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Area of normal stress

  1. Sep 20, 2016 #1
    1. The problem statement, all variables and given/known data
    For σBC end , i dont understand how the author get (20mm)(40mm-25mm) = 300x10^-6 (m^2) ...
    2. Relevant equations


    3. The attempt at a solution
    IMO, , the area should be the circled part (thin rectangular part of the rod) , but i only know one dimension only , which is 40mm , i dont know the another one , how to proceed ?
     

    Attached Files:

  2. jcsd
  3. Sep 20, 2016 #2
  4. Sep 21, 2016 #3

    billy_joule

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    40mm - 25mm is the material either side of the hole.
    The rod end is 40 wide, less 25 mm for the material missing due to the hole.
    This is then multiplied by the rod thickness.
    This is the area of the two rectangles we would see if we cut the rod parallel to the end face and coincident with the pin centre line.
     
  5. Sep 21, 2016 #4
    I
    I still can't visualize it.... Can you help to draw out diagram? The thickness is 20?
     
  6. Sep 21, 2016 #5

    billy_joule

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    The thickness (and pin diameter) is shown on the plan view just above your circled diagram.

    It's just a rectangular prism with a round hole in it, try draw your own diagram, post it if you get stuck.
     
  7. Sep 21, 2016 #6
    i still couldnt imagine , isnt the circle part represent the area ? in the diagram just above my circled part , i didnt see where is the (40-25mm)
    Can you explain further ?
     
  8. Sep 21, 2016 #7

    billy_joule

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    Can you see how the two diagrams show two views of the same assembly?
    Sketch a rectangular prism with a round hole (the rod end) include all the dimensions given, post the drawing.

    I assume you're studying mechanical engineering? You haven't done any technical drawing or CAD yet? You'll be expected to interpret drawings of much more complex parts and assemblies and also produce your own drawings, if you're having trouble with this simple part I'd recommend that you start practicing now so you're prepared.
     
  9. Sep 21, 2016 #8
    like this ? I am not sure though .
     

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  10. Sep 21, 2016 #9

    billy_joule

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    Yes, that's right. If you project backwards you can show the thickness too.

    How much material is left either side of the hole to support any loading?
    Can you see the significance of 40mm - 25mm now?
     
  11. Sep 21, 2016 #10
    the total of 2 red part i add now represent 40 - 25 mm , but where is the 20mm? i didnt see it
     
  12. Sep 22, 2016 #11

    billy_joule

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    The 20mm dimension is next to the 25mm dimension.
    It's given for the fixed support but it's fair to assume they're both the same thickness.
     
  13. Sep 22, 2016 #12
    the diagram is confusing .... From the top view , i found that the rod is quite thick (green line represent the thickness) , However , when we view it from front , it is a flat tod ( very thin) . Or you can draw me a 3d diagram please?
     
    Last edited: Sep 22, 2016
  14. Sep 22, 2016 #13
    t
    do you mean here ( in the photo attached) represent 20mm ? if so , it doesnt make sense , right? Since the diameter of circle already = 25mm , which is > 20mm
     

    Attached Files:

  15. Sep 22, 2016 #14
    Can you label in my diagram that i sketched , where is the 20mm ?
     
  16. Sep 23, 2016 #15
  17. Sep 23, 2016 #16

    billy_joule

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    It's the depth,or thickness of the rod end, into (or out of) the page.
    It can't be shown on your sketch as it is only 2D.
     
  18. Sep 23, 2016 #17
    Since it cant be shown on my diagram , then is my diagram wrong ? in the notes , the area is (20)(40-25) .. did I sketch the diagram wrongly?

    Or , if my diagram correct ? If so , then it's side view , right ?
     
  19. Sep 23, 2016 #18

    billy_joule

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    Your first sketch is right, you just need a top (or bottom, or end) view to show depth.
    Alternatively, you can do an isometric sketch to show all the information.
    You're looking for the area of the two cross hatched sections:
    Gy_Jw5qCEOf8Ti1UfmUGkKcJfmSH4xOauYBuYh0TYXbFlum00Ul6lvKJhweo6r-qFwJD7yn_7Hi4i8Wvtzp=w580-h676-no.png


    Note that we've taken the authors word that this is the smallest cross sectional area of the rod.
    [EDIT: Actually, they do show it's the case]
    It is, but only by a very small margin, if the hole size was reduced to 24mm it wouldn't be the area we need to consider.
    In future, you'll need to prove that you're using the correct cross section.
     
    Last edited: Sep 23, 2016
  20. Sep 23, 2016 #19
    why we need to consider the stress for the area of side view ? Why not from front view ?
     
  21. Sep 23, 2016 #20

    billy_joule

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    What is the definition of normal stress?
     
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