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## How is Clamp Force for a Bolt and Nut Assembly Calculated?

Clamp force is what holds a bolted joint together.

Published charts are available for determining clamp force but we’ve found it’s often useful to understand how these numbers are calculated.

Bolt and nut ratings can be confusing.

Bolts are rated based on the force the material will withstand over a cross-sectional area. Obviously, this cross-sectional area is different for each size of bolt. UN bolts and nuts are rated in pounds per square inch (psi). Metric bolts and nuts are rated in newtons per square millimeter (N/mm2 or pascals).

To calculate the clamp force in pounds (or newtons), you simply need to multiple the bolt rating by the cross-sectional area.

This can be confusing because there are several different types of strength ratings (clamp, proof, yield, tensile, and ultimate) and it’s often not clear which one should be used in the calculation. Also, the cross-sectional area of the weakest part of the bolt is the threaded area and this isn’t a straightforward calculation.

#### Bolt Rating

To determine which bolt rating to use in the calculation we’ll refer to the Stress-Strain Curve graph from our previous blog post (also seen below). The proof load is highest tensile force the bolt can withstand without taking any permanent deformation. For a reasonable factor of safety, the industry accepted value to use for bolt rating in the formula above is 75% of the proof load.

#### Cross-Sectional Area

The cross-sectional area for the threaded portion of the bolt (often referred to as the stress area) is calculated using a formula that accounts for the specific diameter and thread pitch. This is the formula for UN bolts.

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### Example Results

#### Are you having troubles with bolted joints? Give us a call. We’re here to help.

In the next post we’ll explain how to calculate the rotational force (or torque) required to achieve the desired clamp force and factors that can affect the results.

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