The Day of Month function is supported, returning an integer 1-31, the number of the day within a given month. When dragging a Day of Month into a variable, the following tree element is created.
Variable Creation > Input > Variables: SQL Elements pane - Calendar > Day Of Month
Columns and/or other expressions that resolve to a date can be moved over the (empty) branch of the tree.
There are no special properties for the Day of Month function.