Problem $3.$ Statically indeterminate system

Consider the uniform, horizontal beam shown below. The beam is hinged to a wall at A and a weight $W_2=400N$ is attached on the beam at B$.$ Point $C$ represents the center of gravity of the beam, which is equidistant from A and $B.$ The beam has a weight $W1=100N$ and length $I=4m.$ The beam is supported by two vertical rods, $1$ and $2,$ attached to the beam at D and E$.$ Rod $1$ is made of steel with elastic modulus $E_1=200$GPa and a cross$-$sectional area $A_1=500m{m}^2,$ and rod $2$ is bronze with elastic modulus $E_2=80$GPa and $A_2=400m{m}^2.$

The original $($undeformed$)$ lengths of both rods is $h=2m.$ The distance between A and $D$ is $d_1=1$ m and the distance between points A and E is $d_2=3m.$

The free$-$body diagram of the beam and its deflected orientation is shown below, where $T_1$ and $T_2$ represent the forces exerted by the rods on the beam. Symbols ${}_1$ and ${}_2$ represent the amount of deflection the steel and bronze rods undergo, respectively. Note that the beam material is assumed to be very stiff $($almost rigid$)$ as compared to the rods so that it maintains its straight shape.

$($a$)$ Calculate tensions $T_1$ and $T_2,$ and the reactive force $R_A$ on the beam at $A.$

$($b$)$ Calculate the average tensile stresses ${}_1$ and ${}_2$ generated in the rods.