Please provide full workings to show how this problem is solved $($Answers are given$)$

Q$1)$ Use the principle of minimum total potential energy to find the displacements and then the forces in the pin$-$jointed truss shown below. EA is $0\mathrm{.}16106kN$ for all elements.

Answer:

$V=EA[\frac{(0\mathrm{.}8{}_1+0\mathrm{.}6{}_2{)}^2}{25}+\frac{{}_2^2}{23}+\frac{(-0\mathrm{.}8{}_1+0\mathrm{.}6{}_2+0\mathrm{.}8{}_3{)}^2}{25}]$

$-200{}_1-300{}_3$

hence

$V=20480{}_1^2+38187{}_2^2-20480{}_1{}_3+15360{}_2{}_3$

$+10240{}_3^2-200{}_1-300{}_{3}kNm$

${}_1=0\mathrm{.}0329m$;$,{}_2=-0\mathrm{.}0112m$;$,{}_3=0\mathrm{.}0559m$;

$F_{ab}=625kN$;$,F_{bc}=-600kN$;$,F_{bd}=375kN$;