Once you have all the forces in the tank shell from all load combinations (see API 650 section 5.2.2 and 5.11.2 for load combinations), pick a roof-to-shell configuration (using API 650 5.9.5 as a starting point) then review section 5.10 for reference. Note that your roof does not match any of the designs noted in section 5.10.1 but falls under 5.10.2.8. Section 5.10.3 covers allowable stresses for roof components and refers you to ANSI/AISC 360, using ASD only (not LRFD). Note that 5.11 requires that you consider wind uplift loading if the roof does not meet 5.10.4, which yours does not. Add material to the roof-to-shell junction using one of the details in figure F.2 until the hoop stress is within allowables. Your critical load case may be uplift since that induces compression into the upper shell area. There is typically very little stress in this upper section of tank shell from liquid loading so you are usually just designing the roof-to-shell area as a separate structure. The vertical force can be assumed to follow 45 degree lnes downwards, make the vertical attachement tall enough to create a tall enough triangle such that at the bottom of the triangle the compressive stress is within allowables. Typically combining vertical loading from the fixed roof with hoop stress is not considered in API 650 tanks. As a possible guide see E.6.2.2 to see how vertical loads from seismic conditions are treated.
Remember - you read this on the wild wild web and is not a complete nor necessarily reilable response to your question, and although I most likely left out something important I can't think of it right now as I dash off this quick reply to your question.