Summary
In this TLP we have:

Learned how the Young's modulus of a material may be determined using the relationship between the deflection of a cantilever beam δ and the load P applied to it, given by
\[\delta = \frac{1}{3}\frac{{P{L^3}}}{{EI}}\]
where L is the distance from support to point of load application, I is the second moment of area of the beam's cross section, and E is the Young's modulus of the beam's material.

Used measurements of the deflection and load of a steel cantilever beam to determine the Young's modulus of steel as 210 GPa.

Looked at how the asymmetry in the energyseparation graph for atoms in a solid gives rise to an increase in the average interatomic spacing of vibrations as the temperature is increased, the origin of thermal expansion.

Derived a formula relating curvature κ to the length x and deflection δ of a bimaterial strip:
\[\kappa = \frac{{2\sin \left[ {{{\tan }^{  1}}\left( {\delta }/{x} \right)} \right]}}{{\sqrt {\left( {{x^2} + {\delta ^2}} \right)} }}\]

Defined the misfit strain Δε for the two components of a bimaterial strip as
Δε = (α_{A}  α_{B}) ΔT
and quoted a formula relating the curvature κ to the misfit strain, the thickness of the strips h (of equal thickness) and the ratio of the Young's moduli E_{*}
\[\kappa = \frac{{12 \Delta \varepsilon }}{{{h_{}}\left( {{E_*} + 14 + 1 / {E_*}} \right)}}\]

Used measurements of the change in shape of a steelaluminium bimaterial strip immersed in liquid nitrogen to estimate the boiling temperature of nitrogen as 193ºC.

Used measurements of the change in shape of an aluminiumpolycarbonate bimaterial strip immersed in liquid nitrogen to estimate the thermal expansivity of the polycarbonate as 4.5 x 10^{}^{5 }K^{1}.