Please use the Matrix Flexibility method, not the stiffness method.

If you do not know how to do the flexibility method, please don't attempt the question.

Thank you

QUESTION A$2$

$($Total $40$ marks$)$

The frame shown in Figure $A2$ is to be solved by the matrix flexibility method taking the reactions at $A$ as the redundants. Support $D$ is settled downward by $20mm.$ Take joints A$,$ B$,$ C and D as the nodes, $E=200$GPa and $I=5{10}^{6}m{m}^4$ for the frame. Axial deformations of members can be neglected.

Clearly show the sign convention used for the bending moments in the matrices.

A$2($a$)$ Construct the global force matrix $[$Q$]$ for the equivalent forces applied at nodes A$,$ B$,C$ and $D.$

$(10$ marks$)$

A$2($b$)$ Determine the action transformation matrix $[$B$]$ for the member$-$end bending moments at $A,B,C$ and $D.$

$(10$ marks$)$

A$2($c$)$ Determine the reactions at $A,$ and the member$-$end bending moments at $A,B,C$ and D$.$ Draw the bending moment diagram on tension side.

$(20$ marks$)$