Something this tall ought to have a back.

That said, if you dado deep enough (if it was solid wood I would say to do
sliding dovetails) and screw and glue the shelves in, plugging the screw
holes, with the thing squared up when you affix the shelves, the assembly
will be fairly strong.

This tall and you also need to add earthquake straps of some sort anyway. So
that should help prevent any racking.

MikeW

"Alan Smithee" wrote in message
news:iKAIe.119460$s54.20459@pd7tw2no...
I'm building a narrow-tall shelf for a friend. Using three-quarter inch
ply.
It's over 8' tall and about 21" wide. About 7or 8 shelves which I'm
dadoing
into the sides. The friend doesn't want a back on it though and I'm afraid
the whole thing may lack stability. What should I do? Tell 'em it needs a
back or it might fall apart? Reinforce with gussets? Or just glue the
dados
and hit it with some brads and clamp the be-jesus out of it? Thx.