Tightening torque to preload a bolt
 UNF thread :
 SAE Grade Number :
 Preload as percentage of proof strength :
 Thread coeff. of friction :
 Head face coeff. of friction :
 Major diameter d in
 Threads per inch N -
 Pitch P = 1/N 10-3 in
 Pitch diameter dp = d - 0.649519/N in
 Minor diameter dr = d - 1.299038/N in
 Tensile stress area At = π/4 ((dp+dr)/2)2 10-3 in2
 Proof strength Sp kpsi
 Initial tensile stress σi = C1 x Sp kpsi
 Torsional stress1) τ = MG / ( π/16 dr) kpsi
 Equivalent stress σe = (σi2 + 3τ2)½ kpsi
 Thread friction MG lb·in
 Thread friction MG- lb·in
 Head face friction MWD = Fi μhead 1.3 d/2 lb·in
 Initial preload Fi lb
 Total tightening torque MA = MG + MWD lb·in
 1) the equivalent stress is a result of the stress by tension and torsion.
 2) the torsional stress may vanish by relaxation.