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Shear stress on a bar with a bend

  1. Apr 27, 2010 #1
    1. The problem statement, all variables and given/known data

    I have encountered this problem several times in class, but have never really understood it. There is a solid round bar that is fixed on one end, and that bends 90 degrees a ways down. At the free end of the bar there are forces applied in each Cartesian direction.
    Like this: http://farm4.static.flickr.com/3448/4559398860_d6c6e250a0_o.jpg"

    The question is to determine the shear stress [tex]\tau[/tex]xy at point A (on the outer edge of the tube, radially parallel to the z-axis).

    2. Relevant equations

    Torsion - [tex]\tau[/tex] = Tc/J
    Beam - [tex]\tau[/tex] = VQ/It

    3. The attempt at a solution

    I plug in my values in the above equations, and add them up depending on the shear direction, but I don't seem to get the right answer.

    I'm hoping someone can help me with the general idea for this type of problem or point me to a website that explains it clearly.

    Thanks!
     
    Last edited by a moderator: Apr 25, 2017
  2. jcsd
  3. Apr 27, 2010 #2

    Mapes

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    What values are you using for the torque and the shear force?
     
  4. Apr 27, 2010 #3
    Here is what I tried:

    Fx=500lbf
    Fy=-800lbf
    T=Fy14in
    c=r (radius)
    J=pi*r4/4


    which gives torsion shear=-16900psi

    V=Fy
    Q=y'A'
    y'=r
    A'=pi*r2/2
    t=r

    with beam shear=-2844psi

    total shear (xy)=torsion shear-beam shear

    It's been a while since I was actually in Mechanics of Materials, so that might be way wrong though :).
     
  5. Apr 27, 2010 #4

    Mapes

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    It's been a while for me too, but isn't y' the distance to the centroid of the top or bottom half of the cross section?
     
  6. Apr 27, 2010 #5
    ah, yes you are right. Unfortunately I don't have the correct answer in front of me anymore so I can't check if that's all that is wrong.

    Hopefully the other stuff looks right though?
     
  7. Apr 27, 2010 #6

    Mapes

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    Yep, the torsion part looks good.
     
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