QUESTION $3$

$(40$ MARKS$)$

A rigid jointed plane frame is shown in Figure below. The flexural rigidity is the same for all members of the frame or all frame members has a constant EI$.$ Using the principle of "Slope Deflection Equation" and neglecting the effect of side sway and axial deformation $)=(0$ in the frame, answer the following:

Part $1$: Calculate the Fixed End Moment of each member of the frame.

$(10$ Marks$)$

Part $2$: Calculate the relative stiffness $($k$)$ of each member of the frame.

$(5$ Marks$)$

Part $3$: Write the relationship of the end moments and rotations $()$ at each joint of the frame. $(5$ Marks$)$

Part $4$: Write the Slope deflection equations of end moments for each member of the frame.

$(10$ Marks$)$

Part $5$: Calculate the magnitude of the rotations ${}_A,{}_B,{}_C,{}_D,{}_E,$ and ${}_F.(5$ Marks$)$

Part $6$: Calculate the magnitude of the end moment for each member of the frame.

$(5$ Marks$)$