Question $3(25$ marks$)$

$($a$)$ A hollow steel pipe is filled with concrete to form a composite section as shown in Figure Q$3.$ This section has a height of $900$ mm and is subjected to a compressive loading of $110$ kN $.$ The Young's moduli for the steel and concrete are $\backslash ($ E$\_\{$s t$\}=210\backslash$mathrm$\{$GPa$\}\backslash )$ and $\backslash ($ E$\_\{$c o n$\}=35\backslash$mathrm$\{$GPa$\}\backslash ),$ respectively. If the pipe has an outer diameter of $120$ mm and an inner diameter of $110$ mm :

i$.$ Determine the average normal stresses in the concrete and the steel respectively due to the applied loading.

$(12$ marks$)$

ii$.$ Evaluate the axial deformation of the composite section

$(8$ marks$)$