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Mechanic Statics Problem

  1. Apr 15, 2004 #1
    I have a problem for HW that is driving me crazy!
    A copy of the original problem from the text is attached.

    Here is what I have done so far...

    First, I split the area under the force horizontally into two triangles and found the centroid of each.
    Centroid of upper triangle is 3m from left side.
    Centroid of lower tri is 6 m from left side.

    Area force of triangle 1 is 15.75 kN
    Area force of triangle 2 is 6.75 kN

    Total area force is 22.5 kN

    Location to place this equivalent force is 3.9m from left side.

    I believe I am good to this point. Now, to find the reactions at point B and C, I have setup the following equations:

    Sum Fy = By + Cy - 22.5kN - 50kNm/2m - 50kNm/8m = 0
    Sum Ma = 2m*By + 8m*Cy - 22.5kN(3.9m) - 50kNm = 0

    Solving these equations simultaneously I end up with
    Cy = 5.04kN
    By = 48.71kN

    According to the answers in the back of the book (Vector Mechanics for Engineers, 7th ed - Beer, Johnston & Eisenberg) the answers are
    Cy = 15.46 kN
    By = 7.04 kN

    Any help would be greatly appreciated. I am spent on this problem and just cannot see where I am going wrong. I suspect my problem is how I am dealing with the 50kNm torque shown on the diagram.

    Attached Files:

    Last edited: Apr 15, 2004
  2. jcsd
  3. Apr 16, 2004 #2


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    Gold Member

    You've got some extra terms in your force balance equation:

    [tex] \Sigma F_y = 0 = B_y + C_y - 22.5 {\rm kN} [/tex]

    You shouldn't have any terms from your applied moment - it's an applied moment. You'd only consider forces there if you resolved it into a couple or something.
  4. Apr 16, 2004 #3
    OK, I got it now. Thanks Jamesrc. I treated the moment all wrong. You pushed me in the right direction.
    Thanks again.
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