Figure Q$2$ shows a straight rod of circular cross section, of diameter $20$ mm$,$ length

$0\mathrm{.}8$ m and made out of copper. The rod is rigidly supported at one end while the

other end is free to be displaced a distance of $0\mathrm{.}5$ mm$.$ Take the elastic modulus of

copper E $=117$ GPa. The drawing is not at scale.

a$)$ If the coefficient of thermal expansion of copper is $17\backslash$times $10-6$ oC$-1$ find the

temperature change $$T which causes the end B of the rod to touch the wall.

$[5$ marks$]$

b$)$ What is the reaction force at end B if the temperature increases with $2$T$?$

$[4$ marks$]$

c$)$ What is the temperature increase which causes the rod to buckle elastic? Assume

pin joint conditions at end B$.$

$[6$ marks$]$

d$)$ If the rod was rigidly supporter at both ends, what is the temperature raise needed

to cause elastic buckling in the rod?