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Sign of moment in buckling of column

  1. Dec 24, 2016 #1
    1. The problem statement, all variables and given/known data
    Can someone explain why the M is assigned to be anticlockwise here ?

    2. Relevant equations


    3. The attempt at a solution
    When i assign it as clockwise , i will get -P(δ -v) , which is different from the author ... Can i do so ? Why ?
     

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  2. jcsd
  3. Dec 24, 2016 #2
    for the second example here , i can understand that M = -Pv , since M+Pv = 0 at either end when it's in equlibrium. ( I have showed in the working)

    P/s : I know the the sign convention of the bending moment of beam is positive when the beam upwards as shown ...

    For the first example in post#1 , i gt M+P(∂-v) = 0 , so M = - P(∂-v) .
    I am not sure whether is my concept correct or not . My working is in the 3rd photo here
     

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  4. Dec 24, 2016 #3
    Is my concept wrong ? can someone explain it ?
     
  5. Dec 26, 2016 #4

    PhanthomJay

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    Draw a FBD appropriately of an arbitrary cut section of the top part of the deflected column and determine the direction and magnitude of the moment of the applied force P. What must be the direction and magnitude of the internal moment at the cut?
     
  6. Dec 26, 2016 #5
    The moment M has to be counter clock wise at the base because from the given figure the applied force P will try and rotate the column clockwise
     
  7. Dec 27, 2016 #6
    How about the case in post#2 ? Why
    M = -Pv ? For this case , why the M at the bottom = clockwise? since to balance the anticlockwise moment produced by P , the Moment has to be clockwise to counter the effect , am i right ? Just like the case in post#1 ...
     
  8. Dec 27, 2016 #7
    Yes, that's correct. So, note that in post#2 , the assumed direction of the moment in figure (b) is incorrect as it is drawn counter clockwise.
     
  9. Dec 27, 2016 #8
    So , in notes 2 , the assumed direction of the moment should be in clockwise direction . So , M = Pv ?
    But , i checked out so many books and so may links , they still give M = -Pv , so are they all wrong ?
     
  10. Dec 27, 2016 #9
    No , M=-Pv is correct for the assumed internal moments (positive is counter clockwise) as seen in figure (b). The assumed internal moment is counter clockwise in direction and the force P also rotates the column in a counter clockwise motion. So, ΣMoments = 0 , M+Pv=0 , M=-Pv.

    Obviously, since the column is assumed to be in equilibrium, the internal moment will actually be clockwise. This is exactly what the equation tells us, M= - Pv, the negative sign means that the assumed internal moment is equal to PV but is clock wise. But the example doesn't explicitly state this. For mathematical consistency we assign clockwise moments a negative sign, and counter clock wise moments a positive sign.
     
  11. Dec 27, 2016 #10
    Do you mean for all the cases in post 1 and post 2 , the author assumed the internal moment is in counter clockwise direction ?
     
  12. Dec 27, 2016 #11
    Yes, but in case 1 it is not an internal moment but a reaction moment
     
  13. Dec 27, 2016 #12
    It seems that the theory that the author assumed that the moment is counterclckwise all the time is incorrect here . I have 2 example below (from another book) . We can see that in the firstexample ( photo 1 and photo 2) book , the assumed internal moment is clockwise , for another case(photo 3 and photo4) , we can see that the reaction moment is clockwise
     

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  14. Dec 27, 2016 #13
    You can assume any direction to be positive, but for that particular problem, you need to be consistent and carry out the same assumption.
     
  15. Dec 27, 2016 #14
    please refer to the edited post in post #12 .
     
  16. Dec 27, 2016 #15
    It seems that the author of the example in the book that i uploaded doesnt follow the rules , or i missed out something ? can you explain it ?
     
  17. Dec 27, 2016 #16
    I also found that the assumed internal moment always has the same direction with the applied force moment in both example , is this true ? why we need to make that assumption ?
     
  18. Dec 27, 2016 #17
    Assuming a direction is all but a perspective for positive and negative, have a read about the conventional sign convention:
    https://en.wikipedia.org/wiki/Shear_and_moment_diagram#Convention

    Also,
    This is not true, it depends on the situation of analysis. In post #12, question 4.4, the internal moment is drawn counter clockwise and the force P rotates the column clockwise.
     
  19. Dec 27, 2016 #18
    Well , i agree that in 4.4 the assumed moment is counterclockwise , because the moment will turn the beam in U shape (smile curve) . But , i dont understand why in 4.3 , the assumed moment is clockwise , why not anticlockwise ? Because when the assumed moment is anticlockwise , it will bend the beam in U shape
     
  20. Dec 27, 2016 #19
    It doesn't really matter what direction you assume the moment is as long as you adopt a consistent general sign convention: Assume that all counter clockwise moments are'+' and all clock wise moments are '-'.

    Say in our FBD, we drew the unknown internal moment ( call it 'M') counter clockwise, then taking sum of the moments and using the above statement:
    (+M) + (-PV) = 0 , then M=PV. How do we interpret this result? It means that the internal moment is of counter cockwise orientation and of magnitude PV.

    Say in our FBD, we drew the unknown internal moment ( call it 'M') clockwise, then taking sum of the moments and using the above statement:
    (-M) + (-PV) = 0 , then M=-PV. How do we interpret this result? It means that the internal moment is not of clockwise direction (because our answer is negative) , it is of counter clock wise direction and has magnitude PV.

    Have a watch:
     
  21. Dec 27, 2016 #20
    So , shouldn,t the assumed moment is anticlockwise at the beam to enable it to have a curve U shape ? Just like the case below
     

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