Calculate Factor of Safety Against Thread Stripping
with A36 body
When a bolt is fully engaged into a nut or when a screw
has a depth of engagement at least equal to the diameter
of the screw, the thread engagement is adequae. Special
situations arise when the bolt is not fully engaged
into the nut or when the screw is engaged into a much
weaker material. Sufficient design margin against
failure by thread stripping should be provided.
The determination of the required pre-load is outside
the scope of this paper since it is dependent on the
function of the joint, for eg. gasket seating, joint
sealing, etc. A minimum residual pre-load stress of
20% of yield strength of the bolt is recommended by
Ref. 8 for torque retention. Otherwise, torque retention
devices such as lock nuts, jam nuts, lock washers,
staking of threads, locking adhesives, etc would be
If this is an ASTM A193, Gr. B7 bolt, it would not have
reached the plastic range since the von Mises stress
is much less than the yield strength of the bolt (105
Von Mises stress is given by combining tensile stress
with shear stress as follows:
However, Code Interpretation III-1-91-15 states that
Section NB-3232 does not apply to this situation. Thus,
we could instead use Von Mises stress for combining
tensile stress with shear and check against yield for
ASME or non-ASME components
For an ASTM A93, Gr. B7 bolt, the allowable stress intensity
would be 3 Sm,
i.e. 3 x 35 ksi =105 ksi and has not been exceeded.
The shear stress is the highest at the periphery of
the bolt cross-section which is also subject to an
axial tensile stress. For ASME components, the rules
of NB-3232.2 could be used to determine the maximum
allowable stress. This requires calculating the stress
intensity which is defined as twice the maximum shear
stress or the difference between the principal stresses.
: The full applied torque is not experienced by the
cross-section of the bolt since some of this torque
goes to overcome friction under the nut head.
The shear stress is the thread torque divided by the
polar section modulus.
Allowable Tensile Stess:
There is no clear guidance for the maximum allowable
average tensile stress for preload. For ASME components,
ASME III NB-3230 could be used. Provided differential
thermal expansion does not create additional stresses,
the maximum allowable average tensile stress could
be considered as 2 x Sm
since internal pressure would not increase the bolt
loading. For ASTM A193 B7 at a service temperature
of 200 deg. it would be 2 x 32.6 ksi and about 60%
1. Fastener Standards, 6th Edition, Industrial Fasteners
2. AISC Manual of Steel Construction, 8th Edition, 1980
Mechanical Engineering Design, J.E. Slingley & L.D.
An Introduction to the Design and Behavior of Bolted
Joints, by John H. Bickford
5. ASME Boiler & Pressure Vessel Code, Section III,
Development of Design Charts for Bolts Preloaded up
to the Plastic Range, N. Motosh,
Journal of Engineering for Industry, ASME Aug.
Fastener Design Manual, Richard T. Barrett, NASA Reference
Publication 1228, 1990
8. Bolted Joint Maintenance and Applications Guide,
TR-104213, EPRI, December 1995
9. Specification for Structural Joints Using ASTM A325
or A490 Bolts, AISC, 1978
The author wishes to thank Dr. Yinyao Jiang, Dr. Peter
Turula, and Bill Eccles for helping the author understand
some technical points presented in this paper.
The required preload per Table 3 is 12000 lbs. Therefore,
the rotation for 2400 lbs would be:
The bolt in this example has a preload of 2400 lbs.
According to Table 4, the nut rotation for 1/2"
A325 bolt would be 1/3 turn or 120 degrees for a bolt
less than 4 diameters in length.
However, an approximate amount of nut rotation can be
calculated based on Tables 3 and 4 of Reference 9.
Although it is theoretically possible to calculate the
nut rotation as a function of the preload, it does
not correlate well with observations for preloads less
than yield. If tightening to preloads beyond yield
strength is permissible, this is a cost effective and
reliable method and is widely used for structural connections
installing A325 or A490 bolts.
Calculation of Nut Rotation
Note: External threads used and methodology in Reference
Using methodology in Reference 7.
for Carbon Steel; for Stainless Steel use 0.55
(Use the material property for the weaker material)
is the angle of the thread and is 60 degrees for UNC
this is the distance between nut flats for hex nuts
is the effective contact diameter for the threads and
is the average of major and minor diameters; It is
also approximately equal to the pitch diameter.
TPI is threads per inch.
l is lead.
is the effective contact diameter between the nut and
joint surface and is the average of major diameter
and the distance between parallel nut flats for a hex
Determine Torque vs. Tension Relationship
for 1/2" bolt with hex nut as the turning element
Set the parameter, i, according to the size of the bolt.
The following table gives bolt geometry and thread engagement
data for UNC bolts from 1/4" diameter to 1 1/4"
diameter. First row gives the major diamter, second
row gives the minor diamter, third row gives the number
of threads per inch, and the fourth row gives the distance
between nut flats for hex nuts (1/4" to 5/8"
sizes), and heavy hex nuts (3/4" to 1 1/4"
sizes). The last two rows give the thread stripping
areas per inch for external and internal threads respectively.
This information is obtained from References 1 &
Sm is the design stress intensity for the bolt material per ASME B &
The major diameter is the largest
diameter of a screw thread. It is also the nominal size of the bolt.
The minor diameter is the smallest
diameter of a screw thread. Also referred to as root diameter.
The lead is the distance the nut
moves parallel to the screw axis when the nut is given one turn. For a single
start thread used in bolts, screws, nuts, etc., the lead is the same as
the pitch and is the inverse of number
of threads per inch.
The pitch diameter is the diameter
of an imaginary coaxial cylinder cutting the threads at a height where the
width of the thread and groove are equal. The average of major and minor
diameters is approximately equal to the pitch diameter.
The stress area is the effective
cross-sectional area of the bolt that resists bolt fracture.
The thread angle is the included
angle between the flanks of a screw thread.
Calculate Tension in bolt when subject to a known torque
Calcualte max stress in bolt when subject to a pre-load
and determine its acceptability
Calculate factor of safety against stripping failure
for a known thread engagement
Determine whether a torque retention device is required
Calculate nut rotation for a given bolt torque
During maintenance activities in a power plant environment,
the plant engineer is often called upon to make decisions
concerning bolts in bolted connections in a variety
of situations. Most of these bolts are torqued to
achieve a pre-load rather than being tensioned with
a tensioner. Examples include: increasing bolt torque
beyond vendor manual recommended values to stop leaks,
vendor recomendations for torquing are not available,
bolt holes need to be enlarged to install replacement
components, bolts may require trimming to accomodate
replacement component, lack of thread engagement, etc.
The ability to perform a component level analysis
on a bolt, will provide the plant engineer an engineering
tool to make the correct technical decision.
Progress Energy, Southport,
Analysis of Bolt Torquing
ds is the diameter
based on stress
Tensile stress will be calculated using the stress area:
We can either use the results of the long or short formula
for the value of F for this analyis.
Calculate maximum stress on the bolt during the torquing
This short formula gives results which compares well
with the results of the long formula. However, it
is important for the Nut factor to be selected carefully,
since it significantly affects the results.
Nut factors are determined empirically. For values
of Nut factor for various lubricated fasteners See
for unlubricated NEW steel fasteners
There is a simple empirical formula ("short formula")
that is widely used in the industry to calculate the
relationship between Torque and Tension. It is given
Suppose we apply a torque of 20 ft.lb.(240 in.lbs)
Further, it should be noted that only the torques represented
by the first two terms will create a twist in the body
of the bolt.
From this expression, it can be seen that bolt and thread
geometry and the ceofficient
of friction significantly influence the relationship
between torque and
preload. If the above expressions are evaluated it will
be seen that only about 10% of the applied torque works
to achieve the preload and the remainder works to overcome
This expression can be mathematically simplified as
the first term represents the amount of torque to stretch
the bolt and compress the joint
the second term represents the amount of torque required
to overcome the friction between the nut and bolt threads
the third term represents the amount of torque required
to overcome the friction on the face of nut when multiplied
by the preload F.
See Reference 3; "long formula"
Given an applied torque, T, the preload force F in the
bolt is given by
T= F x
is the coefficient of friction assuming non-lubricated
steel bolt and is assumed to the same for friction
between threads and between nut and joint surface.
A more realistic coefficient of friction for fasteners
that has been in service may by 0.35-0.40 rather than