Most failures of bolted joints are due to poor assembly and application of incorrect bolting torque. Hence it is important to ensure correct tightening of bolts to ensure leak free joints.

The torue applied to a bolt is used to overcome the following friction:

- Friction between the threads of bolt and nut.
- Friction between the nut head and the bearing surface (flange outer surface).

## Using Lubricant to reduce friction

A flanged joint when tightened using bolts acts like a compressed spring (see figure). Approximately 50% of the torque applied to a bolted connection is used to overcome the friction at the nut bearing surface and about 35% is dissipated in overcoming the thread friction. The balance of only 15% is available to produce the desired bolt preload. If the thread friction is reduced by application of lubricant a larger value of bolt preload is produced for the same applied torque. Hence special precaution should be taken after application of lubricant because now the same torque can produce sufficient preload to cause the fastener to yield and the bolted joint to fail.

Lubricant should be applied to both nut bearing surface and male threads on bolts. Lubricant used shall be chemically compatible with the bolting and flange material. Particular care should be taken to avoid lubricant chemistry that could potentially lead to stress corrosion cracking. Lubricant should also be suitable for the most severe service temperature.

## Factors affecting Torque values

Factors that affect torque values are flange rating, bolt size, type of gasket and lubricant friction factor.

*Torque Applied T* = \(\frac{kDF}{1000}\) *where*

T = Torque in N-m

F = Bolt load in N

D = Bolt diameter in mm

or

*Torque Applied T = *\(\frac{kDF}{12}\)* where*

T = Torque in ft-lb

F = Bolt load in pounds

D = Bolt diameter in inches

k = Nut factor, tightening factor or k-value

The k-value is not the coefficient of friction. It is an empirically derived correlation factor. The nut-factor depends on various factors including the following:

- Geometric factor - shape or type of threads
- Friction between threads of nuts and bolts
- Friction of nut against the bearing surface of the flange
- Bolt material
- Bolt diameter
- Assembly temperature

Because of a number of factors affecting the torque applied, no two fasteners even from the same lot will not require the same torque values to achieve the same bolt preload. The applied torque may vary between 20-30%.

## How much Bolt Load should you apply

When you apply torque to a bolt, the torque ultimately gets converted into tensile load on the bolt. The value of tension in a bolt should be such that it is within the elastic range, so that the bolt returns to its original condition once the tension is released. By definition, proof load is the applied tensile load that the fastener must withstand without permanent deformation. Acceptable Bolt Load (F) in equation above can vary between 40-75% of the Proof Load. This requires that the target bolt prestress is around 40-75% of the specified minimum yield strength of the material.

Bolt Load = 40-75% of specified minimum yield strength x tensile stress area of the bolt.

We know Modulus of Elasticity Y = \(\frac{Stress}{Strain}\)

If the required bolt preload is 70,000 psi, and knowing Y for carbon steel is 29,000 ksi, then strain is calculated as

Strain \(\frac{ΔL}{L} = \frac{70000}{29000*1000}\)

= 0.0024 inches per inch

Thus longer the joint length, the greater the total elongation will occur in the bolt to produce the desired preload.

## Example Calculation for Bolt Torque

In this example we will calculate the minimum and maximum bolt torque for a 6-inch class 150 flanged joint utilizing spiral wound gasket and ASTM A193 B7 Bolts. The nut factor is considered as 0.18 and the desired gasket seating stress is 7500 psi for spiral wound gaskets. The bolt yield strength for ASTM A193 B7 material is 105,000 psi. The maximum bolt design stress used for calculation is 60,000 psi which is 57% of bolt yield strength. This falls within the values recommended in the preceding paragraph.

**Solution**:

### Calculate Bolt Load and Torque for Gasket Seating

The first step is to calculate the bolt torque required to achieve a gasket seating stress of 7500 psi.

For 6-inch class 150, spiral wound gasket the gasket inside diameter is 7.19" and outside diameter is 8.25". These values are obtained from Table-9 of ASME B16.20.

Based on the ID and OD of gasket the gasket seating area is calculated as 12.854 inch^{2}.......................(1)

The Total Gasket Force is calculated as:

Gasket seating stress x Gasket seating area = 7500 x 12.854 = 96406 lbs.......................(2)

For 6-inch class 150 flange, the bolt size as per ASME B16.5 is 3/4" and number of bolts are 8 nos.

The root area of 3/4" bolt is 0.302 inch^{2}........................(3)

This value is obtained from Table H-1 of ASME B1.1.

Hence Force per Bolt due to gasket seating = Total Gasket Seating Force / Number of Bolts

Force per Bolt for Gasket Seating = 96406 / 8 = 12051 lbs.......................(4)

Bolt Stress (Gasket Seating) = Force per bolt (4) / Root Area of Bolt (3) = 12051 / 0.302 = 39,903 psi.

This is the *minimum bolt torque* for a 6-inch class 150 flanged joint utilizing spiral wound gasket and ASTM A193 B7 bolts.

### Calculate Bolt Load and Torque for Design Bolt Stress

To second step is to calculate the torque required to achieve a design bolt stress of 60,000 psi.

The bolt load to achieve a design bolt stress of 60,000 psi is calculated as

Bolt Root Diameter x Design Bolt Stress = 0.302 x 60,000 = 18120 lbs.......................(6)

This is the *maximum bolt torque* for a 6-inch class 150 flanged joint utilizing spiral wound gasket and ASTM A193 B7 bolts.

Based on Bolt Load of 18120 lbs, check the gasket seating stress does not crush the gasket.

The gasket seating stress based on bolt load of 18120 lbs is calculated as

Bolt load x No. of Bolts/Gasket seating Area = 18120 x 8 / 12.854 = 11277 psi.......................(8)

The above values match the torque values in this article. Note that the applied bolt torque should be larger of the torque required for gasket seating or target bolt design stress.

## What if you have longer bolts projecting beyond the nut

If the bolts project beyond the nut they are susceptible to corrosion and damage if not properly preserved and protected. Corrosion of excess threads can hinder joint disassembly. It is a good practice to fully engage the stud bolt with the nut on one end with bare minimum projection as required by ASME B31.3 so that all excess threads are located on the opposite end. Also a good engineering practice is to limit the bolt lengths so that do not project half an inch beyond the nut unless required for the use of hydraulic bolt tensioners.