Question $1$

a$)$ Two bars are connected and placed between two walls when the temperature is $150C.$ One of the bars is made of steel and the other brass. Determine the force exerted on the $($rigid$)$ supports when the temperature becomes $20C,$ if the steel and brass bar properties are given as:

$E_{st}=200$GPa,$E_{br}=100$GPa

${}_{st}=12x\frac{{10}^{-6}}{C^o},{}_{br}=21x\frac{{10}^{-6}}{C^o}$

$L=300mm,L=300mm$

$A_{st}=200m{m}^2,A_{br}=450m{m}^2$

$(15$ marks$)$

b$)$ The permissible stress for a square timber post with length of side $250mm$ and $3\mathrm{.}5m$ high is $8\mathrm{.}82\frac{N}{m}{m}^2.$ Calculate the safe axial load for the post. How much will the post shorten under this load, assuming that $E$ to be $11,200\frac{N}{m}{m}^2?$ If the length of side was reduced to $150mm,$ how much would the axial load be affected?

$(10$ marks$)$