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Shear flow along a triangular member

  1. Dec 17, 2013 #1
    1. The problem statement, all variables and given/known data
    hHgZXA8.png
    UpGiDPi.png


    2. Relevant equations
    qs1(0)=qs3(5)
    qs2(0)=qs1(5)
    qs3(0)=qs2(6)

    Vy=0

    q(s)=-Vy/Iyy*Q(s)

    Where Q(s)=y*A
    Where y=y coordinate of centroid and A=Area

    3. The attempt at a solution
    To be honest I'm not sure how to separate the q(0) term, nor do I know what the physical significance of q(0) is (it's the shear flow, but is it the total shear flow at point O?). I've tried setting up the problem like:
    qs1(0)=q(0)=qs3(5)=q(0) so q(0)=q(0)
    but that doesn't give me any information. I've also tried:
    qs2(0)=-7.5*Vz*t/Iyy+q(0)
    qs3(0)=-7.5*Vz*t/Iyy+q(0)
     
  2. jcsd
  3. Dec 17, 2013 #2

    SteamKing

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    The shear flow q(s) is a function of the length coordinate s. Along each of the sides s1, s2, and s3, there is a point where s = 0. The location of the shear center suggests that the section is open at some point. If point O is the location where the section is open, what must the value of q(0) be?
     
  4. Dec 17, 2013 #3
    Thanks for the reply.

    Hmm, I see what you are saying. So at s1=0, and the shear at point O is zero, then qs1(0)=-3*Vz*t*(0)^2/(10*Iyy)+q(0)=0 which means q(0) has to equal 0. Can you explain how you know there has to be an open section just from looking at the shear center?
     
  5. Dec 17, 2013 #4

    SteamKing

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    The shear center is located outside of the triangular section. I believe most closed sections have the shear center located somewhere in their interiors. If the section is indeed open, then the shear flow starts with a zero value at the free end of the section. This fact is used when analyzing the shear flow in closed sections.
     
  6. Dec 19, 2013 #5

    nvn

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    into space: The cross section is not open. You can see, from the given diagram, the cross section is closed.

    In section 1 of post 1, why are you listing five values of q(0), a through e? When you state a question, you need to explain what is being listed. Why are you listing those q(0) values? Are you saying this is a multiple choice question? Is this an exam question?

    Wrong. Vy = 0.

    Wrong. Vy = 0. Keep trying. By the way, excellent diagram. Nice work.

    No, it is not. q(0) is just a constant. Your task is to determine the value of that constant.
     
    Last edited: Dec 20, 2013
  7. Dec 21, 2013 #6

    nvn

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    into space: My first sentence in the last line of post 5 might be wrong. You might be right. q(0) might be the total shear flow at point O.
     
    Last edited: Dec 21, 2013
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