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101
101
Strain, Force, and Pressure
Force
is that which results in acceleration (when forces don’t cancel).
Strain
is the change in shape of an object
...
usually due to some force.
(Force is usually called stress in this context.)
Pressure
is force per unit area.
101
EE 4770 Lecture Transparency. Formatted 13:26, 23 December 1997 from lsli10.
101
102
102
Strain
Consider an object in two situations: with and without a force ap
plied.
Let a force be applied along a dimension.
Let
L
1
be the length of the object along the dimension when no force
is applied.
Let
L
2
be the length when the force is applied.
Then the object’s strain is deﬁned to be
L
2

L
1
L
1
.
The symbol
±
is usually used to denote strain.
In most situations, strains of interest will be very small,

±

<
0
.
0001.
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EE 4770 Lecture Transparency. Formatted 13:26, 23 December 1997 from lsli10.
102
103
103
Strain Transducers
Called
strain gauges.
Symbol: no common symbol.
Construction
Flexible card with strip of some conductor arranged in special pattern.
Card is mounted (glued) onto the object being measured.
Conductor is usually a metal or semiconductor.
Pattern is chosen so that strain (to be measured)
occurs along direction of current ﬂow.
Current is passed through conductor.
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EE 4770 Lecture Transparency. Formatted 13:26, 23 December 1997 from lsli10.
103
104
104
Principle of Operation For Both Types
Conductor maintains an almost constant volume with strain.
That is, conductor is not compressible.
Recall that the resistance of a conductor is
R
=
ρ
L
A
, where
L
is its length,
A
is its area, and
ρ
is its resistivity.
Suppose force causes length of the conductor to decrease.
Since volume does not change much, area must increase.
Thus, resistance decreases.
Model Function
H
t1
(
x
)=
R
0
(1 +
G
f
x
),
where
G
f
is a constant
called the
gauge factor.
For metal strain gauges,
G
f
=2.
(An integer!)
For semiconductor strain gauges
G
f
is much higher.
104
EE 4770 Lecture Transparency. Formatted 13:26, 23 December 1997 from lsli10.
104
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105
Complementary Pairs
In some cases the strain
...
in two places on the object
will be of equal magnitude—but opposite sign.
For example, a cantilever beam:
Force
Strain Gauges
The upper part of beam is stretched (positive strain)
and the lower part of beam is compressed (negative strain).
The two strain gauges therefore
form complementary pairs.
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EE 4770 Lecture Transparency. Formatted 13:26, 23 December 1997 from lsli10.
105
106
106
Derivation of Gauge Factor for Ideal Metal
Ideal metal’s properties:
•
Noncompressible. (Does not change volume.)
•
Resistivity is constant.
Consider an Ideal Metal Block
Regardless of strain:
volume is
S
and resistivity is
ρ
.
When unstrained:
call length
L
1
, area
A
1
, and resistance
R
1
.
By standard resistivity formula,
R
1
=
ρ
L
1
A
1
.
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