Jetmaker
Usually, a bolt supported by 2 bearings, as per your diagram, is done to simplify the support of the bolt and make it statically determinate and easy to analyse. If done correctly, it also eliminates the possibility of the bolt and supports being subjected to secondary loads due to error-of-fit, thermal effects, etc.
The bearings are usually either narrow enough not to impose local bending on the bolt, or spherical or self-aligning bearings are used. The introduction of "watch-spring" supports (i.e. stiff sockets) introduces secondary problems similar to the stiff 3 hinge control surface rotation axis.
For your problem, the vertical reactions P1 and P2 remain as per your diagram, and the bearing stress is purely the reaction divided by the bearing area. However, if you have "stiff" bearings (like sockets) you will need to determine the effective rotational stiffness of the supports in terms of their ability to change the deflected shape of the bolt treated as an overhang simply supported beam. Determining a realistic value for the watch-spring stiffness of the bearings may be a tougher problem than you expect. However, if this is possible, then run a simple FEA of the problem, using the watch-spring moment restraints at the mid-points of the supports. The resultant reacting moments (M1 and M2) are then assumed to be approximately reacted within the bearing by a triangular stress distribution, as per a socket over the bearing widths (t1 and t2), and the end peak stresses added to the SS beam reaction bearing stresses.
The stresses are given by:-
f = Pi/(D*ti) + 6Mi/(D*ti^2)
D = Bolt Diam
t = Bearing Width
Hope you can follow this.
Ed.
