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From: dino@euclid.colorado.edu (dino) Newsgroups: alt.folklore.urban Subject: The Tacoma Narrows Date: 28 Mar 1995 01:34:40 GMT Organization: University of Colorado, Boulder Lines: 200 Message-ID: 3l7p3g$nf3@lace.Colorado.EDU References: D6032C.p7@murdoch.acc.Virginia.EDU 95084.163652JSM158@psuvm.psu.edu 3l7bt6$fri@mozo.cc.purdue.edu NNTP-Posting-Host: euclid.colorado.edu

Collapsing bridges seem popular on AFU these days. We have…

branden@hillres22.cc.purdue.edu (Crash) writes:

Queenie (JSM158@psuvm.psu.edu) wrote:

<snip!>

: everything has a characteristic frequency at which it vibrates. When
: sound waves at that frequency are directed at the object, the waves
: merge with the vibrations of the object, intensifying them until the
: object is ripped apart - the principle used by singers to shatter

<snip!>

Yep, that's the 1940 Tacoma Narrows Bridge collapse in Washington state.
Standard fare for freshman-year mechanics courses at reputable science and
engineering-oriented colleges and universities. And your description is
pretty acuurate regarding the phenomena involved.

No it isn't. But I had wanted to knock this one off for a long time, and you gave me the opportunity, so don't feel like I am flaming you.

The following is abstracted from an article in _The American Journal of Physics_, 59 (2), February 1991, pp 118 – 124; the title of the article is:

Resonance, Tacoma Narrows bridge failure, and undergraduate physics
textbooks

From the article's abstract (*'s frame things in italics, all pytos mine):

The Tacoma Narrows bridge disaster of 1940 is still very much in the public
eye today. Notably, in many undergraduate physics texts the disaster is
presented as an example of *forced resonance* of a mechanical oscillator,
with the wind providing an external periodic frequency that matched the 
natural structural frequency. This oversimplified explanation has existed
in numerous texts for a long time and continues this day, with even more
detailed presentations in some new and updated texts. Engineers on the other
hand, have studied the phenomenon over the past half-century, and their
current understanding differs fundamentally from the viewpoint expressed
in most physics texts.  In the present article the engineers viewpoint is
expressed to the physics community ... substantial disagreement exists.
... one misleading identification of forced resonance arises from the
notion that the periodic natural vortex shedding of wind over the structure
was the source of the damaging external excitation. It is then demostrated
that the ultimate failure of the bridge was in fact related to an
aerodynamically induced condition of *self excitation* or "negative damping"
in a torsional degree of freedom. The aeroelastic phenomenon involved was
an *interactive* one in which developed wind forces were strongly linked
to structural motion. This paper emphasizes ... physically as well as
mathematically, *forced resonance* and *self-excitation* [my note: no
masturbation follow-ups, please] are fundamentally different phenomena.
The article closes with a quantitative assesment of the Tacoma Narrows
phenomenon that is in full agreement with the documented action of the
bridge itself in its final moments and a full, dynamically scaled model
of it studied in the 1950s.

(end of abstract)

Some comments from the article:

... Its failure  on November 7, 1940 attracted wide attention at the time
and has elicited recurring references ever since, notably in undergraduate
physics textbooks. ... The main issues in this instance are: What was the
exact nature of the wind-driven occurrences at Tacoma Narrows, and can they
be considered correctly to be cases of resonance? 

<comments on physics texts deleted>

These invoke inferences about the Tacoma Narrows episode that differ
from present engineering understanding of the failure. However, we also
point out below, areas of at least partial agreement. Our aim is to set the
record a bit straighter than it now appears to be -- at least as popularly
understood.

<more comments on physics texts deleted>

II. TEXTBOOK ACCOUNT
Typically, *resonance* is first presented qualitatively along these lines:
 
 In general, whenever a system capable of oscillation is acted upon by 
 a periodic series of impulses have frequency equal to one of the natural
 requencies of the system, the system is set into oscillations of 
 relatively large magnitude.

The article further comments on why the TN bridge episode was described as resonance, commenting on popular accounts in physics textbooks, in which the central span of the bridge resonated (now assumed) until said resonance became so great that it collapsed, and how the wind blowing over the surface and support cables of the TN bridge generated very large wave disturbances that destroyed the unfortunate bridge.

The article continues:

The final, catastrophic event at  Tacoma Narrows did, in fact, fit part of
the above qualitative defintition of resonance -- as we shall discuss --
*if* the more penetrating question of where the "periodic series of
impulses" came from is temporarily set aside, for it was indeed a single
torsional mode of the bridge that wa driven to destructive amplitude by the
wind, as will be discussed at a later point.

<comments on physics books and simple differential equations of oscillators deleted>

The article further comments that after this is told to physics students, an explanation follows, to effect,

  "The wind produced a fluctuating resultant froce in resonance with a
  natural frequency of the structure. This caused a steady increase in
  amplitude until the bridge was destroyed."

The article basically says that this is BS and too simple minded, that physics texts are vague about "just what the exciting force was" and this resulted in the necessary periodicity. Texts will say it was due to "gale winds," or "gusts of wind," et cetera. However, such do not have well-defined periodicity. Further:

Seeking such periodicity must lead to closer investigation of the
aerodynamics of bluff bodies ... The so-called *periodic vortex shedding"
effect is a first, very tempting, candidate to which to attribute the 
necessary periodicity.
Bluff bodies (such as bridge decks) in fluid streams do in fact shed
periodic vortex wakes, tripped off by body shape and viscosity, ...
which oscillate in consequence. ... Unfortunately, this explanation is
incorrect. We now know that this is *not* what occurred at Tacoma Narrows.

The article follows with a section on "Vortex-Induced Vibration," which deals with bluff (non-streamlined) bodies with flow over them and how said flow doesn't follow the contours of the body, breaking away at some points. In short, the article discards this as a cause of the TN's collapse, saying:

It has been now long since demonstarted that from the standpoint of
phenomenology, even such vortex-induced oscillations do not constitute a
case of simple resonance. ... Vortex-induced vibration is clearly not a
linear resonance even if the structure itself has linear properties, since
the exciting force amplitude *F* is a nonlinear function of the system
response.
IV. THE DESTRUCTIVE MECHANISM AT THE TACOMA NARROWS
... took place under a wholly different -- and catastrophic -- set of
circumstances. The wind speed at the time... was 42 mph, and the frequency
he observed for the final destructive oscillation was 12c/m or 0.2 Hz. At
42 mph, the natural frequency of vortex shedding ... be close to 1 Hz,
wholly *out of sync* with the actual... It can be concluded that natural
vortex shedding was *not* the cause of the collapse. This rules out one type
of periodic exciting force implied by a few of our references.

(comments on how engineers want to design bridges that won't collapse in the wind deleted)

The article further comments on how the destruction was duplicated in a scale model bridge built by one Scruton. The physics starts to get involved, and they conclude that the collapse was due to "single-degree-of-freedom torsional flutter" due to "complex, separated flow." In short, the article does conclude:

... if we now identify the source of the periodic impulses as *self-induced*,
the wind supplying the power, and the motion supplying the power-tapping
mechanism. If one wishes to argue, however, that it was a case of
*externally forced linear resonance*, the mathematical distinction between
Eqs. (1) and (3) is quite clear, self-exciting [my note: again, no follow-ups
about masturbation] systems differing strongly from ordinary linear
resonant ones. The texts that we have consulted have not gone this far in
explanation.

It also comments:

We note that numerous instructional texts in mathematics [68-76] allude
to the Tacoma Narrows incident, and most of these, too, could be made
more precise and insightful in the light of the current analysis of the
problem.

They even have some borderline UL-related comments in Closing Remarks:

The Tacoma Narrows incident will remain a celebrated example because of
its spectacular nature and the freak recording of this disaster by
witnessing photographers. The sensational photographs have made it into
an irresistable pedagogical example -- and indeed, much is to be learned
from it. Because it lodges itself so in the memory, it is doubly important
for educators to draw correct lessons from this classic and sensational
event. While it is understandable how so many textbooks have, over the
years, oversimplified the physics involved, it is probably time -- given
the advanced state of the knowledge -- to offer the next generation
of subtler, more complex, and *correct* explanations.

<rest deleted>

OK, I am a math geek, not a physics geek, and glossed over most of the physics myself. However… we may conclude (and a search of the FAQ and cathouse revealed nothing):

F. The Tacoma Narrows bridge collapsed due to simple resonance.

T. It wasn't so simple.

dino "will destroy bridges for food" m.

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