Book$-$

Learning Goal:

To be able to solve three$-$dimensional equilibrium problems using the equations of equilibrium.

As with two$-$dimensional problems, a tree$-$body diagram is the first step in solving three$-$dimensional equilibrium problems. For the free$-$body diagram, it is important to identify the appropriate reaction forces and couple moments that act in three dimensions. At a support, a force arises when translation of the attached member is restricted and a couple moment arises when rotation is prevented. For a rigid body to be in equilibrium when subjected to a force system, both the resultant force and the resultant couple moment acting on the body must be zero. These two conditions are expressed as

${\displaystyle \underset{?}{\overset{?}{}}}F=0$

${\displaystyle \underset{?}{\overset{?}{}}}{M}_O=0$

where ${\displaystyle \underset{?}{\overset{?}{}}}F$ is the sum of all external forces acting on the body and ${\displaystyle \underset{?}{\overset{?}{}}}{M}_O$ is the sum of the couple moments and the moments of all the forces about any point $O.$

These two equations are equivalent to six scalar equilibrium equations that can be used to find up to six unknowns identified in a free$-$body diagram. These equations require that the sum of the external force components in the $x,y,$ and $z$ directions must be zero and the sum of the moment components about the $x,y,$ and $z$ axes are also zero.

Part A

The $J-$shaped member shown in the figure $($Figure $1)$ is supported by a cable $DE$ and a single journal bearing with a square shaft at $A.$ Determine the reaction forces $A_y$ and $A_z$ at support A required to keep the system in equilibrium. The cylinder has a weight $W_B=5\mathrm{.}80lb,$ and $F=2\mathrm{.}00lb$ is a vertical force applied to the member at $C.$ The dimensions of the member are $w=1\mathrm{.}50ft,l=6\mathrm{.}00ft,$ and $h=2\mathrm{.}00ft.$

Express your answers numerically in pounds to three significant figures separated by a comma.

View Available Hint$($s$)$

$$

Part B Complete previous p

Provide Feedback