please show work

Example $1($Problem P$8-6,277,$ Philpot $3$e$)$:

A beam is subjected to equal bending moments as shown

$($where $z$ represents the neutral axis$).$ Determine:

a$)$ The moment of inertia about the horizontal centroidal axis of

the beam cross$-$section.

b$)$ The controlling section modulus

c$)$ The bending stress at $H.$

d$)$ The maximum bending stress in the section.