Subdividing the cross$-$section into the three simpler areas, $A_1,A_2$&$A_3,$ shown

$A_1=4\mathrm{.}5i{n}^2,A_2=5i{n}^2,A_3=6\mathrm{.}5i{n}^2$

For the datum axis shown,

$\frac{?}{\text{b}\text{a}\text{r}}(y{)}_{\text{d}\text{a}\text{t}}=\frac{(0\mathrm{.}5A_1+3\mathrm{.}5A_2+6\mathrm{.}5A_3)(i{n}^3)}{(A_1+A_2+A_3)(i{}^2)}=3\mathrm{.}875(in)$

Moment of inertia

The moment of inertia of area $A_1$ about $z$ axis is given as $I_{Z1}=\frac{(4\mathrm{.}5)1^3}{12}+A_1(3\mathrm{.}375{)}^2=51\mathrm{.}633$

$($i$)$ Moment of inertia of $A_2,$ about $z-$axis is given as $($in ${?}^4)$

$($ii$)$ Moment of inertia of $A_3,$ about $Z-$axis is given as $$ in $($:${?}^4$

Answer fill in blanks

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Required information

Two vertical forces, each of magnitude $P=2\mathrm{.}4$ kips, are applied to a beam of the cross section shown. Assuming $a=5$ in$,b=4\mathrm{.}5$ in and $c=6\mathrm{.}5$ in$,$ determine the maximum tensile and compressive stresses in portion $BC$ of the beam.

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