I just had a job that a base cabinet ended up too large because of a change on site. It was the perfect opportunity to test an actual production sample for structural integrity. 3/4" melamine, 4" nailer and top stretchers, 4" P Bd front kick between sides (sides to floor,) no back. All parts run nested, 8x35mm dowels per AWI standards on bore and insert machine, side dowel holes glued with one shot injection, no other glue used, case clamped probably about 2-3 minutes. The case was four days old.
The un-scientific test: dead blow hammer plus big guy, beat it on the inside until it failed. Result: the failure was the face of the melamine board pulled out in chunks to about the midpoint of the thickness. All the dowels had pieces of board adhered to them. Conclusion: plenty strong.
From contributor M:
If you haven't done many remodels you'd be very surprised at the strength of a box no matter what method of construction is used. I took some cabinets out of a school a few years ago and the construction used some of the thinnest materials I've come a cross. 1/4" sides and 1/8" backs, most everything was tongue and groove, hot glued, and stapled. I literally had to beat these things off the wall with a sledge hammer and they didn't come apart easy. The ones that I got off of the wall intact I also hit with the hammer - hardly any of the joints failed before the wood broke. After seeing these things it made me wonder how much I was over building with 3/4" stock.
We had one a few years back where who ever put the kitchen cabinets up used white silicone caulk to glue the cabinets up and used one big old framing nail through the top rail of each box to hold them in place till the silicone cured! The guy must have gone through cases of silicone, it was everywhere all over the backs, in between boxes, on the floor under them just everywhere. The plumber said that all three toilets he replaced were also glued down with silicone.