Q$1(15$ marks$).$ A two$-$celled thin$-$walled beam with the cross$-$section as shown in Fig. $1$ is subjected to a torque $T.$ Assuming no end constraints and $G$ the shear modulus of the material used, determine the following:

a$)$ Shear flows in the walls $AB,BC,CD,DE,EF,FA,$ and $EB$

b$)$ The twist per unit length of the beam

c$)$ The torsion constant, J

Figure $1$