The primary stress pipe equations in the ASME code, subsection III, Ref. [1], and similar codes add stress contributions from pressure and bending and impose a limit on this sum, while a limit on the pressure hoop stress is imposed separately. The equations constitute interaction formulae for the resistance of the pipe cross-section to the combined action of pressure and bending, similar to the limits on primary membrane and primary membrane plus primary bending stress for a rectangular section. For the latter, an analytical limit load solution is found e.g. in Ref. [2]. In this paper, closed-form limit analysis collapse interaction formulas are derived by means of limit analysis for thin-walled as well as moderately thick-walled straight pipes subjected to internal pressure and pipe bending. The analytical solutions are confirmed by means of non-linear finite element analysis. Moreover, the resistance to combined loading as predicted from the derived interaction formulas is compared to the resistance according to the ASME code primary stress pipe equations and the deviations are elaborated.