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All:

I'm trying to become better educated about the relative strengths of
different types of plywood, and right now I'm dealing with a 3/4" block
of seven-layer oak-veneer plywood.

I'm wondering what would you folks would consider to be the maximum
reasonable span that type of plywood should be expected to sustain for
a shelf holding a 27" tube TV? I'm presently planning a 36" span 22"
deep, secured to the sides of a cabinet via 1/4" dadoes in a solid oak
frame. The cabinet will be backed by 1/4" plywood, glued and screwed to
the shelf from the backside.

I've read some posts that say this type of plywood would be more than
adequate for even larger TV's, but a few others that say it will sag,
but none of the discussions I've seen have talked about how that sag
tendency varies with the number of layers in the plywood, so I have to
plead uncertainty.

Unless you reinforce front and back it is going to sag. I suggest double
thickness with a solid wood trim on the front and back edges.