Cable to be used for the suspension bridge

[NDO]

Homework Statement

The cable to be used for the suspension bridge can safely support a tension of 40 MN.
 Calculate the shortest length of the cable that can be used to construct the bridge.
 Calculate the corresponding value of h.
(Neglect the issue of safety factor).

L = 72

Homework Equations

I have no idea

The Attempt at a Solution

i have been trying to find any equation to find the sag or the length but i need the sag to get the length or i need the load to get the sag.

can anyone give me a point in the right direction

cheers Nathaniel

 

[LCKurtz]

A hanging cable is modeled by a catenary. You might find some helpful information by reading http://en.wikipedia.org/wiki/Catenary

 

[nvn]

NDO: We need to know how the cable is loaded. Have you omitted some information, or a diagram? Also, are the supports at each end of the cable at the same elevation?

From your current post, it almost sounds like the cable is loaded with a uniformly-distributed load w, is of negligible self weight, and both supports are at the same elevation, right? Or wrong?

 

[NDO]

Both supports are at the same height, and i am assuming the weight of the cable and it is a distributed load

here is a link to the photo
http://i908.photobucket.com/albums/ac286/NDO_02/bridge.gif

 

[PhanthomJay]

You have not yet indlcated the cable weight or the uniformly distributed load from the train load and deck. Cables hanging under their own weight form a catenary using the hyperbolic functions (which can be approximated by a parabola when the sag is much less than the span) . When cable weight can be neglected in comparison to the uniformly horizontally distributed dead and live loads, it takes on a parabolic shape. That probably doesn't help with your answer,though, until you come up with the correct relationship (equation) between Tension, Sag, loading, span length, etc., whether it's a catenary or a parabola.

 

[nvn]

NDO: With only the information you posted above, the problem has infinite solutions. You gave us only span length L, cable tension, and an unknown uniformly-distributed load w. Well, for any value you choose for cable length, s, greater than 72 m, there is a corresponding value of w that will cause exactly 40 MN of cable tension.

Therefore, I believe you may be omitting some information that we need to know to be able to solve the problem. Can you post an actual picture of the problem statement, so we can read exactly what it says?

 

[NDO]

click the link to see the q

http://i908.photobucket.com/albums/ac286/NDO_02/bridgetotalq.jpg

i think i had already givin all the info
i think i might have to leave it in terms of w

 

[nvn]

NDO: I agree. Assume the cable has a parabolic shape and is weightless, and probably use only the first two terms of the cable length (series) formula. Solve for cable length in terms of w. Then for part (b), solve for h in terms of w. Post your answers if you want someone to try to check your math.