Lessons From the Failure of a Great Machine
How Galloping Gertie collapsed left us a lasting design legacy.
The Damage
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A bridge inspector checks the damaged cable
WSDOT
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Main cables:
During the collapse, the main suspension cables were thrown violently
side to side, twisted, and tossed 100 feet into the air. They slipped
from their positions in the cable saddles atop each tower. And,
they fell hard on the approach spans. On the north cable at mid-span,
where the cable band loosened, it broke more than 350 wires. Other
wires were severely stressed and distorted. The main cables were
a total loss, but salvage was undertaken. Their only value was as
scrap metal.
Suspender cables:
The violent collapse broke many suspender cables. Some were lost,
some severely damaged, and some undamaged. Their only value now
was as scrap metal.
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View of damaged cables and towers looking
west, February 1943 WSDOT
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View from below the deck at buckled steel
beams WSDOT
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M3-5 Sagging east side span GHM, Bashford
2795
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Towers:
The main towers (West Tower, #4; and East Tower, #5), including
the bracing struts, were twisted and bent. Stress beyond the elastic
limit of the metal resulted in buckling and permanent distortion.
Their only value now was as scrap metal.
Deck-Floor System:
Not surprisingly, the concrete and steel of the center span that
now lay on the bottom of the Narrows was deemed a total loss. The
remainder of the broken concrete on the side spans needed removal.
The floor system had sections that were bent and overstressed. Their
only value now was as scrap metal.
Side Spans:
The loss of the center section, followed by the dropping of the
side spans, caused substantial damage. The events stressed and distorted
the plate girders and floor beams. Some buckled beyond repair.
Piers:
Both the West Pier (#4) and the East Pier (#5) sustained no damage.
The collapse of the center span caused partial sheering of rivets
that attached the towers to the tops of the piers.
Anchorages:
The anchorages for the main cables were undamaged. For building
a replacement bridge, removal of part of the concrete would be necessary
in order to spin the new main cables.
Exactly where were Galloping Gertie's remains
later that day? Weird
Fact
First Investigations-Partial Answers to "Why"
The collapse of the 1940 Tacoma Narrows Bridge stunned everyone,
especially engineers. How could the most "modern"
suspension bridge, with the most advanced design, suffer catastrophic
failure in a relatively light wind?
The State of Washington, the insurance
companies, and the United States government appointed boards of
experts to investigate the collapse of the Narrows Bridge. The Federal
Works Administration (FWA) appointed a 3-member panel of top-ranking
engineers: Othmar Amman, Dr. Theodore Von Karmen, and Glen B. Woodruff.
Their report was the Administrator of the FWA, John Carmody and
became known as the "Carmody Board" report.
In March 1941 the Carmody Board announced
its findings. "Random action of turbulent wind" in general,
said the report, caused the bridge to fail. This ambiguous explanation
was the beginning of attempts to understand the complex phenomenon
of wind-induced motion in suspension bridges. Three key points stood
out:
(1) The principal cause of the 1940 Narrows Bridge's failure
was its "excessive flexibility;"
(2) the solid plate girder and deck acted like an aerofoil, creating
"drag" and "lift;"
(3) aerodynamic forces were little understood, and engineers
needed to test suspension bridge designs using models in a wind
tunnel.
"The fundamental weakness"
of the Tacoma Narrows Bridge, said a summary article published in
Engineering News Record, was its "great flexibility, vertically
and in torsion." Several factors contributed to the excessive
flexibility: The deck was too light. The deck was too shallow at
8 feet (a 1/350 ratio with the center span). The side spans were
too long, compared with the length of the center span. The cables
were anchored at too great a distance from the side spans. The width
of the deck was extremely narrow compared with its center span length,
an unprecedented ratio of 1 to 72.
The pivotal event in the bridge's collapse,
said the Board, was the change from vertical waves to the destructive
twisting, torsional motion. This event was associated with the slippage
of the cable band on the north cable at mid-span. Normally, the
main cables are of equal length where the mid-span cable band attaches
them to the deck. When the band slipped, the north cable became
separated into two segments of unequal length. The imbalance translated
quickly to the thin, flexible plate girders, which twisted easily.
Once the unbalanced motion began, progressive failure followed.
The investigation Board's most significant finding
was simple and obvious: the engineering community must study and
better understand aerodynamics in designing long suspension bridges.
Meanwhile, Professor F. B. Farquharson
continued wind tunnel tests. He concluded that the "cumulative
effected of undampened rhythmic forces" had produced "intense
resonant oscillation." In other words, the bridge's lightness,
combined with an accumulation of wind pressure on the 8-foot solid
plate girder and deck, caused the bridge to fail.
Leon Moisseiff, who was contacted immediately
after the failure, said he was "completely at a loss to explain
the collapse." Moisseiff visited the ruined bridge one week
later, touring under the watchful eye of Clark Eldridge. Moisseiff's
design, while pushing beyond the boundaries of engineering practice,
fully met the requirements of accepted theory at the time.
"Blind Spot"-- Design Lessons of Gertie's Failure
At the time the 1940 Narrows Bridge failed,
the small community of suspension bridge engineers believed that
lighter and narrower bridges were theoretically and functionally
sound. In general, leading suspension bridge designers like David
Steinman, Othmar Amman, and Leon Moisseiff determined the direction
of the profession. Very few people were designing these huge civil
works projects. The great bridges were extremely expensive. They
presented immensely complicated problems of engineering and construction.
The work was sharply limited by government regulation, various social
concerns, and constant public scrutiny. A handful of talented engineers
became pre-eminent. But, they had what has been called a "blind
spot."
That "blind spot" was the root
of the problem. According to bridge historian David P. Billington,
at that time among suspension bridge engineers, "there seemed
to be almost no recognition that wind created vertical movement
at all."
The best suspension bridge designers
in the 1930s believed that earlier failures had occurred because
of heavy traffic loading and poor workmanship. Wind was not particularly
important. Engineers viewed stiffening trusses as important for
preventing sideways movement (lateral, or horizontal deflection)
of the cables and the roadway. Such motion resulted from traffic
loads and temperature changes, but had almost nothing to do with
the wind.
This trend ran in virtual ignorance of
the lessons of earlier times. Early suspension bridge failures resulted
from light spans with very flexible decks that were vulnerable to
wind (aerodynamic) forces. In the late 19th century engineers moved
toward very stiff and heavy suspension bridges. John Roebling consciously
designed the 1883 Brooklyn Bridge so that it would be stable against
the stresses of wind. In the early 20th century, however, says David
P. Billington, Roebling's "historical perspective seemed to
have been replaced by a visual preference unrelated to structural
engineering."
Just four months after Galloping Gertie failed,
a professor of civil engineering at Columbia University, J. K. Finch,
published an article in Engineering News-Record that summarized
over a century of suspension bridge failures. In the article, titled
"Wind Failures of Suspension Bridges or Evolution and Decay
of the Stiffening Truss," Finch reminded engineers of some
important history, as he reviewed the record of spans that had suffered
from aerodynamic instability. Finch declared, "These long-forgotten
difficulties with early suspension bridges, clearly show that while
to modern engineers, the gyrations of the Tacoma bridge constituted
something entirely new and strange, they were not new--they had
simply been forgotten."
An entire generation of suspension bridge
designer-engineers forgot the lessons of the 19th century. The last
major suspension bridge failure had happened five decades earlier,
when the Niagara-Clifton Bridge fell in 1889. And, in the 1930s,
aerodynamic forces were not well understood at all.
"The entire profession shares in the responsibility,"
said David Steinman, the highly regarded suspension bridge designer.
As experience with leading-edge suspension bridge designs gave engineers
new knowledge, they had failed to relate it to aerodynamics and
the dynamic effects of wind forces.
End of an Era
The collapse of Galloping Gertie on November
7, 1940 revealed the limitations of the "deflection theory."
Now, engineers no longer believed that suspension bridges needed
to be stiffened only against the stress of moving vehicles and the
"minor" effect of wind.
The failure of the Tacoma Narrows Bridge
effectively ended Moisseiff's career. More importantly, it abruptly
ended an entire generation of bridge engineering theory and practice,
and the trend in designing increasingly flexible, light, and slender
suspension spans.
Othmar Amman said of the collapse of
the 1940 Narrows Bridge, "Regrettable as the Tacoma Narrows
Bridge failure and other recent experiences are, they have given
us invaluable information and have brought us closer to the safe
and economical design of suspension bridges against wind action."
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Aerial view of 1950 Narrows Bridge WSDOT
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Suspension Bridge Design Since 1940
"Mere size and proportion are not
the outstanding merit of a bridge; a bridge should be handed down
to posterity as a truly monumental structure which will cast credit
on the aesthetic sense of present generations." ---- Othmar
H. Amman, 1954
The end of the 1950s witnessed the construction
of two of the greatest suspension bridges in the world, built by
two of the 20th century's greatest bridge engineers. The Mackinac
Strait Bridge, which opened in November 1957 in Michigan, was the
crowning achievement of David B. Steinman. In New York the Verazzano-Narrows
Bridge, designed by Othmar Amman, was 10 years in the making and
finally opened in November 1964. Both of these monumental spans
directly benefited from the legacies of the failed 1940 and the
successful 1950 Tacoma Narrows Bridges.
Over the course of the last 60 years
since Galloping Gertie failed, bridge engineers have created suspension
bridges that are aerodynamically streamlined, or stiffened against
torsional motion, or both.
Now, wind tunnel testing for aerodynamic
effects on bridges is commonplace. In fact, the United States government
requires that all bridges built with federal funds must first have
their preliminary design subjected to wind tunnel analysis using
a 3-dimensional model.
Failure of the 1940 Tacoma Narrows Bridge
revealed for the first time limitations of the Deflection Theory. Since
the Tacoma disaster, aerodynamic stability analysis has come to supplement
the theory, but not replace it. The Deflection Theory remains an integral
part of suspension bridge engineering. Today, the theory's principles serve
as a model for the complex analytical methods (such as "Finite Element"
computer programs) used by structural engineers to calculate stresses in
the suspension cable system.
Since the 1990s, advances in computer
graphics technology and high-speed processing have enabled such
calculations to be performed on desktop computers. Today, engineers
recognize the importance of a thorough aerodynamic analysis of the
structures they design. Advanced modeling software programs assist
the complex calculations.
Why Did Galloping Gertie Collapse?
For over six decades, engineers have
studied the collapse of the 1940 Tacoma Narrows Bridge. The experts
disagree, at least on some aspects of the explanation. A definitive
description that meets unanimous agreement has not been reached.
The exact cause of the bridge's failure remains a mystery.
Why is it important to know the exact
cause of the 1940 bridge's collapse? Engineers need to know how
a new suspension bridge design will react to natural forces. The
more complete their understanding, the better their problem solving,
and thus, the stronger and safer their bridge. The fact that engineers
still argue about the precise cause of the Galloping Gertie's collapse
is testimony to the extraordinary complexity of natural phenomena.
Today, the 1940 Tacoma Narrows Bridge's failure continues to advance
the "scientific method."
The primary explanation of Galloping
Gertie's failure is described as "torsional flutter."
It will help to break this complicated series of events into several
stages.
Here is a summary of the key points in the explanation.
1. In general, the 1940 Narrows Bridge had relatively little
resistance to torsional (twisting) forces. That was because it
had such a large depth-to-width ratio, 1 to 72. Gertie's long,
narrow, and shallow stiffening girder made the structure extremely
flexible.
2. On the morning of November 7, 1940 shortly after 10 a.m.,
a critical event occurred. The cable band at mid-span on the north
cable slipped. This allowed the cable to separate into two unequal
segments. That contributed to the change from vertical (up-and-down)
to torsional (twisting) movement of the bridge deck.
3. Also contributing to the torsional motion of the bridge deck
was "vortex shedding." In brief, vortex shedding occurred
in the Narrows Bridge as follows:
(1) Wind separated as it struck the side of Galloping Gertie's
deck, the 8-foot solid plate girder. A small amount twisting
occurred in the bridge deck, because even steel is elastic and
changes form under high stress.
(2) The twisting bridge deck caused the wind flow separation
to increase. This formed a vortex, or swirling wind force, which
further lifted and twisted the deck.
(3) The deck structure resisted this lifting and twisting. It
had a natural tendency to return to its previous position. As
it returned, its speed and direction matched the lifting force.
In other words, it moved " in phase" with the vortex.
Then, the wind reinforced that motion. This produced a "lock-on"
event.
4. But, the external force of the wind alone was not sufficient
to cause the severe twisting that led the Narrows Bridge to fail.
5. Now the deck movement went into "torsional flutter."
"Torsional flutter" is a complex
mechanism. "Flutter" is a self-induced harmonic vibration
pattern. This instability can grow to very large vibrations.
Tacoma Narrows Failure Mechanism - original
sketch contributed by Allan Larsen
When the bridge movement changed from
vertical to torsional oscillation, the structure absorbed more wind
energy. The bridge deck's twisting motion began to control the wind
vortex so the two were synchronized. The structure's twisting movements
became self-generating. In other words, the forces acting on the
bridge were no longer caused by wind. The bridge deck's own motion
produced the forces. Engineers call this "self-excited"
motion.
It was critical that the two types of
instability, vortex shedding and torsional flutter, both occurred
at relatively low wind speeds. Usually, vortex shedding occurs at
relatively low wind speeds, like 25 to 35 mph, and torsional flutter
at high wind speeds, like 100 mph. Because of Gertie's design, and
relatively weak resistance to torsional forces, from the vortex
shedding instability the bridge went right into "torsional
flutter."
Now the bridge was beyond its natural ability
to "damp out" the motion. Once the twisting movements
began, they controlled the vortex forces. The torsional motion began
small and built upon its own self-induced energy.
In other words, Galloping Gertie's twisting
induced more twisting, then greater and greater twisting.
This increased beyond the bridge structure's
strength to resist. Failure resulted.
What if . . . ?
Sometimes it is fun and worthwhile to ask the question, "What
if . . . ?," about important historical events. Here's one
with an answer that may surprise you.
What if Clark Eldridge's original design for
the 1940 Tacoma Narrows Bridge had been built, instead of Leon Moisseiff's?
Would it have blown down on November 7, 1940 like Galloping Gertie?
Eldridge's design; elevation detail, May 23,
1938 WSA, WSDOT records
Answer: The bridge would still be there.
That's the opinion of leading bridge engineers who have carefully
studied Eldridge's design, with its 25-foot deep stiffening truss.
"I believe without a doubt," said one senior structural
engineer, "that the bridge would have been aerodynamically
stable for the wind speeds that destroyed Galloping Gertie."
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