Q$3(7$ marks$).$ A$)$ The structure shown in the figure below is loaded by

Case $1)$ a uniformly distributed load on member BC$,(2$ mark$)$

Case $2)$ initial curvature on member CD only, $(2$ mark$)$

Case $3)$ support settlement at D only $(2$ mark$)$

Determine the horizontal displacement at Point B for each case.

B$)$ for the same structure, consider a load case $4$ where all actions act simultaneously

Case $4)$ all actions combined $($Case $1+2+3)$

Determine the horizontal displacement at Point B$,$ and find the support reactions and member force in AB$.(1$ mark$)$

$\backslash$table$[[$Dimensions and section properties$],[$a$,7\mathrm{.}1,$unit: m$],[$b$,3\mathrm{.}4,$unit: m$],[$c$,5\mathrm{.}1,$unit: m$],[$El$,300000,$unit: $kN{m}^2$

Solve only $by$ principle virtual work method With proper real force or virtual force diagrams