Machinery's Handbook, 31st Edition
Fasteners
1653
TORQUE AND TENSION IN FASTENERS Tightening Bolts.— Bolts are often tightened by applying torque to the head or nut, which causes the bolt to stretch. The stretching results in bolt tension or preload, which is the force that holds a joint together. Torque is relatively easy to measure with a torque wrench, so it is the most frequently used indicator of bolt tension. Unfortunately, a torque wrench does not measure bolt tension accurately, mainly because it does not take friction into account. The friction depends on bolt, nut, and washer material, surface smoothness, ma- chining accuracy, degree of lubrication, and the number of times a bolt has been installed. Fastener manufacturers often provide information for determining torque requirements for tightening various bolts, accounting for friction and other effects. If this information is not available, the methods described in what follows give general guidelines for deter - mining how much tension should be present in a bolt, and how much torque may need to be applied to arrive at that tension. High preload tension helps keep bolts tight, increases joint strength, creates friction between parts to resist shear, and improves the fatigue resistance of bolted connections. The recommended preload F i , which can be used for either static (stationary) or fatigue (alternating) applications, can be determined from: F i = 0.75 × A t × S p for reusable connec tions, and F i = 0.9 × A t × S p for permanent connections. In these formulas, F i is the bolt preload, A t is the tensile stress area of the bolt, and S p is the proof strength of the bolt. Determine A t from screw-thread tables or by means of formulas in this section. Proof strength S p of commonly used ASTM and SAE steel fasteners is given in this section and in the section on metric screws and bolts for those fasteners. For other materials, an approximate value of proof strength can be obtained from: S p = 0.85 × S y , where S y is the yield strength of the material. Soft materials should not be used for threaded fasteners. Once the required preload has been determined, one of the best ways to be sure that a bolt is properly tensioned is to measure its tension directly with a strain gage. Next best is to measure the change in length (elongation) of the bolt during tightening, using a microme ter or dial indicator. Each of the following two formulas calculates the required change in length of a bolt needed to make the bolt tension equal to the recommended preload. The change in length δ of the bolt is given by:
F A A E A l A l i d t d t t d # # # # # +
A E F l i # #
(1)
(2)
or
δ =
δ =
In Equation (1) , F i is the bolt preload; A d is the major-diameter area of the bolt; A t is the tensile-stress area of the bolt; E is the bolt modulus of elasticity; l t is the length of the threaded portion of the fastener within the grip; and l d is the length of the unthreaded por tion of the grip. Here, the grip is defined as the total thickness of the clamped material. Equation (2) is a simplified formula for use when the area of the fastener is constant, and gives approximately the same results as Equation (1) . In Equation (2) , l is the bolt length; A is the bolt area; and δ , F i , and E are as described before. If measuring bolt elongation is not possible, the torque necessary to tighten the bolt must be estimated. If the recommended preload is known, use the following general relation for the torque: T = K × F i × d , where T is the wrench torque, K is a constant that depends on the bolt material and size, F i is the preload, and d is the nominal bolt diameter. A value of K = 0.2 may be used in this equation for mild-steel bolts in the size range of 1 ∕ 4 to 1 inch (6.35–25.4 mm). For other steel bolts, use the following values of K : nonplated black finish, 0.3; zinc-plated, 0.2; lubricated, 0.18; cadmium-plated, 0.16. Check with bolt manufacturers and suppliers for values of K to use with bolts of other sizes and materials.
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