online]. Available:http://www.nwrain.com/~newtsuit/recoveries/narrows/narrows.htm [2001, February 8].

United States Geological Survey. (1992, May 13). Tacoma, Washington, United States [Online image].Available: http://terraserver.microsoft.com/image.asp?S=14&T=1&X=168&Y=1635&Z=10&W=2[2001, February 10].

Washington State Department of Transportation. (2008). SR 16 - New Tacoma Narrows Bridge [Online].Available: http://www.wsdot.wa.gov/projects/sr16narrowsbridge/ [2008, March 6].

Washington State Department of Transportation. (2007a). NTPAW Tacoma Narrows Bridge Tour [Onlineimage]. Available: http://www.flickr.com/photos/wsdot/1129855059/ [2008, March 6].

Washington State Department of Transportation. (2007b). View from the Top [Online image]. Available:http://www.flickr.com/photos/wsdot/829349869/ [2008, March 6].