Question $2(40$ pts$)$:

r

A W$25018$ steel column is $5m$ tall and fixed at both ends. The column has an ambient temperature of $25C.$ Assume $E=200$GPa and ${}_y=300$MPa.

a$)$ If the column is heated to a temperature of $85C,$ determine the reaction forces $(P)$ and compressive stress in the column. Assume a coefficient of thermal expansion for steel $=12\mathrm{.}5x{10}^{-6}{C}^{-1}.$

b$)$ Can the column sustain a temperature of $85C$ without failure?

c$)$ What is the maximum temperature able to be sustained by the column without buckling?