How do I calculate an assembly torque?

The following assumes a metric thread form according to ISO 68-1 ISO general purpose screw threads -- Basic profile -- Part 1: Metric screw threads and ISO 724 ISO general-purpose metric screw threads -- Basic dimensions. Also, it is assumed that all assembly torque is used to overcome friction and develop joint preload, so the joint members must be elastic and there must not be any prevailing torque.

M[sub]A[/sub] = F[sub]M[/sub] (0.16 &[ignore]middot[/ignore]; P + 0.58 &[ignore]middot[/ignore]; d[sub]2[/sub] &[ignore]middot[/ignore]; &[ignore]mu[/ignore];[sub]G[/sub] + &[ignore]mu[/ignore];[sub]K[/sub] &[ignore]middot[/ignore]; D[sub]Km[/sub]/2)

where

M[sub]A[/sub] is the assembly torque in N m
F[sub]M[/sub] is the preload in kN
P is the pitch in mm
d[sub]2[/sub] is the pitch diameter in mm
&[ignore]mu[/ignore];[sub]G[/sub] is the thread friction coefficient
&[ignore]mu[/ignore];[sub]K[/sub] is the bearing friction coefficient
D[sub]Km[/sub] = (d[sub]w[/sub] +d[sub]h[/sub])/2
d[sub]w[/sub] is the bearing surface outer diameter in mm
d[sub]h[/sub] is the hole diameter in mm

The target preload F[sub]M[/sub] usually is chosen as a certain percentage of the screw yield stress.

F[sub]M[/sub] = &[ignore]nu[/ignore]; &[ignore]middot[/ignore]; &[ignore]sigma[/ignore];[sub]M[/sub] &[ignore]middot[/ignore]; A[sub]0[/sub]

where

&[ignore]nu[/ignore]; is the percentage of yield stress chosen (90% is standard)
&[ignore]sigma[/ignore];[sub]M[/sub] is stress due to combined tension and torsion
A[sub]0[/sub] is the relevant shank cross-sectional area (Full, reduced, or threaded shank)

&[ignore]sigma[/ignore];[sub]M[/sub] = R[sub]p0.2[/sub] / [1 + 3(3/2 &[ignore]middot[/ignore]; d[sub]2[/sub]/d[sub]0[/sub] &[ignore]middot[/ignore]; {P/(&[ignore]pi[/ignore]; &[ignore]middot[/ignore]; d[sub]2[/sub]) + 1.115 &[ignore]mu[/ignore];[sub]G[/sub]})[sup]2[/sup]][sup]0.5[/sup]

where

R[sub]p0.2[/sub] is the screw yield stress
d[sub]0[/sub] is the diameter corresponding to A[sub]0[/sub]
&[ignore]pi[/ignore]; = 3.141 592 654