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Hi Rusty,

I looked at the responses from two years ago.

The suggestion was to "half-lap" a single layer of 3/4" thick plywood strips together. Basically, you would have three strips each six feet long or so, then cut away half of the thickness for six inches on each end, so that the last six inches of the plywood strip is 3/8" inches thick. This is the half part. Then you glue the halves together and it is 3/4" thick where they overlap. This is the lap part.

However, looking at your picture, there is nothing to keep this whole thing from sagging down away from the wall. Something will have to be done to support the load of this shelf. As drawn, it will not stay up.

Think of what you're proposing as a shelf with a heavy front edge, because that's really what it is.

Shelf supports, or corbels, or something is needed to transfer the load of the shelf to the wall studs. Even a single cleat attached to each stud, and then a length of plywood attached to the cleat and then the shelf will help.
 

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Sorry, I should have said, the beam I show will be in a vertical orientation. The only horizontal element will be a piece of 3/8" or so plywood between the wall and the beam. All it'll be supporting is some rope lights. (See post #6 above).
Hi Rusty,
I was referring to the picture below that you posted.

That looks like a pretty wide horizontal piece. When i look at it, i think that piece plus the 3/4" plywood "beam" will be too heavy for just a cleat above and below. All that's holding that is some screws close to the end of the horizontal "shelf" that are going into the cleat.

Anyway, if all you are doing is rope lights above, why not just use crown molding? Google "crown moulding with rope lights"
 

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The plywood beam is the support, not the thing being supported; it is securely fastened to the wall at either end of it (the walls that are perpendicular to the beam and to "wall" in the drawing).
I see. That does help somewhat. I assume you will be attaching it to studs on the end walls? As Bill said above, 15 ft is a considerable span, so you may want to add an additional support in the middle.
 
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