Most of the time we can change a family's category. We can open the family, click Family Category and Parameters and choose a different category.
An exception to the rule is when we attempt this with a family that is already assigned to the Structural Framing category. Revit will let us think we've succeeded until we try to use the family in a project or reload it.
The special Revityness of structural framing prevents this transition. If you've already loaded and created an instance of the family in a project Revit will generate an error and invite you to delete the family type(s). The moral of the story is "don't because you can't".
An exception to the rule is when we attempt this with a family that is already assigned to the Structural Framing category. Revit will let us think we've succeeded until we try to use the family in a project or reload it.
The special Revityness of structural framing prevents this transition. If you've already loaded and created an instance of the family in a project Revit will generate an error and invite you to delete the family type(s). The moral of the story is "don't because you can't".


