Catenary mesh supported on 3 sides 1

[Lion06]

does anyone know where I can find an equation for horizontal tension reactions for a wire mesh used as a catenary and only supported on 3 sides? I have looked in Roark and can't seem to find anything. I have very limited experience with that book, so I may be looking in teh wrong place.
Any suggestions bould be greatly appreciated.
I have also tried modelling this in RAM Advanse, inputting 0.0000000001 for the Ig of a bending member trying to get it to act as a catenary, but that is not working.

 

[csd72]

StructEIT,

I would model this as supported on two sides as this is how it will actally behave at the unsupported end.

You will actually get diagonal catenaries at the supported end corners (where this is shorter than ther main span). There will be no minor span catenaries as you need two horizontal reactions.

Hope this helps.

csd

 

[Lion06]

I thought about that, but the mesh continues past the support that provides no horizontal reaction so I figured there would be some benefit of that "bearing" only resistance. I wouldn't care about that nuance except that it won't work analyzed as a simple catenary supported on two sides.
This is already in place, so I can't really specify anything different, I am just trying to make the numbers work.

 

[csd72]

Is is a multiple span catenary, is that what you are trying to say?

 

[Lion06]

sort of, but not exactly. The mesh has support on 3 sides. The mesh continues past the 4th side but still doesn't have support at its end. The mesh from the 3rd side spanning to the unsupported edge still seems like it has some support since it goes about 3.5' past the support it is not connected to and is "woven" with the wires spanning the other direction (with supports on both sides).
This is really quite a nightmare to analyze. I initially said that I thought it should be checked as spanning one direction only, but my boss thinks it is getting support from bearing against the 4th side (even though it isn't connected), but I can't find any kind of formula that approximates this.

 

[csd72]

I dont think the fourth side will do anything.

I would design it as one way.

 

[rb1957]

is "RAM Advanse" a non-linear code ?

of course the approach being suggested should be hand calc, no?

 

[Lion06]

rb-
RAM Advanse will apparently not do catenary action. It tells me that my deflections are very large (actually gives me a warning), but gives no reaction parallel to the member.
I can use Roark for a single catenary.

 

[271828]

StrlEIT, I've tried to use typical analysis programs for these problems before and have yet to find one that will work. I've tried RISA, STAAD, and SAP. SAP probably will do this, but I couldn't figure out how, with the correct pretension, etc. You're probably best off doing some kind of manual calc.

These programs fail because of the type of second-order analysis that's used. They use geometric stiffness matrices to account for second-order effects. That won't work for something like a cable. The program must literally move the nodes and do something like Newton-rhapson (sorry if I mis-spelled that) iteration with the tangent stiffness.

 

[Lion06]

Thanks all,
I have one more question. I am looking at Roark page 245 (7th edition), case 6. I am assuming that the P value is the horizontal reaction only and I need to combine that with the vertical reaction to get a resultant reaction.
Can anyone confirm this?

 

[csd72]

Yes, it is the horizontal reaction only. The vertical reaction is the same as for a beam (wl/2).

csd

 

[miecz]

My old Mechanics of Materials book references a Report by W. Ramberg, A.E. Macpherson, and S.Levy titled "Report 748, National Advisory Commitee for Aeronautics, 1942. The book says that the reference contains curves for rectangular plates with large deflections and direct stress.

 

[rb1957]

naca reports are downloadable from the NASA website ...

 

[NITTANYRAY]

If you can locate an old ACI 318-63 code they have moment coefficients for slabs supported on three sides.
If you know your initial mesh drape you can solve for the tensile force using the basic cable equation:
Moment = H*d = w*L*L/8
where:
H is the horizontal force at the support
d is the drape height
w is the uniform load on the mesh

 

[prex]

StructuralEIT,
in the first site below you find a freshly added sheet for calculating a plate in pure membrane behaviour with support on three sides (look under Plates -> Membranes -> Rectangular -> 3 held sides).
This shouldn't be far from your problem, as the influence of shear, that's absent in a mesh, is not very important (and of course should be Poisson=0): it is also possible to derive a sheet with no shear contribution, if you are interested.
Would like to receive your comments upon, if you are still interested.

prex

http://www.xcalcs.com

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