For your wind loads I am not sure if over stressing your poles and causing them to break or permenantly deform will be your method of failure. Your fabric ripping at stress concentrations may be the real point of failue.

For wind loading if you have access to the ASCE #7 code you can take a look at how it handles wind or EN 2005.

To calculate your wind pressure just use P =1/2pV^2 where p is the air density. I would then apply a load factor of 2 to account for dynamic effects. The load factor of 2 is not an item from any code but does have some mathematical basis.

Other factors which make analysis more difficult is that your tent is staked down and guy line limit the defection of the tent. This changes the loading significantly. I suppose you could assume that you have only staked it down at 4 corners of the polls and they were free to deflect as this case would provide the largest stress on the poles. Even doing that I have no idea how you would determine the displacement caused by the wind load acting at the side of your tent without FEA using Shell type elements.

Your idea of dividing the force due to pressure by 3 and applying it to the poles doesn't allow for the displacement of the poles. And your stress level in your pole is almost entirely caused by the displacement.

Failure of the pole will be caused by bending. So one way of looking at the problem might be to find out the flexibility of the pole (can be calculated), find out the maximum curvature before yeilding. Might be provided by the pole vendor or can be calculated from the equations that others have posted. Then calculate the force required to bend the pole that amount and compare that to your wind load / 3 value. However this assumes that the loading is along the axis of the pole. As soon as you start to have non-normal loads none of the above is valid.

Anyway I am just rambling now and don't really have good answers for you.

Edited by GregF on 03/27/2012 17:53:38 MDT.

Snow loading - you didn't mention what thickness of snow?

Wind loading - a guess is as good as anything else. But you don't know the wind speed *at the tent*, and that can be all over the place. Any thick grass or small bushes will deflect the wind upwards. After all, the wind speed at gound zero is actually 0 m/s (zero). I love camping just behind a copse of snow gums. They do wonders in reducing wind speed without creating any vortices.

Furthermore, you don't know how the wind will deflect over the tent. A gusty wind deflects differently from a steady wind. Story: I saw a small helicopter come into a mountain hut in Switzerland once, in a high wind (bread delivery!). The pilot hung the chopper about 10 feet above the ground for a minute, then brought it down gently. What was he doing in that minute? He was rearranging the local wind pattern with the chopper downdraft. It worked.

Weight of fabric - unlikely to matter imho.

Educated guesses (per Franco) - when you have lived in a small tent in gale force winds for many nights, you do acquire an education... :-) :-)

Cheers

> Snow loading - you didn't mention what thickness of snow?

Jennifer mentioned 'All loading values were determined using the National Building Code of Canada'. This makes me think that the snow loading figures are for buildings, potentially with flat roofs. In which case, the loadings are likely to be massively more than can be expected with a tent, especially a dome tent where much of the snow will slide off; it's not a flat roof...

Bent poles don't form semi-circles. Unless you pre-bend them to that shape. Fabric loading compicates the shape even further.

I think we need to determine what level of analysis is required here; is it a college project which is intended to demonstrate some understanding of the basic analytic principles, or are we talking about a real-world product? If the former, we might be tempted to ignore the difficult bits (failures at fabric stress points, etc), and state our assumptions about wind and snow loading (no dynamics, or some simple factor to allow for estimated dynamics).

If a bent pole is subjected to a loading on one side, the entire pole is affected and needs to be analysed (action and reaction).

16mm diameter, 3mm thick 'poles' are very sturdy for a tent. Either it's an enormous tent, or these figures need to be re-addressed. I wouldn't like to try bending a 3mm wall thickness, 16mm diameter pole; it's certainly not a flexipole...

As an engineer, I'd like to think that we can design a tent using analytical methods, and know how strong it will be. But the reality is that almost all tent designs are done empirically, playing with pole configuration in some variable test fixture (e.g. a large wooden base board with lots of holes in to anchor pole ends), and draping/stretching fabric over the top to get the pattern, and then testing in the real world.

Roger. Since one cannot perform the analysis without taking the fabric into account, the constitutive properties are needed. Do you know of a source?

Kevin-
The snow loadings I determined were for buildings with domed roofs. I took the maximum value which occurs when the slope is between 0 and 30 degrees and will apply that to the arch for the cases of uniform snow load and non-uniform load.

This is university design project with an emphasis on materials selection and processing. The objective is to design a "tent" that can be used as an emergency shelter. However, I need to provide some analysis that supports the integrity of the structure when it is subjected to loading. A simplified approach is best. Because of the complexity of a tent, my grader is expecting a lot of justifiable assumptions to be made which will simplify the analysis (or at least I hope he is...). Of course, the only way to really know whether this design works is to build a prototype and test it - this will be stated in the report.

"16mm diameter, 3mm thick 'poles' are very sturdy for a tent. Either it's an enormous tent, or these figures need to be re-addressed. I wouldn't like to try bending a 3mm wall thickness, 16mm diameter pole; it's certainly not a flexipole..."

-- it is an enormous tent at ~2.5m tall. We are following design guidelines set by the UN for emergency shelters. You're right, 3mm also seems too thick. I had chosen an arbitrary value to work around.

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.