Do these shelves seem strong enough?

I put up 3 18"x96" shelves in my basement. Each shelf is a frame of 2x4s, covered with 1/4" plywood. They are securely screwed to the wall in the back. In the front all I have is a 2x4 support screwed to the each side. It looks like a pretty long unsupported shelf, but when I lean about 80 pounds on it right in the middle at the front (presumably the worst possible place) there is no noticable deflection. They will hold no more than 150 pounds each, fairly evenly distributed. Are they sturdy enough, or should I add another support in the middle? It would make putting the big bins (full of my son's scouting gear; 4 sleeping bags seems excessive, but what do I know) up more difficult, but is certainly better than having it break.
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Toller wrote:

Will 150# break an eight foot 2x4? Not in my experience.
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dadiOH
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I suspect it might sag quite a bit over time. You might consider removeable supports in the middle.
Don Young
Don Young
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I don't have a feel for this, but thats not enough to shut me up.
How about: Compromise and put in a middle support for the lowest shelf. Will that make putting in the bins more difficult? Then put the heaviest stuff on the lowest shelf.
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A 2x4 spanning 8 feet will be just fine for anything that doesn't bow or buckle 1/4 ply.
If the shelves show signs of bowing, you can always add a center 1 x 2 face nailed to the 2 x4 s some other day.
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With total load W = 8M/L and L" length and bending moment M = fS and max fiber stress f = 1000 psi and modulus S = bd^2/6 and b" width and d" depth, W = 8fbd^2/(6L) = 8x1000x1.5x3.5^2/(6x8x12) = 255 pounds.
A 2x4 supporting half the shelf might fail with 510 pounds on the shelf.
Nick
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