Problem $1(40$ Marks$)$

For the given configuration both beams have EI $=211{10}^{3}N-m^2$

a$.$ Draw separate free body diagrams for beams AB and CE $(6$ Marks$)$

b$.$ Consider beam $AB$ to find the deflection at point D $(8$ Marks$)$

c$.$ Find the total deflection at point E by using superposition method $(11$ marks$)$

d$.$ Verify your result of part $c$ above by using Castigliano theorem on beam CE $(15$ Marks$)$