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Homework Help: My instinct is conflicting with the stress equation

  1. Nov 28, 2013 #1
    1. The problem statement, all variables and given/known data

    An L-shaped beam is loaded by a bending moment M under an angle ψ with the horizontal axis. M = 200 Nm and ψ = 45°. Determine the maximum tensile stress in the beam and its location(s).


    I added the purple moment-vectors myself, they are the horizontal and vertical components of the applied moment, the black vector.

    2. Relevant equations

    σ = [(Ix*My - Iz*Mx)*x + (Iy*Mx - Iz*My)*y]/(Ix*Iy - Iz²)

    3. The attempt at a solution

    First I calculated the center of gravity, which resulted in the coordinates x=17.61 and y=15.59 with respect to the bottom left corner.
    Then I calculated Ix, Iy and Iz, which I found to be
    Ix = 140 521.35 mm4
    Iy = 111 889.43 mm4
    Iz = -42 639.63 mm4

    Then, when you look at the components of the moment separately, you'll find that for the horizontal component, the top side is in tension and the bottom is in compression. For the vertical component, the left side is in tension and the right side is in compression. This means that, if combined (so in the case of the actual applied moment), the maximum tensile stress will be in the top left corner of the cross section (which has coordinates x=-17.61. and y=19.59 with respect to the center of gravity)

    However, when looking analytically at the stress equation, one can see that the stress will be higher if x would be positive as well. The top corner in the middle has a positive x-value wrt the center of gravity and should, theoretically, have a higher tensile stress. But I always thought that the point furthest away from the vector has the highest stress (since stress varies linearly, thus the farther, the higher) and the top corner in the middle isn't the furthest at all...

    I already calculated the neutral axis but that resulted in the confirmation of my assumption that the neutral axis runs more or less along the moment vector (it has a bit steeper slope, but that doesn't change a thing)

    Does anyone have any idea?

    Sorry for the long post, I just wanted to make sure that everything I had was mentioned.
    Last edited: Nov 28, 2013
  2. jcsd
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