QUESTION $2$:

$(10$ marks$)$

Determine the structure stiffness matrix, joint displacements and member$-$end bending moments of the beam shown in Figure $2$ by the matrix stiffness method. $E$ is constant and I varies as shown in the figure.

Draw bending moment $($on tension side$)$ and shear force diagrams of the beam. All matrix operations and sign conventions must be clearly shown.

Given $E=200$GPa and $I=8\mathrm{.}333{10}^{6}m{m}^2.$Help