$2-$ A thin$-$walled cantilever has a constant cross$-$section of uniform thickness with the

dimensions shown below. It is subjected to a system of point loads as shown below.

A$.$ Calculate the direct stresses at the points $1,2,$ and $3$ of the cross$-$section at the root

and mid$-$span of the beam using

i$.$ Section properties obtained from first part of the assignment.

ii$.$ Section properties calculated using approximations for thin$-$walled sections

iii. Comment on the appropriateness of using approximations for thin$-$walled

sections

B$.$ Propose design changes to reduce the maximum stress by $30\%.$