Hooke’s Law Hooke’s law describes the relation between stress and strain in an
elastic body. An elastic body is one which reverts to its original size
and shape when a deforming force is removed. The law states that so
long as the member remains perfectly elastic, the strain produced is
proportional to the stress applied.
Hooke’s law holds for a certain range of stresses. Within this range,
a graph of stress and strain will be a straight line. The top end of the
range is the limit of proportionality. The yield point marks the limit
of elasticity. The graph below is based on mild steel, but is exagger-
ated for purposes of explanation.
Young’s Modulus Young’s modulus of elasticity appears in strength tables along with
ultimate stress and yield point. Young’s modulus is the ratio of stress
to strain within limits of proportionality. It is a constant for each ma-
terial, does not vary with the cross-sectional area of the
material, and for ferrous metals, is generally the same for tensile or
compressive stresses. The symbol used for Young’s modulus is the
letter “E.”
E stress
strain
=
or E FL
Ae
=
Calculating Stress & Load Stress
s
is equal to the product of Young’s modulus E and strain
e
.
s
e
=×
E
Load F is equal to the product of Young’s modulus E, strain
e
, and
the cross sectional area A of the member.
FE
A
=××
e
Strain Gauges
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