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Understanding a stress equation

  1. Jan 20, 2010 #1
    I really need help understanding how the book created the equation from the book. I would really appreciate help understanding it. The attachment shows an image and the equation.
     

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  2. jcsd
  3. Jan 20, 2010 #2

    Mapes

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    They've divided by dz and canceled out some terms; that might be why it's a little confusing. The force (pressure times area) on the top surface is

    [tex]\left[\sigma_y+\left(\frac{\partial \sigma_y}{\partial y}\right)dy\right]dx\,dz[/tex]

    and the distance (lever arm length) is [itex]dx/2[/itex]. But the force on the bottom surface is

    [tex]\sigma_y\,dx\,dz[/tex]

    which creates a moment in the opposite direction that cancels out part of the moment from the force on the top surface. Starting to make sense now?
     
  4. Jan 20, 2010 #3
    Wow, thanks so much. The cancelling of dz was part of what was confusing me. Also, I was just looking at the diagram incorrectly for no particular reason, but since I saw it wrong initially I could not get it out of my head.

    Also, how do you type formulas into this forum?
     
  5. Jan 20, 2010 #4

    Mapes

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    Just click on the formula to see the markup language.
     
  6. Mar 7, 2010 #5
    tanks
     
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