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Mechanics of materials-homework

  1. Feb 6, 2016 #1
    1. The problem statement, all variables and given/known data

    1–80. The thrust bearing consists of a circular collar A fixed to the shaft B.Determine the maximum axial force P that can be applied to the shaft so that it does not cause the shear stress along a cylindrical surface a or b to exceed an allowable shear stress of 170 MPa.

    upload_2016-2-6_10-10-50.png


    2. Relevant equations

    T=V/A or T = P/A



    3. The attempt at a solution
    This is how I thought I would draw my FBD

    upload_2016-2-6_10-10-28.png

    therefore I thought that if I did the summation of all forces in the x direction, P = Va+Vb
    However, the solution takes it individually, like this:

    T = P/A for a and T = P/A for b and calculates each P. This is confusnig me because, shouldnt the two V (shear forces) equal to the Maximum axial force?

    thanks for any help, Id really like to understand this.
     

    Attached Files:

  2. jcsd
  3. Feb 6, 2016 #2
    I forgot to mention that for my FBD I did two cuts just so I can have a and b in there but I believed that we didnt need the rest.

    I dont want any answers I just need some help with this, thank you!
     
  4. Feb 6, 2016 #3

    SteamKing

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    If you draw a free body diagram of the shaft and the collar attached to it, how many forces will this diagram show? Which is the applied force and which is the reaction?
     
  5. Feb 6, 2016 #4
    Do you mean just of the shaft and collar excluding the a and b surfaces?
     
  6. Feb 6, 2016 #5

    SteamKing

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    The collar is rigidly attached to the shaft, so you can't exclude it.

    You have a thrust P applied to one end of the shaft. What keeps the shaft from accelerating in the direction opposite of P?
     
  7. Feb 6, 2016 #6
    Oh! It should be the normal force correct?
     
  8. Feb 6, 2016 #7
    the normal force that A exerts
     
  9. Feb 6, 2016 #8

    SteamKing

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    Correct.

    The shear area for the collar and the shear area for the thrust bearing are two different values. One of these surface areas will limit how large P can be, subject to the shear stress limit.
     
  10. Feb 6, 2016 #9
    Thank you!
     
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