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.

#### Solution:

Show me the final answerâ†“

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