Bimetallic strip

A metal strip of length l 0 = 20 cm l_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 = 2 mm d = 2\,\text{mm} . At a temperature of T = 0 C T = 0\, ^\circ\text{C} , the bimetallic strip is completely straight.

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

The respective thermal expansion coefficients of zinc and iron are

α Zn = 3 1 0 5 / C , α Fe = 1 1 0 5 / 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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