What Is Poisson's Ratio? Sample Problem And Solution Using Poisson's Ratio
When a homogeneous slender bar is axially loaded, the resulting stress and strain satisfy Hooke’s law, as long as the elastic limit of the material is not exceeded.
In all engineering materials, the elongation produced by an axial tensile force P in the direction of the force is accompanied by a contraction in any transverse direction (Fig. 2.36).† In this section and the following sections (Secs. 2.12 through 2.15), all materials considered will be assumed to be both homogeneous and isotropic, i.e., their mechanical properties will be assumed independent of both position and direction.
It follows that the strain must have the same value for any transverse direction.\ Therefore, for the loading shown in Fig. 2.35 we must have Py 5 Pz. This common value is referred to as the lateral strain.
An important constant for a given material is its Poisson’s ratio, named after the French mathematician Siméon Denis Poisson (1781–1840) and denoted by the Greek letter n (nu). It is defined as
v = - lateral strain / lateral stress.
Sample Problem:
A 500-mm-long, 16-mm-diameter rod made of a homogenous, isotropic material is observed to increase in length by 300 mm, and to decrease in diameter by 2.4 mm when subjected to an axial 12-kN load. Determine the modulus of elasticity and Poisson’s ratio of the material.
Solution:
Click on the image to enlarge and see the solution.
