OpenSpecEngineering

Finds the tightening torque that gives a bolt the preload you want, or the preload a given torque produces. Pick a metric or inch size and thread and the fastener’s condition, then enter a preload or take 75 % or 90 % of the grade’s proof load. Designers and assemblers use it to write torque specifications for bolted joints.

The torque equation

T = K·F·d

T is the tightening torque, F the preload (the bolt’s clamp force), d the nominal bolt diameter and K the nut factor, which lumps together the friction in the threads and under the head [1]. Most of the torque goes into friction, so K decides the preload as much as the torque does. The same torque on a plain, dry bolt (K = 0.30) gives two-thirds of the clamp force it gives on a zinc-plated one (K = 0.20).

A preload set from the proof load is F = 0.75·F_p for a reusable joint or 0.90·F_p for a permanent one [1], where F_p = A_t·S_p. A_t is the tensile stress area: (π/4)(d − 0.9382P)² for a metric thread of pitch P [2], or (π/4)(d − 0.9743/n)² for an inch thread with n threads per inch [5]. S_p is the grade’s proof strength from its standard [2]–[4]. Where the standard gives none, the page uses S_p = 0.85·S_y and says so.

Limits and common mistakes

• K changes with plating, lubricant and even the batch, so a torque gives only an approximate preload. For a critical joint, measure the bolt’s stretch or use turn-of-nut tightening.
• Pick the condition the bolt is in when it is tightened. Oil or anti-seize lowers K, so a torque written for dry bolts can overload lubricated ones.
• The preload is the clamp force before any service load. Check the whole joint with the Bolted Joint Strength calculator.

Worked example

Write the tightening torque for zinc-plated M12 class 10.9 cap screws in a joint that will be taken apart for service.

1. Choose Solve For Torque, given preload, and Bolt Size Metric (ISO).
2. Choose Size M12 and Thread M12 × 1.75.
3. Choose Fastener Condition Zinc plated — K = 0.20.
4. Choose Desired Preload 75 % of proof load — reusable joint, and Bolt Grade Class 10.9.
5. Press Solve. The Solution shows: Required Torque (T): 125.894 N·m
   Tensile Stress Area (At): 84.2664 mm²
   Proof Strength (Sp): 830 MPa
   Preload (F = 75 % of proof load): 52,455.8 N
   Pound-feet: 92.8546 lbf·ft

Check: 0.20 × 52,455.8 N × 0.012 m = 125.9 N·m. On the drawing, round it to a value the wrench can hold, such as 125 N·m.