MecMovies 4.0 : M5.5: Rod and Post in Series

scene 9 of 14

Solve for $F_{1}$ :

$F_{1} - F_{2} - P = 0$

$F_{1} = F_{2} + P$

and substitute the expression for $F_{1}$ into the compatibility equation:

$\frac{(F_{2} + P) L_{1}}{A_{1} E_{1}} + \frac{F_{2} L_{2}}{A_{2} E_{2}} = 0$

Solve this equation for $F_{2}$ :

$F_{2} (\frac{L_{1}}{A_{1} E_{1}} + \frac{L_{2}}{A_{2} E_{2}}) = - \frac{{PL}_{1}}{A_{1} E_{1}}$

$F_{2} = \frac{- \frac{{PL}_{1}}{A_{1} E_{1}}}{(\frac{L_{1}}{A_{1} E_{1}} + \frac{L_{2}}{A_{2} E_{2}})}$