- In the early 1900s, there were two theories
for longspan suspension bridge design.
One was called the Elastic Theory, and the other
was called the Deflection Theory.
The Elastic Theory relied on deep decks,
so this deep deck, the stiffness of those decks
was relied upon for the stiffness of the bridge.
Typically, for Elastic Theory, the span-to-depth ratio
was less than 40.
Again, span being the difference between
the two towers and depth being the
depth of the deck, not the side D,
don't get confused with D.
I'm talking about span-to-depth, the depth of the deck.
So span-to-depth, less than 40 for Elastic Theory.
Deflection Theory led to these thin decks being designed.
And it relied not on the stiffness of the deck,
but it relied on the stiffness of the cables.
The Williamsburg Bridge, for example,
completed in 1903, was based on the Elastic Theory.
So this had a span-to-depth ratio of 40,
and you could see by an image of the Williamsburg Bridge
the very deep deck, that deep truss that was used.
The Manhattan Bridge, in 1909,
was based on the Deflection Theory.
So here, we have a span-to-depth ratio of 61.
So we went from 40 to 61, whereas that ratio,
the larger that ratio gets,
that means the thinner the deck gets.
The Bronx-Whitestone Bridge, completed in 1939,
this was a design by Othmar Ammann,
was also designed by the Deflection Theory,
and now we see a span-to-depth ratio of 210.
So we went from 40, from the Deflection Theory,
now to 210 in the Bronx-Whitestone Bridge.
Now, the Bronx-Whitestone Bridge, when completed,
it was seen to, let's say, dance a little bit.
It would go up and down,
fluctuate a little bit,
and there was a little bit of nervousness
by the people using this bridge.
Ammann kept saying the bridge was safe
and the bridge was safe.
Indeed, it was safe.
But this was an indication of things that were to come.
Let me tell you a little bit about Deflection Theory.
Deflection Theory is a complex mathematical theory.
I am not going to get into the mathematics of it,
but I will just tell you the basic philosophy behind it.
So the philosophy is that the heavier the span weight,
the span weight is related to Q x L.
Q is the load, the line load.
L is the span.
So the heavier that span weight,
the greater the cable tension.
Again, we could go back to the equation
H = QL squared over 8D.
So the larger QL, the larger the H is,
which means the larger the cable tension.
The larger the cable tension, the stiffer the span,
because now you have a larger cable.
So this is the stiffness of the top cable.
So the stiffer the span,
the less you have a need for a deck truss.
And then that results in the elegance of the thin deck.
So this is the philosophy, the thinking,
behind Deflection Theory, which is followed up by,
as I said, really complex mathematical formulations
that were being used in the 1930s
to design longspan bridges.
So now let's look at the effects of the wind,
the dynamic effects of the wind in particular,
and what they had on these longspan suspension bridges.
And in particular, the danger of this
dynamic effect of wind on these very thin decks
designed by Deflection Theory.
So I mentioned that the Bronx-Whitestone Bridge
was moving quite a bit when it was completed
in its design.
And that had to do with the effects
that the wind had on this bridge.
So from the scientific point of view,
let's look at the wind.
From the social point of view,
I'm going to talk a little bit about science
trumping history.
There was no much reliance on science,
and science had such prestige -
the Deflection Theory had great prestige -
that engineers and others forgot to go back
and look at history,
look at empirical data and evidence
of how longspan suspension bridges perfomed in the wind
in the past.
And from the symbolic point of view,
we're gonna look at the deck
and different forms for bridges as they came about,
as engineers and others learned about
these dynamic effects that the wind had on bridges.
So let's go back to the Bronx-Whitestone Bridge.
This had a span-to-depth ratio of 210.
And as I mentioned earlier, when it was completed,
it started to move a bit in the wind
and make people a little bit uncomfortable.
After 1940, some retrofits were made to this bridge.
For example, some cable stays were added,
and a very deep deck truss
was added to this bridge.
So, why this change? What happened?
What happened was the Tacoma Narrows.
So the Tacoma Narrows was completed in 1940,
and it spanned 2,800 feet.
The Bronx-Whitestone, completed only a year earlier,
had a similar span of 2,300 feet.
There're some differences, not only of span
between the bridges.
The Tacoma Narrows was a very narrow bridge,
so proportionately, it was different as well.
This also had a very thin deck.
It had a span-to-depth ratio of 350.
Remember, we started at span-to-depth ratios
of 40 with the Elastic Theory.
Deflection Theory was moving to thin decks,
and we see the extremity of that
with the Tacoma Narrows.
Now the Tacoma Narrows was also,
we could say, a dancing bridge
like the Bronx-Whitestone,
but it was far more dramatic than the Bronx-Whitestone.
It was said that actually, high school kids
would love to drive over this bridge
because it was like driving over a rollercoaster,
and they often would have to close it
because it was just moving too much.
Well, unfortunately, on one November day,
this bridge essentially twisted itself to death.
And there's famous footage,
it's all over the Internet.
I'll show you here in this course,
one of those videos that shows you
the Tacoma Narrows Bridge,
and how it collapsed.
This was on, I wouldn't call it a windy day.
The wind was on the order of 40 miles per hour,
so it wasn't a significant amount of wind.
We can't blame huge wind gusts or hurricane wind loads
to bring down this collapse.
I'll explain after you see the video footage
what happened.
(dramatic music)
- Dawn of a fatal day.
And the wind begins to speak with a roar
that no man can fail to hear.
(dramatic music)
In a 40-mile-an-hour gale,
the center span weaves like a ribbon
in the swinging cliffs that you wouldn't believe possible
unless you could see it, as you do now.
(dramatic music)
There's an automobile caught on the heaving roadway.
The 11,000-ton centerspan twists and springs
the giant cables that support it,
cables of 6300 wireframes, each 17 inches thick.
(dramatic music)
Back out of the danger zone,
all stricken spectators are driven to safety
as the bridge gyrates like a nightmare
high above the river,
twisting, turning, curling!
(dramatic music)
The lone motorist is forced to abandon the car.
He has but a few minutes in which to save himself.
Face to face with fate,
his destiny hanging in the balance.
Will he heed the last warning,
or perish with the doomed structure?
(dramatic music)
But he saved himself by seconds.
(dramatic music)
No structure of steel and concrete
can stand such a strain.
Steel girders buckle and giant cables snap
like puny flint.
There it goes!
(wind blowing)
Engineers are divided as to the cause of the disaster.
Some claim it was the use of solid girders.
Others differ.
But whatever the reason, Tacoma will rebuild,
this time, a bridge that will not provide
a super thrill in the news.
(dramatic music)
Many textbooks will tell you that
the Tacoma Narrows collapsed due to resonance,
resonance of the wind with the bridge,
but this is not true.
It wasn't resonance that brought down
the Tacoma Narrows Bridge,
it was something called self-excitation, or flutter.
So flutter is something you might see
if you see a flag on a flagpole
on a very windy day.
If the day is windy, you don't see the flag
flying straight.
The flag will flutter.
It will oscillate in a direction perpendicular to the wind,
back and forth.
So basically, there's a critical wind speed
at which that flag, and this bridge as well,
will start to oscillate in a direction
perpendicular to the wind in the direction
that it is blowing.
And that is indeed what happened
with the Tacoma Narrows Bridge.
So you see, this twisting motion,
it activated this torsional mode, or twisting mode,
of the bridge, and eventually, as you saw,
the bridge came down.
Now by this time in 1940, there were several bridges
designed with very thin decks.
Not only the Bronx-Whitestone,
but the Deer Isle Bridge in Maine,
a very thin deck.
The Golden Gate Bridge, that I will talk about soon,
also, very thin deck,
and was starting to experience some motions
due to wind.
So the question is,
how could this have happened with so much prestige?
This new science, Deflection Theory,
was so mathematically beautiful,
and soundproof, it semed.
How did this happen?
Well, basically, there was
no study of going to the past.
They had forgotten about the past.
And if you go to the past,
you would have seen empirical evidence of wind
producing vertical oscillations
on many suspension bridges,
and some of them leading to their collapse.
It didn't happen to the Brooklyn Bridge.
Remember that Roebling remembered the Wheeling Bridge,
how the Wheeling Bridge collapsed,
and he added stays to his bridges.
So the Brooklyn Bridge has stays,
and those stays, those diagonal steel wires
that connect the tower to the deck,
they are there to prevent those oscillations
of the deck due to wind.
But again, if you go back in history,
we can see several,
I'm listing eight of them, in history,
where we saw either collapse or damage
due to the effects of wind.
And these examples span from many years,
and also different lengths of bridges.
In the archival literature,
you will see sketches of bridges
that have been drawn in this collapsed mode.
So this has been observed,
this kind of collapse has been observed in the past.
We've studied the Menai Straits Bridge
with Telford.
Now, Menai did not collapse in the wind,
but it did suffer extensive damage due to wind.
So Telford knew about the effects of wind
on his longspan suspension bridges.
And there's other examples, like the Brighton Chain,
another example of a collapsed suspension bridge,
a historical study of that.
So now we have new designs for suspension bridges.
Engineers learned and studied these dynamics effects
that the wind has on these longspan bridges.
So the new Tacoma Narrows now has a very deep truss.
The Deer Isle Bridge now has stays to, again,
control those effects of the wind on the deck.
And the George Washington Bridge was always
safe against the wind.
It had four very heavy cables,
and it had a very wide deck.
But in 1962, a lower deck was added,
and then the form, the cross-section of the deck,
became a shape that would now be very
rigid from a twisting or torsional perspective.
Thin decks are still possible.
This Severn River Bridge, for example,
has air foils in it.
So these air foils essentially, you could say,
slice the wind.
So it interacts with the wind in such a way
that it doesn't pick up this fluttering reaction
of the wind.
So thin decks are still very possible
if you have air foils, or if you have the cross-section
that's in a closed loop,
like a rectangle shape.
Thse are very strong against torsional
movements due to wind-induced excitation.
And as I said earlier, the Brooklyn Bridge is safe.
It has those stays.
Stays are another way of preventing these movements
from the wind.
So Roebling's bridge will not be destroyed by wind,
but Hollywood loves to destroy the Brooklyn Bridge
and other great bridges.
It's just all over Hollywood, which makes me cringe,
not only because I'm a bridge lover,
but also because usually,
they get the anatomy of the collapse wrong.
So let's take a look at what Hollywood is doing
in one example.
So if we take a screenshot of the Batman movie,
Dark Night Rises, we see that the villain
has destroyed the Brooklyn Bridge
and Manhattan Bridge.
They have essentially sliced those bridges
right down the center.
So let's take a closer look at that idea
of slicing a suspension bridge right down the center.
So let's assume that a supervillain
has destroyed a bridge,
very similar to the Batman movie.
And he blows up the bridge
so that the deck and the cable,
the whole center section of that bridge is gone.
My question to you is, if this supervillain indeed
essentially chops this bridge in half,
what would happen to that bridge deck?
Would it be unaffected because it's suspended
from the cable?
Would it be unaffected because it's cantilevering
from the tower?
It's supported by the tower?
Will the bridge collapse, or do you
have no idea what will happen to this bridge?
So the answer is that the bridge will collapse.
And why is that?
It's because the deck is suspended
from the cables, essentially.
If the cable is no longer there,
there is nothing supporting that deck.
The deck is not supported by the towers.
So it goes deck to cable to tower.
So the bridge in this scenario would collapse,
in which case, in that still image
of the Batman movie I showed you,
Hollywood got it wrong.
There is no way that that still image would be real
in a real case.