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_A = F_M (0.16 &[ignore]middot[/ignore]; P + 0.58 &[ignore]middot[/ignore]; d₂ &[ignore]middot[/ignore]; &[ignore]mu[/ignore];_G + &[ignore]mu[/ignore];_K &[ignore]middot[/ignore]; D_Km/2)

where

M_A is the assembly torque in N m
F_M is the preload in kN
P is the pitch in mm
d₂ is the pitch diameter in mm
&[ignore]mu[/ignore];_G is the thread friction coefficient
&[ignore]mu[/ignore];_K is the bearing friction coefficient
D_Km = (d_w +d_h)/2
d_w is the bearing surface outer diameter in mm
d_h is the hole diameter in mm

The target preload F_M usually is chosen as a certain percentage of the screw yield stress.

F_M = &[ignore]nu[/ignore]; &[ignore]middot[/ignore]; &[ignore]sigma[/ignore];_M &[ignore]middot[/ignore]; A₀

where

&[ignore]nu[/ignore]; is the percentage of yield stress chosen (90% is standard)
&[ignore]sigma[/ignore];_M is stress due to combined tension and torsion
A₀ is the relevant shank cross-sectional area (Full, reduced, or threaded shank)

&[ignore]sigma[/ignore];_M = R_p0.2 / [1 + 3(3/2 &[ignore]middot[/ignore]; d₂/d₀ &[ignore]middot[/ignore]; {P/(&[ignore]pi[/ignore]; &[ignore]middot[/ignore]; d₂) + 1.115 &[ignore]mu[/ignore];_G})²]^0.5

where

R_p0.2 is the screw yield stress
d₀ is the diameter corresponding to A₀
&[ignore]pi[/ignore]; = 3.141 592 654