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Moments -- sign convention in beam

  1. Apr 11, 2017 #1
    1. The problem statement, all variables and given/known data
    In this question , we can see that in teh second picture , the 12.86kNm is in clockwise direction at the right of span BC .

    2. Relevant equations


    3. The attempt at a solution
    In meachnic of materials , i learnt that when the beam curve upwards ( U shape) , then it has positive bending moment ... So , I agree that the 1.54kNm clockwise rotation on the left of span AB has POSITIVE moment ... But , i dont agee that the 12.86kNm is in clockwise direction at the right of span BC has POSTIVE value ( it's -12.86kNm on the left , so POSITIVE 12.86kNm is added to bring the moment to 0 at C) ... I think the -12.86kNm on the right of span BC will lead to negative moment
     

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  2. jcsd
  3. Apr 11, 2017 #2

    PhanthomJay

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    Yes, the ends are both fixed and at the left end the deflected curve is upwards, or positive moment by convention, and at the right end the deflected curve is downward so the moment is negative. So the moment is -12.86 at the right end.
    Note when drawing the moment diagram, fixed end moments and applied couples , when acting clockwise , add to the moment diagram as a positive value. That is why at C the cw moment of 12.86 is added as a plus to bring the moment to 0 a hair to the right of C. But by convention, the fixed end moment at C is indeed a negative 12.86. It can get confusing, for sure.
     
  4. Apr 11, 2017 #3
    Do you mean for the clockwise moment 12.86kNm has to become counterclockwise 12.86kNm moment when drawing moment diagram ? This will lead to positive 12086kNm ?

    If it's so , why we have to do so ? Why we have to make the 12.86kNm clockwise moment to become couterclockwise when drawing moment diagram ?
     
  5. Apr 12, 2017 #4

    PhanthomJay

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    No.
    By convention, clockwise moments are negative when acting on a section to the left of it, and clockwise moments are positive when acting on a section to the right of it. Similarly, counterclockwise moments are positive when acting on a section to the left of it, and counterclockwise moments are negative when acting on a section to the right of it. so in your case, the 12.86 moment acts clockwise on a section to the left of it, and is thus negative. Rather confusing I know, so it is always a good idea to roughly sketch in the deflected shape of the beam, and if it faces upward it is a positive moment in that region, and when it faces downward, it is a negative moment in that region.
    Now when drawing your moment diagram from left to right, the fixed end moments point upward when clockwise, and downward when counterclockwise.
    If you are still confused, don't be, because your last sketch showing positive and negative moments is correct.
     
  6. Apr 12, 2017 #5
    As we draw the BENDING MOMENT DIAGRAM from left to right , for FIXED END moment , when it's in clockwise direction , it will bend the beam upwards , so , it's positive ?

    Conversely , if the FIXED END moment is in anticlockwise direction , it will bend the beam downwards , so , it's negative?
     
  7. Apr 12, 2017 #6
    This applied to the moment 12.84kNm only because it's the couple as you mentioned in post#2 ?
     
  8. Apr 12, 2017 #7
    This is same as the when drawing the moment diagram, fixed end moments and applied couples , when acting clockwise , add to the moment diagram as a positive value????
     
  9. Apr 12, 2017 #8

    PhanthomJay

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    The Fixed End Moments do not bend the beam; the loading on the beam between supports causes the bending.

    What I mean is that when drawing the moment diagram starting at the left, as in the example bending moment diagram, at the left support there is a clockwise fixed end moment , 1.54, so you start at 0 and add 1.54 upward to the diagram, then as you proceed to the end you get 12.86 negative moment (- 12.86), and to close the diagram so to speak you add the FEM of 12.86 upward because it is clockwise.
     
  10. Apr 12, 2017 #9
    it is positive 12.86kNm because the clockwise moment will make the left portion of he beam to curve upwards , while the right end in fixed ? Can i explain in this way ??
     
  11. Apr 12, 2017 #10

    PhanthomJay

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    No you cannot. The 12,86 moment is NEGATIVE if you read my prior posts. The section immediately to the left of it curves downward.
     
  12. Apr 12, 2017 #11
    in the previous post , you said my sign convention curve u shape upwards is positive is correct (refer to photo) ? And your current comment stated that when the beam curve 'n' shape is positive ?

    Can you clarify it ?
     
  13. Apr 13, 2017 #12

    PhanthomJay

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    Where did I say that? Upwards U shape is pos mom and upside downU shape is neg mom
     
  14. Apr 17, 2017 #13
    what are you saying ?
     
  15. Apr 17, 2017 #14
    What you mean is like this ? The red part has positive sign convention ?

    But , i also remembered you said that my sign convention positive is correct when the beam bent upwrads ( green part) in post 2 ?

    So , which beam has positive sign convention ? bent upwards or bend downwards ?
     

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  16. Apr 17, 2017 #15

    PhanthomJay

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    As you noted in your very first post attachment 621.png, bent upwards is positive and bent downwards is negative. I thought that was already established. You will also note in that attachment that clockwise moments acting on a section to the right of it, and counterclockwise moments acting on a section to the left of it, are positive moments. You also showed this correctly. The sketch is 100 percent correct.
    You can confirm this by looking at figure 11-10 (b). Notice at the extreme left , the beam bends upwards initially, and the moment M_AB is clockwise acting on he section to the right of it, thus, this agrees fully that the moment M_AB is positive. And notice at the extreme right, the beam bends downward initially, and the moment M_CB is clockwise acting on the section to the left of it, thus, this agrees fully that the moment M_CB is negative.

    Is this clear now?
     
  17. Apr 17, 2017 #16
    No , i show that in that attachment that clockwise moments acting on a section to the right of it, and counterclockwise moments acting on a section to the left of it, are NEGATIVE moments , (curve downwards)
     
  18. Apr 17, 2017 #17
    Can you explain how the negative moment -12.86kNm is brought to 0 at the extreme right end ?
     
  19. Apr 18, 2017 #18

    PhanthomJay

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    What we have here is a failure to communicate. The attachment shows that clockwise moments acting on a section to the LEFT of that moment is NEGATIVE. Please look at the lower sketch in your attachment, the one showing the upside down U deflected shape of the beam. We know that moments are negative in this section. And the clockwise moment at the far right acts on a section to its left. I guess you mean that the clockwise moment lies to the right of the section. Whatever is the way to describe it in words, the sketch is correct.
    Well when drawing moment diagrams, first off, the fixed end (concentrated couple) moments (FEM) at either end don't in theory go to zero, they are what they are, that is, in this example, at the right end, the FEM is negative 12.86 kN-m. In actuality, concentrated moments , just like concentrated point loads, don't exist, because they are applied over zero width, which leads to the infinities that nature despises. But anyway, let's assume the moments start and end at 0. As you draw the moment diagram (after first drawing the shear diagram) from left to right, when you get to the right end , the moment in the beam is -12.86, then in order to close it to 0, you add in the clockwise FEM of 12.86 to get -12.86 + 12.86 = 0. Notice here that when drawing moment diagrams , clockwise moments are always considered positive, and this is unrelated to our previous discussion on moment signage .
    Consider a simple cantilever beam 2 m in length and subject to a downward point load of 10 N at the free end. The free end is at the left of the beam and the fixed end is at the right of the beam. The FEM is 20 N-m clockwise and the beam section it acts on is to its left, thus a negative moment, and of course the beam deflects downward as an upside down 'U' shape of sorts. Now in drawing the moment diagram. starting from the left, the moment in the beam is 0 at the free end, and continues sloping downward to -20 N-m at the fixed end, then since the FEM of 20 N-m is clockwise, you draw a straight line upward back to 0.

    Okay???

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    Last edited: Apr 18, 2017
  20. Apr 18, 2017 #19
    Can you explain how the negative moment -12.86kNm is brought to 0 at the extreme right end ?
     
  21. Apr 18, 2017 #20
    Can you explain this one ? I noticed that the clockwise 12.86kNm clockwise moment acting to the right of span ...
     
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