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

Next, substitute the force-deformation relationships into the geometry of deformation relationship:

$Force deformation Geometry deformation δ_{1} = \frac{F_{1} L_{1}}{A_{1} E_{1}} δ_{2} = \frac{F_{2} L_{2}}{A_{2} E_{2}} \frac{δ_{1}}{380 mm} = \frac{δ_{2}}{760 mm} \frac{F_{1} L_{1}}{A_{1} E_{1}} \frac{1}{380 mm} = \frac{F_{2} L_{2}}{A_{2} E_{2}} \frac{1}{760 mm}$

This equation is known as a compatibility equation. Notice that this equation contains the two unknowns $F_{1}$ and $F_{2}$ . With the compatibility equation and the previously derived equilibrium equation, two equations can be solved simultaneously to determine the unknown forces $F_{1}$ and $F_{2}$ .