18.6 : 훅의 법칙

Hooke's law states that stress applied to a material is directly proportional to the strain it experiences within the elastic limit. For ductile materials, the elastic limit often aligns with the yield point.

The proportionality constant, known as the modulus of elasticity, has the same units as that of stress since strain is a dimensionless quantity.

The physical properties of structural metals are affected by the manufacturing process used. The stress-strain diagrams of pure iron and three different grades of steel show significant variations in yield strength, ultimate strength, and rupture point.

However, they possess the same modulus of elasticity: their stiffness within the linear range is the same. So, if a high-strength steel is substituted for a lower-strength steel in a structure having the same dimensions, it will have an increased load-carrying capacity.

In isotropic materials, like metals, the Stress-strain relationship is independent of load direction. However, for anisotropic materials, such as fiber-reinforced composites, elasticity moduli differ significantly in the directions parallel and perpendicular to the fibers, resulting in different resistances to loading.