Problem $1.$

For the figure below, the force $F=100N.$ At $O,$ the end is fixed

From O to A$,L_{OA}=1000mm,I_{OA}=12\mathrm{.}2e3m{m}^4,J_{OA}=24\mathrm{.}4e3m{m}^4,$ and $E_{OA}=70$GPa and $G_{OA}=27$GPa

From A to B the $l_{AB}=500mm,I_{AB}=12\mathrm{.}2e3mm4,J_{AB}=24\mathrm{.}4e3m{m}^4,$ and a special condition exists where $E_{AB}$ and $G_{AB}$ are so big that the material from $A$ to $B$ cannot bend or twist.

What is the vertical deflection at B$?$

Hint: this is a superposition problem where only OA bends or twists which results in the deflection at $B(answer$ should $be77mm,$ need math done$)$

Show all work and circle the correct solution.

A$.{}_B=77\mathrm{.}0mm$

B$.{}_B=39\mathrm{.}0mm$

C$.{}_B=85\mathrm{.}1mm$

D$.{}_B=0\mathrm{.}488mm$

None of these