New formulas are developed for the torque-tension relationship, various torque components, and breakaway torque values in threaded fastener applications. The three-dimensional aspects of the lead helix and thread profile angles and the kinetic and static friction coefficients are all taken into account. Two scenarios of the contact pressure between threads and under the turning fastener head are considered, namely, uniformly distributed and linearly distributed contact pressure scenarios. The effect of thread pitch, lead helix and thread profile angles, friction coefficients, and fastener geometry is discussed. Results from the new formulas are compared with the approximate torque-tension relationship provided in the literature. A percentage difference analysis indicates that the new formulas provide a significant improvement that would enhance the reliability and safety of bolted connections, especially in critical applications.

1.
Bickford
,
J. H.
, 1997,
An Introduction to the Design and Analysis of Bolted Joints
,
3rd ed.
,
Marcel Dekker
,
New York
.
2.
Bickford
,
J. H.
, and
Nassar
,
A. S.
, 1998,
Handbook of Bolts and Bolted Joints
,
Marcel Dekker
,
New York
.
3.
Juvinall
,
R. C.
, and
Marshek
,
K. M.
, 2000,
Fundamentals of Machine Component Design
,
3rd ed.
,
Wiley
,
New York
.
4.
Jiang
,
Y.
,
Chang
,
J.
, and
Lee
,
C.
, 2000, “
An Experimental Study of Torque-Tension Relationship for Bolted Joints
,”
Int. J. Mater. Prod. Technol.
0268-1900,
16
(
4/5
), pp.
417
429
.
5.
Motosh
,
N.
, 1976, “
Development of Design Charts for Bolts Preloaded up to the Plastic Range
,”
ASME J. Eng. Ind.
0022-0817,
98
(
3
), pp.
849
851
.
6.
Motosh
,
N.
, 1975, “
Load Distribution on Threads of Titanium Tension Nuts and Steel Bolts
,”
ASME J. Eng. Ind.
0022-0817,
97
(
1
), pp.
162
166
.
7.
Shigley
,
J. E.
, and
Mischke
,
C. R.
, 1989,
Mechanical Engineering Design
,
5th ed.
,
McGraw-Hill
,
New York
, Chap. 8.
8.
Maruyama
,
K.
, 1974, “
Stress Analysis of a Bolt-nut Joint by the Finite Element Method and the Copper Electroplating Method (Second Report)
,”
Bull. JSME
0021-3764,
17
(
106
), pp.
442
450
.
9.
Maruyama
,
K.
, 1973, “
Stress Analysis of a Bolt-Nut Joint by the Finite Element Method and the Copper Electroplating Method (First Report)
,”
Bull. JSME
0021-3764,
16
(
94
), pp.
671
678
.
10.
Tanaka
,
M.
,
Hongo
,
K.
, and
Asaba
,
E.
, 1982, “
Finite Element Analysis of Threaded Connections Subjected to External Loads
,”
Bull. JSME
0021-3764,
25
(
200
), pp.
291
298
.
11.
Bretl
,
J. L.
, and
Cook
,
R. D.
, 1979, “
Modeling Load Transfer in Threaded Connections by the Finite Element Methods
,”
Int. J. Numer. Methods Eng.
0029-5981,
14
(
9
), pp.
1359
1377
.
12.
Fukuoka
,
T.
, 1992, “
Finite Element Simulation of Tightening Process of Bolted Joint With Tension
,”
ASME J. Pressure Vessel Technol.
0094-9930,
114
, pp.
433
438
.
13.
Chiang
,
Y.
,
Nassar
,
S. A.
, and
Barber
,
G. C.
, “
Examination of Tightening Torque-Fastening Force Relationship of Bolt-Nut Assemblies
,”
Int. J. Mater. Prod. Technol.
0268-1900, submitted.
14.
Nassar
,
S. A.
,
Barber
,
G. C.
, and
Zuo
,
D.
, 2005, “
Bearing Friction Torque in Bolted Joints
,”
Tribol. Trans.
1040-2004,
48
, pp.
69
75
.
15.
Nassar
,
S. A.
,
Martin
,
P. H.
, and
Barber
,
G. C.
, 2005, “
Thread Friction Torque in Bolted Joints
,”
ASME J. Pressure Vessel Technol.
0094-9930,
127
, pp.
387
393
.
16.
Nassar
,
S. A.
,
El-Khiamy
,
H.
,
Barber
,
G. C.
,
Zou
,
Q.
, and
Sun
,
T. S.
, 2005, “
Bearing and Thread Friction in Fasteners
,”
ASME J. Tribol.
0742-4787,
127
, pp.
263
272
.
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