Q$3$ SLOPE DEFLECTION METHOD $(35$ marks out of total $100)$

For the beam shown below:

$20$mm of settlement at support A

EI constant

a$)$ Identify the unknowns of the problem in the context of the slope deflection method

$[2$ marks$]$

b$)$ Write down the equilibrium equations that you need to consider to determine the problem unknowns

$[2$ marks$]$

c$)$ Calculate the fixed$-$end moments of all beam members

$[6$ marks$]$

d$)$ Write down the slope deflection equations of all beam members

$[6$ marks$]$

e$)$ Calculate the unknown rotations

$[6$ marks$]$

f$)$ Calculate the end$-$member moments

g$)$ Draw the bending moment diagram for the beam