Simple conservative approximation:
When the currents A-B, B-C, and C-A are identical, say X, the currents on A, B, and C are identical and of value X * sqrt(3). The sqrt(3) factor (instead of 2) is due to the current in B from the A-B loads being 60 degrees out of phase from the current in B from the B-C loads (instead of 0 degrees out of phase).
So if you have A-B = B-C = C-A = 15.6, the currents in A, B, and C would be 15.6 * sqrt(3) = 27A. But this neglects the extra 5.2A on B-C. The simple approximation says just add that onto the B and C currents, so you get A = 27A, B = 32.2A, C = 32.2A. This is conservative, as the currents on B and C will be no more that 32.2A.
More accurate:
The 5.2A from B-C is actually at 30 degrees phase difference from the balanced currents from the balanced set of loads. So to get the B and C currents more accurately, we need to add 5.2A and 27A with a 30 degree phase difference. This can be done with the law of cosines, which says for vectors X and Y:
|X+Y|^2 = |X|^2 + |Y|^2 + 2*|X|*|Y|*cos(angle between X and Y).
That means the B and C currents are really sqrt(27^2 + 5.2^2 + 2*27*5.2*cos(30 deg)) = 31.6A. As you can see, a small difference from the conservative approximation.
Cheers, Wayne