I am building a 6 foot long shelf that is going to be supported at the ends
(no option of support in the middle). The shelf needs to support about 50-
70 pounds of weight (stereo equipment), so the "sag" (or deflection) in the
center is going to be a problem. I plan on building the shelf as a hollow
box, and using steel angle iron on the inside as a stiffener.
Just out of curiosity -- what commonly available wood product is best for
resisting deflection under a continuous load (i.e. shelving)? The easily
available ones at my local lumber store are: laminated pine, mdf, playwood
and particle board, I am assuming that the laminated pine would be best,
since all the grain is running longitudinally. Is my assumption correct?
That's pretty much what I had in mind, but with some 1/2 inch steel angle-
iron screwed to the inside of the front and back edges for increased
stiffness. Sounds like my design may be overkill for the application.
I can't imagine 1/2" angle iron bringing much strength at all over 6
ft... and not that much weight either. Or maybe we're thinking
different things. I'm thinking about 1/8" thick steel angle with each
leg being 1/2" wide. Am I missing something??
The angle iron has a modulus of elasticity that is about 15 times that
That 1/2" angle iron gives about as much strength as a 1/2"x2" lip of
oak under the shelf.
Of course, if you put the 2" dimention vertically under the shelf, the
lip is about 16x stronger.
For those who care about the math, the deflection of a beam is inversely
proportional to the width of the rectangular cross section. However,
it is inversely proportional to the *cube* of the height of the cross
Thanks -- those numbers help me a lot. I wanted to create a shelf with
quite a thin cross-section (1.2 inches at most), but then ran into problems
Sounds like the interior piece of iron could be enough to get me what I
I'll put the thing together sometime in the next week (if work permits).
I'll post back and let everyone know how it worked (or didn't).
Thanks to all for their helpful responses. Learning new things is always
fun, especially if I can see the results hanging on my wall :-)
Unfortunately, it has a moment of inertia (even assuming there are 2 of them
as the poster suggested) about 350 times less than the shelf. In the end,
unless 1/2" angle iron is a lot thicker than I think, it doesn't end up
contributing much to the combined moment of inertia, which means it doesn't
reduce deflection in a significant way.
i.e. not very much.
Of course, if the lip is made of tungsten carbide, it would be 30x stronger.
It's also directly proportional to the cube of the length. If the OP could
reduce the width just 6", the deflection would drop about 25%.
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For the sheet goods, on average, plywood would be the best, then particle
board, then MDF for initial sag.
I'm a bit unclear on how you're going to build the shelf as a hollow box.
If you're going to go to that much trouble, and then include a steel angle,
I'd suggest just doubling up on the wood for the shelf. Two of the 3/4"
glued-up pine boards would deflect only about 3/32 at the middle under a
distributed 70 pound load (assuming a shelf depth of 12").
You can get an estimate of sag using the Sagulator at
Are the sagulator numbers good for long-term loading, or just initial
deflection? My experience with purchased bookshelves has been poor --
shelves that progressively sag more as the years go by.
BTW, the loading is not distributed -- almost all of the weight is pretty
close to centered.
From the sagulator: "The Sagulator computes initial sag only. As an
engineering rule of thumb, wood beams/shelves will sag an additional 50%
over time beyond the initial deflection induced by the load."
I'm no engineer... more of a shoot from the hip from experience type.
I think a torsion box with 1/4" glued on ply top and bottom with a
total thickness of 1-3/4" should be strong enough for even the
heaviest stereo equipment.
I think the "sagulator" is just a guide and it has no use in
calculating the strength of engineered assemblies... which is what a
torsion box would be.
We're in luck. I'm a mechanical engineer who specialized in materials
engineering. I wasn't attempting to calculate the strength of a torsion
box. I'm sure it would work. But for the original poster, I'm just
imagining that a couple of 3/4" thick boards that he can buy off the shelf
and laminate together would be easier to deal with and would also be very
Of course the sagulator is just a guide. For one, it doesn't take into
account end conditions, which can have an effect on deflection. It also
makes assumptions regarding the bulk properties of the material that may or
may not be true. And it can't do stuff like figure the deflection if a
thicker piece is applied to the front of the shelf to add rigidity.
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