The concrete pipe elbow has a weight


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.

The concrete pipe elbow has a weight

Image from: Hibbeler, R. C., S. C. Fan, Kai Beng. Yap, and Peter Schiavone. Statics: Mechanics for Engineers. Singapore: Pearson, 2013.

Solution:

Show me the final answer↓

Let us draw a free body diagram around ring B and depict the forces in each cable.

The concrete pipe elbow has a weight

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

 

This question can be found in Engineering Mechanics: Statics, 13th edition, chapter 3, question 3-12.

Leave a comment

Your email address will not be published.