The beam shown has a roller support at A $,$ an

internal hinge $($pin$)$ at B $,$ and a fixed support at C $.$

$W_{AB}=6\frac{k}{f}t$;$x_{AB}=14ft$; and $x_{BC}=10ft$

Sign convention for your answers: assume up$,$ right, and counts rclockwise are positive directions.

Be careful of signs on your answers.

Calculate the magnitude $($absolute value$)$ of the res'stani of the distributed load $W_{AB}.($i$.$e$.,$

if you were to replace $W_{AB}$ with a single concentrated load what would be its magnitude?$).$

$($Make sure you include the units$).$

Arswer:

Units:

Draw an FBD of the entire bea:n$,$ ABC How many support reactions $($appear on your

FBD$?$

three,

four

five

six

Draw an FBD of segmeit AB $.$ Hew many unknowns $($including reactions$)$ appear on your

FBD$?$

two

three

four

five

Draw an FBD of segment BC$.$ How many unknowns $($including reactions$)$ appear on

your FBD$?$

two

three

four

five

Back to your FBD of AB $.$ Calculate the horizontal pin force at B $.$

Answer:

Units:

Still working with your FBD of $AB$ : if you were to sum moments about point $B$ what

would you use for a moment arm for the vertical reaction at $A?$

Still working with your $FBD$ of $AB.$ If you were to sum moments about point $B$ what

would you use for a moment arm for the equivalent load for the distributed load $($from #$1)?$

Answer:

Units:

Still working with your FBD of $AB.$ Sum moments about point $B$ and calculate the

vertical reaction at $A,A_Y.$

Answer:

Units:

Still working with your FBD of $AB.$ Now that you've calculated $A_Y,$ calculate the

vertical pin force at $B,B_Y.$

Answer:

$\_$Units:

Now that you've calculated BY let's start working with the FBD of beam $BC$ that you

drew earlier. The By that you just calculated shows up on this FBD so sketch it in$.$ Be careful

of the direction. Should $B_y$ show up in the same direction that it does on the FBD of $AB$ or in

the opposite direction?

Same Direction

Opposite Direction

Still working with your $FBD$ of $BC.$ At this point what is the only equation that can

use to calculate $C_Y?$

$M_C=0$

$F_Y=0$

$M_B=0$

Still working with your $FBD$ of $BC.$ Calculate $C_Y.$ Answer:

Units:

Still working with your $FBD$ of $BC.$ What equation can you use to calculate $Mc,$ the

moment reaction at fixed support $C?$

$M_C=0$

$F_Y=0$

$M_B=0$

Still working with your $FBD$ of $BC.$ If you were to sum moments about point $C,$ what

would you use for a moment arm for the vertical pin force at $B$ that you calculated

earlier?

Answer:

$\_$Units:

Still working with your $FBD$ of $BC.$ If you were to sum moments about point $C$ what

would you use for a moment arm for $M_C,$ the moment reaction at fixed support C $?$

Answer:

Units:

Still working with your $FBD$ of $BC.$ Calculate $M_C,$ the moment reaction at fixed

support $C.$

Answer:

Units:

The L $-$shaped bracket is subjected to the two concentrated forces

shown. $x=2$;$Y=9$;$x_1=6ft$;$Y_1=5ft$;$Y_2=10ft$;$=70$;

$P_1=282lb$;$P_2=266lb$

Sign convention for your answers: assume up$,$ right, and counterclock wise are pusime

directions. Be careful of signs on your answers.

To calculate the vertical component of force $P_1$ which ratio would you use from the

rise$/$run triangle?

$\frac{Y}{x}$

Y $/$ Hypotenuse

X $/$ Hypotenuse

Calculate the vertical component of force $P_1.$

Answer:

Units:

Calculate the horizontal component of force $P_1.$ Answer:

Units:

To calculate the horizontal component of force $P_2$ would