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If a torque and axial force is applied to a beam with a circular cross section, where along the cross section of the circular beam is the location of the max shear stress, max bending moment, max torque, and max axial stress? Correct me if I am wrong, but from class, I learned that max bending moments occur away at the neutral axis at the top and bottom of the beam (i.e. 90 and 270 degrees). Secondly, I think that the max shear stress occurs at the neutral axis (i.e. 0 and 180 degrees) since that is the apex of the parabolic shear profile but I am unconfident in that answer because I read that fracture points due to shear occur at 45 degrees. Lastly, I am not sure where along the beam the maximum torque and axial stress would occur. Thank you.

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  • $\begingroup$ The shear profile is only (approximately) parabolic for a rectangular section beam, but you are right that for a symmetrical beam the max shear is on the neutral axis. For the torsion loading and torque, a circular beam is exactly the same as a circular rod or bar - the lump of metal doesn't do something different just because humans give it a different name! $\endgroup$ – alephzero Jun 14 '19 at 21:21
  • $\begingroup$ So, orientation is very important for answering your question and I think any answer given will require clarification. When you say axial force, are you saying that it is applying in the direction along the beam? Like if you draw the beam as a circle extruding in and out of page, is the axial force in and out of page? How is the torque applied? Can you supply an FBD - I think that will help people answering your question a lot. $\endgroup$ – Isa Jun 14 '19 at 21:31
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Axial load on a beam does not make any moment or shear. Just normal stress sigma= F/A, stress is evenly distributed over total area of the cross section of the rod.

Maximum shear due to the torque is at the surface of the rod along it's entire length and minimum shear stress is zero at the neutral axis.

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