ISO/TR 16224:2012

Technical aspects of nut design

This Technical Report gives information concerning the design criteria for nuts specified in ISO 898-2 so that, under static tensile overload, the stripping fracture mode is prevented. The design criteria are also applicable to non-standardized nuts or internally threaded elements with ISO metric screw threads (in accordance with ISO 68-1) mating with bolts. However, dimensional factors such as the width across flats or other features related to rigidity of nuts, and thread tolerances can affect the load ability of the individual bolt and nut assemblies. Therefore, it is intended that verification tests be carried out. NOTE The terms "bolt" and "nut" are used as the general terms for externally and internally threaded fasteners, respectively.

Aspects techniques de conception des écrous

General Information

• Status: Published
• Publication Date: 28-Mar-2012
• ICS: 21.060.20 - Nuts
• Technical Committee: ISO/TC 2/SC 12 - Fasteners with metric internal thread
• Drafting Committee: ISO/TC 2/SC 12 - Fasteners with metric internal thread
• Current Stage: 9092 - International Standard to be revised
• Completion Date: 28-Mar-2022

Standards Content (Sample)

TECHNICAL ISO/TR
REPORT 16224
First edition
2012-04-01
Technical aspects of nut design
Aspects techniques de conception des écrous
Reference number
ISO/TR 16224:2012(E)
©
ISO 2012

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ISO/TR 16224:2012(E)
COPYRIGHT PROTECTED DOCUMENT
© ISO 2012
All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized in any form or by any means,
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Published in Switzerland
ii © ISO 2012 – All rights reserved

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ISO/TR 16224:2012(E)
Contents Page
Foreword .iv
1 Scope . 1
2 Normative references . 1
3 Symbols . 1
4 Design principle . 3
4.1 Possible fracture modes in bolt and nut assemblies subjected to tensile load . 3
4.2 Calculation of the fracture loads in bolt and nut assemblies . 3
4.3 Influencing factors on the loadability of bolt and nut assemblies . 6
5 Calculation methods of bolt and nut assemblies in accordance with Alexander’s theory . 8
5.1 General . 8
5.2 Minimum nut height for nuts with specific hardness range . 9
5.3 Minimum hardness for nuts with specific nut height .10
5.4 Proof load . 11
6 Comparison among specified values in ISO 898-2 and calculated results . 11
6.1 General considerations for obtaining the specified values . 11
6.2 Calculation of the minimum Vickers hardness (HV) and the stress under proof load (S ) for
p
individual nuts of style 1 and style 2 . 11
6.3 Consequences for ISO nut design .14
Bibliography .15
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ISO/TR 16224:2012(E)
Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies
(ISO member bodies). The work of preparing International Standards is normally carried out through ISO
technical committees. Each member body interested in a subject for which a technical committee has been
established has the right to be represented on that committee. International organizations, governmental and
non-governmental, in liaison with ISO, also take part in the work. ISO collaborates closely with the International
Electrotechnical Commission (IEC) on all matters of electrotechnical standardization.
International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2.
The main task of technical committees is to prepare International Standards. Draft International Standards
adopted by the technical committees are circulated to the member bodies for voting. Publication as an
International Standard requires approval by at least 75 % of the member bodies casting a vote.
In exceptional circumstances, when a technical committee has collected data of a different kind from that
which is normally published as an International Standard (“state of the art”, for example), it may decide by a
simple majority vote of its participating members to publish a Technical Report. A Technical Report is entirely
informative in nature and does not have to be reviewed until the data it provides are considered to be no longer
valid or useful.
Attention is drawn to the possibility that some of the elements of this document may be the subject of patent
rights. ISO shall not be held responsible for identifying any or all such patent rights.
ISO/TR 16224 was prepared by Technical Committee ISO/TC 2, Fasteners, Subcommittee SC 12, Fasteners
with metric internal thread.
iv © ISO 2012 – All rights reserved

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TECHNICAL REPORT ISO/TR 16224:2012(E)
Technical aspects of nut design
1 Scope
This Technical Report gives information concerning the design criteria for nuts specified in ISO 898-2 so that,
under static tensile overload, the stripping fracture mode is prevented.
The design criteria are also applicable to non-standardized nuts or internally threaded elements with ISO
metric screw threads (in accordance with ISO 68-1) mating with bolts. However, dimensional factors such as
the width across flats or other features related to rigidity of nuts, and thread tolerances can affect the loadability
of the individual bolt and nut assemblies. Therefore, it is intended that verification tests be carried out.
NOTE The terms “bolt” and “nut” are used as the general terms for externally and internally threaded fasteners,
respectively.
2 Normative references
The following referenced documents are indispensable for the application of this document. For dated
references, only the edition cited applies. For undated references, the latest edition of the referenced document
(including any amendments) applies.
ISO 68-1, ISO general purpose screw threads — Basic profile — Part 1: Metric screw threads
ISO 724, ISO general-purpose metric screw threads — Basic dimensions
ISO 898-1, 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
ISO 898-2, Mechanical properties of fasteners made of carbon steel and alloy steel — Part 2: Nuts with
specified property classes — Coarse thread and fine pitch thread
ISO 18265, Metallic materials — Conversion of hardness values
3 Symbols
The following symbols apply in this Technical Report.
2
A actual stress area of the bolt, in mm
s
2
A nominal stress area of the bolt specified in ISO 898-1, in mm
s,nom
2
A shear area of the bolt threads, in mm
Sb
2
A shear area of the nut threads, in mm
Sn
C modification factor for nut dilation
1
C modification factor for thread bending on the bolt stripping strength
2
C modification factor for thread bending on the nut stripping strength
3
d
nominal thread diameter of the bolt, in mm
d basic minor diameter conforming to ISO 724, in mm
1
d basic pitch diameter of the thread according to ISO 724, in mm
2
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ISO/TR 16224:2012(E)
d minor (root) diameter of the bolt, in mm
3
d equivalent diameter of the stress area A , in mm
A s
D nominal thread diameter of the nut, in mm
D minor diameter of the nut, in mm
1
D pitch diameter of the nut, in mm
2
D countersink diameter of the nut, in mm
c
D mean diameter of bell mouthed section of nut in the effective nut height or the length of thread
m
engagement m , in mm
eff
F tensile load, (general)
F bolt breaking load, in N
Bb
F ultimate tensile load, in N
m
F proof load, in N
p
F stripping load of bolt and nut assembly, in N
S
F bolt thread stripping load, in N
Sb
F nut thread stripping load, in N
Sn
F ultimate clamp force, in N
u
F yield clamp force, in N
y
h height of chamfer per end, in mm
c
H height of the fundamental triangle of the thread according to ISO 68-1, in mm
m height of a nut, in mm
m critical nut height giving same probabilities of stripping and breaking failure modes, in mm
c
m effective nut height, in mm
eff
m critical effective nut height giving same probabilities of stripping and breaking failure modes, in mm
eff,c
P
thread pitch, in mm
R tensile strength of the bolt material according to ISO 898-1, in MPa
m
R tensile strength of the nut material, in MPa
mn
R strength ratio
s
s
width across flats of the nut, in mm
S stress under proof load, in MPa
p
x
shear strength/tensile strength ratio
µ coefficient of friction between threads
th
τ shear strength of the bolt material, in MPa
Bb
τ shear strength of the nut material, in MPa
Bn
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ISO/TR 16224:2012(E)
4 Design principle
4.1 Possible fracture modes in bolt and nut assemblies subjected to tensile load
Three fracture modes can occur in bolt and nut assemblies under static tensile overload:
— bolt breaking when the length of thread engagement is long enough, and the strength of the nut or internal
thread material is high enough;
— bolt thread stripping when the length of thread engagement is too short, and the strength of the nut or
internal thread material is relatively high;
— nut thread stripping when the length of thread engagement is too short, and the strength of the nut or
internal thread material is relatively low.
Of these fracture modes, bolt breaking is preferable since it indicates the full loadability (performance) of the bolt
and nut assembly. Furthermore, the thread stripping partially induced in the tightening process is difficult to detect;
therefore, it increases the risk of fracture due to the shortage of the clamp load and/or the loadability in service.
4.2 Calculation of the fracture loads in bolt and nut assemblies
4.2.1 General
As described in 4.1, in the event of static tensile overload during tightening a bolt, screw or stud together with a
nut, three possible fracture modes characterized by three different fracture loads can occur:
— bolt breaking load (F );
Bb
— bolt thread stripping load (F );
Sb
— nut thread stripping load (F ).
Sn
These three loads depend principally on the nut height, the hardness or the material tensile strength of the nut,
the hardness or the material tensile strength of the bolt, and the diameter, pitch and effective length of thread
engagement between bolt and nut.
Furthermore, these three loads are linked; this means that an increase in the hardness of the nut, for example,
induces an increase in the bolt thread stripping load.
[5]
E. M. Alexander defined an analogical model which allows the calculation of these three loads. A bolt and nut
assembly conforming to ISO 898-1 and ISO 898-2 is basically designed in such a way that the assembly should
not fail in the stripping fracture mode when static tensile overload is present, because such a failure could go
undetected. This means that the breaking load in the bolt should be the minimum value between these three loads.
This is the reason different ranges of nut heights and hardness values are defined for regular nuts (style 1) and
high nuts (style 2) as specified in ISO 898-2.
4.2.2 Bolt breaking load (F )
Bb
4.2.2.1 General
Breaking normally occurs at the middle of the free threaded length in grip; therefore, the breaking load has
nothing to do with the specifications of nuts.
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ISO/TR 16224:2012(E)
4.2.2.2 Bolt breaking load for purely tensile loading
For bolts in accordance with ISO 898-1, the tensile strength is defined as the ultimate tensile load divided by
the nominal stress area A :
s,nom
F
m
R = (1)
m
A
s, nom
with
π dd+
 
23
A =
s, nom
 
42
 
where
d is the basic pitch diameter of the thread according to ISO 724;
2
d is the minor diameter of the thread;
3
H
dd=−
3 1
6
where
d is the basic minor diameter according to ISO 724;
1
H is the height of the fundamental triangle of the thread according to ISO 68-1.
According to Equation (1), the stress area A is used as an index to convert the load into stress, or vice
s,nom
versa. The tensile strength R obtained by using Equation (1) for full-size bolt does not perfectly coincide
m
with the material property. For example, smaller bolts of a certain property class, in which the fundamental
deviations of d and d are relatively larger, need higher hardness or material tensile strength than larger bolts
2 1
of the same property class.
Therefore, in the design procedure, the actual stress area A is used instead of A , using the actual
s s,nom
dimensions of d and d . The breaking load F can then be obtained as:
2 1 Bb
FR=⋅A (2)
Bb ms
However, this does not mean that the real stress area can be determined only from the geometry of the thread,
i.e. from the pitch diameter and the minor diameter. It is well known that the loadability of a bolt is affected not
only by dimensions but also by the permanent strain distribution in the free threaded portion, induced by the
[6]
stress concentration effect . The free threaded length affects the permanent strain distribution, and therefore,
the loadability of a bolt. The bolt with a shorter free threaded length tends to endure higher tensile load.
4.2.2.3 Bolt breaking load for tightening loading with the combination of tension and torsion
[7]
VDI 2230 gives the following Equation (3) for the calculation of yield clamp force F :
y
RA
p0,2s
F = (3)
y
2
 
 
3 d P 
2
13++1,155μ
  
th
2 d πd
 
A  2 
 
Equation (3) is based on the maximum distortion energy theory, and assuming the constant yield torsional
stress on the whole sectional area. By using this fracture theory, the bolt breaking load for tightening loading,
i.e. ultimate clamp force F can be calculated by substituting R for R :
u m p0,2
RA
ms
F = (4)
u
2
 
 
3 d P
 
2
13++1,155μ
  
th
2 d πd
 A  2 
 
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ISO/TR 16224:2012(E)
4.2.3 Stripping loads (F , F )
Sb Sn
4.2.3.1 Stripping load for purely tensile loading
[5]
According to Alexander’s theory , the stripping loads F and F for bolt and nut threads can be obtained
Sb Sn
as follows:
FR=⋅0,6 ⋅⋅AC ⋅C

Sb mSb 12
(5)

FR=⋅0,6 ⋅⋅AC ⋅C

Sn mn Sn 13

where
C is the modification factor for nut dilation;
1
C and C are the modification factors for the thread bending effect, which can be obtained as follows:
2 3
2

Cs=−()Ds+−38,( Ds),26 (,for 14≤ 1

23 4

CR=−5,,594 13 682 + 14,,,107RR−+6 057 0,(9353RR for 12 << ,)2
2 s ss ss


= 0,(897 for R ≤ 1)  (6)
 ss

23
CR=+0,,728 1769 −+2,,896RR1 296 ()for 0,4<  3 ss ss

= 08, 997 ()for R ≥ 1
s


RA⋅
mn Sn
with R = .
s
RA⋅
mSb
a
Nut thread stripping.
b
Bolt thread stripping.
Figure 1 — Factors C and C for thread bending
2 3
Figure 1 shows the relationship between the factors C and C in relation to the strength ratio R . This shows
2 3 s
that the strength ratio R determines which thread (bolt or nut) will be stripped when stripping fracture mode
s
occurs although the stripping load is affected by the strength of the mated part (bolt or nut).
[8]
NOTE The experimental and analytical study using FEM shows that the factor C calculated by Equation (6) gives
1
conservative (too small) values for nuts with smaller width across flats. This means that the calculated results for nuts with
small width across flats tend to be safer.
For the calculation of the shear areas in Equation (5), the assumption is that 40 % of the chamfer height is
effective for the actual length of thread engagement m ; see Figure 2.
eff
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ISO/TR 16224:2012(E)
Key
d
major diameter of the bolt
D minor diameter of the nut
1
D countersink diameter of the nut
c
h height of chamfer per end
c
m actual measured nut height
m effective nut height ( = effective length of thread engagement)
eff
a
Detailed sketch of a joint with external and internal thread.
Figure 2 — Effective nut height m for hexagon nuts
eff
Considering the assumption shown in Figure 2, the shear areas A and A for bolt and nut, respectively, can
Sb Sn
be calculated according to Equation (7):

06, m P 1 
eff
A =⋅π ⋅⋅D +−dD
()
  
Sb 1 21
P 2
3
 


 
04, m P 1
eff

+⋅π ⋅⋅D +−dD
()
  
m 2 mm
P 2 (7)
3
  

DD=1,026
m 1


m P 1 
eff
A =⋅π ⋅⋅d +−dD
 () 
Sn 2
P 2
3

 

with m = m − 0,6h (for nuts with chamfer on one end) and m = m − 1,2h (for nuts with chamfers on both ends).
eff c eff c
4.2.3.2 Stripping load for tightening loading
The major effect of the tightening loading on the stripping load is assumed to be the decrease of the shear
areas for both the bolt and nut due to the increase of the nut dilation during the sliding action between threads
and bearing surfaces; see also 4.3.2.3 and 5.2.
On the other hand, the breaking load in tightening [F in Equation (4)] also decreases normally by 15 % to 20 %.
u
4.3 Influencing factors on the loadability of bolt and nut assemblies
4.3.1 Influencing factors based on Alexander’s theory
Table 1 summarizes the influencing factors on Alexander’s theory for the three possible fracture modes
described in 4.2.1, where the magnitude of the effect (direct/indirect/no effect) is indicated for three different
fracture loads as well as for the variable directly concerned.
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ISO/TR 16224:2012(E)
Table 1 — Summary of the factors affecting the loadability of bolt and nut assemblies
Effect on
Item Factor Variable(s) concerned
F F F
Bb Sb Sn
Tensile strength, R
m
Property class
Bolt Shear strength, 0,6 R ○ ○ ●
m
(Hardness)
Factors, C , C
2 3
Shear strength, 0,6 R
mn
Nut Hardness
− ● ○
Factors C , C
2 3
Nut Height Shear areas, A , A − ○ ○
Sb Sn
Nut Width across the flats Factor C − ● ●
1
Actual stress area, A
s
Bolt Thread tolerance class
○ ○ ○
Shear areas, A , A
Sb Sn
Nut Thread tolerance class Shear areas, A , A − ○ ○
Sb Sn
Nut Chamfered height/angle Shear areas, A , A − ○ ○
Sb Sn
Actual stress area, A
s
Bolt/nut D/P ○ ○ ○
Shear areas, A , A
Sb Sn
○ Direct or major effect.
● Indirect or minor effect.
− No effect.
4.3.2 Other factors which are not taken into account in Alexander’s theory but may affect the load-
ability of b
...