Shell & nozzle

Shell OD  D Shell thickness  T Nozzle size Reinforcement pad thickness  t_p

Loads

Design pressure  p Nozzle moment from the RIGID-anchor pipe model  M First pipe leg length  L (straight, anchored far end)

Read it like this. The shell is a rotational spring K_shell in series with the piping's own stiffness K_pipe. A displacement-driven (thermal) load therefore delivers only M × K_shell/(K_shell+K_pipe) — the rigid-anchor model over-states it. Then the local shell check (WRC-107 style: general membrane P_m + local membrane P_L + local bending P_b) is what actually governs, not the stress in the nozzle pipe. Thickening the shell or adding a pad makes the joint stiffer, so it attracts more moment — and still usually wins, because stress falls faster than load rises. Watch both bars move together.

Illustrative model. K_shell ≈ ½·E·a³·(T_eff/R)^1.5 and P_b = 6·(M/a)·ℓ / (b_eff·T_eff²) with shell attenuation length ℓ = √(R·T_eff) and b_eff = a + 2ℓ. These reproduce the right trends and rough magnitudes, not WRC numbers — real work uses WRC 107/537 curves for stress, WRC 297 or shell FE for flexibility. Allowables shown are P_m+P_L ≤ 1.5S and P_m+P_L+P_b ≤ 2.25S with S = 138 MPa, a simplified stand-in for the real code stress-category table.