Calculations for Tent Poles

Since it is a design project my basic assumptions for pole loading caluclations would be as follows

No side loading on the poles.
Fabric failure at stress consentrations.
Failure in the poles are evaluated by two methods. Point loading at the top of the arch and point loading at the end of a pole causing bending. Which ever one produces the lower force would be set to govern the maximum loadings.

If you have a six pole dome design crossing in the center you could assume that the full wind load (wind pressure applied to 2 of the 6 panels) would be applied to one pole. Now this isn't what happens in the real world but it would at least give you some calculations that you could get answers from.

Another method might be to assume fixed points at all guy lines and no deflection of the general tent structure from wind loading. Then your wind problem just disappears but you would have to start looking at the strength of your stakes in the ground and determine a proper length of stake in a given soil type to prevent it from pulling out. And for your pole design just factor in snow loading and bending stress from forcing the pole into its arch shape.

The general problem in this question is that you don't know the displaced shape under wind load or the flexibility of the entire structure put together. And with out the displacement values you can't really compute the stress. You need to solve the [F]=[k][x] equation and right now you have two unkowns. So at least using the above method with well stated assumptions you would get an answer.

The MHW Space Station is 3m tall, and uses 13mm poles. It uses 11 of them, though…

(A friend of mine has one, bought at a car boot sale for a tiny fraction of the RRP. I remembered the poles being a ‘reasonable size’, but had to look up just what size they were. It’s not exactly backpackinglight, although someone did work out that, shared over the 15 occupants, it’s only 1.4kg each…)

;-)

> the constitutive properties are needed. Do you know of a source?
As far as I know, the data does not exist. it is not part of standard fabric testing, which is mainly concerned with tear strength etc – failure modes. Elasticity is not part of that. Note that elasticity will almost be a tensor.

Cheers

> We are following design guidelines set by the UN for emergency shelters.
Set by a committee – right.
You haven't specified the alloy. 1000? 6061? 7075 T9? These have VERY different properties!!!!!
Try 16 mm x 1 mm with a 7001 alloy as a start.

Cheers

Roger. No question a tensor. Can't model it using FEA without it. Thanks.

We've chosen 7075-T6 for its high strength. Information on certain properties of T9 were not readily available.

> We've chosen 7075-T6 for its high strength.
Nice metal, but have you checked for availability in tubing? Not easy. Guess that does not matter for an assignment.

> Information on certain properties of T9 were not readily available.
That's because the T9 grade is not officially recognised by the standards committees or whatever. Basically, 'T9' means 'harder than T8'. How to temper to T9 is known only to Easton. But it's real, and good stuff.

Cheers

"If you can estimate your additional loads (due to snow or wind or whatever) you can add that to your preload to get the total load on the poles."

Ben – is there a straightforward way to add these additional snow/wind loads to the beam equation?
I think i've determined the load values (in kN/m) for each arch but i'm not sure how to combine this with the pre-load or how to determine the moment along the arch so that I can determine the stress at these points.

"is there a straightforward way to add these additional snow/wind loads to the beam equation?"

The pertinent equations are: V = dM/dx (V is shear force), and -w = dV/dx (w is the distributed load).

So my idea is solve for the local moment (M) for the unloaded tent using the beam equation (1st equation in my write-up). You are solving numerically for the curvature (the right hand side of the beam equation), so now you will have a bunch of M values for each node. Numerically differentiate that for shear force at each node, then numerically differentiate shear force for the distributed load. Then add the the external loading (snow, wind, etc) and reverse the calculation. Since you are doing a lot of numerical differentiation you want to make sure you use plenty of data points.

Does that make sense?

Yes, this makes sense. I'll give it a try. Do you have any suggestions on how to relate the stresses in the rods to the induced stresses in the fabric? Or to determine how the fabric sags based on the loading conditions?

well the forces that you calculate on the tent pole are put there by the fabric…. but how to analyze the fabric that is a bit beyond me. It seems like a pretty 3-d problem plus the effects of gravity are important. FEA is probably the only way to solve a problem like that. Plus material properties of fabrics can be tough to come by.

BTW let me know how your project comes out.