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Determine x and y coordinates of resultant force through object

  1. Oct 3, 2012 #1
    1. The problem statement, all variables and given/known data
    The concrete slab supports the six vertical loads shown. Determine the x- and y-coordinates of the point on the slab through with the resultant of the loading system passes.

    Image attached


    2. Relevant equations



    3. The attempt at a solution

    I started off by finding the resultant force. Seeing as how all the forces in the system act in only the z direction I summed them to get:

    Rz = 69Kn - 69kN -42kN - 44kN - 67kN - 59kN
    = -212 kN

    But I'm not sure how I should proceed from this step. I would appreciate any suggestions.
     

    Attached Files:

  2. jcsd
  3. Oct 4, 2012 #2

    tiny-tim

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    Science Advisor
    Homework Helper

    Hi Northbysouth! :smile:

    Assume that it goes through the position (x,y).

    You know it's -212 kN, so what is the moment of that about the x-axis or the y-axis? :wink:
     
  4. Oct 4, 2012 #3
    I've managed to solve it now. I did the following:

    Rz = -212 kN

    Mx = (69kN)(2.3) -(67kN)(3.1+2.3) -(44)(8) -59*(2.3+3.1+2.6)
    = -1027. kNm

    My = 67*2.3 + 44*6.7 + 69*6.7 -69*5.2
    = 552.4 kNm

    Mz = 0

    M = 1166.224 kNm

    Rz*y = -1027.1
    y = 4.8448

    Rzx = 552.4
    x = -2.60566

    Thanks for your help.
     
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