You won't find a stress equation for the hydro-test case in B31.3, it's not there. However, this is a "weight" case - primary loads. Therefore CAESAR II uses the Sustained analysis procedure.
As was pointed out above, your model may be different between the HYD and other load cases. Once you designate a load case as HYD, CAESAR II automatically locks springs and expansion joints (sets their stiffness to rigid). Therefore the global stiffness matrix is different, therefore you end up with a different solution.
One other difference is that B31.3 states corrosion should be removed from the SUS and OCC cases, so be default that is all CAESAR II will corrode. That means if you have corrosion in your job, the SUS case will consider corrosion but the HYD case won't. You can force corrosion to be considered in all load cases by changing the "configuration", set the ALL_STRESS_CASES_CORRODED directive to TRUE.
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Regards,
Richard Ay - Consultant