Solution

Free$-$Body Diagram See Fig. $3\mathrm{.}20($b$).$

Static Determinacy The frame is internally stable with $r=3.$ Therefore, it is statically determinate.

Support Reactions

$+-{\displaystyle \underset{?}{\overset{?}{}}}{F}_x=0$

$(\frac{29\mathrm{.}2+43\mathrm{.}8}{2})(7\mathrm{.}8)(\frac{5}{13})+C_x=0$

$C_x=-109\mathrm{.}5kN$

$C_x=109\mathrm{.}5$kNlarr

$,+C{\displaystyle \underset{?}{\overset{?}{}}}{M}_A=0$

$-29\mathrm{.}2(7\mathrm{.}8)(3\mathrm{.}9)-\frac{1}{2}(14\mathrm{.}6)(7\mathrm{.}8)(\frac{7\mathrm{.}8}{3})-222\mathrm{.}5(7\mathrm{.}2+3\mathrm{.}6)+109\mathrm{.}5kN(3)+C_y(14\mathrm{.}4)=0$

$C_y=216\mathrm{.}03kN$

$C_y=216\mathrm{.}03kNl$

$+1{\displaystyle \underset{?}{\overset{?}{}}}{F}_y=0,$

$A_y-(\frac{29\mathrm{.}2+43\mathrm{.}8}{2})(7\mathrm{.}8)(\frac{12}{13})-222\mathrm{.}5+216\mathrm{.}03=0$

$A_y=269\mathrm{.}27kN$

$A_y=269\mathrm{.}27kN$

Ans.

Checking Computations

$+C{\displaystyle \underset{?}{\overset{?}{}}}{M}_B=-269\mathrm{.}27(7\mathrm{.}2)+29\mathrm{.}2(7\mathrm{.}8)(3\mathrm{.}9)+\frac{1}{2}(14\mathrm{.}6)(7\mathrm{.}8)(\frac{2}{3})(7\mathrm{.}8)-222\mathrm{.}5(3\mathrm{.}6)+216\mathrm{.}03(7\mathrm{.}2)$

$=+0\mathrm{.}024kN-m$~~$0$