Question $1$

$15$ marks

For the composite section shown above in Error! Reference source not found. calculate:

$($i$)$ the position $"$c$"$ of the centroid $($G$),$ in mm$.(2)$

$($ii$){}_{xx},{}_{YY}$ and $J({}_{ZZ})$

$($iii$)$ The least radius of gyration

$($iv$)Z_{YY}$ for point $"$A$"$

$(1)$

$($v$)$ The least section modulus, also stating its reference point

$(2)$

Question $2$

$10$ marks

A steel member with the length of $2$ m and rectangular cross section $(60mm30mm)$ is stretched along its longitudinal direction by an axial tensile force of $72k{N}_{..}$

Young's Modulus E $=200$GPa; Poisson's ratio v $=0\mathrm{.}3$

$($a$)$ Calculate the direct stress $($in MPa$)$ in the member under this load...

$(2)$

$($b$)$ Calculate the longitudinal strain and the extended length $($new length$)$

$($c$)$ Calculate the lateral strain and the change in cross section dimensions