Analysis of Bi-Metal Thermostats

Key Points

• To derive an analytical theory describing the curvature, deformation, and internal stress distributions in bimetallic thermostats subjected to uniform temperature changes.
• Applied classical elasticity theory and beam mechanics to model two distinct metal strips bonded continuously along their length.
• Formulated mathematical equations relating the curvature of the composite strip to layer thickness ratios, elasticity moduli, and coefficients of thermal expansion.
• Derived the standard governing formula calculating the radius of curvature as a function of temperature variation and the ratio of the elastic moduli and thicknesses of the constituent metals.
• Quantified the longitudinal and interfacial shear stress distributions across the bonded surface, defining conditions to prevent mechanical failure during thermal cycling.