THE TWO SUPPORTS
END RESTRAINT OF THE RUN
0MPa bending stress from settlement
Uniform part (harmless)
Differential Δδ = |δA−δB|
Angular distortion β = Δδ/L
Ground verdict
End moment M = c·EIΔδ/L²
End shear / nozzle force V
Stress σ = M/Z vs SA
Nozzle moment vs allowable
What the model does. Only the difference in settlement does work on the pipe. Treating the run as a prismatic beam of length L with a relative support movement Δδ: M = c·EIΔδ/L², and the end shear is 12EIΔδ/L³ (c=6) or 3EIΔδ/L³ (c=3), with c = 6 for a run held against rotation at both ends (the usual guided case), c = 3 fixed–pinned, c = 0 pinned–pinned — a truly free-to-rotate run picks up no stress at all, it just tilts. E = 203 GPa. Angular-distortion bands follow Bjerrum's classic chart. Real work needs the settlement profile from the geotechnical report, the actual support stiffnesses, and the vendor's nozzle allowables.