It is important to distinguish stiffness, which is a measure of the load needed to induce a given
deformation in the material, from the strength, which usually refers to the material’s resistance to
failure by fracture or excessive deformation. The stiffness is usually measured by applying relatively
small loads, well short of fracture, and measuring the resulting deformation. Since the deformations
in most materials are very small for these loading conditions, the experimental problem is largely
one of measuring small changes in length accurately.
Hooke3 made a number of such measurements on long wires under various loads, and observed
that to a good approximation the load P and its resulting deformation δ were related linearly as
long as the loads were sufficiently small. This relation, generally known as Hooke’s Law, can be
written algebraically as
P = kδ