# 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.

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

#### Solution:

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

$F_{BC}=F_{BD}=283$ lb