What height beam do I need to support a weight? Howto calc horiz load?

[SteveWasiura]

I'm going to build a swingset/gym in my 4yr old's bedroom so during the winter he can satisfy his climbing needs without climbing on me

How can I calculate the height (or thickness) of the beam I will need to use to support his weight, and perhaps the weight of a couple of his friends, too?

The beam will be lag bolted into studs in the wall, with an approximate distance of 10 feet between the walls. Assume my sons weight at about 30 lbs, but multiply it by 10 to allow for friends and monkey business.

Would a standard 2x4 stud mounted with the 1-1/2" side parallel to the floor be enough of a height (3-1/2") to support a 300 lb weight at any point along the beam (I think the worst location is directly in the center - the furthest point from each support). Or should I go with a 2x6 plank with the 5-1/2" side as the height?

I would appreciate a physics formula to determine this to convince my wife

 

[Cliff_J]

A 2x4 is quite strong - in statics we calculated you could use just 2x4s to support the floors in your house but the 'bounce' you'd have with every step would be unnerving and furniture would have to be picked very carefully.

Here's a quick table for using lumber for spans, look at the difference in spans going from 2x4 to 2x6:
http://www.usplasticlumber.com/_files/Trimax- JoistModeSpanTables.pdf

For the engineering terms you could go here:
http://www.engineersedge.com/strength_of_materials.htm

You'll note that the bending (flexural modulus) goes by a power of 3. So a 2x6 is 1.6 times thicker than a 2x4 so its going to bend 4x less. Or a 10ft span is going to bend 8x as much as a 5ft span. You merely cube the difference. The joint table above is going to include a safety margin and other stuff well below failure so its quite conservative.

You are getting maximum strength by placing the lumber on its edge. Even on its face (weak side) and over an 8 ft span you can walk up a 2x4 as an adult and not break it. It will flex like mad but its surprisingly tough.

Go to a home center with the wife and try to break a 2x4 and you'll both see what I mean.

Cliff

P.S. The likely weak point where failure might occur would be the lag bolts you use and number of them. This should obviously be over-done for safety. That and some sort of really good paint to reduce the chance of slivers.

 

[Artman]

You can expect this beam to move in both directions horizontally and vertically. You also do not want flexure even if it is strong enough not to break because flexure will stress the studs supporting the beam.

Have you considered creating a T, L or I beam shape by using 2x4s glued and bolted together to counter sideways motion and torque? Maybe overkill, but flexure could put cracks in gypboard or plaster walls or ceiling.

 

[SteveWasiura]

Over my head

Sorry, I took a look at both of those links and I feel I am in over my head. I don't understand Modulus of Elasticity, etc.

Plus they are talking about joist spacing, but I'm having a hard time understanding how to correlate that to a single beam span across to end anchor points.

in the usplasticlumber table, I assume this is for plastic wood, so I'm not even sure the numbers should be used for tree wood...

for an example at 120F, they list a span for 100 psf Live Load. Does this mean 100 pounds per square foot, and if I want to have the 2x4 beam support 300 pounds in it's middle (again assuming that's the weakest point) I can only have a span of 25 inches? That's too short of a distance, and the 2x5 beam does not appear to be much better. I need to span a 10ft horizontal.

The other page with calculations confused me. Can you sugest other websites or search terms that I could use to try and find a method to calcualte this? thanks

 

[Cliff_J]

Sorry Steve, I tried to make it as simple as possible but most links I'd found were for statics and calculus based. In short, each joist/beam does need to support a part of the weight and its a big number and with lots of margin of error.

Very short - you could infer from the chart the relative strength and the 2x6 is close to twice the span of the 2x4.

If you went into your attic you'll find your rafters are likely a truss constructed from 2x4 segments. Mine is and even with my weight or my brothers weight (over 300lbs) we can walk on them without noticable deflection. If it did deflect much, the drywall on the ceiling below would crack. Sure the drywall prevents lateral movement, and a truss supports the 2x4 at an interval in-between the load bearing walls, but in the vertical plane, even over an 5-6ft span, the 2x4 is plenty strong enough - so 30lbs is very small in comparison.

You want the moment of inertia for a pine 2x4, it appears the modulus of elasticity is 1,800,000 or so for wood from a quick internet search. Then plug that into a calculator like the following link and you get the deflection.
http://www.engineersedge.com/beam_bending/beam_bending2.htm

Then you could examine the tensile strength or shear and much more simply just find a website where a civil engineering class has tested a 2x4 to failure.

That's why I suggested visiting a home center. A simple pine 2x4 is very strong and a 2x6 is way overkill.

Cliff