Strain Gages
By Dr. Sotiris Omirou
The electrical resistance strain is a metal wire or metal foil
strip which is wafer-like and can be stuck onto surfaces like
a postage stamp.
Strain-gauge
Typical bonded strain gages
When a strain gauge is bonded to an object, and the
object changes in size, the resistance of the strain
gauge will change. The resistance R is given by the
expression:
R= ρ l/A
Where:

l is the length of the wire in meters

ρ is the resistivity of the material in ohm meters

A is the cross-sectional area of the filament in m2
When strain gauges measure the changing dimensions of an
object, they are measuring strain. Strain is the ratio of the
change in dimension of an object to the original dimension
Mechanical strain
ε = ΔL / L
When subject to strain, its resistance R changes, the
fractional change in resistance ΔR/R being proportional to
the mechanical strain i.e.
Electrical strain
ΔR/R= G . ΔL/L
where G is the gauge factor (1.8 – 2.2)
R varies between 50 Ω and 2KΩ
Potential Divider
Potential Divider with differential amplifier
Wheatstone Bridge



The four arms of the bridge
circuit are formed by the
resistance R1 to R4.
The corner points 1 and 4 are
connected to the input
voltage Vin
The corner points 2 and 3 are
connected to the output
voltage Vo.
R
2
R
2
1
1
4
R
3
3
R
4
Vin
V
o
Quarter strain gauge bridge with differential amplifier
Half strain gauge bridge with differential amplifier
Full strain gauge bridge with differential amplifier
Interpretation of results
(Example 1)
Meter reading
(Example 2)
Meter reading
Strain Gages - review
 Strain = Elongation / Original Length
 Change in length = Change in electrical
resistance
 Electrical Resistance change is very small,
too small to be accurately measured using
ordinary voltmeters
Wheatstone Bridge
Converts a change in
electrical resistance
from a strain gage to a
change in voltage
 Changes in strain are
linearly related to a
change in voltage
output


Voltage change is too
small to be accurately
measured and for this
reason an amplifier is
used