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Bimetallic strip

A metal strip of length l0=20cml_0 = 20 \,\text{cm} consists of a layer of iron (Fe) and a layer of zinc (Zn), which are welded together with each having a thickness of d=2mmd = 2\,\text{mm}. At a temperature of T=0CT = 0\, ^\circ\text{C}, the bimetallic strip is completely straight.

What is the radius of the curvature rr of the strip at a temperature of T=100C?T = 100\, ^\circ\text{C}?

The respective thermal expansion coefficients of zinc and iron are

αZn=3105/C,αFe=1105/C.\alpha_\text{Zn} = 3\cdot 10^{-5}/^\circ\text{C},\quad \alpha_\text{Fe} = 1\cdot 10^{-5}/^\circ\text{C}.


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