Beam bending of a Non-Straight Beam
Beam bending of a Non-Straight Beam
(OP)
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. photobucke t.com/albu ms/y157/To wlie42h/Ge ar_Lever_P roblem.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!
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.
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!





RE: Beam bending of a Non-Straight Beam
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
RE: Beam bending of a Non-Straight Beam
corus
RE: Beam bending of a Non-Straight Beam
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
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RE: Beam bending of a Non-Straight Beam
No more things should be presumed to exist than are absolutely necessary - William of Occam
RE: Beam bending of a Non-Straight Beam
Mike Halloran
Pembroke Pines, FL, USA
RE: Beam bending of a Non-Straight Beam
RE: Beam bending of a Non-Straight Beam
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.
RE: Beam bending of a Non-Straight Beam
Tunalover
RE: Beam bending of a Non-Straight Beam
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