Span is the important issue here that is missing. If you add a center
support in the shelf, you can assume that the span is halved and more
than double the load.
9000 lbs is wrong.
My framing book offers the following advise...for 3/4 inch plywood with
48 inch spacing between supports plan for a load of 40 lbs per square
Now there are several issues with this.
1) this assumes the load is live, not dead.
2) It assumes that the supports are down both sides
3) It assumes that the support offers a resting area of at least 1 inch
on each side
4) It does not assume a constant load
You will see some sag in the shelf boards on a constant load over a long
period of time.
A shelf tab in the center back of the shelf will help a lot.
Also, something else I've done in the past is to glue a strip into a
dado which is located not far from the front edge of the shelf. Also,
I further assume that the rear edge of the shelf is fixed to the back
(plywood or somesuch) and the ends are themselves located in dados.
That'll hold up pretty well.
However, the look of the shelf is definitely affected by adding that
strip. It might not be acceptable for his design.
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