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Statics Equilibrium problem

  1. May 16, 2016 #1
    Question:

    Three forces of magnitude 45 kN, 24 kN and 12 kN are applied to the truss connection as shown. Knowing that the connection is in equilibrium, determine the magnitude of the forces C and T.

    fI9E29j.jpg



    Equations:

    Fx = 0
    Fy = 0

    My attempt:

    Fx=0:

    -24kN + Tcos40 + Csin20 = 0

    Fy = 0:

    45kN + Tsin40 - Ccos20 = 0

    By substitution:

    Divide first equation by sin20:

    2.24T + C = 70.17 kN ---> C = 70.17kN - 2.24T (Plug that C into equation 2.)

    Tsin40 - (70.17kN - 2.24T)(cos20) = -45kN

    2.75T = 20.94

    T = 7.62kN (Plug that back into equation 1 to find C)

    C = 53.10 kN

    However the answer is supposed to be C = 44.89kN and T = 4.35kN

    What am I doing wrong?
     
  2. jcsd
  3. May 16, 2016 #2

    robphy

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    How do you get your Fx equation?
     
  4. May 16, 2016 #3
    For a start sign convention:
    ∧ +ve & >+ve

    v=0
    -24 + CCos70 = TCos40 +12​
    h=0
    -CSin70 = TSin40 +45

    from here you should be able to get answer​
     
  5. May 16, 2016 #4
    I think you missed the 12 kN in your Fx equation. I didn't go through the math though.
     
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