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## How Much Rotation Angle is Needed to Tighten a Fastener?

Hint: not as much as you think.

To answer this question, let’s start with an example of a fastener assembly with a 3/4″ x 10 Grade 5 bolt and nut and a 2” clamp distance, as shown in figure 1. Figure 1

For this example, once the nut face and the bolt head contact the clamp surface, the nut only needs to rotate 15° (as shown figure 2) to go from essentially zero clamp force to a full clamp force of 21,300 lbs. How is this possible? Figure 2

#### 1.

The distance between each thread is known from the thread call out. For example, on a metric M24 x 3.0 thread it’s quite simple. The 3.0 indicates the distance between each thread. Of course, it has to be a bit more complicated for the inch or UN series threads. On a 3/4” x 10 thread, the 10 indicates threads per inch. To calculate the distance between threads, 1” is divided by 10. The result is 0.10” between each thread. An illustration of this is shown in figure 3.

#### 2.

The distance the fastener will travel relative to the center axis with one complete rotation (360°) is equal to the distance between each thread. An illustration for a 3/4 x 10 thread is shown in figure 4 below. Figure 4

#### Rotation Angle Calculation

In our previous post, we showed the calculation for bolt stretch required to achieve full clamp load. In the example of a 3/4″ x 10 Grade 5 bolt and nut and a 2” clamp distance, this stretch amount is only 0.0043”. Knowing that one rotation (360°) will stretch the bolt 0.100” (or one pitch), this calculation used to determine the rotation angle needed to achieve this stretch amount:

Using the example above: (0.0043 / 0.100) x 360 ≈ 15°

Here’s a link to a spreadsheet that can be used to calculate clamp load, torque, bolt stretch, and rotation angle for any know clamp distance and fastener type. A screenshot of the spreadsheet is shown below.

#### Final Note

The details above are a simplified description of the situation that can be used for practical purposes. We’ve shown that it only takes a small amount of rotation of the bolt or nut to go from almost no clamp force to full clamp load in a bolted joint. In an actual assembly situation, most of the rotation after the nut contacts the clamp surface is only pulling the joint together. After this “snug” torque is achieved, the specified tightening angle starts from this point. The amount of rotation pulling the joint together and not actually adding to the clamp force will be dependent on the condition of the assembly, finish of the clamp surfaces, and materials used.

• Condition of the assembly – some rotation and clamp compression may not go toward tightening the joint but bending the components in to place if they are not flat or parallel.
• Clamp surface finishes – cast or rough surfaces will embed in each other during the initial tightening process
• Material – if the components being clamped together have softer material, part of the rotation will go toward compressing these materials and not stretching the bolt.

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