Bars AB$,$ BD$,$ and BE are shown in the figure. End A$,$ end D$,$ and end E are fixed. Load is applied at C: P$=10$ kips$\frac{40pt}{B}ar$ sAB,$BD,$ and $BE$ are shown in

the figure. End $A,$ end $D,$ and end $E$ are fixed.

Load is applied at $C$:$P=10$kips. The bar

lengths: $AB=4ft,BC=2ft,CD=$

$4ft,$ and $BE=6ft.$ The cross$-$section

areas: $4i{n}^2$ for $AB,$ and $2i{n}^2$ for $BD$ and $BE.$

The Young's modulus is given: $E=30$

${10}^3$ksi. Knowing that the deformations of $BD$

and $BE$ are equal: ${}_{BD}={}_{BE},$ determine:

$($a$)$ the reaction forces at end $A,$ end $D$ and end

$E$

$($b$)$ the deformations ${}_{AB},{}_{BC}$ and ${}_{CD}$