$(2.)$ The cross section of a solid beam is shown in the figure viewed opposite axis $x.z_C=5\mathrm{.}2368cm,A=190c{m}^2.I_z=5103\mathrm{.}3c{m}^4$ and $I_y=2612\mathrm{.}68c{m}^4.$

$s=10cm$

$t=6cm$

$h=8cm$

$u=5cm$

$V=36kN$

$M=12kNm$

a$)$ Find the direction and magnitude for the maximum shearing stress in the section.

Prepare a qualitative diagram of the distribution of shearing stresses. Specify the location and magnitude of the maximum shearing stress.

b$)$ Assign a right$-$handed coordinate system $(u,v,x)$ to point A where $v-x$ is the plane of stress. Indicate axes precisely.

c$)$ Find the magnitude and direction of principal stresses at point $A($estimate directions of principa stresses by superposition of effects of normal and shearing stresses$).$ Display your results in a sketch viewed in front of $u$ with axes $x$ and $v$ directed to the right and down, respectively.

d$)$ What is the mechanical meaning of the first principal direction of strains?