"Koz" wrote in message
...
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).
True, which is why I mentioned 'ideally' :-) A 1/2" sag would be
acceptable, 1/4" would be better.
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 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.
*note* *note* *Calculations below are quick and dirty and I may
goof...this is not trying to be perfect, just show the process*
No problem. I greatly appreciate the walkthrough
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?
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) .
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.
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.
Koz (who obviously wanted to avoid work today)
I hope I helped you accomplish your goal :-) Thanks again!
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