PLEASE SOLVE ON PAPER.

FOR EACH PROFILE SECTION:

STEP $1$:

Use the formulations for the change of axes given below and

Calculate the moments of inertia with respect to the $x^{\text{'}}$ axis $($Ix$),$ the $Y^{\text{'}}$ axis $($Ir$)$

and the product moment of inertia with respect to the $x^{\text{'}}-Y^{\text{'}}$ axis coordinate

system $($Ixr$)$

Note: The angle between $x$ and $x^{\text{'}}$ axis is equal to $30$

STEP $2$:

Using the formulations for ${}_m,$ Imax and Imin

Calculate the orientations of the principal axes $({}_m)$

Calculate the principal moments of inertia $(I_{\text{m}\text{a}\text{x}}$ and $I_{\text{m}\text{i}\text{n}})$

STEP $3$:

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