External Pressure Calculation (ASME Section VIII, Div. 1)

Applies to: Cylindrical shells (UG‑28), Heads (UG‑33)

References: ASME BPVC Section VIII Div. 1; ASME BPVC Section II Part D, Subpart 3 (Vacuum Charts & Tables—e.g., Table G & HA‑5)

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1. Scope & Applicable Rules:

When a vessel component is subject to external pressure (vacuum), the buckling capacity must be verified using the ASME chart method:

1. 1. 1. Cylindrical shells: UG‑28 (External Pressure)
      2. Heads : UG‑33 (External Pressure on Heads)
      3. Material data & charts: ASME Section II, Part D, Subpart 3 (Figures/Tables such as Figure G & HA etc.)

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2. Data Required:

Collect and confirm the following before starting:

• • Geometry:
    1. External (outside) diameter, Do​
    2. Corroded thickness, t (use t=tnom−CA)
    3. Equivalent outside spherical radius, (Ro​)
       1. Ro=Ko⋅Do
          where Ko​ is the head-shape factor
  • Material
    1. Material designation (e.g., SA‑240 S32205)
    2. Applicable vacuum chart/table (e.g., Table HA‑5)
    3. Elastic modulus, (E) at design temperature, taken from Section II Part D Subpart 3 curves/tables for the specific material
  • Design Conditions

1. 1. 1. Design external pressure, P
      2. Design metal temperature, T

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3. Geometric Ratios:

Compute the ratios required to enter the charts:

1. 1. For heads:
      1. Ro/t
   2. For shells (UG‑28):
      1. Length ratio L/Do/
      2. Thickness ratio Do/t

These ratios determine the Factor A position on the charts.

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4. Determine Factor A:

• • Ellipsoidal Head (UG‑33 / chart method)

1. • 1. As per UG‑28(d), calculate the geometry-based factor: A  =  0.125/(Ro/t)
   • Cylindrical Shell (UG‑28)
     1. Refer to Table G using the ratios L/Do​ and Do/t to obtain Factor A.
     2. Use linear interpolation between chart points where needed.

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5. Determine Factor B (Material/Geometry)
   1. Using ASME Section II, Part D, Subpart 3 (e.g., Table HA‑5), find Factor B corresponding to your Factor A and design temperature.
   2. Apply interpolation for intermediate temperatures and A values not directly listed.

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6. Calculate Maximum Allowable External Pressure Pa​
   1. As per UG-28:
      1.   Pa  =  4B/3(Do/t)  For cylindrical shells (UG‑28 (c))
      2.   Pa  =  B/(Ro/t)  For Heads (UG‑33 & UG-28 (d))
   2. Compare Pa​ with the design external pressure P.

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7. Acceptance Check & Design Changes
   1. Acceptance criterion:
      Pa  ≥  P
   2. If not satisfied:
      1. Add stiffener rings (UG‑29) as applicable
      2. Increase thickness t
      3. Change geometry
      4. Select a different material (higher Yield Strength)
      5. Reduce design external pressure (if process allows)

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8. Worked Example (Ellipsoidal Head)
   1. Given Data
      1. Do=510 mm
      2. tnom=6 mm, CA=1 mm ⇒ t=5 mm
      3. Design External Pressure = 0.101 MPa
      4. Outside diameter (D) = 510 mm                → use for Do/t
      5. Outside crown radius (Ro) = 448.45 mm  → geometry parameter & B
      6. Nominal thickness (tnom) = 6 mm
      7. Corrosion allowance (CA) = 1 mm
      8. Corroded thickness (t) = tnom - CA = 5 mm
      9. Material: SA‑240 S32205
      10. Design Temperature = 45 °C
      11. Design Pressure (P) = 1.01 MPa
      12. E(45∘C) = 193,378 MPa
      13. Chart selection: Table HA‑5 (vacuum chart for this material)
      14. Shape coefficient (Ko)  = 0.87931 ⇒ Ro=Ko⋅Do=448.45 mm
   2. Ratios
      1. Ro/t=448.45/5=89.69
      2. Do/t=510/5=102
   3. Factor A
      1. A=0.125(Ro/t)=0.125/89.69=0.001394
   4. Factor B (from Table HA‑5)
      1. B(45∘C)=129.3957 MPa
   5. Allowable External Pressure (use Pa=B/(Ro/t))
      1. Pa   =  B/(Ro/t) = 129.3957/89.69 ⇒ 1.4427 MPa
      2. Check: If Pa  ≥  Pdesign
      3.   1.4427 MPa ≥ 1.01 MPa ⇒ Meets Code Requirements

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