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I'm working on this reactions problem. I know M(ay) is equal to 0, but I haven't been able to figure out how to solve for the tension in cable BC, forces A(x) and A(y), or moments A(x) and A(z). I've tried summing moments and forces every way I can think of, but keep coming up short and could use some help!

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    $\begingroup$ This looks like a homework problem. Demonstrate what you have tried, sot that other people can help you. $\endgroup$
    – NMech
    Commented Apr 6, 2021 at 2:48
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    $\begingroup$ $M_{Ay}$ is not equal to zero. $\endgroup$
    – NMech
    Commented Apr 6, 2021 at 6:06

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In this problem, you have at A $$ F_{Ax}, F_{Ay}, M_{Ax}, M_{Ay},M_{Az} \text{ not equal to zero}$$

only $ F_{Az}$ is equal to zero.

and also at point C, one force with magnitude $F_{C}$, and components you can derive from the direction of the wire

$$\vec{BC} = \begin{bmatrix} -L_1\\ -L_3-L_2\\ L_4 \end{bmatrix}$$

you can estimate the direction (unit vector) of the force from $$\vec{e}_{BC} = \frac{\vec{BC}}{\|BC\|}$$

where:

  • $\|BC\|=\sqrt{L_1^2 + (L_2-L_3)^2+ (-L_4)^2}$

From $\vec{e}_{BC}$, you can determine the components of the force at C:

$$\vec{F}_C = \frac{1}{\|BC\|}\begin{bmatrix} -L_1\\ -L_2+L_3\\ L_4 \end{bmatrix}\cdot F_{C}$$ where $F_C$ is the magnitude of the wire force.

As you can see you have a total of 6 unknowns ($F_{Ax}, F_{Ay}, M_{Ax}, M_{Ay},M_{Az}, F_c$), and 6 equations:

  • 3 equilibriums of Forces along x, y, z
  • 3 equilibriums of moments along x, y, z (I would pick point A as reference, to calculate the moment, to simplify my life).

The rest I leave to you.

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Resolve the cable by the upward force equals F at B. So do the sin/cos thing to get the cable tension. Then get the horizontal component of the cable which will come a moment about Az. F produces an additional moment about Ax from the force at B.

The key is resolving the cable tension via its x and z components, with the z component = F.

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