Question: Consider the given figure with a force acting at D . Draw the free - body diagram of member ABD. Determine the reactions at A

Consider the given figure with a force acting at

D .

Draw the free

-

body diagram of member ABD. Determine the reactions at A and

E .

Strategy. The figure shows a simple machine. Note that drawing a FBD of the structure completely attached together would allow you to see two reactions at pin A and at pin

E .

For a twodimensional problem, we can only solve up to three unknowns for any free

-

body diagram. We need to reduce the number of unknowns or draw multiple FBDs

(

we have not covered how to do this yet for machines

) .

Identifying two

-

force members will reduce the unknowns by one. Identifying three

-

force members will also reduce the unknowns by one. This problem has one of each. The unknowns should initially be:

A_{x}, A_{y}, E_{x},

and

E_{y}

since there are two pins.

Task

1 .

Identify the two

-

force member. It is attached at no more than two places and has no additional forces applied to it

.

Draw a FBD of the member itself, knowing the line of action of the forces at the ends pass through both attachment points. Draw this member in compression. Note that instead of both

E_{x}

and

E_{y}

at the pin at

E,

there is only one unknown, the magnitude of the force at

E, F_{B E} .

The unknowns have been reduced. The unknowns should now be:

A_{x}, A_{y},

and

F_{B E} .

Task

2 .

Identify the three

-

force member. The sum of attachment points and applied forces on the member is exactly three. Draw a FBD of the member. The

200 -

lb applied load has a known line of action. By identifying member

B E

as a two

-

force member, we know the line of action of

F_{B E}

as well. Draw

F_{B E}

pointing at

B

from

E .

Locate the intersection point of the

200 - l b

force and

F_{B E} .

Instead of writing

A_{x}

and

A_{y}

at point

A,

we know the third force must pass through the same intersection point as the other two forces. Define the line of action for the force at

A, F_{A} .

The unknowns should now be only:

F_{A}

and

F_{B E} .

Task

3 .

Use the FBD to apply equilibrium and solve for the two unknowns. Express your answer as a force and small angle from the horizontal axis.

Further. With known reactions, can you find the values for the initial four unknowns:

A_{x}, A_{y}, E_{x},

and

E_{y} ?

After identifying the two

-

force member, there were three

Consider the given figure with a force acting at

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