QUESTION $1$

$[25$ MARKS$]$

The $11m$ long beam shown in Figure Q$1$ below has a hinge support at $A,$ and the supports $B,C$ and $D$ are rollers. Use the flexibility method to do the following:

$($a$)$ Sketch the primary structure

$[3]$

$($b$)$ Determine the displacements at $B$ and $C$ of the primary structure

$[6]$

$($c$)$ Determine the flexibility coefficients

$[8]$

$($d$)$ Write the compatibility equations

$[2]$

$($e$)$ Determine the reactions at the supports

$[6]$

$EI$ is constant along the length of the beam.