Depicted here is a
"Floating" countertop, for a handicap bathroom addition, with no visible means of support on one end - for easy wheelchair access.
The architect had drawn a wood panel for support at the end, but I wanted to give the wheelchair more room and freedom to approach the sink.
The countertop sits on a small base cabinet at one end, and is supported by a welded square-tube steel brace on the other.
I worried some during construction, but it turned out to be extremely rigid.
When laying out the tile, we decided it would be more user-friendly if we clipped the corner at 45 degrees, a last-minute change made with a reciprocating saw (sawzall).
Here you can see the steel brace lagged into the stud prior to sheetrock.

Torsion-box type construction served to stiffen the
countertop.
The tile base was cement, troweled in place with the use of screeds - small strips of wood leveled front to back, and with each other.
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