h a l f b a k e r yWhy not imagine it in a way that works?
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The deck is kept under very, very high tension between anchorages on each river bank, so no supports required in between. Really a very flat suspension bridge but with the tension so high it doesn't need a stiffening girder.
Various Bridge Sims
http://www.chroniclogic.com/
Chronic Logic produced some awesome bridge-building/simulation games - seriously worth a look. [zen_tom, Aug 16 2007]
Amusing property of a catenary
http://www.sunsite....ation/catenary.html
[Ling, Aug 17 2007]
Another interesting catenary trick
http://web.njit.edu.../pastimes/catenary/
[Ling, Aug 17 2007]
[link]
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Do we own stock in the unobtanium mines, Mr. Mudd? |
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Like that one over the Thames near that museum. It bounced and made people feel ill so they spent ages trying to fix it. |
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We do, Mr Caeli, we do. We also live next to the River of Disturbing Dreams and the Peak of Unattainable Aspirations. It's nice. |
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I think it is actually not possible to pull a cable tight enough so that it experiences no droop(albeit the droop can be made quite small) There are bridges that use a tensioned cable to maintain the shape of the road deck that would otherwise droop(the deck is in compression the cable in Tension) Pre-stressed concrete bridges use compression to offset the tension. In all situations you have a dynamic interplay between tension and compression to keep the bridge in place. |
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So this is just the swinging bridge from every jungle movie ever made, made heavier and pulled up a lot tighter? |
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[Baconbrain] It's called a Burma rope bridge. |
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The primary difficulty with a purely-tension bridge is that the required level of tension will be proportional to the load times the ratio between the span between support points and the height difference between the support points and the midpoint of the bridge. If a bridge had to connect tunnels on either side of a chasm, said tunnels emerging a considerable distance below the clifftops above, the most practical method of construction could be to build anchors on the clifftops and hang support cables between them; the navigable part of the bridge could be flat and level using such an approach. |
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Generally, though, it's better to build a suspension bridge using a pair of support columns that are as close together as practical; the taller the columns are, the less tension will be required (but the more material will be required for the towers themselves). In many suspension bridges, the only parts of the bridge under significant compression are the pilings and the tops of the anchors. Most such bridges have stiffening trusses, parts of which will be under intermittent compression, but the loads on such trusses are comparatively minor. Some bridges like the Brooklyn Bridge use diagonal cable stays rather than stiffening trusses; I would expect newer bridges use trusses rather than cable strays because they're cheaper. |
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There is no level of tension sufficient to sway-proof a bridge without using cable stays or other means of stiffening. |
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This would be better if it could be under a little bit more tension. |
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If the bridge could be built from a piece of iron which was longer than the gap that it crossed, the iron would bulge upwards in the middle. The bulge quantity would be gauged to perfectly match expected droop, thus cancelling out and producing a perfectly straight bridge. |
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[Bungston] No. No no very no. As soon
as you adjusted things so that the
bridge was just level, it would go
"badoing" and pop itself into an
inverted arch shape. |
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Try it. Take a plastic ruler horizontally
between your palms; push inward so it
starts to bulge upward. Then add a
downward load by pushing it down with
your chin. If you keep pushing hard
inward, and then also push down just
enough to flatten the ruler, it'll flip into
a downward bow. It may or may not
make the badoing noise. |
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[Bung]; that's a pretty clever idea, however as [Max] says, it will simply turn over if you allow it to get anywhere near level. The problem is a "piece of iron" or perhaps even steel (let's pretend we're somehwere past 1800, eh?) will have massive self-weight. Think about it, even on a scale. practically no tensioned structures are made out of solid metal, simply for weight reasons. Engineers hundreds of years ago worked out that trussed structures can have a better strength:weight ratio. |
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Essentially what you are suggesting is analogous to pre-tensioning structures, which is pretty much standard practice nowadays anyhow. |
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//It's called a Burma rope bridge.// Oh, thanks. I've only been on them in Missouri and in Mexico. |
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Here's a fun trick: Fasten a chain tightly between a heavy truck and an immovable object. Make it good and taut. Now, grab the middle of the chain and pull sideways, so as to bend the chain. The truck will move--a little. That's basic physics. |
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Now, replace the chain with a bridge deck under very, very high tension, and replace the pull of your hand with the weight of a very large truck. One end of the bridge will move--a little. And it will all fall down in a twanging heap. That's basic physics. |
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The truck will not move, not even a nanometer. The material in the rope will expand. |
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Sorry, [global], I was changing that rope to chain whilst you wrote. (It seems that a chain would stretch less.) I have bent the bed of a pickup with this rig. |
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Where did you find an immovable object? |
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The thing is, I have an irresistable force I'd like to introduce it to to see what would happen... |
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/ Where did you find an immovable object? / |
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It was in the back of my station wagon. Turns out that's why my mileage was so bad. |
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Sorry, in my example above, I forgot about the time I got a pickup truck out of the mud, by myself, using a rope. I got the rope between the bumper and a handy fencepost, pulled the rope tight using a trucker's hitch, then jumped on the middle of the rope. The truck moved a few inches. I tightened the rope again, jumped again, and got a few more inches. On my third jump, the fencepost snapped off (it wasn't immovable), but I had a stump left to tie to, so I kept going, and got it done. |
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The relationship between the tension of a rope and the flatness of the catenary curve is probably an asymptotic function. I mean, you can't get it straighter than straight, so the force has to climb to the infinite. |
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I can't draw the vectors here, but I do know that in hoisting, a spreader bar will compress and collapse if the angle of the harness is too flat. A tension bridge is the converse, perhaps, but it will go boom. |
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This is one of those ideas that seems new and different. But that's only because to people who build bridges it is so obviously wrong that they don't even consider it. |
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If it is loosened up enough to be buildable, it is really just a Burma rope bridge. So what's new about it? "Burma rope bridge, really tight."? |
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baconbrain: The relationship between sag and tension is indeed nasty as things get flat. Overhead trolley (tram) wires and suspension bridges show a solution, though: have the main cable sag significantly at the bottom, but then use cables of various lengths to tie that to the object one wishes to be horizontal. This will yield a much more stable structure than simply trying to pull a cable tight. |
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Which is what the proposed idea wishes to avoid. But can't. |
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BTW, I once read a VERY long mathematical explanation of why a suspension cable changes its curve from a catenary to a parabola during bridge construction. It's a lot simpler to just think of the bridge as a graph of a thrown ball. But either way, the posted idea cannot work. |
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The explanation for the curve change is very simple: when the cable is only supporting itself, it has roughly the same weight per lineal foot over its entire length. When it is supporting a bridge, the portions near the middle support less weight per lineal foot than those nearer the edges (at the center, each foot of cable supports a foot of bridge; if the slope at the edge is 1, then each foot of cable only supports about 0.7 feet of bridge.) |
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