I have a question, what part does yield or tensile strength play in the above formula?
Perhaps we jumped a bit ahead of ourselves. Let's back up a little.
How much clamping force do we need to keep a joint from coming apart?
More than the forces that are trying to take it apart.
Bolts come in various grades which determine their strength; called yield load.
SAE 2 = 43500 psi
SAE 5 = 95700 psi
SAE 8 = 136300 psi
We are really only interested in the higher grade bolts SAE 8.
The maximum clamping force that can be exterted by a bolt is determined by the
yield x bolt area.
The bolt area will depend on whether it is fully threaded, partially threaded or has a reduced shank.
Assume a 3/8 -24 SAE grade 8 with a shank diameter of 3/8".
Max clamping force = yield (136,300 psi) * bolt area (0.110 in2) = 14,993 lbs
If that clamping force is too small, a larger bolt should be used.
If the clamping force is too great for the the material being used (avoid crush), a
smaller or lower grade bolt can be used.
The bolt should be torqued to the yield limit just at the point of leaving the elastic range and entering the plastic range. A very close approximation to yield point can be determined by bolt stretch equal to about 0.2% or 0.002 times bolt length.
Bolt length, diameter and thread pitch are then used to determine angle torque.
Angle = Length x .002 x 360/Pitch (in inches)
For a 4 inch bolt. 3/8-24 we have:
4.0" x .002 x 360/0.0419" = 68.7 degrees.
This angle torque is measured from the pre-load torque point, where all the slack and clearances have been taken up. This should not include compressing a head gasket.
The advantage of the angle torque system is that it does not require the knowledge of thread, washer, head or nut friction, or of surface finish and lubrication. Friction does not matter. But, it does require the correct yield point force, and correct bolt diameter. A fully threaded bolt is quite different than a reduced shank bolt.
With a little bit of work, an excel spreadsheet can be constructed to accomodate a range of bolt grades, diameters, lengths, and thread pitches. To confirm clamping pressure, a product called FujiFilm can be used.