Strength of Screw Threads – Thread Stripping

The Strength of Screw Threads – Thread Stripping

Thread stripping is a complex phenomenon that occurs in a threaded joint under tensile load. When designing a joint with a threaded interface it is necessary to ensure that the length of thread engagement is sufficient to ensure that the integrity of the joint is not compromised by thread stripping. It is also preferable to ensure that the limiting failure mode is tensile rupture of the bolt, rather than thread stripping.

This article demonstrates, through the use of a recognised standard (BS 3580:1964), that a threaded joint is likely to be acceptable, provided that the tensile strength of the material forming the internally threaded part is equal to, or greater than that of the material forming the externally threaded part, and the length of thread engagement is equal to or greater than the nominal thread diameter. The effect of material dissimilarities are also discussed.

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Bearing Stress and Bolts Bolt Tightening Methods

This page is divided into the following sections:

  1. Introduction
  2. Taking Account of Thread Stripping in Design
  3. How do we Ensure that Thread Stripping is Prevented?
  4. Using the Bolted Joint Geometry Database
  5. A Useful Rule of Thumb
  6. Final Note

References

  1. http://www.boltscience.com/pages/strength.htm
  2. BS 3580:1964 – Guide to design consideration on the strength of screw threads
  3. ISO 898-1:2013 – Mechanical properties of fasteners made of carbon steel and alloy steel. Part 1: Bolts, screws and studs with specified property classes – Coarse thread and fine pitch thread
  4. BS ISO 965-1:2013 – ISO general purpose metric screw threads — Tolerances Part 1- Principles and basic data
  5. BS 3643-1-2007 – ISO metric screw threads – Principles and basic data
  6. BS 3643-2:2007 – ISO metric screw threads. Specification for selected limits of size

Relevant Downloads

TME_TEC_INF_SHT_ME_001_v01.0_SECURED.xlsx (583 downloads) Bolted Joint Geometry Database.
Copyright 2018 www.themechanicalengineer.com

1. Introduction

It is sometimes necessary for the engineer to design a bespoke threaded connection which does not incorporate a typical bolt / nut interface. Examples of such connections may be through-bolts or studs for pressure vessels or threaded bars with couplers for structural connections. In these cases, it is necessary to consider the capacity of the internal and external threads relative to each other and to the bolt section. It should be noted that the internally threaded part is the hole and the externally threaded part is the bolt. For example, consider the case of a standard Grade 8.8 stud bolt which engages with a female thread form cut into S355 structural grade steel as presented in Figure 1.

 

Thread Stripping

Figure 1 – Stud Bolt Engaged in Steel Material

For a typical configuration such as the one presented in Figure 1, it is usual to ensure that the limiting failure mode is by tension across the bolt section and not by stripping of the threads.  The tapped hole (or nut) should support more load than the bolt. I.e. it is necessary to ensure that there is a sufficient length of thread engagement (L_{e}) of the stud bolt into the structural steel to ensure that the bolt fails in tension across its section before the threads strip (see Section 2.1 for further details). Before moving on, it is probably a good idea to define some of the key terms in this context.

1.2 Thread Stripping

Thread stripping is a complex phenomenon that occurs in a threaded joint under tensile load. The failure is characterised by shear across a reduced thickness thread ridge. The reduced thickness of thread ridge is caused by bending or crushing of the thread form, nut dilation/radial expansion of the internal thread and necking under tension of the bolt shaft. The contact of the internal and external thread flanks generates the axial load in a bolt and this creates a shear force across the threads. The line of action which the shear load is carried is dictated by the relevant strengths of the internal and external thread materials.

Bending and crushing of the thread form reduces the shear area by basically just mashing the thread into a squashed and elongated shape. I can’t think of a better way to describe it than that. Nut dilation in combination with bolt necking due to tensile action reduces the overlap between threads and therefore reduces the available thread shear area. A good image of thread crushing and discussion of related effects can be found here [1].

1.3 Thread Engagement

The length of thread engagement (L_{e}) as presented in Figure 1, is defined as the axial distance through which the fully formed male and female threads are in contact. To give the simplest example: the length of thread engagement of a nut which is fully screwed onto a bolt is approximately equal to the thickness of the nut. It is often convenient to think of the length of engagement in terms of the number of full threads in “engagement”. It should be noted that the length of thread engagement is distinct from the depth of thread engagement, which is the distance that the threads overlap in a radial direction.

1.4 Nut Dilation

Nut dilation or radial expansion is the increase in the radial size of the internally threaded part in response to the radial portion of the contact load acting on the thread flank. Nut dilation reduces the depth of thread engagement. This pushes the contact area of the threads further away from the thread root and the thicker base of the thread ridge, thereby reducing the shear area of the thread which would be available to resist tensile loads in the joint. The magnitude of nut dilation is a function of the radial hoop stiffness of the fastener. I.e. a very wide nut with a small threaded hole will expand much less than an internally threaded, thin-walled pipe / tube. Therefore, it is especially important to take care when designing threaded joints in which one or more parts have relatively low radial (hoop) stiffness, as this presents a much higher risk of thread stripping.

2. Taking Account of Thread Stripping in Design

Taking into account thread stripping is a very simple process. The bolted connection is designed as normal and the required number of size of fasteners are selected. All that remains is to size a sufficient length of engagement to ensure that the bolt fails in tension across its section before the threads strip, whilst taking into account the combination of internal and external materials selected.

2.1 Why do We Want the Bolt to Fail in Tension Before the Thread Strips?

The answer to this question is perhaps not that obvious. Clause 2.2 of the (very) old, but still current and confirmed (i.e. good to use) British Standard, BS 3580:1964 [2] states that it is desirable, where possible, to design a threaded joint such that failure under tensile load occurs by breakage across the core cross-section of the threaded portion of the bolt and not by thread stripping. This is true for the following reasons:

2.1.1 Safety – Detection of Failure

Failure by thread stripping begins with bending of the thread form and ends by shearing of the internal or external threads. This failure tends to be gradual in nature and will be progressive when assembly of the joint is repeated. This type of damage to the threads is not easy to detect.

Let’s say for example, that a bolt thread has been damaged by over-tightening (over-torquing) during assembly. In this case, the engineer has very limited indication that the damage has occurred. The joint could then enter service and the only indication that the thread was damaged may arise too late after a dangerous thread stripping failure has occurred. In contrast, when the thread capacity is greater than the core capacity, then over-tightening will result in the bolt breaking before the structure is put into service.

When over-tightening (over-torquing) a bolt beyond yield, the bolt can suddenly feel slightly easier to torque (tighten). This is because the bolt material has entered the plastic regime where the application of additional load produces proportionately more elongation than it would in the elastic regime. When you feel a bolt becoming easier to tighten due to yielding then you have a clue that it may be about to break. Unfortunately, no amount of wishful thinking or “backing off a quarter of a turn” will now help you escape this predicament. It is irreparably damaged and must be condemned. If you were to give the spanner (wrench) another little turn then the bolt head or nut would probably snap clean off.

2.1.2 Serviceability

A less important factor is that it is generally much easier to remove a broken bolt from a female threaded hole than it is to repair a stripped thread. If the female thread has been cut in an expensive and complex assembly, then you may now suffer costly and time-consuming setbacks if the thread is ruined. You could re-machine the thread, but that generally means bringing whatever it is back to a workshop and setting it all up again.

2.1.3 Economy

Finally, thread stripping indicates an uneconomic use of the bolt material and that the full strength of the bolt has not been “developed” (put to good use).

2.1.4 Summary

For a reliable design, the potential of failure by thread stripping of both the internal and external threads must be avoided and it is important to ensure that the appropriate material choices are made for the internal and external threaded components.

3. How do we Ensure that Thread Stripping is Prevented?

Appendix A of BS 3580:1964 [2] provides a useful and relatively easy to follow method. The method is presented for both Unified and Whitworth thread forms; however, I will only provide the Unified version as Whitworth threads are essentially obsolete and the ISO Standard thread form (ISO 898-1:2013 [3]) is based on the Unified form.

The fundamental premise of the BS 3580:1964 method is based on the estimation of a shear area across the limiting thread and the comparison of this shear area against the tensile stress area of the bolt. Essentially, the method aims to ensure that the length of thread engagement is sufficient to ensure that the limiting thread shear area is greater than two times the bolt tensile stress area. I.e. the limiting failure mode will be due to bolt tensile rupture, rather than thread shear, if:

(1)   \begin{equation*} AS_{s} \geq 2A_{s} \end{equation*}

3.1 Thread Shear Areas

The shear areas of the internal and external threads are different. The internal thread shear area is larger than the external thread shear area. When considering a unified (ISO Standard) thread form, the internal shear area is around 30-40% greater than the external shear area. Appendix A of BS 3580:1964 provides the formulae to determine the effective thread shear areas of both the internal and external threads.

3.1.1 The Effect of Thread Tolerance

The shear area formulae provided in Appendix A of BS 3580:1964 are based on upper and lower limits of specific thread dimensions in accordance with the appropriate tolerance class for the threads being considered. It should be noted that the tolerance classes 6g/6H in accordance with ISO 965-1:2013 [4] are considered default values and should be considered appropriate for standardised fasteners which have been commercially produced in accordance with EN ISO 898-1:2013 [3]. Looser and tighter fit tolerances result in lesser and greater effective thread shear areas, respectively.

3.1.2 The Effect of Dissimilar Material Properties

When the externally and internally threaded parts are manufactured from the same material, then it is sufficient only to determine the external thread shear area. However; when the parts are manufactured from dissimilar materials it is necessary to take into account the relative strength between the internally and externally threaded parts. See Section XX for further details.

3.1.3 External Thread

The thread shear area of the external thread is the effective area at a diameter equal to the maximum minor diameter of the internal thread. The formula for external thread shear area (AS_{s}) of a unified thread form is as follows:

(2)   \begin{equation*} AS_{s} = \pi \, n\, K_{n,max}\left(\frac {1}{2n}+ 0.577(E_{s,min}-K_{n,max})\right)} \end{equation*}

Where:

AS_{s} = external thread shear area (mm²)
n = number of threads per mm
K_{n,max} = maximum minor diameter of internal thread (mm)
E_{s,min} = minimum effective (pitch) diameter of external thread (mm)

Determining K_{n,max}

  • The maximum minor diameter of the internal thread, K_{n,max}, as defined in BS 3580:1964 is the maximum permissible minor diameter of the internal thread in accordance with the appropriate tolerance class for the thread. The minor diameter of the internal thread is referred to as D_{1} in the standard BS 3643-1:2007, which defines the geometrical properties of ISO metric thread profiles, for further information on this subject, see our page here.
  • The value of the maximum minor diameter of the internal thread, K_{n,max} can be found in Table 1 of BS 3643-2:2007 [6]. The information is also included in our downloadable Bolted Joint Geometry Database.

Determining E_{s,min}

  • The minimum effective pitch diameter of the external thread, E_{s,min}, as defined in BS 3580:1964 is the minimum permissible pitch diameter of the external thread in accordance with the appropriate tolerance class for the thread. The pitch diameter of the external thread is referred to as d_{2} in the standard BS 3643-1:2007, which defines the geometrical properties of ISO metric thread profiles, for further information on this subject, see our page here.
  • The value of minimum effective pitch diameter of the external thread, E_{s,min} can be found in Table 1 of BS 3643-2:2007 [6]. The information is also included in our downloadable Bolted Joint Geometry Database.

3.1.4 Internal Thread

The thread shear area of the internal thread is the effective area at a diameter equal to the minimum major diameter of the external thread. The formula for internal thread shear area (AS_{n}) of a unified thread form is as follows:

(3)   \begin{equation*} AS_{n} = \pi \, n\, K_{n,max}\left(\frac {1}{2n}+ 0.521(D_{s,min}-E_{n,max})\right)} \end{equation*}

Where:

AS_{n} = internal thread shear area (mm²)
n = number of threads per mm
E_{n,max} = maximum effective (pitch) diameter of internal thread (mm)
D_{s,min} = minimum major diameter of external thread (mm)

Determining E_{n,max}

  • The maximum effective pitch diameter of the internal thread, E_{n,max}, as defined in BS 3580:1964 is the maximum permissible pitch diameter of the internal thread in accordance with the appropriate tolerance class for the thread. The pitch diameter of the internal thread is referred to as D_{2} in the standard BS 3643-1:2007, which defines the geometrical properties of ISO metric thread profiles, for further information on this subject, see our page here.
  • The value of the maximum effective pitch diameter of the internal thread, E_{n,max} can be found in Table 1 of BS 3643-2:2007 [6]. The information is also included in our downloadable Bolted Joint Geometry Database.

Determining D_{s,min}

  • The minimum major diameter of the external thread, D_{s,min}, as defined in BS 3580:1964 is the minimum permissible major diameter of the external thread in accordance with the appropriate tolerance class for the thread. The major diameter of the external thread is referred to as d in the standard BS 3643-1:2007, which defines the geometrical properties of ISO metric thread profiles, for further information on this subject, see our page here.
  • The value of the minimum major diameter of the external thread, D_{s,min} can be found in Table 1 of BS 3643-2:2007 [6]. The information is also included in our downloadable Bolted Joint Geometry Database.

3.2 Calculating Required Length of Engagement

As discussed previously, it is preferable to ensure that the threaded portion of the bolt (externally threaded part) will break by tensile failure before either the external or internal threads strip. Therefore, we want to ensure that a sufficient length of engagement is specified, taking into account a possible difference in material strength between the internal and external threads. For this reason, BS 3580:1964 [1]  states that the limiting shearing strength of the threads should be taken as one half of the bolt tensile strength, which provides a small factor of safety. I.e.:

(4)   \begin{equation*} AS_{s} \geq 2A_{s} \end{equation*}

3.2.1 Internally and Externally Threaded Parts Manufactured from the Same Material

Where the internally and externally threaded parts are manufactured from the same material, the length of engagement is calculated as follows:

(5)   \begin{equation*} L_{e} = \frac {2 A_{s}}{AS_{s}} \end{equation*}

Where:

L_{e} = the length of engagement of a threaded connection that will develop the maximum strength of the connection with external and internal threads manufactured of materials of equal tensile strength (mm). I.e. The length of engagement required to ensure that the bolt snaps before the threads strip.
A_{s} = the tensile stress area of the bolt, as determined using the formula from Annex A.3 of BS 3643-2:2007 [xx], which is explained on our page here.

It should be noted that this formula already includes the aforementioned safety factor.

3.2.1 Internally and Externally Threaded Parts Manufactured from Dissimilar Materials

Where the external and internal threads are manufactured from dissimilar materials of different tensile strengths, BS 3580:1964 [1] defines a factor J describing the relative strength in shear of external threads with respect to internal threads. The factor J is computed from the following formula:

(6)   \begin{equation*} J = \frac{AS_{s}f_{u.ex}}{AS_{n} f_{u.in}} \end{equation*}

Where:

J = a factor describing the relative strength in shear of external threads with respect to internal threads
f_{u.ex} = the tensile strength of the externally threaded material (N/mm²)
f_{u.in} = the tensile strength internally threaded material (N/mm²)

The length of engagement of a threaded connection of differing materials is subsequently adjusted to breakage of the bolt before thread stripping. The adjusted engagement length, Q is calculated using the following formulae:

(7)   \begin{equation*}  \begin {split} & if\,\,J < 1, Q=L_{e} \\ & if\,\,J > 1, Q=J\times L_{e} \end{split} \end{equation*}

Where:

Q = the adjusted length of engagement of a threaded connection to account for variation in material strength (mm). I.e. The adjusted length of engagement required to ensure that the bolt fails in tension, before the threads strip.

It should be noted that the consideration of dissimilar materials is only relevant if the internally threaded part has a lower tensile strength than the externally threaded part, as the lesser of the two shear stress areas is that of the externally threaded part, AS_{s}.

4. Using the Bolted Joint Geometry Database

We have developed and made available for download Bolted Joint Geometry Database that includes all of the required reference information to complete a thread engagement check following the BS 3580:1964 method.

4.1 Relevant Thread Dimensions

The dimensions, D_{s,min}E_{s,min}E_{n,max} and K_{n,max} are listed in the worksheet tab titled “Thread_Tol_DB” of the database workbook. The appropriate columns are highlighted in Figure 2.

Bolted Joint Geometry Database Extract - Thread Stripping

Figure 2 – Extract from Bolted Joint Geometry Database

4.2 Thread Shear Areas

The internal and external thread shear areas, calculated using Equations 2 and 3 above are also listed in the worksheet tab titled “Thread_Tol_DB” of the database workbook. The appropriate columns are highlighted in Figure 3.

Bolted Joint Geometry Database Extract - Thread Stripping

Figure 3 – Extract from Bolted Joint Geometry Database

4.3 Required Length of Engagement

The required length of thread engagement, L_{e} (mm) assuming that both the internally and externally threaded parts are manufactured from the same material is calculated using Equation 5 above and listed in the worksheet tab titled “Thread_Tol_DB” of the database workbook. The appropriate column is highlighted in Figure 3.

5. A Useful Rule of Thumb

When the internally and externally threaded parts are manufactured from the same material, there is a common rule of thumb which states that provided the length of engagement is not less than the nominal diameter of the bolt, then the limiting failure mode will be failure by tension across the bolt section and not failure by stripping of the threads. I.e. failure by thread stripping is avoided if:

(8)   \begin{equation*} L_{e} \geq d \end{equation*}

This is proven as true for all bolts assessed using the BS 3580:1964 method, except a select number of thread combinations with the loose fit tolerance class 8g/7H. The proof of this check is performed in worksheet tab titled “Thread_Tol_DB” of the database workbook. The appropriate columns are highlighted in Figure 3.

In conclusion, a threaded joint is likely to be acceptable, provided that the tensile strength of the internally threaded material is equal to or greater than that of the externally threaded part and that the length of thread engagement is equal to the nominal thread diameter.

6. A word of Caution

Based on the above methods, it may appear to be possible to continually increase the thread strength by increasing the length of engagement. However, this is not true in practice due to the distribution of load through a threaded joint. Figure 2 of BS 3580 provides an estimate of the theoretical load distribution through a threaded interface and predicts that approximately 30 to 40% of the tensile load in a connection is taken in the first thread, with the decreasing non-linearly to approximately zero after an engagement length of around one nominal diameter. After an engagement length of one nominal diameter, there is no appreciable increase in strength. Once the applied load has exceeded the first thread’s capacity, it will fail and subsequently cause the remaining threads to fail in succession.

Further information is provided in the article on thread load distribution.

7. Final Note

Clause 2.5 of BS 3580:1964  explicitly states that “…formulae based on ‘shear areas’ are unrealistic, as they incorrectly assume that shear occurs in threads not previously deformed by bending, and that the internally threaded member suffers no radial expansion…”. However; the standard then goes on to state that “…Despite the inadequacy of formulae based on the ‘shear area’ of undistorted threads, this approach is at present the only one generally applicable to the calculation of stripping strength…”. Therefore, in the absence of an alternative recognised method, documented in a reputable standard, the method presented is BS 3580:1964 provides an adequate verification and is one which can be relied upon.