Miter Bend Formula to Calculate Length, Angle of Cut, Weight, and Cut-back of the Miters? (With PDF)

In the Piping and Pipeline Engineering field, Miter Bend plays an important role because standard Elbows are not easily available and economical for larger pipe sizes. The site Engineer or the Fabrication supervisor is responsible for the perfect delivery of the joints made for the miter bend.
This article will provide detailed calculation procedures for finding out the required dimensions, angles of cut, and weight of the pipe.

What is a Miter Bend?

A Miter Bend or Miter Elbow is prepared by mitering (angle cutting) and welding pipe ends of the cut pieces, usually at 45° and 90° to form a corner. There are two types of miter bend, one non-perpendicular bend & another is 3-D bend. Miter Elbow/Bend is made from miter-cut pieces of pipe. The Miter pieces also called gores, There are two end gores and two middle gores in a 4-piece Miter bend.

Standards Associated with Miter Bend

• AWWS (American Water Work Association): For sizing and the number of cuts/miter.
• ASME B16.9: For end preparation of the miters

Note: According to ASME B31.3, the number of miters is restricted to a maximum of 5.

Important Points about Miter Bend

• Miter bends are not standard pipe fittings.
• It is also called a fabricated bend.
• Highly skilled welders and fitters are required for perfect miter bend preparation.
• Used mainly in general services (category “D” fluid).
• If used in process lines then above 14” pipe size.
• Used above 6” for utility lines.
• Miter bend can be fabricated with 2, 3, 4, & 5 miters.
• The number of cuts will be a maximum of 5.

Note:
1. The number of miters will be decided according to the pressure and temperature of the line.
2. Application size range can vary from company to company.

Limitations of Miter Bend

• Poor strength because of the more number of joints.
• Higher pressure drop.
• Higher turbulence.
• Higher risk of corrosion because of more numbers of weld joints.
• Less strength.
• Not suitable for pigging.
• High-skilled manpower is required.

Advantages of Miter Bend

• Low cost.
• No thinning required
• It can be made at the site or in the workshop.

Inputs Required for Calculation

Pipe/Line Size	Schedule Number	Material Type	Bend Angle	Number of Cut	Radius of Bend
8″	SCH 120	CS (Carbon Steel)	90	3	2.5 D

Steps for Calculation

Step-1: Write down the available data(refer to Table No. 1)

We have,

D = 8”,     OD (Outer Diameter) of pipe =  219 mm
Schedule- SCH120
Material- CS (Carbon Steel)
Bend Angle = 90°
No. of cuts = 4
R = 2.5 D = 2.5*8*25.4 = 508 mm

Step-2: As per the number of cuts, Sketch the drawing as below (refer to Fig. 2)

Step-3: Find the Angle of the Cut (refer to Fig. 2 for all the steps)

We know,

Step-4: Find the Center Line Length (CL₁) of the First Miter

We know from Pythagoras,s formula,

Important Note:

1. The first and last miter always will be of the same length at each point.
2. Except for the last miter, all the miter’s length will be double of the first miter at every point.

Therefore,

            CL₂ = CL₁ * 2 = 272 mm
            CL₃  = CL₁ * 2 = 272 mm
            CL₄ = CL₁ = 136 mm

Step-5: Calculate the Inside and Outside Radius (IR & OR) of the bend.

We know from fig. 2,

Step-6: Calculate the Inside Length (IL₁) of the First Miter.

We know from Pythagoras formula,

Therefore,

            IL₂ = IL₁ * 2 = 214 mm
            IL₃  = IL₁ * 2 = 214 mm
            IL₄ = IL₁ = 107 mm

Step-7: Find out the Outside Length (OL₁) of the First Miter

We know from Pythagoras’s formula,

Therefore,

            OL₂ = OL₁ * 2 = 330 mm
            OL₃  = OL₁ * 2 = 330 mm
            OL₄ = OL₁ = 165 mm

Step-8: Find the “Length of Pipe required” for the Miter Bend.

Length of pipe required = CL₁ + Cutting allowance + CL₂ + Cutting allowance + CL₃ + Cutting allowance + CL₄
Note- Cutting allowance depends upon the cutting method used, we are assuming 5 mm, refer to Fig. 3.

Thus,
         L = 136+5+272+5+272+5+136
        L = 831 mm

Step-9: Calculate the Weight of the Pipe.

Check the Plain End Mass in the code book under the code “ASME B36.10 for 8” SCH 120 Pipe (refer to Fig. 4).

Plain End mass is given 90.44 kg/m as per ASME B 36.10 M
Now,
find the weight using the following formula-

Weight of the Pipe = Plain End Mass * Length of Pipe ( in meter)

Weight (W) = 90.44 * 0.831 = 75 kg.

Step-10: Get the Cut-back (optional).

Cut-back = CL₁ – IL₁

Cut-back = 136 – 107 = 29 mm

Few more useful resources for you.

Piping Elbows vs Bends: A useful literature for piping engineers
Piping Elbow or Bend SIF (Stress Intensification Factor)
Tee Connection: A short literature for piping engineers
Technical requirements for Pipes & Fittings for preparation of Purchase Requisition
“Pipe Coupling”-A short Introduction for the piping professionals
Comparison of Pipe and Tube (Pipe Vs Tube)
Details about Spectacle Blind and Spacers