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As a general rule, a bolt should engage a distancegreater than or equal to its outer diameter. The number of threads engaged can then be calculated from the number of threads per inch on the bolt. So if you are using a 1/4-20 bolt, meaning it has 1/4" diameter and 20 threads per inch, you should engage the bolt 1/4" into the hole, or 5 threads. (20 threads/inch x 1/4 inches)

Why: The shear stress on the threads will be equal to the tensile stress in the shank of the bolt. This means that once you thread the bolt in a distance greater than its diameter, the shank itself will fail before the threads shear off the bolt under tensile load.

Sources: Design of Machinery class at Purdue University, page 10 of the following MIT article: http://web.mit.edu/2.75/resources/FUNdaMENTALs%20Book%20pdf/FUNdaMENTALs%20Topic%206.PDF

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