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Homework Help: Statics - 3 Dimensional Equilibrium

  1. Jun 14, 2010 #1
    Moment about an axis - Statics - 3 Dimensional Equilibrium

    1. The problem statement, all variables and given/known data
    The member is supported by a pin at A and a cable BC. If the load at D is 300, determine the x, y, z components of reaction at these supports.
    i.e Find the reactions at A and the tension in the cable BC

    2. Relevant equations
    Since it is in equilbrium.
    [tex]\Sigma F = 0[/tex]
    [tex]\Sigma M = 0[/tex]

    3. The attempt at a solution
    The most confusing part for me, is moment about an axis. (If possible, please tell me, how to find moment about an axis - the direct method and through the vector matrix).

    Correct me, if i am wrong.

    rBC = 0.3i - 0.6j + 0.2k
    |rBC| = 0.7
    uBC = 1/0.7 (0.3 i - 0.6j + 0.2k)

    TBC = |TBC|/0.7 (0.3i - 0.6j + 0.2k)

    [tex]\Sigma Fz = 0[/tex]
    [tex] = -300 + Az + TBC(0.2 / 0.7)[/tex]
    Az is unknown, so to determine Az - we find moment about the x axis of B.
    This will give, Az = 0
    [tex]\Sigma Fz = 0[/tex]
    [tex]= -300 + TBC(0.2/0.7) = 0[/tex]
    TBC = 1050 N.

    [tex]\Sigma Fx = 0[/tex]
    Ax + 1050(0.3/0.7) = 0
    Ax = -450 N

    [tex]\Sigma Fy = 0[/tex]
    Ay - 1050(0.6/0.7) = 0
    Ay = 900N

    Thats what i could do max (i think im right), now only moment about Y-axis w.r.t a and moment about Z-axis is left, w.r.t a again. (May and Maz).
    Please tell me how to get this part, with 2-3 methods to get moment about an axis (Direct and through matrix).

    Thanks a lot =)

    Attached Files:

    Last edited: Jun 14, 2010
  2. jcsd
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