An engineering question

[Jeff Mackay]

Any engineers in the crowd? I"m designing a window seat. The idea is a bench "suspended" in front of the window. I have two floor registers beneath the bench where I'll put some columns to support the bench. Total length of the bench will be about 13 feet.

So the question is: will a 2x4 support a weight of about 500 lbs (two adults) over a 7 foot span with minimal deflection? How about a 2x6?

I found some beam calculators online, but they're above my head.

[Jeff Mackay]

I think I just found my answer. According to http://newstore.southernpine.com/images/ref207.pdf the smallest header for a 4-foot span is a single 2x6. The smallest header for an 8-foot span is a single 2x10. Although I'm reasonably certain the weight required to be supported by a bench is lower than that required to be supported by wall framing, I think I'll play it safe, use a framework of 2x6's with a support at the center that will reduce the span to less than 4'.

[Nick Laeder]

You could also make the bench a torsion box. That would help out quite a bit. Or LVL or some other material for your support in lieu of framing lumber.

[Brian Tymchak]

Hi Jeff,

If I understand your requirements correctly, here is what Sagulator says.

If you consider a 2x4 (of Eastern White Pine, straight grained, no knots) as being a shelf that is 1.5" wide and 3.5" thick (in other words using it on edge), and using 4' spans, and putting a load of 500 lbs on it at the center, the sag would total .1". That's actually better than I thought it would be. In actuality, that is a worst-case scenario. You would not be putting a 500 lb point load on the center of the span, but would spread it out a bit. A uniform distribution of 500 lbs across the span yields .05" sag, so your real load would be somewhere between the uniform and center scenarios. Sagulator also notes that these are initial deflections. Beams and shelves will sag an additional 50% over time. It says a target allowable sag should be .02" per foot. The measures I provided here are totals, so divide those by 4 to get per foot measures.

If you use something a bit more sturdy than pine, say white ash, the sag is lower by about 20%.

I'm not exactly sure of your design. You say the bench will be "suspended". I'll make an assumption here in that you would most likely use 2 2x4s, tied together in some type of frame under the seat. The sag drops to .05" (center load), and .03" (uniform load). I assume you will use something on top of the 2x4 frame as a seat which will actually help strengthen the assembly and the sag will drop a bit more. Sagulator says this construction could support over 1000 lbs uniform load.

Bottom line is that you should be able to build a very sturdy structure using just 2x4s over 4' spans.

For comparison, if you use a 6.5' span, the total sag with 2 pine 2x4s on edge under the seat, the sag computes to .22" (~1/4") over the span, .033" per foot. That's a little higher than sagulator's recommendations of .02" per foot. So, if you use 2x6s (1.5"x5.5") instead of 2x4s, your total sag would be .06" or .009" per foot (and support over 2000 lbs uniform load). You could actually rip those 2x6s down some if you want to. 2 1.5"x4.5" boards would get you sag calculations of .10" total and .016" per foot ( supporting about 1200 lbs uniform load).

And lastly, if you use 2 2x6s on 4' spans, your sag will be .01" total, .003" per foot with 500lbs center loaded. This construction, according to Sagulator, could support ~6000lbs uniformly load... A very, very sturdy bench indeed!

Lot's of numbers I know. Hope this helps!
Brian

[Jim Galvin]

Jeff

That example you got from that website equates to having 320 lbs per foot on that 2X6 for the four foot span. Thats quite a bit of load.

Jim

[Jeff Mackay]

Hi Brian,

Thanks for the help. The sagulator is exactly what I was looking for! I got my inspiration from Frank Lloyd Wright's living room at Taliesin, where he had benches surrounding a sitting room that appeared to "float". I'm trying for a similar effect with a window seat in an alcove in my family room.

The bench will be about 13 feet long, with two "columns" supporting the bench about 2 feet from each end. The columns will be about 15" wide by about 18 inches deep, to allow for HVAC returns.

I'll construct the bench seat from a framework of 2x4s, 9" on center, topped with a layer of 3/4" cherry veneer ply, a layer of 1/4" birch ply below, and a 5.25" solid cherry edging board mitered to the cherry ply on top. The top of the bench will be covered with upholstered cushions.

I used the sagulator to calculate sag for a white pine shelf that is 18 inches in depth with a thickness of 3.5", and an edging strip of cherry that is 5.25" thick, with a depth of .75". I'm effectively making it into a a 3.75" thick torsion box, supported by two columns that are a foot wide each. With a load of 750 lbs (three good sized adults sitting in the six foot span), I should still only get a sag of .001" per foot, assuming a uniform load distribution.

Does this sound right? Thanks again for the help.

Jeff

[Brian Tymchak]

Ah. I see. Torsion boxes (aka stressed-skin panels), very cool. Also very strong.

One correction I would make with your calculations - you really don't have an 18" deep shelf of white pine. You have a 4.5" deep shelf, which is the total width of the 3 2x4s running the length of the bench. (Since you are tying those 2x4s together in a framework all supporting the load, they tend to act like a solid piece of lumber.) The rest of the shelf width adds no structural strength since it is air. Then the cherry strip is considered an edging strip. I'm surprised it makes that much of a difference. Also if the shelf is fully supported by the columns and not the back wall, then I would use the "Floating" shelf attachment option. Total sag I computed was .09, with .014 per foot, which is very acceptable.

That's without the plywood skins. Those will definitely help. Skinning the 2x4 frame will provide more ridgity to the structure, but I don't know how to calculate deflection of torsion boxes. Even though it's not quite a correct model, just adding the 1" of thickness (3/4" +1/4") to account for the plywood skins, for a total thickness of 4.5, drops the sag to .05 total and .008 per foot. I think you would get better results from a torsion calculation. Technically, I think you would get a stronger torsion box if the upper and lower skins were the same type and thickness. I think it balances the stresses across the frame. But, bottom line is that I think your design is going to be very sturdy.

I downloaded a document a while back that dealt with torsion design but I never went through it. Here's the link to that, with no endorsement of the content other than it appears at first glance to be fairly technical:

http://gp.com/BUILD/DocumentViewer.a...elementid=3815

Also, you could search here on the Creek for Torsion box or Stressed-Skin Panels and maybe find some info. I remember reading a few threads over the last year or so. Maybe there's someone on the Creek that can kick in some advice at this point.

Sounds like a fun project! Good luck!

[Ben Hatcher]

Jeff, a tortion box acts like a solid piece of lumber of the same size, but without the weight. If you were to look at the stresses in a beam, you'll see that the vast majority of them are carried by the outside edges of the piece. The middle section serves no purpose other than to keep the outside skins a predetermined distance apart. Your 4" panel will be more than adequate. You can even go thinner on the plywood if you'd like. I'd use 1/2" or perhaps even 3/8". The structure has to hold all of the weight applied to it, load and itself. Drop 30# of plywood weight and you add 30# of load that it can carry.

[Matt Ellis]

Ian Kirby has written several articles about torsion box construction. It you're a member of FWW, you can see them here:

http://www.finewoodworking.com/Works...F.aspx?id=2072

-matt

[Jeff Mackay]

Hi Brian,

I took a look at the document. Looks like it's meant more for construction purposes (building construction), but it was interesting.
Jeff

[Jeff Mackay]

Ben,

I'm sure you're right, but 3/4" cherry ply is what I have on hand. And since cherry ply is almost as expensive as the real thing, I think I'll just go ahead use what I have. I'm going with the 5 1/4 overall thickness because that's the thickness of the beams and crown (if I ever get it installed) in that room.

Jeff

[Jeff Mackay]

A progress report. I built the framework of 2x4s and set it in place today, supported at both ends by 1.5 inch cherry cleats. With a 12'-8" span, and no attachment to the back wall beneath the window, I get about 1/2" of sag with just me sitting on the bench.

I figure that's good. I still plan to lag it to the studs, 16" on center, glue/nail 3/4" plywood to the top and bottom, and add a 5.25" cherry front to it. If it still sags noticeably, I'll add a diagonal support beneath at the center of the bench.

[Brian Tymchak]

A progress report. I built the framework of 2x4s and set it in place today, supported at both ends by 1.5 inch cherry cleats. With a 12'-8" span, and no attachment to the back wall beneath the window, I get about 1/2" of sag with just me sitting on the bench.

I figure that's good. I still plan to lag it to the studs, 16" on center, glue/nail 3/4" plywood to the top and bottom, and add a 5.25" cherry front to it. If it still sags noticeably, I'll add a diagonal support beneath at the center of the bench.

Jeff,

I guess I misunderstood something in your first posts. 12'8" span is quite a bit longer than I used in my calculations with Sagulator. I used 7'9" as the longest span taking into account 2' overhang on either end and 2 15" wide columns centered about the 2' mark on either end. (13' -2' -2' - 2*7.5") = 7'9". Sorry for the bad assumption. I guess I should have called that out better.

Brian

[Jeff Mackay]

No Brian, my fault. I decided to forgo the columns if I could, which increases the span to over 12' between the ends. I'll lag screw the torsion box to studs 16" on center. So I won't necessarily have to worry about sag anymore. I might, however, have to worry about pulling the lag screws out of the studs, since the weight will be carried by a combination of the torsion box, the cleats on each end, and the lag screws into the studs.

I can always add diagonal supports, columns, or whatever I need if it doesn't work out.

[Thom Porterfield]

Jeff:
Don't depend on lag screws. You'll waste a lot of time and wind up wishing you'd found another way.

The way I would approach your problem is to dig holes into the wall adjacent to each stud and bolt on a 1x4 on each side so that the 1x4 sticks into the room the depth of your bench minus the thickness of the rim member (2 -- 1x4 lookouts every 16").

You have room for (2) 3/8" bolts in a 1x4 and that "sandwich" condition is the strongest bolted wood joint there is. Once the "lookouts" are in place, build your torsion box around them. The resulting structure is stout enough to dance on.

If you are worried that 1x4s won't be strong enough, build a test and check it out. They are. But if you're still worried, use a 1x6 and make the bottom edge tapered so that your rim is the desired dimension.