Problem $2$: a$)$ Draw the q$,$V$,$M diagrams for the I$-$beam shown below. a$)$ What is the maximum bending stress and where does it occur? b$)$ For I$-$beams, it is often necessary to consider the effects of transverse shear. Where along the beam would you expect the maximum transverse shear to occur? Is this the same location as the maximum bending stress? c$)$ Determine the transverse shear stresses at the location of maximum transverse shear stress. $($Here$,$ there are $4$ locations of interest for the transverse shear stresses along the cross$-$section: i$)$ at the neutral axis, ii$,$iii$)$ on either side where the thin web meets the wide flange, and iv$)$ at the outer surface$)$ d$)$ What is the maximum shear stress at each of these locations? $($Hint: You will have to determine the bending stress at each location and use that to find the maximum shear stress$)$