$(55$ PTS$)$ Given the I$-$beam and cross$-$section shown in the figure below $($Hint: Think equivalent load$)$:

a$.$ Draw the overall free body diagram for beam $($figure $1)$

b$.$ Find the reaction forces at the pin at A and the roller at B$.$

c$.$ Replace the $10$ kN loads on the rigid bars with an equivalent load at points B and C and

draw the FBD of the beam with the equivalent loads in the diagram below $($figure $3).$

d$.$ Draw the shear and moment diagram for the entire beam.

e$.$ If the beams cross$-$section $($figure $2)$ has the dimensions shown, find the location of the

centroid bar$($y$).$

f$.$ Find the Moment of Inertia about the centroidal axis $($I$.$e$.$ I$\_($x$)).$ For a rectangle

I$=(1)/(12)$bh$^(3)$

SHOW ALL WORK AND DRAW FREE BODY DIAGRAMS