As someone else said, A 516 is not "close" to A 513. The ASTM numbers are just names and don't mean anything. A higher number just means the spec was written at a later date.
You can buy individual specs from ASTM for nonshocking costs. ASTM A 513 costs $42:
http://www.astm.org/Standards/A513.htmand you can download it immediately.
You can also buy books of specs:
http://www.astm.org/BOOKSTORE/BOS/section01.htmIf most of the specs you want are all in one volume, it might be worth your while.
D1.1 has a limited (though still pretty long) list of *prequalified* base metals. For everything else, you can run a PQR--which it looks like you're running anyway.