A padded nozzle on a 1.8 m drum
A NPS 10 nozzle with a reinforcing pad on a 1800 mm cylinder, worked by WRC 537. The inputs are invented; the numbers are what the calculator gives. Change them in the box at the end and the result moves.
1. The inputs
- Shell: 1800 mm inside diameter, 22 mm thick, 3 mm corrosion allowance, S = 138 MPa.
- Design: 1.2 MPa at 150 °C.
- Nozzle: 273.1 mm outside diameter, 12.7 mm wall. Pad: 420 mm diameter, 16 mm thick.
- Loads at the junction: P = 2000 N, shears 1500 N, moments 2, 1.5 and 1 kN·m.
2. Geometry parameters
The bulletin works from the shell mean radius, the thickness where the nozzle meets the shell, and how big the attachment is.
- Thickness at the nozzle edge T = 22 + 16 − 3 = 35 mm (shell plus pad, less corrosion).
- Mean radius Rm = 912.5 mm, so the shell slenderness γ = Rm / T = 26.07.
- Corroded nozzle radius r0 = 273.1 / 2 − 3 = 133.55 mm, so β = r0 / Rm = 0.128.
3. Pressure stress
Pressure alone loads the shell before any attachment load: hoop 57.03 MPa and longitudinal 28.52 MPa, which is half. These are added to the local stresses at each point.
4. Stress at the nozzle edge
Stress in MPa at four points round the nozzle, on the outer (u) and inner (L) surface.
| Point | σφ | σx | τ | Combined |
|---|---|---|---|---|
| Au | 85.3 | 20.6 | 0.36 | 85.3 |
| AL | 94.7 | 35.0 | 0.36 | 94.7 |
| Bu | 95.9 | 33.6 | 0.15 | 96.0 |
| BL | 89.9 | 24.1 | 0.15 | 89.9 |
| Cu | 49.3 | 40.9 | 0.15 | 49.3 |
| CL | 63.6 | 49.2 | 0.15 | 63.6 |
| Du | 62.0 | 48.6 | 0.36 | 62.0 |
| DL | 52.4 | 43.6 | 0.36 | 52.5 |
The highest combined stress is 95.95 MPa. The pad edge, where the shell is thinner than under the pad, is lower: 67.7 MPa.
5. The checks
With S = 138 MPa the limits are 1.5S = 207 MPa for local primary membrane stress Pl and 3S = 414 MPa for Pl + Pb + Q.
- Nozzle edge: Pl = 92.93 MPa, ratio 0.45. Pl + Pb + Q = 95.95 MPa, ratio 0.23.
- Pad edge: Pl = 59.46 MPa, ratio 0.29. Pl + Pb + Q = 67.7 MPa, ratio 0.16.
- Nozzle neck: longitudinal Pm = 12.49 MPa against 138, shear 1.57 MPa against 96.6.
Every ratio is below 1, so the case passes. The governing check is Pl at the nozzle edge, at 0.45. Most of the stress here is pressure, not the attached loads: enter a radial load of 2000000 N, a thousand times more, in the box below and Pl at the nozzle edge reaches 287 MPa, over 1.5S, and the case fails.
Try it
Result
PASS
WRC 537 local stress at the nozzle and pad edges, against the ASME VIII-2 limits. 2 engine notes are in the full report. A quick check, not a design record.
How the bulletin method works: The bulletin method and the quick reference.