STRAIN MEASUREMENT
CONTENTS
INTRODUCTION
ELECTRICAL RESISTANCE STRAIN GAGES
TYPES OF STRAIN GAGES
STRAIN GAGE SIGNAL CONDITIONING
CALIBRATION
WHAT IS STRAIN?
lateral
axial
Strain is the amount of deformation of a body to an applied force
For axial direction from the figure above
a 
L
Usually in m (x10-6)
L
Because of Poisson strain phenomena, D will be contracted in lateral direction,
with magnitude depends on Poisson ratio (n)
L
n 
a
n is the property of material, for example, steel has 0.25≤n≤0.3
CONTENTS
INTRODUCTION
ELECTRICAL RESISTANCE STRAIN GAGES
TYPES OF STRAIN GAGES
STRAIN GAGE SIGNAL CONDITIONING
CALIBRATION
MEASURING STRAIN
The most common method for measuring strain is using strain gauge
Strain gage is a device whose electrical resistance
varies in the proportion of the amount of strain
A
in the device.
The most widely used strain gages
is the bonded metallic strain gage
The resistance of the conductor of the strain gage
R  
L
A
If differentiated this equation become:
A D
dA
A
where r = resistivity of conductor material
L =conductor length
A = cross-sectional area of conductor
dR
2
2
R
dD
D
Lateral strain
Then the equation :
dR
R

d


d


dL

L
  a 1  2n
dA
A

GAGE FACTOR
Strain gage factor, S is defined
dR
R

d

  a 1  2n
d
S  1  2n  


dR
S 
R
a
usually around 2 for metallic strain gage
a
If the surface of a structure is in the biaxial stress condition there will
be a transverse strain that will affect the strain gage output
dR
can be described with transverse gage factor, St
St 
R
t
and
Transverse sensitivity
Usually small (less than 0.01)
Kt 
St
Sa
CONTENTS
INTRODUCTION
ELECTRICAL RESISTANCE STRAIN GAGES
TYPES OF STRAIN GAGES
STRAIN GAGE SIGNAL CONDITIONING
CALIBRATION
TYPICAL METALLIC FOIL STRAIN GAGE
single element strain gage
two element rossete
three-element rossete
used in pressured
diaphragms
CONTENTS
INTRODUCTION
ELECTRICAL RESISTANCE STRAIN GAGES
TYPES OF STRAIN GAGES
STRAIN GAGE SIGNAL CONDITIONING
CALIBRATION
STRAIN GAGE SENSITIVITY
Strain measurement involves a very small quantity (a few me)
Therefore to measure strain, requires accurate measurement of
a very small change of resistance
Example:
To measure a strain of 500 m, with strain gage factor= 2
Than R=Sx = 2x500 m or 0.1%
If the strain gage has R=120 W (typical for a strain gage to measure strain)
R=0.12 W (it’s a very small resistance change)
To measure such a small change in resistance, a bridge circuit is needed
to convert this change in resistance to the change in voltage
STRAIN GAGE BRIDGE CIRCUIT
WHEATSTONE BRIDGE
For the Wheatstone bridge arrangement

R3
R4
V o  

 R 2  R 3 R1  R 4

V s


For example strain gage is in R3
The initial resistance of strain gage is R3i
Then to balance the bridge
R3iR1-R4R2=0, then if the strain is strained
R3=R3i+R3
Vo  Vs
R1  R 3
( R 2  R 3 i   R 3 )( R1  R 4 )
R3 small compared to R3i and can be neglected
Vo become linier function of R3 then
 R 2  R 3 i 2
 a  Vo
V s SR 2 R 3 i
EXAMPLE
A single strain gage has a nominal resistance of 120 W and a gage factor
of 2.06. For a quarter bridge with 120 W fixed resistor, what will be the
voltage output with a strain of 1000 mstrain for a supply voltage of 3 V?
Solution:
Using equation
 a  Vo
1000 x10
6
 R 2  R 3 i 2
V s SR 2 R 3 i

V out (120  120 )
2
3 x 2 . 06 x120 x120
V out  1 . 544 mV
SEVERAL BRIDGE ARRANGEMENT
quarter bridge circuit
half bridge circuit
full bridge circuit
Temperature compensation
Any change in resistance of RG caused by change
in temperature will be compensated by the dummy
gage resulting in only strain imposed in active RG
will be detected
CONTENTS
INTRODUCTION
ELECTRICAL RESISTANCE STRAIN GAGES
TYPES OF STRAIN GAGES
STRAIN GAGE SIGNAL CONDITIONING
CALIBRATION
CALIBRATION METHOD
•Introducing small resistance change at the gage and calculating equivalent
strain in the gage using shunt resistor in parallel with gage
•Mounting a strain gage on a cantilever beam into one arm of Wheatstone
bridge and observing deflection as known strain is applied to the gage,
then using deflection formula for cantilever beam deflected a distance d
etc
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