Vessel

Shell OD  D Shell thickness  t Saddle spacing  L  (fixed → sliding) Material  → α

Service & supports

Metal ΔT above installation Slide friction coefficient  μ Weight carried by the SLIDING saddle  W Saddle + pier lateral stiffness  k

Read it like this. Only one saddle is fixed. Everything measured from that point grows by ΔL = α·L·ΔT and that growth has to happen somewhere. With a working slide the price is only the friction force μ·W, and it is the same whether the vessel grows 2 mm or 60 mm — friction does not care about travel. With a seized slide the price becomes k·ΔL, which scales with travel and with how stiff you made the pier. That is why a stiffer, "better" foundation is worse once the slide stops working.

Illustrative model. The seized force is the elastic demand k·ΔL, capped at full axial restraint E·A·α·ΔT (A = π·(D−t)·t, E = 190 GPa hot). In reality something yields long before that: anchor bolts shear, the pier cracks, the base plate tears, or the shell buckles at the saddle horn. The number is what the structure is being asked for, not what it will survive. Real designs also check Zick saddle-horn and circumferential stresses, wear-plate extent and saddle angle — not covered here.