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Question about shear flow / stress

  1. Jan 5, 2017 #1
    1. The problem statement, all variables and given/known data
    For QB , why shouldnt the QB = red part only ?

    2. Relevant equations


    3. The attempt at a solution
    Is there anything wrong with the solution given ?
    Since When we 'cut ' the boards , the b is the red part which in contact with the other board , right ?
     

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  3. Jan 9, 2017 #2

    PhanthomJay

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    Nothing wrong with solution. Remember when determining bolt shear, use the full area of connected part when determining Q.
     
  4. Apr 21, 2017 #3
    Sorry to bump this but when finding QB why can we not use one of the boards on the left or right? Why the center board?
     
  5. Apr 21, 2017 #4

    PhanthomJay

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    You can do it that way and get the same result without having to divide by 2 when you use the center board, because now there is just one shear plane instead of 2 when using the first method.
     
  6. Apr 21, 2017 #5
    But I was thinking that only works here because the boards are the same dimensions.

    In a question like this below (b), if I use one of the side boards I get a different (wrong) answer than if I use the center board.

    main-qimg-28763a636910916c63557f31d77183d8?convert_to_webp=true.png
     
  7. Apr 24, 2017 #6

    PhanthomJay

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    Part b is a bit more tricky than part a because in part b, the longitudinal shear flow across the nail is into the plane of the page (z direction) on the yz side face of a cubic element, in contrast to part a where the longitudinal shear flow across the nail is into the plane of the page (z direction) on the xz top face of a cubic element. Consequently, in part b, the shear flow is horizontally distributed across the top board, so you need to find Q based on the area of the board in between the nailed joints, and the vertical distance from its centroid to the neutral axis. Then divide result by 2 when determining shear flow, because there are 2 shear planes.
    Alternatively, you could use the Q of the area outside of the top cuts, but when so doing, you must use the full area , that is, the area of both vertical pieces times the vertical distance of its centroid to the neutral axis. This a more tedious way of finding it.
    Part b is a stronger connection than part a, because the Q in part b is less.
     
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