Calculations for Tent Poles

[Liam de la Bedoyere]

Hi everyone

My name is Liam and I am designing a small 2 man tent for a project but I need to show some math calculations showing how much stress and strain there is on my tent poles.

I assume that it depends on the length and the angles that they are at but if anyone has some suggestions or accurate equations that you think would help me I would be very much appreciative.

Liam

[Ben H.]

I haven't looked at this stuff since I was an undergrad, but this is the beam equation:

Most undergrad textbooks assume small deflections so the bottom right side of the equation is neglected. Unfortunately, a tent pole does not undergo small deflections, so most standard solutions can't be used. Hopefully someone else around here has more experience and can give you a better answer. If you don't get a better answer and the above equation does not scare you too much, then let me know and we can try to move forward.

[Kevin Beeden]

> Unfortunately, a tent pole does not undergo small deflections, so most standard solutions can't be used.

Not only that, but it's supporting a stressed membrane (assuming it's a flexi-pole, geodesic tent), which adds to the problem of trying to identify the bent pole shape and loading.

Having figured out that I couldn't figure out what the pole shape ought to be, I gave up analytical methods of designing tent panels, and went empirical…

If the OP figures out the maths, please post a thread on it; it would be very welcome…

[Ben H.]

I thought about this some more. I was spending a lot of time thinking about boundary conditions that should be used to solve the equation. Then it struck me, most tents have a series of clips or sleeves that constrain the pole to a design shape. What force is applied? It is exactly the correct force to get the designed shape. The force isn't your known quantity, but… shape is! Now look at the equation I posted… it is also in terms of shape. If you have a graphical representation of the shape of you tent pole, you can numerically differentiate, plug it into the above equation, and solve for the applied moment. OP, let me know if this makes any sense to you or you need additional help.

[Kevin Beeden]

> I was spending a lot of time thinking about boundary conditions that should be used to solve the equation. Then it struck me, most tents have a series of clips or sleeves that constrain the pole to a design shape.

Yes, that was the way I'd thought of attacking a numerical solution to tent design, using some form of simulated annealing of a fabric mesh, based on the boundary conditions (be they a set of fixed pole anchor points, pole lengths, and fabric stresses (including catenary edges for the panels)). I'd got to the point of thinking about modelling a fabric as a mesh of cells, each comprised of four rigid, fixed length elements (representing the warp and weft fibres) joined flexibly at the corners, with springs across the corners (representing the bias movement of the fabric). Then I got distracted by something shiny…

[Daryl and Daryl]

"Then I got distracted by something shiny"

I finally found part of this discussion that I could understand.

[Ben H.]

Ok, this is what happens when you ask a nerd a question. I made a little write-up on how to calculate maximum stress on a tent pole. A note about engineering analysis. I am a mechanical engineer but I am not a structural engineer. I am confident in this analysis but I do not have the back ground to suggest what kind of safety factors need to be applied for design purposes. This only calculates the static load (i.e. with the tent set-up in you garage). In actual use (wind load, bending the poles to set-up the tent, or falling on your tent in the middle of the night after a pee run) can significantly increase the load a tent pole will see. Let me know if you have any questions.

[Peter Nielsen]

I have a buddy that use to work for cascade designs and we were just talking about tent design the other day. I was very surprised to find out that there is very little design calculations done on tents. most of the design is based on experience of what works and testing.

[Jennifer D]

I'm working on a similar project but need to figure out if my structure will fail under different load conditions. My tent is a hexagonal dome consisting of 3 semi-circular aluminum rods. The loading conditions i'm considering are: a uniform snow load, a non-uniform wind/snow load, and a wind only load. If anyone has any suggestions on how to do this analysis with hand calculations it would be very much appreciated!
I should state that a major assumption is that the frame will support the loading and as a preliminary assessment, I can neglect support from the fabric.

Thanks in advance,

Jennifer

[David Drake]

Both the OP and the last poster might want to look at this:

http://www.backpackinglight.com/cgi-bin/backpackinglight/storm_resistance_ultralight_shelters_part_1_intro.html

Good stuff for background, and I believe is available to non-members.

Edit: Checked again, and it is subscription-only. However, there are extensive forum comments on the article they are available without subscription.

[Ben H.]

Jennifer, I don't mean to be nosy, but what is your background? Did you understand the analysis I presented and could you perform it? I can try to help you but I need to know where you are at.

[Tim Zen]

Don't forget buckling.
Ignore the finite deflection as it just changes the loading which you are estimating.

Can you analyze something simple like a flat tarp on two poles?

[Jennifer D]

Ben, I'm a materials engineering student so structural engineering is not my expertise. However, I think I did make sense of the method you presented. I divided one arched rod into 16 points and used the equations you presented to determine the bending stresses at each joint as a result of it taking the shape I defined. In my case, I'm using semi-circular rods so the equation was SQRT(r2 – (x-r)2). Since the resulting maximum stress value (which occurred at the apex of the arch) is less than the maximum tensile stress of aluminum i've concluded that the rod can take the shape of the arch and will not fail due to bending. In reality, the rods are 16 individual segments press-fit together, however i'm pretty sure in the above analysis I consider the arch to be one uniform rod.
If I design each rod to be slightly pre-bent, this further alleviates the stresses.
I'm not sure how to determine whether the entire frame (3 crossing arches) will fail under each loading condition I mentioned. I don't have access/knowledge to FEA software, so i'm trying to come up with a valid way of assessing the structure using hand calculations.
I've been looking for calculations for arches and think these would qualify as two pinned (two hinged) which are indeterminate. This further complicates my analysis.
Hope you could lead me in the right direction.
Thanks for your response!

Jennifer

[Ben H.]

Jennifer,

Sounds good. I am a Thermo/Fluid Engineer so this isn't my strong suit either, but I'll see if I can help. The analysis I presented tells you the pre-load on the tent. As you mentioned, you can alleviate some of the pre-load by deforming the poles to your desired shape. 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.

I would compare these stresses to the yield strength, not the tensile strength and appropriate factors of safety need to be applied. Also as Tim mentioned above, the failure mode for a tent pole is most likely buckling. We should think some more about that. I will keep thinking about this problem. Let me know additional ideas or comments you have.

-Ben

[Greg F]

For wind loading I would use a dynamic load factor of 2 and then apply it as a static pressure load. This assumes no shape factor of your tents ability to shed wind and as long as there are no standing wave effects (tacoma narrows bridge) than a dynamic load factor of 2 should be conservative.

You have now got me thinking on if the pipe stress software I use could be used for tent design. It uses line elements so I question whether it would work. Failure due to axial buckling is not consdiered, and local collapse of the tube would not be considered. But failure to do yeilding of the tubes would and that should be the primary failure of a tent pole that is overloaded.

I suspect though it only considers small degree bends to piping when it analyses the flexibility of the system and since the small angle approxamation isn't valid here. So likely it is back to hand methods.

What is the D/t ratio of a tent pole? (diameter over thickness) If it is less than 50 you can approxamte the effects as a line element and it will greatly decrease the complexity of the calculation. Although I would have to verify that for large bend angles.

[Franco Darioli]

Interesting thread…
This is how is done in the real world :
http://www.youtube.com/watch?v=QQ3Vkks25dM
Franco

[Roger Caffin]

Snicker.
They started off with a poor basic design, and spent several years trying to make it work. I doubt the guides were really happy with it at the end, but management probably got tired of waiting. Ah well, the guides got some fun trips out of it.

It's a 2-man tent which weighs 5.17 kg (11.4 lb). Light-weight, eh? And it looks no different from any other heavy geodesic tent on the market. That's not how they build extreme weather tents in New Zealand or Northern Europe: I wonder why (=sarcasm). And it takes several guys to pitch it in bad weather. Sheesh.

OK, tent poles.

Trying to do useful tent pole calculations is almost impossible. The reason is not to do with the pole; it's because the main reinforcing mechanism keeping the pole straight is the fabric around the pole – assuming the poles are sleeved in the fly. OK, on a pop-up tent (or some geodesics) where the fly is thrown over the top the fabric does not help very much – which is why pop-ups collapse so easily and geodesics are so heavy. Bad initial design. Sleeving is essential.

Why can't you model the effect of the fabric? Because the loads depend totally on exactly (and I mean exactly) how the tent is pitched, how strong the wind is, how much stretch there is in the fabric, where the guy ropes are and how much tension they have, whether the poles can slide under the fabric (as in pop-ups), …

Wha does matter is to calculate the minimum bend radius the material can handle, and to make sure the actual bend radius (at the top of the arch) has a big safety margin over that (for storms etc). You can put a pre-bend into the aluminium poles, and that helps enormously, if done correctly. Been there, done that (both the right way and the wrong way). And sleeve the poles in the fly, don't throw the fly over them.

Cheers

[Franco Darioli]

That video clip I posted was only meant to show how and indirectly why tents are built and tested like that.
Roger has explained very well the problem with pole theory versus how they behave in reality.
That is also why you cannot often enough just put a different skin on a tent (say from taffeta nylon to silnylon to Cuben) and expect it to work.
Franco
BTW, I would suppose that Roger also starts with an "educated guess" on how it will work when he makes his own, however I would expect that by testing in the real world he gets a better idea then just working figures on a computer.

[Jennifer D]

Some additional comments:

I am assuming that even though the arches cross over each other at the apex, I can still treat each rod individually – that is, I do not consider the effect of the topmost one on the other two, etc.
All loading values were determined using the National Building Code of Canada.

For uniform snow load, I assume that I can take the total value (4.73kN/m) and divide it by number of arches (3), to get the loading on 1 arch = 1.575kN/m. Using this value, I would then have to determine the support reactions and moments.

For non-uniform load (wind & snow), only half the tent would be loaded. This case is more complicated because at any given time 3-4 half-arches are loaded depending on the orientation of the tent (think of a top down view of a circle with load on only one side). In this case, I was going to divide the total load (2.80kN/m) by 3 (3 half-arches) = 0.93kN/m, take one arch and determine the support reactions and moments if only half is loaded by this value.

For wind, I have a specified external pressure acting statically normal to the tent surface – this is either directed towards the surface or as a suction away from the surface. This value is 2.27kPa (for wind speed of 20m/s). To analyze the effect on the arches, at any given time 3 half arches will be exposed to wind (think half the tent from a side view), To get a force value, I would multiply the pressure value by the projected area (cross-section of tent) (P=F/A) then divide the force by 3 and analyze the effect on one arch.

I don't know if my thinking is correct in any of these instances.
I also don't know if I should be including the self-weight of the tent because the fabrics we have chosen are pretty heavy (it is supposed to be a "winter" tent with an insulation layer).

Thanks for looking into this! I should let you know that i'm running out of time to complete this analysis for my project. I was relying on a SolidWorks model and SolidWorks simulation and recently determined that it can't be done since the fabric is too thin to mesh.

Thanks again.

Jennifer

[Jennifer D]

Greg – i've chosen a rod of outer diameter=16mm and thickness = 3mm as preliminary dimensions. I was hoping to be able to adjust these values once I know the effect of the loads.

[Greg F]

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.

[Roger Caffin]

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

[Kevin Beeden]

> 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.

[Tim Zen]

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

[Jennifer D]

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.

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