eFunda: Torque and Tension in Bolts
engineering fundamentals Torque and Tension in Bolts
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The required torques for fastening common steel fasteners can be found in the Bolt Torque Calculator.

Torque and Tension in Bolts

Bolt, one of the most widely used fasteners in the industry, is usually tightened by applying torque to the head and/or nut. As the bolt is tightened, it is stretched (preloaded). Preload tension is necessary to keep the bolt tight, increase join strength, create friction between parts, and improve fatigue resistance. The recommended preload force Fi is

For reusable connections: 

For permanent connections: 

where At is the tensile area of the bolt and Sp is the proof strength of the bolt. Although the above formulae look rather straightforward, the preload tension Fi is not easy to measure or control. A common practice is to relate the preload tension Fi to a quantity that is easier to measure, the applied torque T. This torque, usually achieved by a torque wrench, the turn-of-nut, or an indicating washer, is

where d is the nominal outside diameter of the bolt and K is the correction factor that depends on the material, size, surface friction, and threading of the bolt. For most small to mid size bolts, K is between 0.15 and 0.3.

As a rough approximation:

dry (un-lubricated) mid-size steel bolts: K = 0.2
non-plated black finish: K = 0.3
zinc-plated: K = 0.2
cadmium-plated: K = 0.16
lubricated: K = 0.15 ~ 0.18

A more complicated torque formula is given as

where P is the lead (pitch) of the thread, Db is the average mean diameter of the bolt, Dn is the average mean diameter of the nut, k is the coefficient of friction, and is one half of the thread angle (usually 30°). This formula, although more complete, is seldom used, for the large errors (sometimes as much as 25%) involved in torque wrench readout usually renders using a more accurate formula pointless.

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