Section through M-M and N-N
Free Body Diagram to the Left of M-M
$\Sigma M_G = 0$
$6\left( \frac{5}{\sqrt{29}}F_{DF} \right) = 15(200) + 10(200) + 5(400)$
$\frac{30}{\sqrt{29}}F_{DF} = 7000$
$F_{DF} = \frac{700}{3}\sqrt{29} ~ \text{kN} = 1256.54 ~ \text{kN tension}$ answer
$\Sigma M_F = 0$
$6F_{GI} = 15(200) + 10(200) + 5(400)$
$6_{FGI} = 7000$
$F_{GI} = \frac{3500}{3} ~ \text{kN} = 1166.67 ~ \text{kN compression}$ answer
$\Sigma F_V = 0$
$F_{FG} + \frac{2}{\sqrt{29}}F_{DF} = 200 + 200 + 400 + 400$
$F_{FG} + \frac{2}{\sqrt{29}}\left( \frac{700}{3}\sqrt{29} \right) = 1200$
$F_{FG} = \frac{2200}{3} ~ \text{kN} = 733.33 ~ \text{kN tension}$
Free Body Diagram to the Left of N-N
$\Sigma M_I = 0$
$10\left( \frac{5}{\sqrt{41}}F_{FH} \right) = 20(200) + 15(200) + 10(400) + 5(400)$
$\frac{50}{\sqrt{41}}F_{FH} = 13,000$
$F_{FH} = 260\sqrt{41} ~ \text{kN} = 1664.81 ~ \text{kN tension}$ answer
$\Sigma F_V = 0$
$\frac{6}{\sqrt{61}}F_{FI} + \frac{4}{\sqrt{41}}F_{FH} = 200 + 200 + 400 + 400$
$\frac{6}{\sqrt{61}}F_{FI} + \frac{4}{\sqrt{41}}\left( 260\sqrt{41} \right) = 1200$
$\frac{6}{\sqrt{61}}F_{FI} = 160$
$F_{FI} = \frac{80}{3}\sqrt{61} ~ \text{kN} = 208.27 ~ \text{kN compression}$ answer
