Fundamental Engineering Concepts - Mathematics and Statistics for the Environment - page 241

DID YOU KNOW?

Cork has a Poisson ratio of practically zero. This is why cork is used as a stopper in wine
bottles. As the cork is inserted into the bottle, the upper part that is not yet inserted will not
expand as the lower part is compressed.

Modulus of elasticity— Ratio of stress to strain, for stresses below the elastic limit. By check-
ing the modulus of elasticity, the comparative stiffness of different materials can readily
be ascertained. Rigidity and stiffness are very important considerations for many machine
and structural applications.
Poisson's ratio— Ratio of the relative change of diameter of a bar to its unit change of length
under an axial load that does not stress it beyond the elastic limit. Stated differently,
Poisson's ratio (υ) is the negative ratio of transverse to axial strain. When a sample object is
stretched (or squeezed) to an extension (or contraction) in the direction of the applied load,
it corresponds to a contraction (or extension) in a direction perpendicular to the applied
load (Gercek, 2007).

d
d

ε
ε

d
d

ε
ε

d
d

ε
ε

trans
axial

y
x

z
x

υ =− −= −=

where
υ = Poisson's ratio.
ε trans = Transverse strain, which is negative for axial tension (stretching) and positive
for axial compression.
ε axial = Axial strain, which is positive for axial tension and negative for axial
compression.

Note: Later, in our discussion of hydraulics, we talk about pressurized piping systems. When the
air or liquid in a pipe is highly pressurized it exerts a uniform force on the inside of the pipe,
resulting in a radial stress within the pipe material. Due to Poisson's effect, this radial stress
will cause the pipe to slightly increase in diameter and decrease in length. The decrease in
length, in particular, can have a noticeable effect upon the pipe joints, as the effect will accu-
mulate for each section of pipe joined in series. Obviously, a restrained joint may be pulled
apart or otherwise prone to failure. This could result in a catastrophic spill of piping contents
onto nearby personnel and into the environment.

Tensile strength— Resistance to forces acting to pull the metal apart, a very important factor
in the evaluation of a metal (see Figure 11.10).
Compressive strength— Ability of a material to resist being crushed (see Figure 11.11).

Force

Force

FIGURE 11.10 A metal with tensile strength resists pulling forces.

Force

Force

FIGURE 11.11 Compressive strength is the ability of a metal to resist crushing forces.