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Suspension Bridges of Disbelief (hackaday.com)
152 points by szczys on Nov 19, 2015 | hide | past | web | favorite | 41 comments

This is a really well done piece.

Totally unrelated, but I've always been fascinated by suspension bridges. When I was 12 I built one out of Lego blocks with a road deck 5 feet long, using fishing line for the cabling. I couldn't get past a few feet at first, my towers would break in half. I glued the blocks. It helped, for a bit. Finally I realized that the cables shouldn't be affixed to the towers, that they should be draped over them and anchored at the ends.

Then I got my first knex set and learned how cantilevers work.

The idea of gluing Lego makes me feel really uneasy for some reason.

Great article, but the following line irked me a bit.

> played by Vancouver’s Lions Gate Bridge, the only non-iconic bridge on this list.

Vancouvers still the 3rd largest city in Canada and I think most Canadians would consider Lions Gate to be ionic in its own right. It's certainly a stunning location spanning across the Burrard Inlet into Stanley Park.

Anyways, it's not important enough to worry too much about.

The other bridges discussed are iconic throughout the world. Merely being iconic to most Canadians is not really in the same league.

Vancouver spends too much time in movies masquerading as an American city to ever be iconic.


With the current exchange rate we'll have another wave of movies pretending Canadian cities are American cities.

Shame, because aside from real estate prices, Vancouver is a jewel.

Nice video on the topic: https://vimeo.com/138807572

> The other bridges discussed are iconic throughout the world.

I don't think they are. The only iconic North American bridge is the Golden Gate Bridge — this is widely recognised.

Worldwide, I'd add Tower Bridge [1], but I'm struggling to think of another bridge that is so widely known that it's instantly recognizable by a significant number of people.

[1] If you don't the name and don't recognise it, then I'm probably wrong: http://cdn.rsvlts.com/wp-content/uploads/2012/12/Tower-Bridg...

Indeed, for me not being either from US or UK, Golden Gate and Tower Bridge are the only two iconic bridges I can think of. These I would recognize both by name and shape, anything else would probably be half a guess.

Perhaps the Brooklyn Bridge? https://en.wikipedia.org/wiki/Brooklyn_Bridge

If shown a picture yesterday, I wouldn't have been able to name it. I think I would have known it was in New York, but when I visited it wasn't one of the sights — unlike Tower Bridge and the Golden Gate Bridge. (Perhaps I don't watch enough American TV shows; it's the kind of thing that would be in the intro-credits showing the setting is NYC.)

I think it's like the Forth Bridge near Edinburgh or Charles Bridge in Prague. They're extremely well known nationally, and may well be tourist attractions, but would most people know about them before visiting the area?

Why is the shape of the cable a parabola and not a catenary? I've always been taught that the shape a cable makes hanging between two supports is a catenary. Isn't a suspension bridge the same thing?

The parabola is the equilibrium shape of a cable which is supporting an even load per unit horizontal distance. The catenary is the same for an even load per unit cable length.

As for why, it's been a few years since I had to derive this, but it goes something like this:

* The horizontal component of the force in the cable doesn't change along its length

* This leads to the fact that the extra vertical load picked up in the cable, per unit horizontal length as you approach the support, is proportional to the change in slope of the cable per unit length

* The change in slope is the second derivative of the cable height, and since it is a constant the cable shape is parabolic

Fun extra fact - the parabola is the equilibrium shape because the cable can resist tension but not bending. If you reverse the sign on all the equations then they still work, but your parabola is pointing away from the direction of gravity and you have only compression, no bending, in the material. That's why arch bridges are shaped like a parabola too.

Wikipedia says [0] it's "due to the weight of the roadway being much greater than that of the cable".

[0] - https://en.wikipedia.org/wiki/Catenary#Suspension_bridge_cur...

Yeah, catenary is the shape a cable makes when under its own weight, and with only its own tension holding it up.

If you hang a single 1lb weight in the middle of a clothes line, it forms very nearly a perfect V. That's because the 1lb totally dominates the 1/2 oz that the rest of the line weighs.

Right, but isn't the roadway's weight uniformly distributed along the length of the main cable?

Maybe a linear weight distribution favors the parabola, while a curved weight distribution (i.e. the cable's own weight when hanging free) causes the catenary? That makes sense to me, there's more weight per linear meter at the ends than in the center when considering just the cable's weight.

The reason for this is how the force distributions are applied.

A catenary forms when self weight is the driving force. In other words, when the weight per unit length of the cable is the same. For a bridge, the weight of the deck is much alrger than the cable. The weight of the deck is the same per unit horizontal length which is not the same as the unit length of the cable due to the curvature.

It's uniformly distributed along the length of the roadway. The arc length of the main cable between the suspension cable hanging points is greater near the towers where the slope of the main cable is steep, than closer to the center of the span.

My favorite lines:

The soldiers continue to battle Godzilla and the drivers motor across the bridge to safety, all oblivious to the physics errors that spared their lives.

and the parenthetical:

(I must note that the bridge featured in the movie’s climax is a cantilever bridge and therefore outside the scope of this article.)

This is really great. A couple of my favourite quotes so far:

"Most of the structural elements have no purpose, and bridges are instead supported by a mix of perplexing whimsy, directorial ignorance, and nothing."

"(Not that it really matters because apparently nothing matters, but the Golden Gate Bridge isn’t long enough to span the distance depicted even if the structural forces could be resolved.)"

Tangentially related. What caused cable-stayed bridges to so increase in prominence over the past few decades? I did some reading and they've become a popular choice for bridges and have advantages (e.g. not requiring really solid anchoring for the ends of the cable) but I haven't run across a good explanation about what made the design popular where it hadn't been before.

Does the increased use of pre-stressed concrete have anything to do with it?

T Y Lin discusses some neat aspects of bridge design that touch on this in his oral memoirs. [1]

IIRC, cable-stayed bridges have the advantage of being able to be cantilevered from the tower out during construction. Their disadvantage of compressive load on the deck goes nicely with prestressed concrete's strength.

The whole memoir is really good.

> Lin: This was all concrete. Except the cables. See, cable bridges are really prestressed concrete. To tighten the cables against the concrete, but put the cables outside; for ordinary beam, the cables are inside. When the bridge gets too long it is cheaper to put cables outside, so it s really a type of prestressed concrete bridge. They call it cable-stayed bridge. It's post-tensioned concrete. So, okay.

[1] https://archive.org/details/fatherprestressed00tylirich

Then the underlying reason would be price. Prestressed concrete can't compete with steel in strenght/weight ratio. But the strenght/price ratio makes it good choise for some budget designs.

There was a terror plot against the Brooklyn Bridge in 2002.[1] It didn't get that far, but the plan was feasible - to get inside the anchorage where the cable strands fan out to be individually anchored into concrete, and cut them one at a time, using gasoline-powered saws, until the cable failed.

Security had been tightened up, though. From 1985 to 2001, the anchorage was used for art exhibits, but that stopped after 9/11. The plotters gave up on that plan, since they would have needed hours or days of uninterrupted access.

[1] http://www.nyc.gov/html/nypd/html/pr/plots_targeting_nyc.sht...

Sounds like a suicide plot. Standing next to a steel cable that's holding up a bridge, and cutting it until it breaks? They'd probably have more success using thermite on the cables, though they'd need to smuggle lots and lots of it.

In the "I, Robot" movie there is a ruined suspension bridge that ignores physics. That was not the most serious problem with that film.

About a decade ago I was thinking about spider-man swinging down a NY Avenue, his web going from building on one side to a building on the other (you know the scenes I'm talking about), and I realized it just couldn't be. Pretty quickly he'd touch the ground. Gave a good explanation to my friends and half of them didn't get it, the other half thought I was wrong/stupid because of course you can swing down an avenue like spiderman. Now I got the itch to call these same friends and tell them about these bridges. Thanks!

Sounded like all of your friends didn't get it and I don't get it either, enlighten me!

My take is this - to maintain height he would have to switch sides on the upswing. If he's attached to the side of a building he would hit that building first before achieving any upswing.

(Unless of course the web is pulling him in. Possibly it contracts after it hits the buildings, or it reels in somedow)

You can turn forward momentum directly into upswing. So if he does switch at the low and high point of a swing, it might work. At low point he would shoot bit backwards, at high point bit forwards.

He doesn't need to maintain height, but energy.

The thing is, he doesnt swing in a straight line. he goes forward but also in a zig zag path, so the web would end up getting longer and longer each time.

Other than the silly gore that clip from Final Destination V was really an interesting portray of a suspension bridge coming apart. I would think it would come apart faster after watching other bridge accidents actually caught on video

What would actually happen in the pictured Dark Knight scenario where a relatively small part of the middle of the the bridge disappears? It seems like if the road deck is sufficiently rigid the vertical suspenders near the middle would realign and provide at least some of the tension force previously supplied by the removed suspension cable. Is there any reason why the bridge must fall?

It's not clear from the picture, but the article says

> Explosions sever the suspension cables and the road decks all at once

If the cables weren't severed, then it sounds reasonable to me that the rest of the bridge would stay up, although the outer parts would probably droop slightly as the cable in the middle lost some weight.

But if the explosions did actually sever the cables, then the article makes it pretty clear that the whole thing should have collapsed.

"Americans don’t build real bridges anymore, or maintain the ones that we have"

I can't speak for all bridges in general, but since the author takes the Golden Gate bridge as an example, I can tell you it's maintained. Many pieces have been replaced over the (past) 4 years I've crossed it, including structural pieces. Heck they even document some of it / how its done on the bridge itself...

They also re-built half the Bay bridge from scratch (other side of San Franciso). Granted, for this one the work-force was mainly Chinese (but a large part of it was still American).

So yeah, don't start off with false facts, specially if you have valid points afterwards, since I'd generally just stop reading at this point and figure you're just full of yourself throw stuff you think sound cool and can't be verified.

Also here's some REAL suspension bridge collapses... it's not so far off in some (obviously not all) movies...




The author partook in hyperbole (I thought it was obvious that it was hyperbole.. but heh), but was referencing stuff like this:



The first article really is a fairly sensationalized piece on bridge infrastructure failures. The headline bridge, the one on I-10, was "functionally obsolete" because the guardrails were of a design that wasn't up to what modern bridges would have. The scouring that occurred because flash flooding isn't completely predictable, and washes can and do occasionally try to change course.

The second bridge in the example was even worse. Someone died /demolishing/ a bridge. Unless I'm missing something, rebuilding a deficient bridge is kinda the opposite of neglecting infrastructure. Yes, there's an infrastructure problem, but the article in question just muddies the issue with near classic yellow journalism.

They are all off in the exact way the author describes. Those are in no way counter examples.

The scene he mentions from The Dark Knight Rises (the bridge is at the very end): https://www.youtube.com/watch?v=UsoYwysCdfY

Yeah. Hollywood proves that storytellers don't need to do research to be popular. Just watch any movie about hackers.

I think the same bridge problems also occur for the 1998 movie version of Godzilla. There, it gets stuck in the Brooklyn Bridge which refuses to collapse despite the cables being pulled out.

Suspending belief?

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