Question $2$

$1\backslash \%.$ WL

The structure in Fig. Q$2$ consists of a cantilever, encastr$$ at Node $1,$ and with a flexural rigidity of $\backslash ($ E I$=800\backslash$mathrm$\{$kNm$\}^\{2\}\backslash ).$ It is propped at Node $2$ with a truss member of axial stiffness $\backslash ($ E A$=400\backslash$mathrm$\{$kN$\}\backslash ).$

Assuming elastic behaviour and ignoring axial deformation, use the stiffness method to analyse the structure.

$($a$)$ Calculate the vertical deflection, $\backslash (\backslash$Delta $\backslash ),$ and rotation, $\backslash (\backslash$theta $\backslash ),$ at Node $2.$

$[12$ marks$]$

$($b$)$ Compute the reactions.

$[9$ marks$]$

$($c$)$ Draw the Bending Moment Diagram and sketch the deflected shape.