Fastener engineer here!

Torque is a means to an end. The end goal is actually to stretch the screw. The screw behaves like a rubber band. As you stretch it out, it wants to return to its original length. As it does so, it squeezes the components you are fastening together. This is typically called clamp load. This clamp load is difficult to measure directly, requiring modifications to include an expensive load cell or ultrasonic measurement. Neither of these are practical in any production environment, and basically impossible at home. Torque on the other hand is really easy to cheaply measure.

What dictates how much clamp load you can get for a given torque is the friction you have to overcome as you tighten and how much clamp load the bolt can sustain. The total load be the proof load of the part and is based on the grade. Friction primarily comes from the contact between the threads and the contact between the underside of the screw's head and your joint components. This friction is also what prevents the screw from coming loose on its own. The amount of friction must be controlled so that you require a consistent amount of torque to reach a consistent amount of clamp load. This is typically done by careful control of the screws finish and application of lubricants.

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There is a pretty simple formula for figuring out approximate torque if you know a few things about the components.

T = KDP

T= torque

K= dimensionless friction value for the entire joint. Takes into consideration the finishes and geometry of all of the components. Can be approximated in non-critical joints, for safety critical should always be experimentally derived.

D= nominal thread diameter

P= clamp load, often 75% of the proof load of the bolt

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If for example I wanted to figure out what torque I should tighten a 1/4-20 grade 5 hex cap screw into a joint that has a matching nut or a tapped hole at least 3/8 deep:

K= .22 (typical for zinc plated parts, would change if using something with significantly different geometry like a flange bolt, different finish, or with lubricant added.)

D= .250 in

P= 2025 lbf (75% proof load)

.22 * .250 * 2025 = 111 in-lb

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One consideration for the DIY at home is that lubrication will often reduce the amount of friction, meaning LESS torque is required to reach the required clamp load. The consequence here is that the torque value your service manual says you should use may actually be enough to damage the threads if you use lubricants that were not originally used during manufacturing.