Short Snippet on Bolted Joints

I once thought a screw was a very simple mechanism, you screw a screw into a nut or threaded hole and boom you connected something to something else. Yet the more I needed to understand and actually do analysis with them I realized just how great of an invention it is. While it is credited to Joseph Whitworth, who standardized production of bolts and nuts, ancient peoples from the 1st century CE have started using wooden screws and metal screws became more common in the 15th century.

I did some napkin maths literally. But here is my derivation of the bolt and material behaving like parallel springs when encountering an external load P. This was really confusing to me at first because the bolt is in tension under a preload and the material is in compression under the same preload initially. Conceptually text books do not really explain how the bolt load equation is derived or why the a bolt under preload will have a higher mean stress but a lower alternating stress when under cyclic loading. This would input into fatigue analysis using a Goodman curve. So conceptually, we want to think of the preload making the joint stiff, and the joint would have some type of inertia to resist external loads to an extent. In detail, this would entail when pulling on the bolt, the material under compression is relieved, this causes the bolt to actually have more freed up pull to oppose an additional tension force P. So the bolt actually does not have to stretch as long as it would normally have to if it were under additional tension by itself. This results in mathematical equivalency to having the material and the bolt be parallel springs, although physically it is not what happens. Very tricky indeed. So if one needs the load on the bolt, it would be the preload plus the fraction of the spring constants (K1/(K1+K2)) times the applied tension load P. For the load on the material side compression is negative so (K2/(K1+K2))*P-Preload would be the expression.

There are usually 3 major things to look for: bolt and material yielding using a failure criterion like distortion energy (Von mises), fatigue failure of bolt and joint, and slipping and gapping.

The next thing I would want to cover would be Fatigue and also gapping and slipping analyses.