The concrete pipe elbow has a weight of 400 lb and the center of gravity is located at point G. Determine the force F_{AB} and the tension in cables BC and BD needed to support it.
Image from: Hibbeler, R. C., S. C. Fan, Kai Beng. Yap, and Peter Schiavone. Statics: Mechanics for Engineers. Singapore: Pearson, 2013.
Solution:
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Let us draw a free body diagram around ring B and depict the forces in each cable.
Note how the weight of the pipe must go through F_{AB}. Also note that F_{BC}=F_{BD} due to symmetry.
Let us write an equation of equilibrium for the y-axis forces.
+\uparrow \sum \text{F}_\text{y}\,=\,0
400-F_{BC}\cos45^0-F_{BD}\cos45^0=0
(Note again that F_{BC}=F_{BD} due to symmetry.)
400-2F_{BC}\cos45^0=0(Solve for F_{BC})
F_{BC}=283 lb
Final Answer:
F_{BC}=F_{BD}=283 lb