Problem $3(25$ points$)$

$3$a$)$ For the truss shown in Figure $3$a do the following:

$1)$ Calculate the reactions at $\backslash ($ A $\backslash )$ and J$.$

$2)$ Use the method of joints to calculate the force in members $\backslash ($ A D $\backslash )$ and $\backslash ($ A B $\backslash ).$

$(3$ points$)$

$3)$ Use a smart section cut to determine the force in member BC$.$

$(2$ points$)$

$(4$ points$)$

$3$b$)$ A computer program is used to solve a given $2-$D truss, resulting in having to solve a system of linear equations $\backslash ($ A x$=$b $\backslash )($where x is comprised by the unknown member forces followed by the unknown reactions as explained in the lectures$).$ It is given that $\backslash ($ A $\backslash )$ is a $\backslash (16\backslash$times $16\backslash )$ matrix $($again the rows and columns are ordered as explained in class$).$ Assume that there are $3$ unknown reactions $\backslash ($ R$\_\{1\},$ R$\_\{2\}\backslash ),$ and $\backslash ($ R$\_\{3\}\backslash ).$

Questions $1-4$ do not assume a known truss configuration. $($That is$,$ the truss may be different than the specific truss considered in the later part of questions $5-10).$

$1.$ How many members does this truss have?

$(1$ points$)$

$2.$ Let $\backslash ($ A$(8,5)=\backslash$frac$\{\backslash$sqrt$\{3\}\}\{2\}\backslash ).$ Make a statement of the form "member $\backslash ($ X $\backslash )$ is connected to joint $\backslash ($ Y $\backslash )".$

$(2$ points$)$

$4$