Machinery's Handbook, 31st Edition
1658 TORQUE AND TENSION IN FASTENERS The most common methods of bolt tension control are indirect because it is usually difficult or impractical to measure the tension produced in each fastener during assembly. Table 2 lists the most frequently used methods of applying bolt preload and the approximate accuracy of each method. For many applications, fastener tension can be satisfactorily controlled within certain limits by applying a known torque to the fastener. Laboratory tests have shown that whereas a satisfactory torque tension relationship can be established for a given set of conditions, a change of any of the variables, such as fastener material, surface finish, and the presence or absence of lubrication, may severely alter the relationship. Because most of the applied torque is absorbed in intermediate friction, a change in the surface roughness of the bearing surfaces or a change in the lubrication will drastically affect the friction and thus the torque tension relationship. Regardless of the method or accuracy of applying the preload, tension will decrease in time if the bolt, nut, or washer seating faces deform under load, if the bolt stretches or creeps under tensile load, or if cyclic loading causes relative motion between joint members. Table 2. Accuracy of Bolt Preload Application Methods Method Accuracy Method Accuracy By feel ± 35% Computer-controlled wrench Torque wrench ± 25% below yield (turn-of-nut) ± 15% Turn-of-nut ± 15% yield-point sensing ± 8% Preload indicating washer ± 10% Bolt elongation ± 3 − 5% Strain gages ± 1% Ultrasonic sensing ± 1% Tightening methods using power drivers are similar in accuracy to equivalent manual methods. Elongation Measurement.— Bolt elongation is directly proportional to axial stress when the applied stress is within the elastic range of the material. If both ends of a bolt are acces sible, a micrometer measurement of bolt length made before and after the application of tension will ensure the required axial stress is applied. The elongation δ in inches (mm) can be determined from the formula δ = F t × L B ÷ E , given the required axial stress F t in psi (MPa), the bolt modulus of elasticity E in psi (MPa), and the effective bolt length L B in inches (mm). L B , as indicated in Fig. 2 , includes the contribution of bolt area and ends (head and nut) and is calculated from: (6) where d ts is the thread stress diameter, d is the bolt diameter, L s is the unthreaded length of the bolt shank, L j is the overall joint length, H B is the height of the bolt head, and H N is the height of the nut. 2 2 L d d B ts = a L H L L J + + − + B S k H s N 2 # a k
H N
L S L J
H B
L B ( ) 2 d ts d
( L S ) H B 2
d
d ts = thread stress dia.
H N 2
L J L S
1 2
1 2
H N
H B
Note: For Headless Application, Substitute 1/2 Engaged Thread Length
L B
Fig. 2. Effective Length Applicable in Elongation Formulas
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