# Pipe held up by a chain

I've got a question that I've been struggling with for a while...
I've got a pipe held up by a chain. Picture a pipe bent into an arch,
held up by a chain suspended below. I've put a gif of this on my
website:
. Periodically, there are
struts from the pipe to the chain that hold the shape together and hold
the pipe above the chain. The entire structure is supported vertically
only, so the ends are free to move.
I've done the analysis using both a catenary and a parabola; the results
are essentially the same for both.
I am unclear as to the end conditions. The pipe arch is flatter than
the chain, so the horizontal reactions are greater than the chain. I
figure that some of the horizontal reactions go into raising the pipe,
thus reducing the stress in the chain and increasing bending moment on
the pipe....
Direct measurements indicate that the tension in the chain is about 1/3
of that predicted by a parabola/catenary, and I am at a loss to explain
this amount of discrepancy....
Any thoughts, discussion, suggestions?
If the tensile load is less than you expected, then the compression load on the pipework is ipso facto, greater than you expected. You are not sketching the struts or diagonals that connect the upper and lower parts of this structure which may be called a girder.
At least if you think "girder" you will not be expecting so much (or any?) horizontal reactions.
Regards
Brian Whatcott
If the end are not fixed horizontally, the horizontal components from the arch and the chain must be identical, for static equilibrium. There can be no 'shedding' from one to the other.
Assuming normal sizes for components of this type, the mass of the chain will be very much less than that of the arch (and vertical struts, and any load that may be in the arched pipe) and hence the chain will hang very nearly as a series of straight links, rather than as a catenary or parabola.
The problem is far from trivial, as it is highly redundant (assuming reasonable stiffness and strength of the pipe arch). If you have acces to an FE solution method, this might be the easiest approach to use! 8-) Might be worth turning the problem upside down, and assume that a pipe arch is being used to stress a chain through vertical struts.
Keith Civil Solutions
Yup, thanks. I finally figured that one out.... One of those really dumb*ss oversights.... (Heck, I got numbers from the computer, it must be right...)
As near as we can measure, the connection points where the chain meets the struts lie on a catenary / parabola. The links are straight, but the overall geometry is that of a hanging chain.
We're also doing FE analysis as well as empirical design.... This is so we can start with some realistic geometries to feed the welders and the FE guys.... A reality check on all the other stuff.
Thanks again.

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