What size steel beam to hang hammock?

Hi,
I want to install two posts to hang a hammock. For aesthetic reasons I dont want to camber them away from one another as typically
suggested. What size steel tube would I need such that deflection is basically non-existant with a typical 1-person weight on the hammock? (lets say 200 lbs) The posts would be 6' above ground, 4' below ground. The hammock would hang from the top of the posts.
I was thinking 3" diameter but I'm not sure if the minimum sidewall (1/8") would be acceptable or if I should go thicker.
What size would be equivalent to a 6x6 wood post for this application? (ie. primarily bending strength)
Thanks!
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www.efunda.com look for cantilever calculations
--
Anthony

You can't 'idiot proof' anything....every time you try, they just make
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Thanks, but that site costs money to signup (it seems they let you do 2 free calculations first).
Also, I cant quite figure out how E and I are affected by sidewall thickness?

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bob smith wrote:

It's also going to depend a lot on whether you like a good solid sag in the hammock or whether you like it tight as a fiddle string so there is very little sag when the kids do a running jump on it. There are several websites that deal with catenary sag and the tension applied at the tie points for a given weight and sag. From there you can calculate basic beam deflection using formulas in Machineries handbook or similar based on your preference about how far the tops of the posts can deflect under the weight.
I'd also probably fill the pipe with concrete. It will add a little more strength against deflection and will make the posts seem less "springy" if you choose a size on the low end of the strength scale.
Personally, I'd go fairly large and thick walled on the pipe as I think it looks better (people perceive it as SOLID) and even when the rust gremlins start taking over (rust never sleeps) there will be pleanty of material there for a long time to keep things standing.
Koz
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free
Thanks. I dont want any sag as a result of the posts, ideally the posts would be completely deflection-free.
I will probably fill the pipe with concrete, and I will definitely be setting them in the ground with concrete.
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bob smith wrote:

The posts will ALWAYS deflect under the load. The question is, how much deflection is not visible to you (or you may not care if they move 1/2" inward).
With regards to he hammock itself, as you approach zero deflection (straight line hammock) the amount of tension on the posts will approach infinity....there will always be some sag. The reason I bring this up is somethwere between straight and hitting the ground in the middle is the place you like it. If you like it to be taught, this will apply a huge force on the posts (ignoring post deflection at this point). If you can tolerate a foot or two of center bow, the forces will be better. Everyone's different on this and cutting the bow in half applies 4 times the force on the end of the post so it does matter a lot.
*note* *note* *Calculations below are quick and dirty and I may goof...this is not trying to be perfect, just show the process*
So, doing it the easy way and assuming the load on the hammock is evenly distributed from post to post you can use the formula below to approximately calculate the tension on the end of the post: T= (3(L^2)W)/2S where T = tension, L = span in feet, W = weight and S sag in inches
So, let's assume posts 12 feet apart, a 200 pound guy, and that you want the center to sag only 6 inches under the weight you have a tension on the posts of : T = (3*144*200)/(2*6) T= 7200 pounds. Huge, aint it? Small amounts of catenary sag cause huge amounts of tension on the posts. Also remember that what's holding the posts in the ground needs to counteract this force..4' above ground and 2' below can act as a lever and pry itself out.
For safety, you have to assume that the full 7200 pounds is on one end (it's actually jumping back and forth as you move).
So, assuming the pipe is fixed under the ground and the hammock attaches 4 feet above the ground, the formula for end point deflection from machinery's handbook can be used: D=(WL^3)/(8EI) where D = deflection (inches), I = Moment of Inertia of the beam, W = load on beam end (pounds), E = modulus of elasticity of the material, L = length of the beam (inches) . (engineers are gunna kill me for not using SI units here but who cares?)
Assuming that 1/4" deflection is about the maximum allowed we can re-arrange the equation and start plugging in numbers: I = (7200*48^3)/(8*E*.25) From the table for E, steel is about 30,000,000. so, I = about 13
Now we're getting somewhere....looking at a table of I for pipe, you're looking at a 5" sch 20 (or 4" sch 80) hollow pipe or greater to meet that deflection.
(can calculate on any pipe using (.7854OR^4-.7854IR^4) where OR outside radius and IR = inside radius
Ok, so that's worst case. Most people will allow more sag than 6 inches in the middle of the hammock and the loads on the posts will be lower. Run some numbers yourself to see what comes out right in the real world.
Koz (who obviously wanted to avoid work today)

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True, which is why I mentioned 'ideally' :-) A 1/2" sag would be acceptable, 1/4" would be better.

The sag comes from the hammock itself stretching, not the posts. I hope this is what you mean. For example, if the hammock was tied to two large trees the trees would not bend but the hammock would not be stiff as a board. I want to simulate that scenario.

No problem. I greatly appreciate the walkthrough

Considering E = 1,800,000 for wood, the following numbers crank out:
steel 6" .25" I = 13 steel 6" .5" I = 6.5 steel 12" .25" I = 6.5 steel 12" .5" I = 3.25 wood 6" .25" I = 221 wood 6" .5" I = 110 wood 12" .25" I = 110 wood 12" .5" I = 55
I for a 6x6 beam = bh^3/12 = 76, equivalent I for a steel pipe = about 5. Note that the typically recommended 6x6 wood beam seems to fall somewhere in the middle of these numbers, a good compromise.
To meet an I=5 you need 3" schedule 160, or 3.5" schedule 40 (or a little more than 4.5" diameter hollow structural steel with a 1/8" minimum sidewall).
The middle option sounds promising.

I hope I helped you accomplish your goal :-) Thanks again!
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Koz wrote:

Heck no -- I'm an engineer and I think English units are perfect for this kind of calc! SI is a real pain when the inputs and outputs are English anyway (weight, dimensions, especially of the pipe/tube/beam and the tables of I and S in the books). With all the infrastructure in the US built around English units, it'll be a looong time before we can get SI-dim'd raw materials, hardware, etc. as easily as English ones. Long live the King!
SI is great for dynamics, though--them darn slugs and lb-masses...
David
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But if you clear your browser cache, you can do 2 more :)
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Anthony

You can't 'idiot proof' anything....every time you try, they just make
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dont
(lets
(ie.
I'm far from an engineer, so I'm unable to provide specifics, but by your description, with 4' of pipe underground, I'd be totally surprised if you weren't satisfied with a plain piece of 3" schedule 40 pipe. It should be the least expensive material you can buy, and is very close to your specifications. Wall thickness is greater than the 1/8" you mentioned (it's almost double @ .216"), and the OD would be 3.500" instead of 3".
I fully agree with the idea of filling the pipe with concrete, but I'd also cap it when finished, well enough to prevent water from entering. If you could keep it dry inside, you'd have no rusting except from the outside in, and that would take a long time to destroy the pipe----perhaps not in your lifetime. If you could tolerate the looks of galvanized pipe, even that wouldn't be an issue.
One thing------I'd set these pipes in concrete, not just dirt. I've watched guys install chain link fence---simply pouring bags of concrete premix into the holes, adding water after the fact. No need to premix the concrete before pouring. Makes the job a lot easier, and seems to work just as well.
Harold
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(1/8")
How does schedule 40 compare with HSS pipe structurally? same basic alloys and production?

also
in,
The pipe will be covered with wood to provide a clean look.

just
Oh yeah, definitely. I'll definitely be setting them in concrete.
Thanks!

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Bob, I hate to say what I am going to say, but if you are like me, you will hang this hammock and then will basically never use it. Are you sure that you want to do it.
i
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    Aha! You have moved from alt.net, so I'm seeing your original articles again.
    Enjoy,         DoN.
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snip----
Sorry, I'm not familiar with the term HSS where pipe is concerned----care to elaborate?

also
you
in,
your
that
That could still let in some water. I'd be careful to preclude any water entering the top, which will certainly not be to your advantage. You could do something as simple as cover the top with black visqueen, draping it over the sides, before covering it with wood. Anything to prevent water from entering the top.
Harold
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alloys
to
HSS = hollow structural steel. schedule 40 actually doesnt seem any cheaper by weight, I can get 1/8" sidewall HSS for about half the price. I guess theres no free lunch any way you dice it!

outside
could
over
Agreed. There will probably be a little 'hat' at the top or something. Even a plastic endcap would be sufficient.

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bob smith wrote:

I think that would be marginal depending on how tight the hammock is strung.

Harold's suggestion of 3" sched 40 pipe should be ok but is not quite as strong as a 6x6 post of good wood.
Note that E is a property of a material and is approx. 30E6 for any steel. Formulae for I for various geometries are given in Machinery's Handbook. For 3" sched 40 pipe, I=3 in^4 approx.
Note also that you don't have a simple cantilever beam. You have an eccentricly loaded column carying both compression and bending.
Ted
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A few years ago I helped my son put some posts in for a hammock. The hammock came with a recomendation to use 6 by 6 wood posts. We used 4 by 6 posts with the 6 inch being the depth of the beam. To provide the soil resistance of a six inch post, we put a foot or so of 2 by 6 at the bottom of the 4 by 6 so as to have the 6 inch diamension resisting the movement of the post at the bottom of the hole. We then dug a trench about two feet long and maybe 8 inches deep intersecting the hole. And nailed some 2 by 6 across the 4 by 6 on the hammock side of the 4 by 6.
I doubt if anyone can follow this without a picture. But the result was a really solid post.
Dan
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I think I get what you're saying. Thats an interesting suggestion, thanks. In my case the two posts are also forming two footers for an 18" high deck. So, the deck will actually be holding the posts apart too, and I think the strength of this will be similar to what you have done.

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Hey Bob,
I'm too big and too old to desire a hammock any longer. But if it was me, I'd at least string a top spreader beam in there too, at least the size of the uprights. That way, you could convert it use as kids swings, or a soccer style goal, or a clothes line, or some other good use, once you get too old for the hammock too. And be sure to remember the enormous "side loads" any hammock swinging puts on any of this.
Take care.
Brian Lawson, Bothwell, Ontario. XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXxX

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Our company designs shoring for excavations. Based on typical cantilever shoring designs I'd say you need W21x122 grade 50 steel beams, 18' embedment, centered in 30'' dia drillholes filled with structural concrete. That should take care of any pesky deflection in the beams.
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