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Stiffness of column when fixed versus pin fixed

  1. Aug 2, 2012 #1
    Guys when i study earthquake , they told me that the column stiffness is 12EI/L3 if column is fixed -fixed and 3EI/L3 if column is pin -fixed, so how they get this, i try to study stiffness Matrix and it gives you big matrix for frames not Only one factor like 12EI/L3
    please explain
     
  2. jcsd
  3. Aug 2, 2012 #2

    PhanthomJay

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    Re: Stiffness

    They are not talking about the stiffness of the joints, just the stiffness of the member framing into the joint with a lateral load is applied at the joint. If both ends are fixed at the joints (translation but no relative rotation), K = 12EI/L^3, which is the inverse of its end deflection for a fixed-guided beam subject to point load at the joint, and if it's fixed pinned, then K = 3EI/L^3, the inverse of the deflection of a cantilever with a point load at joint
     
  4. Aug 2, 2012 #3
    Re: Stiffness

    Thank you very much. i didnt get it ,could uou provide me with something to read , in order to understand it.Please
     
  5. Aug 2, 2012 #4
    Re: Stiffness

    What do you mean by the inverse of the deflection of a cantilever with a point load at joint?? and how it is equivelent please expalin
     
  6. Aug 2, 2012 #5

    PhanthomJay

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    Re: Stiffness

    The deflection of a cantilever with a point load F at the free end is FL^3/3EI. It's stiffness, K, or spring constant if you will, per Hooke's Law F=kx, is

    F=kx

    k = F/x
    k = F/(FL^3/3EI)
    k = 3EI/L^3
    which is the inverse of the deflection under a unit load.
    You are asking why, I think, you use the cantilever stiffness for a fixed pinned column in a frame with a load applied at the joint. That's because the joint translates, and the deflected sahpe is equivalent to the cantilever's deflected shape. For the fixed-fixed case with joint translation, the stiffness is equivalent to that of a beam fixed at one end and free to translate but not rotate at the other, in which case K = 12EI/L^3, which youcan find in beam tables.
     
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