A T$-$beam supports the external load as shown in figure in addition to its self$-$weight. The beam is made of steel $($unit weight of steel is $7850k{g}^{\text{'}}{m}^3)$ and cross$-$section is shown in figure below. Self$-$weight of the beam must be considered.

$($i$)$ Calculate the maximum bending and shearing stress

$($ii$)$ Sketch the bending and shearing stress distribution diagram and

$($iii$)$ Deternine the percentage of shear carried by the web alone.