The full history of the B31 standards is discussed in the forward to ASME B31.3 (and it's likely in the other B31 documents as well). In case you don't have one handy, it starts off as follows:
"Responding to evident need and at the request of The American Society of Mechanical Engineers, the American Standards Association initiated Project B31 in March 1926, with ASME as sole administrative sponsor. The breadth of the field involved required that membership of the Sectional Committee be drawn from some 40 engineering societies, industries government bureaus, institutes, and trade associations.
Initial publication in 1935 was as the American Tentative Standard Code for Pressure Piping. Revisions from 1942 through 1955 were published as separate documents the various industry Sections..."
Anyway, the full history provided in B31.3 is about a page and a half and provides all the detail you might be looking for.