## Trunnion Calculation Formula – MW. Kellogg Method

Any attachment to the pipe shell such as Trunnion, have to be designed so that the pipe shell bending and pressure stress due to load imposed to the pipes upon the pipes do not exceed the total allowable stress of the pipe.

**Bending Stress:**

Where,

- SB = Bending Stress in pipe shell, psi
- f = load induced by the attachment, lbs per linear inch along the edge of the attachment
- R = Outside Radius of PIpe Shell, Inches.
- t = Corroded Wall Thickness = Wall + Corrosion Allowance., plus the thickness of reinforcement pad, when Pad is required), inches

**2. Pressure Longitudinal Stress or also known as Longitudinal Primary Stress**

Where,

- SPL = Longitudinal Pressure Stress, Psi
- P = Internal Pressure at Design Conditions, Psi
- R = Outside Radius of the pipe shell, Inches
- t = Corroded Wall thickness = Wall Thick + Corrosion Allowance

**3. Circumferential Pressure Stress: or also known as Hoop Primary Stress.**

Where:

- SPC = Circumferential Pressure Stress, Psi
- P = Internal Pressure at Design Conditions, Psi
- R = Outside Radius of the pipe shell, Inches
- t = Corroded Wall thickness = Wall Thick + Corrosion Allowance

**4. Total Allowable Stress, S = is the total of the Allowable Bending Stress and Internal Pressure Stress:**

- Normal Operating Conditions = 2.0 x Sh
- Short Time Operating Conditions = 2.4 x Sh
- Normal Thermal Conditions Only = 1.25 . Sc + 0.25 Sh
- Short Time Operating with Thermal = 1.5 (Sh = Sc)
- Test Conditions = 2.4 x Sc

**Sh = Basic Allowable Stress at Design Temperature, Psi**

**Sc = Basic Allowable Stress at Atmospheric Temperature, Psi**

The total Allowable Stress must not exceed 30,000 Psi.

**5. Load Induced by Attachment, f , is used to calculate the localized bending stress, and consist of two type:**

- Loading Due to Longitudinal Bending,
*f**l = f longitudinal as lbs per Inch, where ML = Longitudinal Bending Moment as in-lbs.* - Loading Due to Circumferential Bending,
*fc**= f Circumferential as lbs per Inch, where Mc = Circumferential Bending Moment as in-lbs.*

Therefore, the value of** f **to be used for bending stress calculation is as below:

- Load Due to Sustained Effect for ( Longitudinal Bending and and Direct Axial Force),
**f1 = FL + 1.5 FA**

- Load Due to Sustained Effect for ( Circumferential Bending and and Direct Axial Force),
**f2= 1.5 (FC+ FA)**

We then need to compare the Combined Circumferential Stress and Combined Longitudinal Stress against the Allowable Stress.

**Combined Circumferential Stress = Circumferential Bending Stress + Hoop Primary Stress.****Combined Longitudinal Stress = Longitudinal Bending Stress + Longitudinal Primary Stress**