This chapter discusses the mathematical method used to calculate the elongation of a material under tensile force and elasticity of a material.

EO 1.7STATE Hooke's Law.

EO 1.8DEFINE Young's Modulus (Elastic Modulus) as it relates to stress.

EO 1.9Given the values of the associated material properties, CALCULATE the elongation of a material using Hooke's Law.

Hooke's Law

If a metal is lightly stressed, a temporary deformation, presumably permitted by an elastic displacement of the atoms in the space lattice, takes place.          Removal of the stress results in a gradual return of the metal to its original shape and dimensions.  In 1678 an English scientist named Robert Hooke ran experiments that provided data that showed that in the elastic range of a material, strain is proportional to stress. The elongation of the bar is directly proportional to the tensile force and the length of the bar and inversely proportional to the cross-sectional area and the modulus of elasticity.

Hooke's experimental law may be given by Equation (2-3).

This simple linear relationship between the force (stress) and the elongation (strain) was formulated using the following notation.

The quantity E, the ratio of the unit stress to the unit strain, is the modulus of elasticity of the material in tension or compression and is often called Young's Modulus.

Previously, we learned that tensile stress, or simply stress, was equated to the load per unit area or force applied per cross-sectional area perpendicular to the force measured in pounds force per square inch.

We also learned that tensile strain, or the elongation of a bar per unit length, is determined by:

Thus, the conditions of the experiment described above are adequately expressed by Hooke's Law for elastic materials. For materials under tension, strain (c) is proportional to applied stress G.

where