I am building a 52" x 18" x 2" (actual dimensions) white oak bench for
a small alcove that is surrounded on 3 sides by walls.

To support the bench, I am thinking of using white oak cleats along the 3
supporting sides and screwing up through the cleats into the bench so
that there are no (obviousy) visible fasteners

Would a running 3/4" x 2" cleat along 3 sides of the bench be
sufficient to support the bench under easonable use? (say maximum of
3 adults or 4 children sitting on it).

Assume that the cleats will be screwed into the studs every 16 inches
using a 3 1/2" deck screw. Assume also that 3" deck screws will be
used to screw up through the cleat into the bench.

Thanks