A symmetric cross$-$section is formed by connecting a channel

section to an unequal flanged I$-$section by means of bolts as

shown in Figure Q$1$ on page $3.$ The geometrical properties of

the sections are given in Table $1$ and Table $2.$

Material Properties:

$=200$ GPa $$ Young$$s Modulus

$=76\mathrm{.}9$ GPa $$ Shear Modulus

$!""=250$ MPa $$ Allowable flexural stress

a$.$ Show that the location of the centroid and the second

moments of inertia of the new cross$-$section are

$$# $=36\mathrm{.}66$ mm $($from the top surface of the I$-$section$)$

$$$$ $=23\mathrm{.}02\backslash$times $10\%$ mm&

$\text{'}\text{'}=9\mathrm{.}83\backslash$times $10\%$ mm&