Should API 650 section V.7.2 be applied if the roof has rafters but no columns? My vote is no, but a senior engineer here says the opposite. Any thoughts or clarification would be appreciated.
That section wouldn't apply, as it is for self-supporting roofs without rafters. However, you would need to do similar checks for your roof plate and roof structure/rafters, and those checks are not covered by Appendix V.
Looks like I'll need to show the senior engineer this definition:
5.10.1.a: A supported cone roof is a roof formed to approximately the surface of a right cone that is supported principally
either by rafters on girders and columns or by rafters on trusses with or without columns.