Calculation for a straight pipe under external pressure is referenced in section 304.1.3 of ASME B31.3. As per this section, to determine wall thickness and stiffening requirements for straight pipe under external pressure, the procedure outlined in the BPV Code, Section VIII, Division 1, UG-28 through UG-30 shall be followed, using as the design length L, the running centerline length between any two sections stiffened in accordance with UG-29.

As an exception, for pipe with D_{o}/t < 10, the value of S to be used in determining P_{a} shall be the lesser of the following values for pipe material at design temperature:

- 1.5 times the stress value from Table A-1 of ASME B31.3, or
- 0.9 times the yield strength tabulated in Section II, Part D, Table Y-1 for materials listed therein (The symbol D
_{o}in Section VIII is equivalent to D in ASME B31.3 Code.)

In piping systems which are subject to vacuum, it is likely that the external pressure may govern the required wall thickness specially for large bore and thin walled piping. Calculations for determining wall thickness in external pressure are required to be done in case the pipe is subject to vaccum conditions or offshore pipelines which are subject to hydrostatic head where the external pressure will depend on the water depth. Failure of piping due to external pressure can occur at lower pressure due to elastic buckling as the pipe geometry is weaker in compression than in tension. The external pressure at which elastic buckling occurs is called the critical elastic pressure. The length of pipe at which the critical stress is achieved is called the critical length of pipe. Any cylinder which exceeds the critical length is considered to be of infinite length because the additional length does not contribute to stiffness of the pipe. The critical length L_{c} is given by the following equation:

L_{c} = 1.11D\(\sqrt{\frac{D}{t}}\)

Calculations for external pressure as per ASME, Section VIII, Division 1 requires first the calculation of a parameter A, which is a function of geometry, and then calculation of parameter B, which depends on A and a material property curve.

## Steps in calculating the wall thickness for external pressure

We have to first start by considering the wall thickness available for external pressure. Unlike calculations for internal pressure, the calculations for external pressure is more of a verification for determining the suitability of pipe for the external pressure.

### Step 1

Assume thickness available for pressure

t = T - M - c

where

T = Nominal pipe wall thickness

M = Mill Tolerance

c = sum of mechanical allowances.

### Step 2

Calculate D_{o}/t and L/D_{o}

For L/D_{o} > 50 use a value of L/D_{o} = 50 where

D_{o} = Pipe Outside Diameter

L = Maximum unstiffened length of pipe. Calculate the maximum distance between flanges, stiffening rings, pipe caps, elbows etc. Flanges, heads, and stiffeners that comply with ASME BPVC, Section VIII, Division 1, para. UG-29 are deemed to be stiffeners.

### Step 3

Refer to ASME Section II, Part D, subpart 3 Figure-G to determine factor A.

### Step 4

Use the value of factor A determined above. Then go to the figure (material temperature charts) based on the applicable piping material and determine factor B.

### Step 5

Calculate Allowable External Pressure P_{a} if the value of factor B is determined.

P_{a} = \(\frac{4B}{3(\frac{D_o}{t})}\)

or if the value of factor A falls to the left of material/temperature lines and value of factor B cannot be determined, use the equation below

P_{a} = \(\frac{2AE}{3(\frac{D_o}{t})}\)

where

E is the Modulus of Elasticity

If value of P_{a} is less than the external design pressure, select a higher value of pipe wall thickness and repeat the above calculations until P_{a} is ≥ the external design pressure.

### Step 6

Also verify that the pipe wall thickness satisfies the hoop stress equation.

## Example Calculation for External Pressure

The following section illustrates with an example how the external pressure calculation is performed. The figures from ASME Section II Part D have been used for illustration. Use the applicable figures from ASME to perform the actual calculations.

**Example**

Calculate for a 40" pipe to ASTM A106 Gr. B, the required wall thickness to withstand full vacuum conditions (15 psi or 100 kPa) assuming there is no stiffener in the straight section of pipe for over 100m length. The corrosion allowance for pipe is 1.6mm and no other mechanical allowances are to be considered. Consider a mill tolerance of 12.5% and design temperature of 300°F.

**Solution**:

Let us start with a 40" pipe with nominal wall thickness of sch STD which is 9.53 mm.

For purpose of calculation D_{o} is converted to mm = 40 inches x 25.4 = 1016mm

and L is converted to mm = 100,000mm

**Step 1**

Calculate Pressure design thickness

t = 9.53mm - Mill tolerance (1.19mm) - Corrosion allowance (1.6mm) = 6.74mm

(*Note that mill tolerance of 12.5% = 9.53 x 0.125 = 1.19mm*)

**Step 2**

Calculate D_{o}/t and L/D_{o}

D_{o}/t = 1016/6.74 = 151

and L/D_{o} = 50 since actual L/D_{o} = 100,000/1016 = 98.5 is greater than 50

**Step 3**

Refer to ASME Section II, Part D, subpart 3 Figure-G to determine factor A

From Chart as shown in figure below value of A = 0.00005

**Step 4**

Use the value of factor A determined above. Then go to the figure (material temperature charts) based on the applicable piping material and determine factor B.

For carbon steels with specified minimum yield strength 30,000 psi and over, curve Figure CS-2 is applicable for determining value of B.

**Step 5**

Calculate Allowable External Pressure P_{a}

It is noted that factor A is on left side of the curve. Hence, allowable external pressure will be calculated using the equation

P_{a} = \(\frac{2AE}{3(\frac{D_o}{t})}\)

Hence P_{a} = 2 x 0.00005 x 29 x 10^{6} / (3 x 151) = 6.4 psia

The selected pipe wall thickness is not suitable for vacuum. Hence let us perform Iteration 2 with higher wall thickness.

**Iteration 2**

**Solution**:

Let us now try with a 40" pipe with nominal wall thickness of sch XS which is 12.7 mm.

For purpose of calculation D_{o} is converted to mm = 40 inches x 25.4 = 1016mm

and L is converted to mm = 100,000mm

**Step 1**

Calculate Pressure design thickness

t = 12.7mm - Mill tolerance (1.5875mm) - Corrosion allowance (1.6mm) = 9.5125mm

(*Note that mill tolerance of 12.5% = 12.7 x 0.125 = 1.5875mm*)

**Step 2**

Calculate D_{o}/t and L/D_{o}

D_{o}/t = 1016/9.5125 = 107

and L/D_{o} = 50 since actual L/D_{o} = 100,000/1016 = 98.5 is greater than 50

**Step 3**

Refer to ASME Section II, Part D, subpart 3 Figure-G to determine factor A

From Chart as shown in figure below value of A = 0.000098

**Step 4**

Use the value of factor A determined above. Then go to the figure (material temperature charts) based on the applicable piping material and determine factor B.

For carbon steels with specified minimum yield strength 30,000 psi and over, curve Figure CS-2 is applicable for determining value of B.

**Step 5**

Calculate Allowable External Pressure P_{a}

It is noted that factor A is on left side of the curve. Hence, allowable external pressure will be calculated using the equation

P_{a} = \(\frac{2AE}{3(\frac{D_o}{t})}\)

Hence P_{a} = 2 x 0.000098 x 29 x 10^{6} / (3 x 107) = 17.7 psia

The selected higher pipe nominal wall thickness of 12.7mm is suitable for vacuum.