I have a 208 volt three phase AC supply. We want to attach one 18 amp single phase load to A-B and another identical single phase load to B-C. There is no load attached to A-C. There are resistive loads. My question is: How much current flows in Leg B? These two loads are the only connections to the supply. The neutral is not used.

If the loads draws 18 amps on A and B, and then 18 amps on B and C then
18 + 18 = 36 amps on the B phase.
Can you explain why you have asked this question? Were you expecting a
different result? If so, what were you expecting?

Thank you for your reply. Because the source is a 3 phase AC supply I was wondering if the 120 degree off-set between phases would make a difference. If these were DC power sources through resistive loads then the Ohm's law calculation would indicate 36 amps in the B leg. I know that calculating current flow in 3 phase loads requires the use of the square root of 3 in the calculations. That is why 3 phase circuits cause ma a bit of confusion at times. I could just set it up on a bench and just measure with an amp clamp meter.