The figure below shows a single symmetrical cross$-$section consisting of a vertical and a horizontal tab, both of length e and thickness t$.$ The horizontal tab is located at a distance of $30/4$ from the top of the vertical tab as shown in the figure. The cross$-$section is generally considered thin$-$walled data.

Question $1$

Show that the elastic center $C$ of the cross section is located at a distance of o from the top of the cross section, just as shown in the figure.

Question $2$

Determine the moment of inertia $/$ of the cross$-$section in relation to the elastic center $C$ of the cross$-$section, expressed by a and $t$

Question $3$

A beam is made of steel with shear modulus $G0$GPa and has the above crosssection with dimensions a $50mm$ and $15mm.$ Calculate the beam's torsional stiffness GK$,$ specifying appropriate units.