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Determine the Maximum Tensile and Compressive Stresses in the Beam

  1. Mar 27, 2013 #1
    1. The problem statement, all variables and given/known data
    Two vertical forces are applied to a beam of the cross section shown. Determine the maximum tensile and compressive stresses in portion BC of the beam

    I have attached an image of the question

    2. Relevant equations

    σ = P/A +/- My/Ix

    Ix = Ix + Ad2 ---> parallel axis theorem

    3. The attempt at a solution

    I calculated the centroid to be:

    x = 4.5 in

    y = 3 in

    I did this by dividing the shape into two rectangles, determining the centers of those rectangles from an arbitrarily assigned origin, O, which I assigned to be at the bottom left of the lower rectangle.

    I then used the parallel axis theorem to calculate the Inertia, Ix

    P = 0 because the sum of the forces is 0.

    M is the greatest moment value, which I found to be 600 kip-in.

    My confusion is how do I determine the y value? I believe that the greatest tensile and compressive stresses would be at the bottom and top of the bar respectively, but my notes indicate that the correct y-values are 3 in for the tensile stress and 5 in for the compressive stress. I had thought that the y values was from the centroid of the cross-section which makes me think it should be 3 in for the max compressive and tensile forces.

    Can anyone clarify this for me?

    I know the final answers are

    8.82 ksi T

    14.72 ksi C
     

    Attached Files:

  2. jcsd
  3. Mar 27, 2013 #2
    Never mind, I figured it out.
     
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