Question $3$

Part I:

A composite column using concrete$-$filled double skin rectangular hollow section $($RHS$),$ with overall $($outer$)$ dimensions of steel tube is shown in the Figure $($not to scale$).$ The space between the two rectangular hollow sections and the inner steel tube is filled with concrete. Detailed geometric dimensions and design properties for steel tubes and concrete are provided below:

Cross$-$sectional and steel properties of the RHS:

Outer steel tube height $=500mm$

Outer steel tube width $,=250mm$

Inner steel tube height $,=300mm$

Inner steel tube width $,=125mm$

Thickness of outer steel, $t,=5mm$

Thickness of inner steel, $t,=5mm$

Modulus of elasticity, $E_a,=210k\frac{N}{m}{m}^2$

Design yield strength, $f_{yd},=355\frac{N}{m}{m}^2$

Infilled concrete properties:

Modulus of elasticity: $E_{cm}=33\mathrm{.}5k\frac{N}{m}{m}^2$

Characteristic concrete cylinder strength: $f_{ck}=60\frac{N}{m}{m}^2$

Design concrete cylinder strength: $f_{cd}=40\frac{N}{m}{m}^2$

For this question, you can assume the design concrete compressive strength to be $1\mathrm{.}0f_{cd}$ instead of $0\mathrm{.}85f_{cd},$ to consider the confinement effect.

$($i$)$ Calculate the steel contribution ratio of the given cross$-$section, and check whether the given cross$-$section behaves as a composite member or standalone steel member or standalone concrete member.

$($ii$)$ Based on plastic theory, construct a multi$-$linear axial load$-$moment $($N$-$M$)$ interaction curve $[$major $($y$-$y$)$ axis only$]$ for the above composite column subjected to combined compression and major axis bending in accordance with Eurocode $4.$

$[15$ marks$]$

Part II:

$($a$)$ State at least four advantages of composite column over hollow steel or concrete columns, and state why imperfections are incorporated in the structural analysis of composite columns.

$[2$ marks$]$

$($b$)$ In Eurocode $4,$ state how does the second order imperfection is considered in the design of composite column.

$[3$ marks$]$

$($c$)$ State the limitations for simplified method in determining the resistance of composite member in combined compression and bending in accordance with Eurocode $4.$

$[2$ marks$]$