6.5Margin of Safety on Tightening

ECSS-E-HB-32-23A, Space Engineering — Threaded Fasteners Handbook

Last Updated 29 Oct 2026

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When specifying the torque tightening method for fastening, it is important to check the ability of the fastener to sustain the torquing. The stress occurring during the tightening process is composed by a tension caused by the increasing preload and a shear stress caused by the application of the torque. These two stresses are combined by the shape deformation energy hypothesis according to the Von Mises equation,

\sigma_{v.m.} = \sqrt{\sigma_{V,\max}^{2} + 3\tau_{\max}^{2}} \tag{6.5.1}

where σ V , max is the maximum axial stress in the fastener due to preloading, and τ max is the maximum shear stress due to remaining torsion in the fastener.

The total torque applied to the fastener during torque application $M_{app}$ is reacted by two moments;

the moment of friction forces in the thread, and

the moment of friction forces under the bolt head or nut

Due to equilibrium of moments, the maximum shear stress within the fastener's shank (or the adjacent non-engaged thread) is related to the moments due to under-head friction and the externally applied torque by,

\tau_{\max} = \frac{M_{app,\max} - M_{uh,\min}}{W_{p}} \tag{6.5.2}

where the minimum under-head frictional torque is given by,

M_{uh,\min} = \frac{d_{uh}}{2} (F_{V,\max} - F_{\Delta T^{+}}) \mu_{uh,\min} \frac{1}{\sin(\lambda / 2)} \tag{6.5.3}

and the polar section modulus is,

W_{p} = \frac{\pi d_{0}^{3}}{16} \tag{6.5.4}

It is important to note that the prevailing torque makes a significant contribution to the torsional stress in the fastener shank. Equation [6.5.2] includes this effect via the Mapp,max term. To minimise preload scatter it is recommended to measure (and compensate for) the prevailing torque each time a fastener is tightened.

After the shear stress in the fastener exceeds its yield point a state of total plastic deformation is reached, whereby the torsional stresses through the cross section are constant. To include this effect, the polar section modulus is corrected to,

W_{p}' = \frac{\pi d_{0}^{3}}{12} \tag{6.5.5}

From Equations [6.3.5] and [6.3.22] the maximum pretension stress is given by,

\sigma_{V,max} = \frac{F_{V,max} - F_{\Delta T^{+}}}{A_{0}} \tag{6.5.6}

The Margins of Safety on tightening are:

Yield: $MoS_{ti,y} = \frac{\sigma_{y}}{\sigma_{v.m.}} - 1$ [6.5.7]

Ultimate: $MoS_{ti,ult} = \frac{\sigma_{ult}}{\sigma_{v.m.}} - 1$ [6.5.8]

Figure description:

Text: ECSS
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No factors of safety are used in Equations [6.5.7] and [6.5.8] since all uncertainty sources are already included in FV,max .

If the MoS for yield is positive, the MoS for the ultimate is always positive. Therefore, the ultimate MoS in Equation [6.5.8] is not normally needed. One possible exception to this is yield controlled tightening methods (see Section 12.3).