Two metallic strips are bonded at $\backslash (425^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ to form a bi$-$metallic strip $($stress free at $\backslash (425^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )).$ The Young's modulus, coefficient of thermal expansion, and the geometry of the cross$-$section for each material are below. The bonded strip was then cooled to $\backslash (25^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ).$ Due the residual thermal stress, the strip bends. Calculate the bending curvature.

a$.$ Calculate the relative moment of inertia $\backslash (\backslash$mathrm$\{$I$\}\_\{\backslash$mathrm$\{$r$\}\}\backslash ),$ and bending stiffness $\backslash (\backslash$mathrm$\{$E$\}\_\{\backslash$mathrm$\{$r$\}\}\backslash$mathrm$\{$I$\}\_\{\backslash$mathrm$\{$r$\}\}\backslash ),$ using the procedure you learned from the "bending of beams made of different material". Pick material $1$ as the reference.

b$.$ Using the procedure learned for deriving the internal forces for non$-$bending case $($e$.$g$.$ tube and core$),$ find the internal forces, $\backslash (\backslash$mathrm$\{$P$\}\_\{1\}\backslash )$ and $\backslash (\backslash$mathrm$\{$P$\}\_\{2\}\backslash ),$ in each part that are needed to keep the bi$-$metallic strip straight.

c$.$ Releasing the force at the ends is equivalent to applying reverse forces. Calculate the moment produced by the reverse forces.

d$.$ Calculate the curvature.