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Re: Flexure vs. Cable Action in a solid rod.

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Michael Gregory wrote:

Any help? Is there someone or some other reference that I can turn to? I have searched the internet and have not turned up any good leads. Is there any software available that will analyze a catenary shaped member? Are there any references, research papers or other documents that indicates at what point a solid element may begin to behave as a cable? Thanks!!
There's a whole chapter in Timoshenko's Strength of Materials volume 2 about beams with combined axial and lateral loads. The answer to your question depends on the boundary conditions. If you assume rigid spanwise support, axial loading starts to develop whenever the rod has any deflection at all. That's because the length of the deflection curve is longer than the original straight line between the posts. Timoshenko shows how to calculate the corresponding axial load and superpose the direct and axial stresses. You can compare the stress from the direct load to that for transverse loading only to see where one or the other dominates. There's always some contribution from direct loading but you can assume the boundary between the two behaviors as the point where the difference is less than usual engineering accuracy--probably about 5%.

It's trickier when you have elastic supports like stanchions supporting the rods because they also deflect under load which reduces the axial load on the rod. but you can figure this out pretty easily by hand. If you have multiple spans all the rods have full axial support, except for the ones at each of the ends of the rail where the stanchions can deflect inward unless they're pretty well braced.

This effect is fairly easy to figure manually, but if your EOR is an old shell-back who believes you can analyze the world by assuming it's a cantilever beam, your work is cut out for you. Just make sure you've designed your connections to account for the full direct loading and the beam reactions both, and that you've taken steps to assure that you've eliminated any local yielding that might make the rod sag or the connections loosen. Anyone old enough to remember the coated wire clothes lines and how they'd sag. You'd tighten the wires up and put a little pre-tension so they were nice and straight, and the next couple of laundry loads and a nice breeze would have them sagging again because the wires stretched. Even after a detailed explanation of all that, my mother was singularly unimpressed -- what good was engineering college if she'd have to use clothes poles all he life.


Christopher Wright P.E. |"They couldn't hit an elephant at
chrisw(--nospam--at)skypoint.com   | this distance" (last words of Gen.
.......................................| John Sedgwick, Spotsylvania 1864)
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