The rigid beam ABCD is supported by the two struts steel $(E=200$GPa $)-$ strut $1$ attaches to the beam at $B$ and strut $2$ attaches to the beam at $D$ as shown. Strut $1$ has a rectangular cross$-$section of $20$ mm by $40$ mm $,$ while strut $2$ has a rectangular cross$-$section of $10$ mm by $40$ mm $.$ The applied load $P$ is $150$ KN $.$ You may assume that deformations are small.

a$)$ Determine the stresses in the two struts.

b$)$ Determine the reactions at the support at $A.$

c$)$ Determine the deflection of point D at the end of the rigid beam.