Since we always recommended using set screws (the longest set screws we've found are 4 inches long) and they do penetrate the bracket by about ¾ of an inch, we suggest that when using the aluminum bracket, the maximum thickness should not exceeded 5 ½ inches.
When using the steel bracket we can go much thicker, since the steel bracket comes in different sizes. Starting at 2 ½ inches high and increasing all the way up to 7 inches high in ½ inch increments. A 7-inch steel bracket could do a 9 inch thick shelf.
That said, if we go any higher, one needs to use thicker steel (more than 10 gauge). This becomes very expensive and will always be a custom order.
That aside, in theory, there is no height limit in steel.
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