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What is the best type of swing set?

Swing set loading.

  • Actual question: what is the formula for the deflection of an intermediately loaded simply supported beam from multiple point loads? Reason for the question so you can question my assumptions (and know that I'm not doing homework): I am building a swing-set, from pretty much standard swing set parts, but want to deviate from the standard dimensions a bit - in particular, I want to make the top beam in a single bay setup 1.75' longer than the usual 10'. I am doing this so I can hang a longer bench swing that would hold a couple of people, so this is more length supporting more load, and I want to calculate some things. More inside! First, my assumptions - I feel like if I calculate the deflection from static loading in both the standard 10', two swing configuration, and the deflection from static loading on my 13.75', 1 swing, 1 bench configuration and compare them, I'll get an idea if I'm being insane or just not within normal tolerances for a public swingset. I'm okay with the latter. This is ultimately for use at little outdoor parties of the sort where I can set up a swing-set, and burning man - but out in the suburbs, not a super highly trafficed location. If it ultimately bends it's not going to be unattended long enough to lead to disaster, and I can handle losing a piece of pipe... but I want that to be less than 100% likely within the first 10 minutes. I also know that load from swinging is going to be much different from static load, but I am hoping that it varies linearly! So part one of my question is - is that assumption close to correct? It's easy enough to find that the maximum deflection from a single load here http://en.wikipedia.org/wiki/Deflection_(engineering)#Intermediately_loaded_beam, and I've found the constants I believe I need (moment of inertia and modulus of elasticity) for the 2" schedule 40 steel pipe that I plan on using. But it doesn't seem like I could just add the results of the 4 loads I have from two swings, and I can't find an expansion of that after reading a few chapters of the textbooks I can find online (or a path to deriving it. I am not that clever.) So as I said, the real question is: what is the formula for the deflection of an intermediately loaded simply supported beam from multiple point loads? And what percentage crazy am I being. I'm sure it's a little, I just don't want it to be a lot.

  • Answer:

    what is the formula for the deflection of an intermediately loaded simply supported beam from multiple point loads? If you're really interested in deriving this from first principles, you probably want http://en.wikipedia.org/wiki/Euler%C3%A2%C2%80%C2%93Bernoulli_beam_equation Basically, the equation for the deflection would be E I w''''(x) = Σ (mi g δ(x - xi) ) where E is the elastic modulus of the beam material, I is the second moment of area, mi are the masses of the loads, xi are their positions, and δ(x) is the Dirac delta-function. This is a fourth-order differential equation, but at least it's linear.

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You may also wish to consider the strength of the pipe at the joints. If you are using threaded rather then welded construction, be aware that the threading will cut quite deeply into the pipe. Note that a failure here will be a catastrophic failure, not just a bent pipe.

ryanrs

Have you calculated the worst-case deflection by using the center-loaded beam formula? Maybe your pipe works fine in that scenario, in which case you're done. As to the dynamic load from centripetal acceleration, if your swingers traverse a 180 degree arc, reversing direction at the 3 o'clock and 9 o'clock positions, then the centripetal force will be 2*m*g. Add the static force of m*g from their normal weight gives a total of 3*m*g, or 3 times their normal weight. If they make a full 360, then maximum force at bottom dead center will be 5 times their normal weight. Of course actual people won't be swinging in perfectly smooth arcs, so there will be jerks that increase peak forces above these numbers. On the other hand, the more flexible the pipe, the lower the force will be during these short term excursions.

ryanrs

It does occur to me that the straps would only prevent tipping, not keep the structure rigid.

flaterik

Thanks ryanrs! I have thought of that, and was hoping to get away with heavy duty 18" forged steel stakes and ratchet straps, one per leg. I should probably be drawing force diagrams for that. This whole adventure is a bit safety 3rd, I know. I'm trying to avoid it jumping up to safety 4th or 5th, though. I did my maths and the deflection on a 10' pole with two 200 pound people is 0.55"; a 12'9" pole with 3 200 pound people is 1.56". Kind of an alarming ratio, but still a worst case (IE if it's at the center, which it wouldn't be) deflection angle of 1.2 degrees. I... still have no idea how okay that is. But it's enough that I am looking for more info, not just jumping into it.

flaterik

Note that the swing set kits you linked require substantial concrete anchors at each leg. Don't expect to get away with skipping this part. The concrete is necessary to keep the frame rigid (see http://ask.metafilter.com/241059/Swing-set-loading#3496933).

ryanrs

I've got PATRAN/NASTRAN open and ready to go if you want an FEA solution :-) Though as per the other's I'd use superposition. End constraints are probably not purely simply supported, but you could bound them by trying the fixed / pinned solutions.

trialex

1: I have a copy of The Machinery's Handbook right here at my desk and can easily reference it for deflection data on very specific loading scenarios if you want to MeFi mail me. It confirms dforemsky's equation for that basic scenario. 2: I think modeling as simply-supported is fine. The deflection (or potential deflection) of the cross beam would have to be quite high for the rigidity/counterforce of the endpoint fixture to influence the dynamics appreciably. Plus, if you are modeling for strength, the act of tossing out the moments at the end is giving you a little safety margin implicitly. 3: If I am you, I model the current loading arrangement and solve for the highest deflection and the highest stress. Then when I design the new scenario, I set those levels as design criteria and find out what is necessary from a crossbar/loading arrangement. Good luck man!

milqman

The ends are not threaded, and I'm using http://www.jensenswing.com/products_detail.php?proid=135 - which is also what determined the pipe material. 2" schedule 40 actually has a 2 3/8" OD. I assumed that my assumptions were incorrect for determining the ACTUAL deflection, but I'm going to look at the comparison between the cases to make my determination. Thank you all!

flaterik

Sorry, backseatpilot. I misread your first answer.

dforemsky

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