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Finding the stress of a rigid beam

  1. Apr 5, 2009 #1
    The question is simple.

    i want to find the stress of a rectangular beam freely supported at both ends. A load F is acting in the middle.

    I know that stress = moment / inertia

    also inertia = (b h ^3 ) / 12
     
  2. jcsd
  3. Apr 5, 2009 #2
    I think you have your equation wrong. I think what you want is
    sigma = M*c/I
    so, figure out M, c, and I and go to it.
     
  4. Apr 5, 2009 #3
    can you explain please how to proceed with that. i have been struggling for days
     
  5. Apr 5, 2009 #4
    i know that both sides there are 2 vertical forces acting upwards F/2
     
  6. Apr 5, 2009 #5
    You'd have to find out the maximum moment which is at the middle, by multiplying either reaction by the half-span (distance from end to middle).

    As Dr. D said, the maximum (bending) stress is My/I.
    M has already been determined above, you'd need to determine for the beam cross section
    y = distance between the neutral axis and the distance at which stress is required (usually top or bottom edge)
    I = second moment of area.

    You only have to do a little google search to find out how these quantities are calculated, if you missed your class and do not have a textbook on Strength of Materials.
     
  7. Apr 6, 2009 #6
    if the length is L and the load is at the middle.

    The moment, M is L/2 x F /2 ?

    is y also L/2 ?
     
  8. Apr 6, 2009 #7
    Look at what mathmate said about y. The neutral axis is a horizontal line (for a horizontal beam). Do you want the bending stress at a point L/2 above the neutral axis, which in this case is the midplane?
     
  9. Apr 8, 2009 #8
    The maximum moment and hence highest stress is indeed situated at x = L/2, however the flexure formula above is used to calculate the stress distribution within a certain cross-section, as such the y is a coordinate within this cross-section. It has nothing to do with the dimensions of the beam itself. The distribution will look like this:

    http://en.wikivisual.com/images/3/3a/Internal_Forces_and_Stresses_from_Bending.png

    If your goal is to calculate the maximum stresses then the above equation may be used whereby y is the largest distance from the neutral axis (as already stated), and would in this case be h/2.
     
    Last edited: Apr 8, 2009
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