How do I work out the tightening torque for an M10 grade 8.8 bolt, and what does the washer do?

The goal of tightening is preload, the tension in the bolt that clamps the joint; torque is only an indirect way of getting it. A common target is about 75 percent of the bolt's proof load for a joint that may be reassembled.

For M10 coarse thread the tensile stress area is 58 mm². Property class 8.8 has a proof strength of 580 MPa in sizes up to M16, so the proof load is 58 × 580 = 33.6 kN and the target preload is 0.75 × 33.6 = 25.2 kN.

Torque and preload are linked by T = K × d × F, where d is the nominal diameter and K is the nut factor that lumps together thread geometry and friction. K is about 0.2 for plain or zinc-plated steel as received and about 0.15 when oiled; special lubricants go lower.

With K = 0.2: T = 0.2 × 0.010 m × 25,200 N = 50 N·m. With K = 0.15 the same preload needs only 38 N·m. That is the spread in your tables. It also shows the danger: 50 N·m applied to an oiled bolt gives 50 / (0.15 × 0.010) = 33.3 kN, right at the proof load. A torque value is only meaningful together with the lubrication condition it assumes.

It helps to know where the torque goes. Roughly half is spent on friction under the turning head or nut, about 40 percent on friction in the threads, and only around 10 percent actually stretches the bolt. A modest change in either friction therefore changes the preload a lot, and even with a calibrated torque wrench the preload scatter is commonly quoted as about ±25 percent.

Where that is not good enough, preload is controlled more directly: torque plus a measured angle of turn, measuring bolt elongation, or load-indicating washers. For engines, structural steelwork and anything safety-critical, the manufacturer's or code-specified procedure overrides any general calculation.

The washer does both of the things you heard. A hardened flat washer gives the turning face a smooth, consistent surface to slide on, which keeps K repeatable and stops the head from galling a soft or painted part.

It also lowers the bearing pressure on the joint surface. Under the head alone, the contact ring is roughly 15 mm outside diameter around an 11 mm clearance hole, about 82 mm², so 25.2 kN gives around 300 MPa, more than soft materials such as aluminium alloys, plastics or painted surfaces can take without indenting. A standard 20 mm washer over the same hole has about 219 mm², for about 115 MPa. Indentation after tightening relaxes the bolt stretch, and with it the preload, so the washer protects the clamp force. It must be hard and thick enough to do so; a thin soft washer just dishes.

On why preload matters so much: in a properly preloaded joint the clamped parts are much stiffer than the bolt, so when the working load fluctuates the bolt sees only a small fraction of the change and the rest is taken by the parts unloading slightly. The bolt's stress hardly cycles, which is what protects it from fatigue. An under-tightened bolt sees the full load swing on every cycle, and once the joint can slip sideways the nut rotates loose.

So a bolt that keeps coming loose under vibration is usually a preload problem first. Adequate preload, enough clamped length and clean seating faces do more than most locking devices added afterwards.