Q$5.(2014$ midterm$)$

The circular stepped shaft is made of bronze and aluminum sections and has the dimensions and properties shown below. The support on the right is a rigid, fixed support. After the forces of equal magnitude are applied, the system undergoes a temperature increase of $125F($assume the stepped shaft is unstressed before the forces are applied$).$ Calculate

a$)$ The magnitude of the forces $F$ so the gap just closes after the temperature increase without inducing a force at the left support

b$)$ The resulting stress in sections $AB$ and $CD$

c$)$ The resulting strain in sections $BC$ and $DE$

d$)$ The deflection of point C

Answers: $F=27\mathrm{.}19$kips,${}_{AB}=0,{}_{CD}=9\mathrm{.}71$ksi$(C),{}_{BC}=7\mathrm{.}4510-4,{}_{DE}=-2\mathrm{.}2010-4,de{l}_C=0\mathrm{.}00429in$ to the left.