mandee,
Air cooler header box is usually modeled as a rigid element and weight distributed among various bays (For bays, Refer API661 Figure 2) which is also shown by Jozm in his attachment. The header box movement is decided by the air cooler design. If the design is even pass (Inlet and outlet nozzles on same side the tube expansion is not included (as it allowed to expand on the other side) but if the air cooler is odd pass (Inlet nozzle on one side of the header box and outlet nozzle on other side) than the expansion of the tubes should be included at the respective header boxes. The lateral displacement of the header box(perpindicular to tubes) can be taken as 12mm on one side or 6mm on each side (depends on the design). You should refer the vendor drawing for various details.
In Jozm attchment Rz should be included at nodes 1120 & 1020 because the rotation of the header box will not be govern by the piping as the Air cooler is a massive structure. I hope that experts will agree with me.
Hope it will help
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Rajinder