Compatibility Equation  
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The figure shows an aluminum bar of dimensions 30 millimeters by 24 millimeters sandwiched between copper bars of dimensions 30 millimeters by 12 millimeters above and below it. The bars are held in place by pins on either end.

The force-temperature-deformation relationships for the copper and aluminum axial members are:

Substitute these two expressions into the geometry of deformation equation:

to derive the compatibility equation: