MecMovies 4.0 : M5.7: Rigid Bar and Two Axial Members

Equilibrium equation:

$\sum_{} M_{A} = F_{1} (380 mm) + F_{2} (760 mm) - P (1, 520 mm) = 0$

Compatibility equation:

$\frac{F_{1} L_{1}}{A_{1} E_{1}} \frac{1}{380 mm} = \frac{F_{2} L_{2}}{A_{2} E_{2}} \frac{1}{760 mm}$

Solve the compatibility equation for $F_{1}$ :

$F_{1} = F_{2} (\frac{A_{1}}{A_{2}}) (\frac{E_{1}}{E_{2}}) (\frac{L_{2}}{L_{1}}) (\frac{380 mm}{760 mm})$

$= F_{2} (\frac{420 {mm}^{2}}{320 {mm}^{2}}) (\frac{70 GPa}{105 GPa}) (\frac{700 mm}{500 mm}) (\frac{380 mm}{760 mm}) = 0.6125 F_{2}$