timbob; you do not say how thick the plastic is which could be important to looking at alternative methods of fastening the steel sheet to the plastic. Is the plastic also sheet or do you plan on putting the rivets into a boss? You might want to look into using a Hi-Lo, Plastite, PT, or a similar thread forming fastener designed for use in plastic. If the flex modulus of the plastic is above 1,000,000 (as many filled thermoplastics may be)you may have to look at a thread cutter. I have had extensive experience with fastening into plastic and have found riveting to be the most economical but the most difficult to control due to forces mentioned by Ron. They are also the most difficult to repair as the rivet has to be drilled out and a larger one installed, not without some damage to the material.
When you start to worry about clamp load on plastic you must remember the creep characteristics of the plastic being used. Many tests have proven that clamp in plastic will approach 0 very quickly at room temperatures and even faster at elavated temperatures due to the creep phenomena. It can also be a function of the initial clamp induced into the plastic.
There is an excellent book on Fastening into Plastic by Ken Gomes that discusses the many different approaches into several different type plastics. It can be found by searching authors on Amazon.com or barnes-noble.com. I do not recall the name of it right now but most of Ken's books deal with plastic and aluminum since both materials act very similar.
Good Luck. Bill P.
CSFT, Inc.