Hello Mr Maleki
You do not mention the code of construction. In ASME Section VIII, Division 1, the code does not specifically address supports. However, PWHT is a procedure to lessent the likelihood of brittel fracture, and as the skirt is on tension, at least some to the time, my personal opinion is that PWHT should be considered for skirts.
Usually, a skirt is thinner that the vessel components, so the MDMT for the skirt may be lower that the MDMT for the vessel.
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Sincerely,
Ray Delaforce
CADWorx & Analysis Solutions
Hexagon PPM