A horizontal circular plate weighing 60 lb is suspended as shown from three wires that are attached to a support at D and form 30° angles with the vertical. Determine the tension in each wire.

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Accepted Answer

[latex]\begin{aligned}& \Sigma F_{x}=0: \& \quad-T_{A D}\left(\sin 30^{\circ} ight)\left(\sin 50^{\circ} ight)+T_{B D}\left(\sin 30^{\circ} ight)\left(\cos 40^{\circ} ight)+T_{C D}\left(\sin 30^{\circ} ight)\left(\cos 60^{\circ} ight)=0\end{aligned}[/latex]

Dividing through by 30° and evaluating:

[latex]\begin{gathered}-0.76604 T_{A D}+0.76604 T_{B D}+0.5 T_{C D}=0 \qquad & (1)\\Sigma F_{y}=0: \quad-T_{A D}\left(\cos 30^{\circ} ight)-T_{B D}\left(\cos 30^{\circ} ight)-T_{C D}\left(\cos 30^{\circ} ight)+60 \,\mathrm{lb}=0 \ ext { or } \quad T_{A D}+T_{B D}+T_{C D}=69.282 \,\mathrm{lb} \qquad& (2)\\Sigma F_{z}=0: \quad T_{A D} \sin 30^{\circ} \cos 50^{\circ}+T_{B D} \sin 30^{\circ} \sin 40^{\circ}-T_{C D} \sin 30^{\circ} \sin 60^{\circ}=0 \ ext { or } \quad 0.64279 T_{A D}+0.64279 T_{B D}-0.86603 T_{C D}=0 \qquad& (3)\end{gathered}[/latex]

Solving Equations (1), (2), and (3) simultaneously:

[latex]\begin{gathered}T_{A D}=29.5 \,\mathrm{lb}\blacktriangleleft \T_{B D}=10.25 \,\mathrm{lb} \blacktriangleleft\T_{C D}=29.5 \,\mathrm{lb}\blacktriangleleft\end{gathered}[/latex]

Question 2.120: A horizontal circular plate weighing 60 lb is suspended as s...

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