Introduction to External Pressure Design

Designing pressure vessels for external pressure (often referred to as vacuum design) is a critical task for mechanical and piping engineers. Unlike internal pressure, where the primary failure mode is tensile yielding, external pressure causes failure through instability or buckling. This buckling can occur at stresses far below the yield strength of the material.

In this guide, we break down the rigorous procedures defined by ASME Section VIII, Division 1 (UG-28 through UG-33) to ensure your vessel stays rigid under external loads.

1. Cylindrical Shells (UG-28)

The calculation for cylindrical shells depends on the ratio of the length to the diameter and the diameter to the thickness. ASME uses a trial-and-error iterative process involving geometric charts.

Step 1: Assume a Thickness ($t$)

Start with a trial thickness (often the thickness required for internal pressure).

Step 2: Determine Geometric Ratios

Calculate the ratios $L/D_o$ and $D_o/t$, where:

• L: Design length of the vessel section between stiffening rings or heads.
• D_o: Outside diameter of the shell.
• t: Nominal thickness minus corrosion allowance.

Step 3: Factor A

Using the $L/D_o$ and $D_o/t$ ratios, enter Section II, Part D, Subpart 3, Figure G to find Factor A. This is a dimensionless coefficient representing the strain.

Step 4: Factor B

Using Factor A, enter the applicable material chart in Section II, Part D (e.g., Figure CS-1 for Carbon Steel). Move horizontally to find Factor B.

Step 5: Calculate Allowable External Pressure ($P_a$)

If Factor A is on the curve:

If Factor A is to the left of the curve:

2. Spherical Shells (UG-28.1)

Spheres are inherently stronger under external pressure, but the calculation procedure differs slightly.

The Calculation Steps:

1. Calculate Factor A using the formula:
   $$A = \frac{0.125}{R_o/t}$$
   Where $R_o$ is the outside radius.
2. Determine Factor B from the material chart using Factor A.
3. Calculate Allowable Pressure:
   $$P_a = \frac{B}{R_o/t}$$

3. Ellipsoidal and Torispherical Heads (UG-33)

Heads under external pressure are calculated based on an Equivalent Spherical Radius ($K_1 D_o$).

Once the equivalent $R_o$ is determined, use the same procedure as the Spherical Shell section above.

4. Stiffening Rings (UG-29)

When the shell thickness becomes economically unfeasible, engineers add stiffening rings. These rings reduce the "effective length" ($L$), thereby increasing the allowable external pressure.

Moment of Inertia Requirement ($I_s$)

The stiffening ring must have a required moment of inertia calculated by:

Where $A_s$ is the cross-sectional area of the ring and $L_s$ is the distance between rings.

Common Mistakes in Calculations

• Ignoring Corrosion: Always use the "corroded" thickness for calculations.
• Temperature Impact: Factor B is highly dependent on the Design Temperature. Using the wrong chart results in unsafe designs.
• $L$ Calculation: Forgetting to include one-third of the depth of the heads in the total length $L$.

Summary Table for Quick Reference