# calculate shelf beam size based on load?



## yocalif (Nov 11, 2010)

click on image for larger view

I was already to go out and buy materials, to construct garage shelving, but I realized I forgot to design in storage for lumber (2x4s, board stock). I didn't want to put lumber on top, so I needed to go under. So the only easy way I came up with to do this, was create an 10' open space, which requires a beam to support the weight of the shelves above. This would require some kind of beam. The wood would lay on a cart and roll in or out from under the shelving like a drawer.

10ft span,
Approx total weight max 1500lbs.
The back side of the shelving will be supported by wall studs, so the beam only needs to support half the weight or 750lbs.

Can a 4x4 typical HD pine lumber, with 10' span support the estimated weight? If not will a 2x4 pinned to the 4x4 thus giving 4x6x10' provide the necessary span support?

I tried using several different online calculators to solve this problem but most asked for varibles that I wasn't familiar with.

I finally came on this formula which is fairly easy to understand:


> Total load in pounds = FBd^2 / 9L.
> 
> 
> Fill in the parts of the formula that are already known. L stands for the span of the beam, in feet. In the example, the beam spans the 10-foot width of the roof. The total load is 4,000 pounds. F stands for the beam's fiber strength in bending, which depends on the species of wood. For the initial calculation, F can be estimated at 1,000. Now the example formula is 4,000 = (1,000)Bd^2 / (9 x 10).
> ...


Plugging in 1000 lbs and 4" the result was about 4.75 x 4. 

However I couldn't find any source for the beam's fiber strength.

Anyone have a link to beam's fiber strength resource?


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## mdntrdr (Dec 22, 2009)

4X4 will sag under its own weight.

I would use a pair of 2X6 with 3/4 ply glued and sandwiched between 2 bys.


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## byron9393 (Nov 19, 2010)

I would use a pair of 2X6 with 3/4 ply glued and sandwiched between 2 bys.[/QUOTE]

Ditto:


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## jstange2 (Dec 5, 2010)

Or you could get a 12 inch by 10 foot LVL and rip down the middle. Use construction adhesive with 3 inch screws and you would have a 5 13/16 inch by 3 1/2 inch beam. We use LVLs on window and door headers when they start getting over 12 feet wide or the roof or floor bearing on it are too far to the next bearing point (more load on header). I like overkill.

Edit.... 5 13/16 because they usually come as 11 7/8 inch wide. Might be able to get 5 7/8 inch if you triple check your setup before ripping.


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## Shoester (Dec 18, 2010)

Ha! Wish I had my Statics and Strengths of Materials book for my Theory of Structures class on me...it has charts for all different beam sizes and the loads they can safely carry. If you haven't solved your problem by Monday, I'll chime in when I get my hand on it.


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## yocalif (Nov 11, 2010)

what is LVL?

I should switch to using 2x6 the 
AWC span charts for 10' show that a 2x6 can support about a 500 lbs, based on 1000 wood fiber strength which is at the weak end of fiber strength. So doubling with 2 2x6 should provide the necessary support.

From the replies above is it necessary to glue or can I just bolt the 2x6s together, although there is no reason why I can't add glue, I'm just asking to learn if there is really a structural benefit to adding the clue?

Also you guys experience with framing, how should I tie the beams to the two vertical post? What should the diameter of the posts be? Is it ok to only use the thicker posts diameter below the 2x6s beams and then switch back to to single 2x4 above? Actually the 2x4 would run the full height from bottom to top tied to the thicker post section under the beam, is this ok? Rem, this is really just garage shelving, but I am trying to think ahead in case serious weight is put on those shelves.


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## woodnthings (Jan 24, 2009)

*I wouldn't rely on calculations*

For this project unless you have considerable Strength of Materials experience, static loads involving calculus if I recall from 50 yrs ago.
You don't have a "simple" concentrated load in the middle of a beam, you have a bunch of distributed loads, some on the wall, some transferring to the end supports. It would require a lot of calculations to come up with the correct answer. JMO

I would just over-build it ...seat of pants guesstimate. The Micro lam beams are a good idea, pricey tho. A box beam made of 3/4" on both faces and spacers inside comes to mind, maybe 4" deep/thick or so, yeah I know wasted space, but not much. Your 10' length will be an issue for plywood though.
Also two 2"x 12" would probably work screwed and glued. 
If you use 2 X 12's for the shelves, more of the load will be transferred to the end verticals. A 3/4" back glued to all the shelves will transfer the loads to the back wall. The object here is to make the entire structure "load bearing" rather than just the beam on the bottom.  bill
BTW a piece of steel channel or box across the very front will solve any sagging issues. But still make the structure as above.


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## jstange2 (Dec 5, 2010)

LVL.....laminated veneer limber. Basically 1 3/4 inch thick plywood using special resins for adhesive. http://www.homeconstructionimprovement.com/what-is-a-microllam/


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## jstange2 (Dec 5, 2010)

You could get a piece of flat iron 1/8 inch by 5 1/2 inches and sandwich between 2 2×6. Glue with construction adhesive, use at max 3 inch screws, and predrill from one side just through the metal.


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