Question $3(25$ marks$)$

$($a$)$ The column shown in Figure Q$3$ below is constructed from high$-$strength concrete and six steel reinforcing bars. The Young's modulii for the steel and concrete are Est $=210$ GPa and $E_{\text{c}\text{o}\text{n}}=35$ GPa respectively.

i$.$ If the column is subjected to an axial force of $175$ kN $,$ show that using a bar diameter of $43\mathrm{.}8$ mm for the steel bars will result in $40\%$ of the load being carried by the concrete with the remainder carried by the steel;

$(12$ marks$)$

ii$.$ Hence, evaluate the axial deformation of the column

$(5$ marks$)$

iii. Evaluate the average normal stresses in the concrete and in each steel bar

$(4$ marks$)$

$($b$)$ An axially loaded steel bar that is restrained at only one end is located outdoors in the west of Ireland. Its initial length is $2000$ mm $.$ How much will it deform by from summer to winter if the average temperatures are $14\mathrm{.}5C$ and $5\mathrm{.}5C$ respectively? Take ${}_{st}=12\frac{{10}^{-6}}{}C.$

$(4$ marks$)$