I need to design a screwed joint as follows:
Two aluminum sheets, 3mm thick each, sandwich a sheet of mild steel, also 3mm, with hole, as in the picture below. The aluminium sheets are parts of bought-in components and I cannot add holes to them. The steel part is my design and I can shape it as I want.

I want to use a self-drilling screw to drill through the two sheets, going through the center of the hole, so as to clamp the parts together (there will be a template to position the screw from the outside so that it finds the hole).
The conditions of application necessitate that I add a loose nut on the other side, tightening the whole joint after the screw has drilled through.
The Problem:
It is not a problem to design and size a normal screw/nut joint for this application, which is what I would do if I could add holes in the aluminum.
As things are, I need to use self-drilling screws. Searching through fastener suppliers I cannot find a self-drilling screw which is not self-tapping as well. Self-tapping screws have non-ISO threads, sharper and with grooves through them.
Standard nuts are not designed for this type of screw thread. How will this affect the joint calculations and strength?
Thanks.
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