Learning Goal:

To be able to solve three$-$dimensional equilibrium

problems using the equations of equilibrium.

As with two$-$dimensional problems, a free$-$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 $W_B=5\mathrm{.}10lb,$ 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$)$

$lb$

X Incorrect; Try Again; $5$ attempts remaining