Problem $3(32$ pts$.)$ For the shown truss below with a vertical load of $10$ kips applied at joint C $,$ and assuming that members AC and BD are not connected at their mid$-$span and AE is constant, $($i$)$ determine the force in the member BD$,$ and $($ii$)$ state whether your answer in part $($i$)$ would change if a new member is added between pin supports A and D$.$ Circle one: Yes or No$.$

$SI=(m+r)-2n=(5+4)-24=1$

Select $R_1=F_{BD}(tension)$

$N_{AC}FBD$ joint

$N_{DC}{3}^4-(C{)}^{45}$

${\displaystyle \underset{y=0}{\overset{?}{}}}{10}^k$

$-N_{n-1}-N_{Ar}(3)-0$

${30}^{\text{'}}$