From: dino@euclid.colorado.edu (dino)
\nNewsgroups: alt.folklore.urban
\nSubject: The Tacoma Narrows
\nDate: 28 Mar 1995 01:34:40 GMT
\nOrganization: University of Colorado, Boulder
\nLines: 200
\nMessage-ID:
\nReferences:
\nNNTP-Posting-Host: euclid.colorado.edu<\/p>\n
Collapsing bridges seem popular on AFU these days. We have…<\/p>\n
branden@hillres22.cc.purdue.edu (Crash) writes:
\n>Queenie (JSM158@psuvm.psu.edu) wrote:<\/p>\n
>: everything has a characteristic frequency at which it vibrates. When
\n>: sound waves at that frequency are directed at the object, the waves
\n>: merge with the vibrations of the object, intensifying them until the
\n>: object is ripped apart – the principle used by singers to shatter<\/p>\n
>Yep, that’s the 1940 Tacoma Narrows Bridge collapse in Washington state.
\n>Standard fare for freshman-year mechanics courses at reputable science and
\n>engineering-oriented colleges and universities. And your description is
\n>pretty acuurate regarding the phenomena involved.<\/p>\n
—<\/p>\n
No it isn’t. But I had wanted to knock this one off for a long time, and
\nyou gave me the opportunity, so don’t feel like I am flaming you.<\/p>\n
The following is abstracted from an article in _The American Journal of
\nPhysics_, 59 (2), February 1991, pp 118 — 124; the title of the article is:<\/p>\n
Resonance, Tacoma Narrows bridge failure, and undergraduate physics
\n textbooks<\/p>\n
From the article’s abstract (*’s frame things in italics, all pytos mine):<\/p>\n
The Tacoma Narrows bridge disaster of 1940 is still very much in the public
\n eye today. Notably, in many undergraduate physics texts the disaster is
\n presented as an example of *forced resonance* of a mechanical oscillator,
\n with the wind providing an external periodic frequency that matched the
\n natural structural frequency. This oversimplified explanation has existed
\n in numerous texts for a long time and continues this day, with even more
\n detailed presentations in some new and updated texts. Engineers on the other
\n hand, have studied the phenomenon over the past half-century, and their
\n current understanding differs fundamentally from the viewpoint expressed
\n in most physics texts. In the present article the engineers viewpoint is
\n expressed to the physics community … substantial disagreement exists.
\n … one misleading identification of forced resonance arises from the
\n notion that the periodic natural vortex shedding of wind over the structure
\n was the source of the damaging external excitation. It is then demostrated
\n that the ultimate failure of the bridge was in fact related to an
\n aerodynamically induced condition of *self excitation* or “negative damping”
\n in a torsional degree of freedom. The aeroelastic phenomenon involved was
\n an *interactive* one in which developed wind forces were strongly linked
\n to structural motion. This paper emphasizes … physically as well as
\n mathematically, *forced resonance* and *self-excitation* [my note: no
\n masturbation follow-ups, please] are fundamentally different phenomena.
\n The article closes with a quantitative assesment of the Tacoma Narrows
\n phenomenon that is in full agreement with the documented action of the
\n bridge itself in its final moments and a full, dynamically scaled model
\n of it studied in the 1950s.<\/p>\n
(end of abstract)<\/p>\n
Some comments from the article: <\/p>\n
… Its failure on November 7, 1940 attracted wide attention at the time
\n and has elicited recurring references ever since, notably in undergraduate
\n physics textbooks. … The main issues in this instance are: What was the
\n exact nature of the wind-driven occurrences at Tacoma Narrows, and can they
\n be considered correctly to be cases of resonance? <\/p>\n
These invoke inferences about the Tacoma Narrows episode that differ
\n from present engineering understanding of the failure. However, we also
\n point out below, areas of at least partial agreement. Our aim is to set the
\n record a bit straighter than it now appears to be — at least as popularly
\n understood.<\/p>\n
II. TEXTBOOK ACCOUNT<\/p>\n
Typically, *resonance* is first presented qualitatively along these lines:<\/p>\n
In general, whenever a system capable of oscillation is acted upon by
\n a periodic series of impulses have frequency equal to one of the natural
\n requencies of the system, the system is set into oscillations of
\n relatively large magnitude.<\/p>\n
The article further comments on why the TN bridge episode was described as
\nresonance, commenting on popular accounts in physics textbooks, in which
\nthe central span of the bridge resonated (now assumed) until said resonance
\nbecame so great that it collapsed, and how the wind blowing over the surface
\nand support cables of the TN bridge generated very large wave disturbances
\nthat destroyed the unfortunate bridge.<\/p>\n
The article continues:<\/p>\n
The final, catastrophic event at Tacoma Narrows did, in fact, fit part of
\n the above qualitative defintition of resonance — as we shall discuss —
\n *if* the more penetrating question of where the “periodic series of
\n impulses” came from is temporarily set aside, for it was indeed a single
\n torsional mode of the bridge that wa driven to destructive amplitude by the
\n wind, as will be discussed at a later point.<\/p>\n
The article further comments that after this is told to physics students,
\nan explanation follows, to effect, <\/p>\n
“The wind produced a fluctuating resultant froce in resonance with a
\n natural frequency of the structure. This caused a steady increase in
\n amplitude until the bridge was destroyed.”<\/p>\n
The article basically says that this is BS and too simple minded, that
\nphysics texts are vague about “just what the exciting force was” and this
\nresulted in the necessary periodicity. Texts will say it was due to “gale
\nwinds,” or “gusts of wind,” et cetera. However, such do not have well-defined
\nperiodicity. Further:<\/p>\n
Seeking such periodicity must lead to closer investigation of the
\n aerodynamics of bluff bodies … The so-called *periodic vortex shedding”
\n effect is a first, very tempting, candidate to which to attribute the
\n necessary periodicity.<\/p>\n
Bluff bodies (such as bridge decks) in fluid streams do in fact shed
\n periodic vortex wakes, tripped off by body shape and viscosity, …
\n which oscillate in consequence. … Unfortunately, this explanation is
\n incorrect. We now know that this is *not* what occurred at Tacoma Narrows.<\/p>\n
The article follows with a section on “Vortex-Induced Vibration,” which
\ndeals with bluff (non-streamlined) bodies with flow over them and how said
\nflow doesn’t follow the contours of the body, breaking away at some points.
\nIn short, the article discards this as a cause of the TN’s collapse, saying:<\/p>\n
It has been now long since demonstarted that from the standpoint of
\n phenomenology, even such vortex-induced oscillations do not constitute a
\n case of simple resonance. … Vortex-induced vibration is clearly not a
\n linear resonance even if the structure itself has linear properties, since
\n the exciting force amplitude *F* is a nonlinear function of the system
\n response.<\/p>\n
IV. THE DESTRUCTIVE MECHANISM AT THE TACOMA NARROWS<\/p>\n
… took place under a wholly different — and catastrophic — set of
\n circumstances. The wind speed at the time… was 42 mph, and the frequency
\n he observed for the final destructive oscillation was 12c\/m or 0.2 Hz. At
\n 42 mph, the natural frequency of vortex shedding … be close to 1 Hz,
\n wholly *out of sync* with the actual… It can be concluded that natural
\n vortex shedding was *not* the cause of the collapse. This rules out one type
\n of periodic exciting force implied by a few of our references.<\/p>\n
(comments on how engineers want to design bridges that won’t collapse in the
\n wind deleted)<\/p>\n
The article further comments on how the destruction was duplicated in a scale
\nmodel bridge built by one Scruton. The physics starts to get involved, and
\nthey conclude that the collapse was due to “single-degree-of-freedom torsional
\nflutter” due to “complex, separated flow.” In short, the article does conclude:<\/p>\n
… if we now identify the source of the periodic impulses as *self-induced*,
\n the wind supplying the power, and the motion supplying the power-tapping
\n mechanism. If one wishes to argue, however, that it was a case of
\n *externally forced linear resonance*, the mathematical distinction between
\n Eqs. (1) and (3) is quite clear, self-exciting [my note: again, no follow-ups
\n about masturbation] systems differing strongly from ordinary linear
\n resonant ones. The texts that we have consulted have not gone this far in
\n explanation.<\/p>\n
It also comments:<\/p>\n
We note that numerous instructional texts in mathematics [68-76] allude
\n to the Tacoma Narrows incident, and most of these, too, could be made
\n more precise and insightful in the light of the current analysis of the
\n problem.<\/p>\n
They even have some borderline UL-related comments in Closing Remarks:<\/p>\n
The Tacoma Narrows incident will remain a celebrated example because of
\n its spectacular nature and the freak recording of this disaster by
\n witnessing photographers. The sensational photographs have made it into
\n an irresistable pedagogical example — and indeed, much is to be learned
\n from it. Because it lodges itself so in the memory, it is doubly important
\n for educators to draw correct lessons from this classic and sensational
\n event. While it is understandable how so many textbooks have, over the
\n years, oversimplified the physics involved, it is probably time — given
\n the advanced state of the knowledge — to offer the next generation
\n of subtler, more complex, and *correct* explanations.<\/p>\n
OK, I am a math geek, not a physics geek, and glossed over most of the
\nphysics myself. However… we may conclude (and a search of the FAQ and
\ncathouse revealed nothing):<\/p>\n
F. The Tacoma Narrows bridge collapsed due to simple resonance.<\/p>\n
T. It wasn’t so simple.<\/p>\n
dino “will destroy bridges for food” m.<\/p>\n
