Question $1$

$[25$ marks$]$

Consider the frame shown in Figure Q$1$ for which all elements have constant stiffnesses EI$.$ Implement the flexibility method by removing the vertical support at A to create a statically determinate system. The Product Integral Table is included at the back of this examination paper.

a$)$ Sketch the Primary and the Secondary Structure for the application of the Flexibility Method and define the Compatibility condition.

b$)$ Find the displacement at the position of the $[3$ Marks$]$ implementing Virtual Force Method.

c$)$ Find the displacement at the position of the release in the Secondary structure by implementing Virtual Force Method.

d$)$ Apply the compatibility condition to obtain the reaction at the release $A.$

$[6$ Marks$]$

e$)$ Draw the bending moment diagram for the frame.

$[3$ Marks$]$

$[5$ Marks$]$