Beam bending of a Non-Straight Beam

[TomJackUK]

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:

http://i5.photobucket.com/albums/y157/Towlie42h/Gear_Lever_Problem.jpg

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!

 

[MikeHalloran]

The maximum loading condition is Willy T. Ribbs doing clutchless shifts for half a race. You know a guy is really trying when he gets out of the car still grasping the top half of what appears to have once been a very sturdy gear lever.

Which is to say, for a hand calc, I would assume the shift lever is fixed at its weakest plane, its major axis is horizontal, and a gorilla is jumping on the distal end of the lever, treated as a cantilever beam.



Mike Halloran
Pembroke Pines, FL, USA

 

[corus]

Resolve your forces so that you have one parallel to the two pinned restraints, and one 90 degrees to it. You can work out the bending stress at the red pivot fronm the sum of the moments. Same thing would apply at the angled junctions, though you'd need to add in a stress concentration factor for the fillet radii there. Your results should give you a rough comparison with the FE model.

corus

 

[GregLocock]

The bending moment at any point along the gearlever is F*the distance perpendicular to F from the point. As such the kinks don't really make much difference.


The max stress is y*M/I, where y is the distance of the furthest point in the cross section from the neutral axis, that is, r, if you have a circular cross section.




Cheers

Greg Locock


New here? Try reading these, they might help FAQ731-376

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[HamishMcTavish]

you're using FEA for a GEAR lever? am i missing something?

No more things should be presumed to exist than are absolutely necessary - William of Occam

 

[MikeHalloran]

21st century engineering is scary, isn't it?



Mike Halloran
Pembroke Pines, FL, USA

 

[rb1957]

we have the tools ... we can re-analyze him ...

 

[flash3780]

Resolve the stresses at your cut plane into shear force, tension force, and bending moment. From there, you should be able to get a stress distribution using standard beam theory. Be sure to look carefully at your connection between the shifter and the gearbox; that's likely your most highly stressed location.

If you're trying to determine the flexibility of the shifter, you could chop the beam into three straight sections and resolve out the displacements of each.

A truly curved beam could be calculated with Castigliano's method; there should be some literature out there if you decide to look at an arc-shaped beam.

 

[Tunalover]

Castigliano's Theorum is useful for non-straight beams. Don't ask me to do it though.



Tunalover

 

[RolMec]

Hi TomJackUK,

cf. attached sketch, there is a rough hand calc.
If you want to know the stress level along the lever, it's (going from the point where the force is applied) increasing bending stress till the first bend, then increasing bending stress + increasing torsional stress till the second bend then increasing bending stress + constant torsional stress.

Regards

Roland