Question $1(65$ points$)$

The frame system has pin supports at A and $F,$ internal hinge at $C$ and supports the loading shown below. The flexural rigidity of elements $AB,DF$ is $2EI$ and of elements $BC$ and CDE is $EI,$ where $E=30$GPa and $I=800{10}^{6}m{m}^4$

For the frame system Assume Different Values for $1,(s)2,h1,h2,w1,w{2}_{?}$

a$.$ Find the reaction forces

b$.$ Draw the bending moment diagram indicating key values

c$.$ Draw the deformed shape

d$.$ Find the horizontal displacement at $B$ and the rotation at $F$ using the principle of virtual work. Ignore the shear and axial deformations of the frame system