7.10Thread Failure by Shear Pull-Out

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

Last Updated 29 Oct 2026

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7.10.1 Introduction

To guarantee the pull-out (striping) strength capacity of the thread a certain length of the engaged thread, Leng , is necessary. In nut-tightened joints the full length of the female thread is normally engaged, i.e. Leng = Ln . For manufacturing reasons, threaded hole joints often only have engaged thread for only a portion of the hole’s length.

Fastener systems with ‘normed’ nuts are completely bearing capable when the strength class of the nut is at least as high the strength class of the fastener.

It is recommended to use nuts with lower stiffness than the fastener in order to give more uniform load transfer through the threaded interface. If calculations indicate that the female thread is too weak, it is important to consider the use of a thread insert of higher strength (e.g. a helicoil). The calculation methods presented in this section are applicable to any thread system, including helicoils.

7.10.2 Failure of the Female Thread

The critical fastener load for failure of the female thread is given by,

F_{ult,th,n} = \tau_{ult,n} * A_{th,n} * c_{1} * c_{3} \tag{7.10.1}

where; $\tau_{ult,n}$ is the ultimate tensile shear strength of the material forming the female thread, $A_{th,n}$ is the surface area around the female thread that is assumed to fail during thread pull-out, and $c_{1}$ & $c_{3}$ are empirical coefficients (derived for ISO metric threads) accounting for the depth of supporting material behind the female thread and the strength ratio of the two threads (see equations [7.10.4], [7.10.5] and [7.10.6] below).

The female thread’s failure surface area is calculated by (see Reference 7.2),

A_{th,n} = \pi d \left( \frac{L_{eng,eff}}{p} \right) \left[ \frac{p}{2} + (d - D_{2}) \tan(\theta) \right] \tag{7.10.2}

where p is the thread pitch, and D2 is the pitch diameter of the female thread, θ is the half angle of the thread groove, and Leng,eff is the effective length of engaged thread given by,

\text{Leng,eff} = \text{Leng} - 2^{*}p \tag{7.10.3}

which accounts for the beginning portion of the engaged thread, which does not transmit any significant load (1,0p on the upper part and 1,0p on the lower part of the engaged length, for a total of 2p).

The coefficient c1 is either 1,0 for a threaded hole, or calculated by the following equation for a threaded nut:

c_{1} = 3.8 \left( \frac{s_{w}}{d} \right) - \left( \frac{s_{w}}{d} \right)^{2} - 2.61 \tag*{[7.10.4]}

where sw is the wrench size as indicated in Figure 5-5.

Equation [7.10.4] is only valid for metric threads with 1.4 ≤ ቀ 𝑑𝑑 ቁ≤ 1.9.

The coefficient $c_{3}$ is given by,

c_{3} = 0,897 \quad \text{for } R_{s} \geq 1,0, \text{ or} \quad [7.10.5]

c_{3} = 0,728 + 1,769R_{s} - 2,896R_{s}^{2} + 1,296R_{s}^{3} \quad \text{for } 0,4 < R_{s} < 1 \quad [7.10.6]

where for $R_{s} \leq 0,4$ : $R_{s} = 0,4$

where; $R_{s}$ is the shear strength ratio of the female and male threads according to;

R_{S} = \frac{\tau_{ult,n} A_{th,n}}{\tau_{ult,b} A_{th,b}} \tag*{[7.10.7]}

where; $\tau_{ult,b}$ is the ultimate tensile shear strength of the material forming the male thread and $A_{th,b}$ is the failure surface area of the male thread calculated by (see Reference 7.2),

A_{th,b} = \pi D_{1} \left( \frac{L_{eng,eff}}{p} \right) \left[ \frac{p}{2} + (d_{2} - D_{1}) \tan(\theta) \right] \tag*{[7.10.8]}

where D1 is the minor diameter of the female thread and d2 is the pitch diameter of the male thread (see Section 5.4).

If the both threads are steel, Equation [7.10.7] can be replaced with;

R_{s} = \frac{\sigma_{ult,n} A_{th,n}}{\sigma_{ult,b} A_{th,b}} \tag{7.10.9}

where; $\sigma_{ult,n}$ and $\sigma_{ult,b}$ are the ultimate tensile strengths of the female and male thread materials respectively.

Table 7-4 - <<deleted>>

Using equations [7.10.2] and [7.10.3] the necessary length of engaged thread can be expressed as,

l_{eng,req} = \frac{F_{th} p}{c_{1} c_{3} \tau_{ult,n} \pi d \left[ \frac{p}{2} + (d - D_{2}) \tan(\theta) \right]} + 2p \tag{7.10.10}

where Fth is the axial load transmitted by the thread, from both maximum preload and the applicable proportion of the axial applied force, as defined by the joint stiffness ratio.

The most unfavourable case for the load-bearing capacity of the threaded joint is when the external diameter $d$ of the bolt thread is at the lower tolerance limit and the pitch flank diameter $D_{2}$ of the nut thread is at the upper tolerance limit. Equation [7.10.10] for finding the necessary length of thread engagement is for this reason modified as follows for the case when the effective thread dimensions are not known:

l_{eng,req,min} = \frac{F_{th} p}{c_{1} c_{3} \tau_{ult,n,min} \pi d_{min} \left[ \frac{p}{2} + (d_{min} - D_{2max}) \tan(\theta) \right]} + 2 p \tag{7.10.11}

7.10.3 Failure of the Male Thread

Normally the fastener’s material strength is higher or equal to that of the nut, so when ‘normed’ nuts with equal or lower material strength to the fastener are used, there is no need to calculate failure of the male thread.

If the fastener's material is weaker than the nut or insert, $R_{s} > 1$ from Equation [7.10.7], the analysis is the same except for Equation [7.10.1] in which the variables, $\tau_{ult,n}$ and $A_{th,n}$ , are replaced by $\tau_{ult,b}$ and $A_{th,b}$ respectively and it is important to use the correction factor $c_{2}$ (derived for ISO metric threads) instead of $c_{3}$ .

Thus, the strength of the male thread is calculated by,

F_{ult,th,b} = \tau_{ult,b} A_{th,b} c_{1} c_{2} \tag{7.10.12}

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where $\tau_{ult,b}$ is the ultimate shear strength of the fastener material, $A_{th,b}$ is the failure area of the male thread as calculated by Equation [7.10.8], and the coefficient $c_{1}$ is calculated as for the female thread.

The coefficient $c_{2}$ is given by,

c_{2} = 1,187 \quad \text{for } R_{\text{S}} \geq 2,2, \text{ or} \quad \text{[7.10.13]}

c_{2} = 5,594 - 13,682R_{\text{S}} + 14,107R_{\text{S}}^{2} - 6,057R_{\text{S}}^{3} + 0,9353R_{\text{S}}^{4} \quad \text{for } 1,0 < R_{\text{S}} < 2,2 \quad \text{[7.10.14]}

The minimum required engagement length is calculated as follows:

l_{eng,req,min} = \frac{F_{th} p}{c_{1} c_{2} \tau_{ult,n,min} \pi d_{min} \left[\frac{p}{2} + (d_{2min} - D_{1max}) \tan(\theta)\right]} + 2 p \tag{7.10.15}

7.10.4 Margin of Safety on Thread Pull-Out

The margin of safety on shear pull-out of the thread under the external load is calculated by,

MoS_{th,A} = \frac{F_{th,crit}}{F_{A} sf_{ult}} - 1 \tag{7.10.16}

and for the overall load,

MoS_{th,tot} = \frac{F_{th,crit}}{F_{V,\max} + \Phi_{n} F_{A} sf_{ult}} - 1 \tag{7.10.17}

where Fth,crit is the critical thread failure load (lower of the male and female thread strengths).

No MoS calculations are necessary for yield failure of the thread.