Beam Bending of a Non-Straight Beam

[TowlieUK]

Hi all,

I am designing a gear lever for a small race car, and am looking to validate my FEA of the lever through the use of hand calculations.

The beam is not straight, and i have never tackled a problem like this before. I am using Roarks Formulas for Stresses and Strains, however am struggling to grasp what it is trying to tell me what to do!

The beam bends in this manner:

The beam bends at 26 degrees and then back again 26 degrees to get it back to the vertical. The force, F, is applied in the Z direction (into the page) and the lever itself is pivotted about the green line (ie. it can 'rock' backwards and forwards). At the bottom the lever, in reality, is free to move a bit, but for this analysis i was thinking of just having it pinned to demonstrate the maximum loading condition.

Could anyone help me with the theory to obtain the Stress and bending moments of the beam. As I said i have been going through the Roarcks book but to no avail.

Many thanks!

 

[nvn]

TowlieUK: If the vertical distance of force F from the green line is y = h1, then the maximum bending moment occurs at the green line and is Mx = h1*F. If the horizontal distance of force F from the red dot is x = a1, then the beam is also subjected to torsion at the green line, and the torque is T = a1*F. Therefore, it currently appears you do not need to use curved beam theory to analyze the beam.