Typically hanger design is a "two load case, one pass" affair: restrained weight to get the hot load, then a free thermal to obtain the travel. Once you have these two values, you pick the hanger. At this point, the hanger preload and stiffness are inserted into the model and "your" load cases are analyzed.
But what happens if the hanger stiffness is significant compared to the stiffness of the nearby piping? Sometimes the hanger affects the behavior of the piping system.
Some people/organizations want to perform a second free thermal with the hanger inserted. If the resulting travel results in a different spring being selected, then the new spring is inserted and the process is repeated (this is the iteration you refer to).
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Regards,
Richard Ay - Consultant