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Buckling of column connected to beam

  1. Aug 13, 2016 #1
    1. The problem statement, all variables and given/known data
    In this question, we are interested inthe buckling of column, so we should calculate the moment of inertia (Ixx) or (Iyy) at the column,right?

    2. Relevant equations


    3. The attempt at a solution
    Why the author calculate (Ixx) and (Iyy) using the cross sectional area of beam?
    is it wrong?
    And for critical load applied at y-axis (Pcr_y) , why the Le used is 3000 , why not 250mm?
     

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  3. Aug 13, 2016 #2

    PhanthomJay

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    The author is using the column cross section in determining the buckling load of the column. The beam in the middle provides lateral weak axis column support at the column mid point.
     
  4. Aug 13, 2016 #3
    do you mean the load is applied at the beam to detremine the buckling of column?
    Since the column and beam are connected , so , we can use the Ixx or Iyy about the cross sectional area of beam to calculate the buckling of column?
     
  5. Aug 13, 2016 #4

    PhanthomJay

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    Buckling loads in the usual sense are compressive axial loads. This problem asks what is the max compressive axial load that can be applied to the top of the column before it buckles. The cross section of the beam has nothing to do with the buckling of the column. The beams transfer vertical loads to the columns, yes, but the problem example wants to show how beams can reduce the effective length of the column when determining weak axis column buckling
     
  6. Aug 13, 2016 #5
    is It true that the load is applied in this direction? uploadfromtaptalk1471131132083.jpg
     
  7. Aug 13, 2016 #6

    PhanthomJay

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    Not true. The solution gives the max vertical load for P applied downward at the top of the column.
     
  8. Aug 15, 2016 #7
    do you mean the load is applied in this direction ?
     

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  9. Aug 15, 2016 #8

    PhanthomJay

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  10. Aug 15, 2016 #9
    then , why we need to consider the moment of inertia about the cross sectional area of beam ? or i misunderstood something ? the 250mm x300mm is not cross sectional area of beam ?
     
  11. Aug 15, 2016 #10

    PhanthomJay

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    That is the cross section of the column, which should have been more clearly shown,
     
  12. Aug 15, 2016 #11
    Can you explain why we need to consider the moment of inertia about the cross sectional area of beam? We are interested in the buckling of column, so we should consider the moment of inertia of the column, right?
     
  13. Aug 16, 2016 #12

    PhanthomJay

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    Yes , the dimensions given are for the column. You do not need to consider the cross section of beam.
     
  14. Aug 16, 2016 #13
    why there are two force applied which is 771kN and 2138kN? only 1 force can be applied at the top and bottom portionof the column to determine the critical load of the column,right?
     
  15. Aug 16, 2016 #14

    PhanthomJay

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    That is correct. Critical load is determined by using the lesser of the 2 values calculated. In this case, major axis buckling controls due to the higher l/r ratio.
     
  16. Aug 17, 2016 #15
    can you explain why the Le for Pcr_y is 3000 ? i could only understand the Le for Pcr_x is 6000
     
  17. Aug 17, 2016 #16

    PhanthomJay

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    The middle beam provides lateral support at the column mid point on the weak axis direction. That cuts it's effective length in half against weak axis buckling. No such mid point support is provided against major axis buckling by this beam.
     
  18. Aug 17, 2016 #17
    ,do you mean the beam divided the column into 2 parts?
     
  19. Aug 17, 2016 #18
    ,do you mean the beam divided the column into 2 parts?
     
  20. Aug 17, 2016 #19
    you already said that the middle beam provides lateral support at the column mid point on the weak axis direction. That cuts it's effective length in half against weak axis buckling?
    Why there's no support provided by this beam?
     
  21. Aug 17, 2016 #20

    PhanthomJay

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    The beam is pinned to the column at one end and at the other end of the beam it is connected to a wall or another column which is not shown in the figure. Once again the beam keeps the column from deflecting in the direction of that beam so it cannot bulge out and buckle at that point. But since the beam is pinned to the column at that point, it can't prevent the column from buckling about the major axis since the beam would just rotate and not provide support on that direction, only the other direction along the beam. Assuming ideal pins here. So in reprieve, effective length is 6000 for major
    axis buckling and 3000 for minor axis buckling.
     
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