Tightening torque  to preload a bolt
 Metric thread : -
 Initial tensile stress : σt = Rp0.2 
 Thread coeff. of friction : thread =
 Head - face coeff. of friction : head =
 
 pitch P mm
 pitch diameter d2 mm
 root diameter d3 mm
 tensile stress area At =π/4 d02 ; d0=(d2+d3)/2 mm2
 ultimate tensile strength Rm  MPa
 yield strength Rp0.2 MPa
 tensile stress σt = σ't x Rp0.2 MPa
 torsional stress τ = MG / ( π/16 d3) MPa
 equivalent stress σe = (σt2 + 3τ2) MPa
 thread friction MG Nm
 thread friction MG- Nm
 head face friction MWD = Fi μhead 1.3 d/2 Nm
 Total tightening torque MA = MG + MWD Nm
 Initial preload Fi = σt At kN
 Load at Yield F02 = Rp02 At kN
 Load reserve Pb=F0.2 - Fi kN
  1) stress by torsion is relaxed after tightening.
  2) equivalent stress should remain below the yield strength (linear elastic).
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