Question $1[20$ Marks$]$

A cast$-$iron pipe with an outside diameter of $500$ mm and $30-$mm thickness is used as

a short column $2,5$ m long. The inside of the column is filled with concrete. If the column

is to carry a compressive load of $1200$ kN$,$ calculate the stresses induced in the cast

iron and concrete as well as the amount by which the column shortens.

Econcrete $=14$ GPa and Ecastiron $=140$ GPa

Question $2[30$ Marks$]$

A precast concrete beam has a cross$-$section as shown in the Figure $1,$ with respect

to X$-$X and Y$-$Y axis. $($all dimensions are in millimetres$).$

$2\mathrm{.}1$Calculate the point of centroid $[8]$

$2\mathrm{.}2$ Calculate the second moment of area about x$-$x$,$ Ixx $[7]$

$2\mathrm{.}3$Calculate the second moment of area about y$-$y$,$ Iyy $[4]$

$2\mathrm{.}4$Calculate radius of gyration,rx and ry $[4]$

$2\mathrm{.}5$Calculate the elastic section modulus $[2]$

$2\mathrm{.}6$Calculate the plastic modulus $[5]$

Figure $1$

TOTAL $=50$ MARKS