Mechanics of Materials · Torque and preload
Gravity's invoice, paid at the wrench
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Gravity's invoice, paid at the wrench

A bolt does not hold things together by being strong. It holds them together by being STRETCHED, and the tension you put in at assembly — the preload — is the whole point of the exercise. The trouble is that nobody can see tension. What a fitter can see is a torque wrench, and the bridge between the two is the nut factor.

T=KDFT = K D F — read aloud T equals K D F. TT is the tightening torque in newton-metres. KK is the nut factor, a bare number around 0.20 for a plain as-received thread and nearer 0.15 lubricated. DD is the nominal bolt diameter in millimetres. FF is the preload, the clamp force in the bolt — in this chapter, kilonewtons. Keep those two units together and the arithmetic is a gift: millimetres against kilonewtons puts TT straight into newton-metres, because the two thousands cancel. M12 at K=0.20K = 0.20 for 30 kN is 0.20×12×30=720.20 \times 12 \times 30 = 72 N·m, and that is the number a torque table prints.

Now the part that should unsettle you. KK is not a property of the bolt; it is a property of the JOINT on the day — thread finish, lubricant, surface under the head, whether the nut has been run down once already. Around 90 per cent of your torque goes into friction under the head and in the threads and never becomes tension at all. Scatter of ±25 per cent on the achieved preload is normal for torque control, and that is why anything that really matters gets tightened by angle, by bolt stretch, or by a load-indicating washer. Torque is the cheapest method, not the good one.

Units guide, they do not confess. Push them through: a bare ratio, times a length, times a force, is a length times a force — a newton-metre. If your rearrangement leaves anything else standing, it is wrong, no appeal. Units that DO cancel never prove you right; the check runs one way only.