Y $=34\mathrm{.}5$

Do $=250\mathrm{.}33$

A composite column with a configuration shown in Figure Q$4$ is fixed at the base. The outer steel

tube diameter is D$\_($o$)$mm and the hollow ratio $($ratio of inner tube diameter to outer tube diameter$)$ is

$0\mathrm{.}7.$ Both steel tubes are having a similar thickness of $5$ mm $.$ An axial load of PkN is applied at the

top of the column through a rigid plate. Given the elastic modulus of concrete and steel, E$\_($c$)=32$GPa

and E$\_($s$)=205$GPa, concrete compressive strength, f$\_($cu$)=$Y MPa and steel yield strength, f$\_($y$)=275$MPa.

Solve the followings:

a$)$ Generate the equilibrium and compatibility equations for this condition. $(2\%)$

b$)$ If the failure of the column is governed by concrete crushing, find the maximum axial load P $.$

$(15\%)$

c$)$ At the maximum load in $($b$),$ calculate the axial forces and normal stresses in the outer and inner

steel tubes. $(8\%)$

Figure Q$4$