PLEASE SOLVE ON PAPER.

FOR EACH PROFILE SECTION:

STEP $1$:

Calculate the moments of inertia with respect to $x$ axis $($Ix$),$ Y axis $($Iy$)$ and

the product moment of inertia with respect to $x-Y$ axis coordinate system $($Ixy$)$

STEP $2$:

Calculate the coordinates of the centroid $(\stackrel{}{x}$ and $\frac{?}{\text{b}\text{a}\text{r}}(Y))$ with respect to $x_{-}Y$ axis

coordinate system.

STEP $3$:

Calculate the moments of inertia with respect to the centroidal $\stackrel{}{x}$ axis $(\frac{?}{\text{b}\text{a}\text{r}}(I)),$

the centroidal $\frac{?}{\text{b}\text{a}\text{r}}(Y)$ axis $(\frac{?}{\text{b}\text{a}\text{r}}(I))$ and the product moment of inertia with respect to the

centroidal $\stackrel{}{x}\frac{-}{b}ar(Y)$ axis coordinate system $($y$)$

STEP $4$:

Use the $I_x,I_y,I_{xy}$ values that you obtained in STEP$1$ and draw MOHR'S CIRCLE.

Formulations for the change of axes:

$I_{x^{\text{'}}}=\frac{I_x+I_y}{2}+\frac{I_x-I_y}{2}cos2-I_{xy}sin2$

$I_{y^{\text{'}}}=\frac{I_x+I_y}{2}-\frac{I_x-I_y}{2}cos2+I_{xy}sin2$

$I_{x^{\text{'}}{y}^{\text{'}}}=\frac{I_x-I_y}{2}sin2+I_{xy}cos2$

NOTE: Conduct STEP$1,2,3,4$ FOR EACH PROFILE SECTION.

HINT: USE PARALLEL AXIS THEOREM WHEN NECESSARY.