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General loading, shear and moment relationships

  1. Nov 20, 2009 #1

    Hi everyone,

    I'm struggling to get my head around the convention of internal moments and shear forces of a loaded beam.

    I just can't seem to make any sense of why F is facing upwards and F+dF is facing downwards. It's driving me absolutely insane. Surely both of them will be facing upwards to cancel out wdx?

    Please help =/

    Thank you.
  2. jcsd
  3. Nov 20, 2009 #2


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    Hi emRage! :smile:
    No, the F upward shown on the left of the section matches the F downward (not shown) on the right of the next section to the left (Newton's third law!).

    And the next section to the right will similarly have an F + dF upward on its left (not shown), and that matches the F + dF downward shown.

    To look at it another way …

    the wdx is a very small amount, and tends to zero as dx tends to zero.

    It must therefore be "cancelled" by an equally very small amount …

    and that isn't going to be the rather large F + F + dF, is it? :wink:
  4. Nov 20, 2009 #3
    Thank you tiny-tim,

    Now my next question is:

    The arrows for F and F+dF are facing that way to cancel out the hidden F and F+dF. Why do the (visible) arrows have to face that particular direction? Because if I were to change the direction they are facing, that would change the shear force and bending moment equilibrium eqtns am I correct?

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  5. Nov 20, 2009 #4


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    They don't have to.

    If you put the arrows that way round, and then solve the equations, you'll find that F will come out negative.

    In some problems, it isn't at all obvious which way up they should be, so you just have to make a guess, and if the guess turns out wrong it doesn't matter … you'll have, say, -3N up instead of 3N down … same thing. :smile:
  6. Nov 21, 2009 #5
    Thanks for ur help, Ok so here's the next question,

    C-section beam of 300mm , Sy = 1000N
    Finding bending stresses 100mm from the point of load...The force causes compression on top and tension on the bottom hence bottom stresses should be +ve and top stresses -ve.

    100mm from the point of load would mean a bending moment of 1000x100 = 100000Nmm in the positive sense about x-axis.

    The bending moment caused by Sy in this case is +ve Mx (moment in the x-axis). Am I correct?

    I'm getting positive values at the top corners and negative at the bottom corners for bending stress which is clearly wrong!


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  7. Nov 21, 2009 #6


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    uh-uh, can you please start a new thread?

    (and can you make it clear where the point of application of the force is?)

    Then other members will come in and help …

    all this stress and moment is getting a bit out of my depth. :redface:
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