If the piping system is linear, then L3 & L4, below, give the same results:
L1: T1
L2: W
L3: T1+W
L4: L1+L2 (algebraic)

If the system is not linear, e.g. there are +Y supports, then L3 need not be the same as L4. This is because the stiffness matrices from L1 & L2 may not be identical.

The B31.3 piping code has little to say about incorporating nonlinear response into the analysis. Liftoff of supports (a nonlinear response) is considered in the longitudinal stress due to sustained loads in B31.3 Appendix S.

For combining load cases in CAESAR II (like L4 above), you can sum the stress magnitudes (what we call scalar summation) or you can sum stresses "algebraically", in which case the SIGNED loads are combined and the stress is a product of these resultant loads. Our interpretation of B31.3 is that the signs should not considered in the sustained plus occasional stress evaluation. So this stress combination should be "scalar"rather than the typical (default) "algebraic".