$[40$ pts$]$ The beam shown below is subjected to equal bending moments of $M_z=12$kip. ft $,$ and a shear force of $10$ kips $.$ The cross$-$sectional dimensions$/$properties are:

$b_1=3\mathrm{.}0in.,d_1=1\mathrm{.}0in.$

$b_2=0\mathrm{.}5in.,d_2=3\mathrm{.}0in.$

$b_3=2\mathrm{.}0in.,$ and $d_3=0\mathrm{.}5in.$

$c_1=1\mathrm{.}727in$

$I_c=13\mathrm{.}17i{n}^4$

Please:

a$.$ Determine the stresses acting on the element located at point H $($located at the junction between the upper flange and the web$).$ Draw these stresses on the element provided below.

b$.$ Determine the principle stresses and the maximum shear stress at this location. Draw these stresses on appropriate elements rotated from part a$.$

c$.$ Based on principles discussed in this course, explain why the stresses at point H may be important for the design of this beam.