HelpQUESTION $3$:

$(10$ marks$)$

Determine the structure stiffness matrix, joint displacements in terms of El$,$ member$-$end bending moments and reactions of the frame shown in Figure by the matrix stiffness method. Joint $G$ is a rigid connection with a link support preventing horizontal displacement. $E$ is constant and I varies as shown in the figure.

Draw bending moment $($on tension side$)$ and shear force diagrams of the frame.

All matrix operations and sign conventions must be clearly shown.