Most of the piping systems I deal with are in relatively low seismic zones so horizontal acceleration alone is considered. In some projects with much higher seismic values, the horizontal and vertical components will be combined.

The Caesar II user guide shows multiple methods of doing this, without providing much guidance on why you'd choose one method over another, other than saying "sometimes you want to do this".

Below is a condensed version of the load cases.

Method 1:
L1 = Operating
L2 = Operating + U1 (horizontal) + 0.67U2 (vertical)
L3 = Sustained
L4 = L2 - L1 (algebraic)
L5 = L3 + L4 (abs or scalar)

Method 2:
L1 = Operating
L2 = Operating + U1 (horizontal)
L3 = Operating + U2 (vertical)
L4 = Sustained
L5 = L2 - L1 (algebraic)
L6 = L3 - L1 (algebraic)
L7 = L5 + L6 (SRSS)
L8 = L4 + L7 (abs or scalar)


What drives the decision to use either method? From a quick test the stresses appear almost identical while restraint loads are different due to the different combination of loads in the operating cases.