Tightening
torque to preload a bolt 

Metric thread : 
 
Initial tensile stress : σ_{t }= 
·R_{p0.2}

Thread coeff. of friction : µ_{thread
}= 

Head  face coeff. of friction : µ_{head }= 


pitch P 
mm 
pitch diameter d_{2} 
mm 
root diameter d_{3} 
mm 
tensile stress area A_{t }=π/4
d_{0}^{2 }; d_{0}=(d_{2}+d_{3})/2 
mm^{2} 
ultimate tensile strength R_{m} 
MPa 
yield strength R_{p0.2} 
MPa 
tensile stress σ_{t} = σ'_{t} x R_{p0.2} 
MPa 
torsional stress τ = M_{G }/ ( π/16
d_{3}^{3 }) 
MPa 
equivalent stress σ_{e} = (σ_{t}^{2
}+ 3τ^{2})^{½} 
MPa 
thread friction M_{G} 
Nm

thread friction M_{G} 
Nm

head face friction M_{WD} = F_{i} μ_{head}
1.3 d/2 
Nm 
Total tightening torque M_{A }= M_{G} + M_{WD} 
Nm 
Initial preload F_{i }=
σ_{t }·A_{t} 
kN 
Load at Yield F_{02 }=
R_{p02 }·A_{t} 
kN 
Load reserve P_{b}=F_{0.2 } F_{i} 
kN 
^{1)} stress by torsion is
relaxed after tightening.
^{2)} equivalent stress should remain below the yield
strength (linear elastic). 

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