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Suppose I have a bolt that goes through a hole in a plate and is under tension. If I place a washer between the bolt head and the plate, does static frictional force (torque actually) really double? I'm assuming the bolt, washer, and plate are all of the same material for simplicity.

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No it doesn't, and it isn't meant for that either. A standard flat washer, that is. It's meant to give the nuts and bolts a better support, and it protects the material against the nut which may otherwise scratch it upon tightening.

A washer may even reduce the friction on the nut, since the fastened material may in many cases have a higher friction against the nut than the washer does. That's why we either use lock washers, or nylock nuts, flange serrated nuts, or other types of self securing nuts.

For your good understanding, it doesn't matter what kind or how many washers or nuts you apply, the one with the least friction determines the total friction. Like the weakest link determines the strength of a chain.

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You have made a very common mistake - if you want to increase the static friction, you have to decrease the torque! So yes, a well designed fastener system that includes washers can significantly reduce the torque needed to achieve a given tension on the bolt. And it is the tension, not the torque applied to get there, that provides the friction and stiction. This is done by controlling the radius of the pressure. It is common practice to want the blind side to stick more than the side being turned. Easy to do if you think about it. Also, for torque critical applications, washers provide a more consistent torque to tension relationship.

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