Stress in Bolt Due To Bending

Hello,

I am new to this forum, so I apologize in advance if I break any forum rules.

I am currently trying to figure out whether a bolt will elongate due to bending moment. I have attached an image of what I am trying to analyze. Basically, in my mind, I am envisioning this problem almost like a cantilever beam with one end fixed type of problem. On the free end of the beam, a load will be applied in the downward direction. Assuming that the beam does not fail before the bolts do, the beam will bend downwards. Theoretically, this will cause the bolts to elongate and bend.

I am not concerned with the beam bending, but rather with the bolt bending. I understand that as long as the stress in the bolt does not exceed the yield strength of the bolt, no permanent deformation will occur. I have looked through various different sources (including Shigley's), but I have not found anything that fits my application just right.

Any type of help/suggestions/guidance would be greatly appreciated.

I would use a simple lever calculation to determine the force applied by the moment force then add that load to the loading on the bolt from torque.

See:
[url]https://www.engineersedge.com/simple_levers_menu.shtml[/url]

and

[url]https://www.engineersedge.com/calculators/torque_calc.htm[/url]

Force/area = lbs/in^2 then compare to bolt rating.

The tension results from a bending moment on the face of the connection that is equal to the applied force times the distance the force is from the contact surface of the connection. ... The tensile force in each bolt is found by multiplying the tensile stress by the bolt area.

I'd use the inside edge of the 'heel' in your sketch as the point where the moments would be calculated. Force x horizontal distance to that point being equal to the bolt force x bolt centerline to the same point. If your sketch is roughly to scale the bolt force will be higher of course.

As Kelly Bramble points out you must add the clamping force to obtain the total force applied to the bolt.

If there is sufficient clamp force to keep the the boss on the the lever from actually lifting or rotating, then no significant bending is likely to occur. The clamping force should be significantly higher than the moment force. Perhaps ten times.


Now be advised that there is always some movement whenever a force is applied to a mechanical part. The bolt stretches from the initial clamp load and also a little from the force needed to counteract the moment. The boss under the bolt is compressed a bit from the initial clamp force and will expand, particularly in the section that is furthest from the lever force. If this expansion does not approach the level of compression from the clamp load things are good.

Without actual dimensions and material specifications and loads, the forces cannot be estimated. You will have to use those factors to evaluate the conditions.