A gauge used to measure strain is termed as a strain gauge.

This gauge can be mechanical, optical,

or electrical. An ordinary scale can be used to measure the strains. But the least count of an ordinary
scale is 0.5 mm, if the gauge length of specimen is 100 mm, then least count of strain measurement
is (0.5/100) 0.005 5000 microstrain. But for accurate determination of strains at a point the least
count of strain measuring instrument should be 1 strain. A mechanical extensometer known as

count on measurement scale is 0.5 mm. Then least count of change in length on gauge length is
4.166 10–4 10–4 1.666 10–5
or 16.66 microstrain. The use of this extensometer is too cumbersome and mechanical elements in the
extensometer possess heavy inertia forces and dynamic strains cannot be recorded. There are optical
extensometers, where the mechanical levers are replaced by optical levers such as Tuckerman’s optical
gauge but the operation of this gauge necessitates the employment of a highly skilled mechanic.
In order to achieve the least count of 1 microstrain and recording of dynamic strains, electrical
gauges have been developed. The principle of operation of these gauges is that change in magni-
tude of electrical signal is directly proportional to the strain being measured. There are capacitance,
inductance, and resistance strain gauge, but the inertia effect of capacitance and inductance strain
gauges is large which render these useless for dynamic strain measurement. To overcome the defect
of large inertia and friction in mechanical systems, electrical resistance strain gauges have been devel-
oped which are known as inertialess strain gauges. An electrical resistance strain gauge should have
following characteristics.
(i) Strain can be measured with least count of 1 microstrain.
(ii) Strain is measured at a point, therefore the size of the gauge (i.e. its length and breadth) should
be as small as possible.
 (iii
(iv
by a calibration constant. The gauge should have a stable calibration constant.
(v) Operation of system using electrical resistance strain gauge should be simple.
(vi) Output of strain gauge should be linear.
(vii) Strain gauge elements can be suitably used in transducer applications.
(viii) Output from the gauge during read out period should be independent of changes in temperatures
and environmental parameters.

We have learnt that there are three strains in a two-dimensional case. An ordinary

gauge length. To determine the state of stress at a point, it is essential that three strain components
must be determined by recording strains in any three directions at a point.

measurement of strain must be very small in size. This has been made possible by making use of a thin
electrical conductor in the form of a wire. If a wire is adhered onto the surface of a specimen such that
specimen strains are transmitted to the wire, as shown in Figure 8.l, then for a tensile strain, length of
the wire will increase and its area of cross-section will decrease. Consequently, the resistance of the
wire will increase. This change in resistance is proportional to the tensile strain. In other words, if the
change in resistance is measured, then the surface strain on the specimen can be determined. This is
the basic principle of an electrical resistance strain gauge.
In order to have a considerable initial resistance of the wire and a small gauge length, a very thin

. If a strain gauge is fabri-

, strain

This is normally shortened by making a grid but at the expense of gauge width and induced cross-
sensitivity.
 Now say R is the resistance of the wire of an alloy
used for strain gauge as shown in Figure 8.3.

(8.1)

where
L length of the wire, and
A area of cross section of the wire.
Differentiating Eq. (8.1) and dividing both sides by R, we get

Say the initial wire diameter d0.

Final wire diameter df .
Then

where v is the Poisson’s ratio of the material of the wire.

change in area,

and

putting the value of df in terms of d0

neglecting higher order term.

(8.3)

Strain sensitivity of the metallic alloy used in conductor is

For most commonly used alloys in the manufacture of strain gauges, SA is given in the following table.

For general static strain measurement, strain gauges of advance alloy are used while for dynamic strain
measurements, strain gauges made of isoelastic alloy are used.
The strain sensing wire in the form of a grid is carried between two thin carriers with the help of an
adhesive. The backing materials which carry the wire grid are fabricated from paper, phenolic, epoxy,
polyester, plastic, or ceramics. The gauge is bonded directly to the surface being analysed with the help
of a thin layer of adhesive as shown in Figure 8.4. The adhesive serves to transmit strains from the
-
tion is employed for gauge lengths greater than 6 mm.

Strain sensitivity of a straight conductor of an alloy is

where is the uniform strain along the conductor. When the wire is wound in the form of a grid, the

register a resistance change proportional to the lateral (cross) strain yy

as shown in Figure 8.5.

where lateral strain, yy

v0 xx.
 The strain gauge is calibrated on a mild steel specimen and in the above expression, vo
Poisson’s ratio of mild steel. If this gauge factor is used to convert resistance change to strain in any
-
rected by taking into account the cross-sensitivity factor of the gauge.

(8.4)

where l length of straight segment, and

r radius of end loop as shown in Figure 8.6.
The derivation of Eq. (8.4) is beyond the scope of this book. The reader can note that to reduce the
effect of cross-sensitivity K, radius of loop should be as small as possible. But reduction in loop radius
r introduces high bending stresses in wire and cold working in wire.

following relationships:
 true strains,
(8.5)

(8.6)

where and

some other cases, this error may be large particularly when one strain level is very high and other is
very low.

gauges, thin metal foil gauges are used.

The grid element in thin foil gauges is many times wider than it is thick and therefore provides a
larger ratio of bonding area to cross-sectional area than that in a wire grid gauge. Because of larger
area, the foil gauges have better heat dissipation property. Cross-sensitivity effects in thin foil gauge
are much smaller than those in wire grid gauges because cross-section at the ends is much greater than
the cross-section along the straight segment as shown in Figure 8.7.
 -

Sometimes the testing period is long or the readout period of the gauge is very long, then stability or
freedom from zero drift of the gauge installation becomes a prime consideration. Changes in tempera-

gauge installation increases by T, then

(i) The gauge will elongate

(ii) The base material upon which the gauge is mounted will also elongate

(iii) The resistivity of the gauge material, ,

Combined effect of these three factors will be

where

Sg strain sensitivity of the gauge, gauge factor.

If , gauge is subjected to a mechanical strain. ( – ) T, which does not occur in the
specimen due to load and R occurs due to apparent strain .
If , then there is no mechanical strain , but still the gauge will register a change of resistance
is not zero.
There are two approaches to achieve temperature compensation in a gauge system, i.e. (i) com-
pensation in the gauge so that net effect of three factors is cancelled out and (ii) compensation in the
electrical system for the effects of the temperature change.
In producing temperature compensated gauges, it is possible to obtain compensation by perfectly
(

of expansion.
Two alloys A and B are carefully selected so that they both
respond to temperature changes but exactly in the opposite sense.
By properly selecting the lengths of the wires of the two materials,
as shown in Figure 8.8, the temperature effects can be cancelled out
and a gauge with a low temperature response over a limited range
in temperature can be successfully produced.
The second approach will be discussed while dealing with the
electrical circuits used for strain measurement.

Electrical resistance strain gauges are manufactured with a gauge factor accurate to 0.5 and
a resistance accurate to about . But during experimental analysis, several parameters can

resistance strain gauges demands a thorough knowledge of all these parameters such as adhesive,
strain cycles, heat dissipation, time, humidity, moisture, hydrostatic pressure, etc.

The wire or a foil type strain gauge is mounted on a specimen with an adhesive which serves the vital func-
tion of transmitting the strain from the specimen to the gauge sensing element without distortion. While
employing the adhesive, it is essential that the surface of the specimen be properly prepared and absolutely

thoroughly degreased by scrubbing it with acetone. At the same time, the bottom side of the gauge is
cleaned with acetone just prior to its placement. After the gauge is installed, the adhesive must be exposed
to proper combination of pressure and temperature for a suitable length of time to ensure complete cure.
The curing process is quite complicated since adhesive expands because of heat, experiences a
reduction in volume due to polymerization, exhibits a contraction upon cooling, and many a times

output from the strain gauge.

The adhesives generally used for strain gauge installation are (i) Duco cement (cellulose nitrate), (ii) Bake-
lite (Phonelic) cement, (iii) Epoxy, (iv) v) Ceramic cement.
Cellulose nitrate
amount of solvent is to be removed by evaporation. By placing a strain gauged component in an air
circulating oven at 130°F, the time required for curing is appreciably shortened and complete cure can
be affected in a day or two.
 Once the gauge is completely dried, it must be immediately water proofed otherwise the cellulose
nitrate cement will begin to absorb moisture from the atmosphere and it will expand. This expansion

Phonelic cement is cured by a combination of pressure and heat over a given interval of time. Phonelic,
a combination of phenol and formaldehyde during curing, release water as a by-product and it is neces-
sary that this water be removed and any porosity produced as a result of the formation of water vapours
pressure will accomplish this task.
If the gauge is to be employed at temperature in excess of 350°F, thin gauge installation with
phenolic cement should be subjected to a minimum of two temperature cycles to this higher temperature
before measurements are made.
Epoxy consists of a monomer and a hardening agent which induces polymerization. It is a thermosetting
plastic and exhibits higher bond strength.
The amount of hardener added to the monomer is extremely important because the heat distortion

to 10 by

expansion of the epoxy.

Cynoacrylate cement is quite unusual in that it requires neither heat nor catalyst to induce polymer-

to trigger the process of polymerization.

and gentle pressure is applied for about a minute or two to induce polymerization. The shelf life of this
adhesive is very short, i.e.
Ceramic cement is used for very high temperature applications. Strain sensing wire is carried
between two strippable carriers. The carrier is removed during application of the gauge and a ceramic

combined with phosphoric acid. This blend is mixed with a solvent such as isopropyl alcohol and an

so as to form a thin layer of insulation between gauge grid and specimen. A second layer of ceramic
cement is then applied to bond the gauge element.

element is often cold worked and hysteresis and zero shift effects are evident. The cold working
induces resistivity changes in the gauge alloy and due to hysteresis, the gauge output deviates from a
linear relationship with the applied strain.

before it is used to record the strain. This strain cycling stabilizes the gauge and improves the accuracy
of the strain measuring system to a considerable extent.
After many thousands or millions of cycles, the gauge begins to fail in fatigue and incorrect readings
are obtained. In general, foil gauge is more satisfactory than wire type gauges for fatigue applications
because foil gauges withstand a large number of cycles before failure. For wire gauges, the point of
To avoid this failure, gauges with dual leads are employed as

not abrupt. Instead, a crack usually initiates in the foil near

the soldered terminal on the tab and slowly propagates
across the width of the conductor until the circuit opens.

output of strain gauges, particularly of those which are not

temperature compensated. The temperature of the gauge
-
tions and by the power dissipated in the gauge in the form
of heat when it is connected into a Wheatstone bridge or
a Potentiometer circuit. The dissipated heat depends upon
voltage applied to the gauge and the gauge resistance.

where P power in Watts, W,

I gauge current, Amperes, A,
R gauge resistance, ohms, , and
V voltage across the gauge in volts.

of adhesive, etc. which govern the heat dissipation.

Power densities which can be tolerated by a gauge are strongly related to the specimen which serves
as the heat sink. For thin steel sections, power densities 0.0015 to 0.003 W/mm are allowable. In other
resistance, 10 mm gauge length, the current should be limited to

Moisture is absorbed by both the adhesive and the carrier and the gauge performance is affected in
many ways. The moisture decreases the gauge to ground resistance, degrades the strength and rigidity
of the bond, and thus reduces the effectiveness of the adhesive. Moreover, the presence of water in

eroded. All these factors introduce errors in the measurement of strain. Therefore, it is necessary that
strain gauge installation should be moisture proofed. For the general laboratory work, where the read-

from moisture in air.

For more severe applications, such as exposure of strain gauge to sea water, it is essential to build up
In applications like pressure vessels, the normal pressure will produce a small change in resistance of the

therefore it is preferable that foil type gauges should be employed on the even surface of the pressure
vessel. The bubbles in the adhesive cannot be tolerated because the hydrostatic pressure will force the
sensing element into any void beneath the gauge and erroneous resistance changes will be recorded.
Dummy gauge required for temperature compensation should not be placed in the pressure vessel but
it should be mounted on a small block of the material from which the pressure vessel is fabricated.
By employing non-conducting hydraulic oil as the pressurizing medium, it is possible to avoid the

If a strain gauge is installed on or near an electrical equipment producing relatively high magnetic

lines and current will be generated affecting the gauge output. For example, a strain gauge installed on

Isoelastic alloy is magnetostrictive, i.e. the dimensions of the alloy change in relation to the strength

Sometimes the readout period of output from a strain gauge is very long, i.e. several months or even
years, and the specimens cannot be unloaded to determine the error due to zero drift. During this long

to do so and the error developed due to each of the factors can be considerable.
If readout period of the strain gauge is long, following precautions must be taken at the time of
gauge installations:
(i) The advance foil temperature compensated gauges should be used which are most stable gauge.
(ii) The gauge length should be kept as long as possible for better heat dissipation.
(iii) The carrier material can be either Bakelite or epoxy and should not be paper because of its
tendency to creep.
 (iv) The strength, rigidity, and creep resistance of the adhesive can be improved by employing about

(v) The gauge should be cured by following normal procedure and then subjected to a postcure
treatment at 175°F for at least a week.
(vi -
ence due to water or change in humidity.
To account for the zero drift during the long readout period, the position of the active and dummy
gauges should be reversed and reading should be taken in both normal position (A) and reversed posi-
tion (B) as shown in Figure 8.11(a) and (b). If the active and dummy gauges are reversed in the electri-
cal circuit and two readings are taken, the instrument drift will add to one and will subtract from the
other. The true strain will be given by the mean of the two readings.
During the long readout period, readings should be taken after the thermal equilibrium is estab-
lished, i.e.
thermal equilibrium.

Electrical resistance strain gauges are employed on the surface of a specimen to establish the state of
yy
,
yy
, and xy
with respect to x-axis. The
longitudinal strain recorded by the strain gauge will be

The principal strains at the point will be

The principal stresses will be

where E Young’s modulus and v Poisson’s ratio of the material.

To determine the principal stresses at any point, it is essential that three unknowns xx, yy, and xy
should be determined. Therefore if the strains are measured in any three directions, then state of strain

Following combinations of strain gauges or strain gauge rosettes are used.

1. A single strain gauge can be used if
the direction of one principal stress is
known and the other principal stress is
zero as shown in Figure 8.13.

shown in Figure 8.14(a) is used where

directions of both the principal stresses are known and p1 0 and p 0.
Figure 8.14(b) shows a two-element rectangular rosette made from thin foil gauges with
theiraxes at right angle.
3. A three-element rectangular rosette as shown in Figure 8.15 is employed to completely determine
A
, B, and C. Then strains

4. A four-element rectangular rosette is employed to verify the accuracy of the rosette analysis.
Four-strain gauges are employed at an angular interval of 45° as shown in Figure 8.16. If the
strain readings are A c B D, then the analysis is accurate.
5. A three-element delta rosette is shown in Figure 8.17. Strain readings in directions and
C are
xx A
6. A four-element Tee-Delta rosette is used again to check the accuracy of strain measurements.

the fourth strain gauge element, as shown in Figure 8.18, is provided to check the validity of
the analysis. Strain readings will give
Problem 8.1 A two-element rectangular rosette was used to determine the two principal stresses at a
p1 and p 75 N/mm
xx
, yy and xy when 30°.

Solution: Principal stresses p1 and p have been obtained through strain readings along principal
xx
along x directions which is inclined at 30° from direction 1 will be

137.5

Stress,

Shear stress,
Problem 8.2 The following apparent strains were obtained with two-element rectangular rosette

Determine the true strains xx and yy if cross-sensitivity factor K 0.01. Determine the error which
would have occurred if the cross-sensitivity of the gauge had been neglected.
Solution: The expression for true strain in x direction is

where v0 is the Poisson’s ratio of the material on which the gauge is calibrated. In the problem value
of v0 is not given, therefore

then

Similarly true strain in y direction,

True strains,

xx
700 m/m

yy
m/m

Error in the measurement of, xx

Error in the measurement of, yy

Problem 8.3 The following observations are made with a
rectangular rosette mounted on a steel specimen
A
800 m/m

B
–100 m/m

C
.
Determine the principal strains, principal stresses, and prin-
cipal angles 1 and with respect to x-axis.
For steel E v 0.3
Solution: Strains,

xx A
800 m/m
yy C
m/m

xy B
– C
–100 m/m

Principal strains,

–50 – 851.47 m/m

Principal stresses,
Principal angles,

1
–1°40'48"

Problem 8.4 The following observations were made with a delta rosette mounted on an aluminium

A
800 cm/cm

B
400 cm/cm

C
0 cm/cm.

Determine principal strains, principal stresses, and principal

angles if for aluminium E 680 10 N/mm , v 0.33.
Solution: Strains,

0.75 yy
– 0.433 xy
40

or 0.75 yy
– 0.433 xy
m/m
Moreover

0.75 yy
0.433 xy
0

0.75 yy
0.433 xy
m/m

1.5 yy
0 or yy
0
Thus,
0.433 xy

xy
m/m
Principal strains
 400 – 461.88 –61.88 m/m

Principal stresses

Principal angles

Problem 8.5 Following readings were recorded through a four-element rectangular rosette mounted
on an aluminium specimen. If the measurements are accurate, determine principal strains.
Solution: In this set of readings, strains

Since A C B
, the strain measurements are accurate.
D

Strain components

Principal strains
 m/m.
Problem 8.6 For a Tee-delta rosette, the following data are recorded from the four gauge element.

A
500 m/m

B
50 m/m

C
150 m/m

D
300 m/m

Solution: xx A
m/m

(i)

(ii)
From Eqs (i) and (ii)
yy
300 m/m

The data are valid because strain gauge element at D in the y direction has correctly recorded the
strain , i.e. 300 m/m.

8.1 A two-element rectangular rosette was used to determine the two principal stresses at a point. If
principal stresses are p1 and p –60 N/mm xx
, yy, and xy if

Ans.
8.2 The following apparent strain data were obtained with two-element rectangular rosette
'xx m/m
'yy 400 m/m

Determine true strains xx and yy if K 0.015. Determine also the error which would have
occurred if cross-sensitivity of the gauges had been neglected.
Ans. strain, –0.5 , – 4.7
8.3 The following observations were made with a rectangular rosette mounted on an aluminium
specimen.

A
m/m

B
70 m/m

C
70 m/m

Determine the principal strains, the principal stresses.

For aluminium, E 68 kN/mm , v 0.33.
Ans. strain, 3.6 N/mm , –137.5 N/mm
8.4 The following observations were made with a delta rosette mounted on a steel specimen.

A
400 m/m

B
m/m

C
m/m
 Determine principal strains, principal stresses, and principal angles. For steel E ,
v 0.3.
Ans.

8.5 A four-element rectangular rosette is mounted on an aluminium specimen. The following

observations are made
A
300 m/m

Determine principal strains and principal stresses. For aluminium E 68 kN/mm , v 0.33.
Ans. [741.55 strain, 158.45
8.6 For a Tee-Delta rosette the following data are recorded from the four gauge elements. Comment
on the validity of the data present.

Ans.

The change in resistance R of a strain gauge is proportional to the applied strain . In order to deter-
mine the strain, the change in resistance R is measured accurately in terms of voltage output E of
an electrical circuit in which gauge is connected. The two most commonly used electrical circuits are
(i) Potentiometer circuit and (ii) Wheatstone bridge circuit.

Rg is connected in a series
with the ballast resistor Rb. A current Ig passes through the gauge as the voltage applied between
terminals a and c is V.

Now let us say that resistances Rb and Rg change to Rb Rb and Rg Rg respectively.

Voltage across terminals of the gauge,

(8.8)
 From Eqs (8.7) and (8.8)
Change in voltage,

neglecting the higher order terms,

where .

If we take r 1, i.e. Rb Rg, then temperature compensation is achieved.

Let us assume that Rg is due to the applied strain and Rb 0, then

Now

where Sg gauge factor

and

So, (8.10)
 circuit sensitivity,

where

r should be greater than 1, i.e. Rb Rg. Then temperature

compensation will not be achieved.
Ratio of Rb and Rg Sg
Ig Rg, which is determined entirely by the selection of the strain gauge.

Normally E is in volts and E -

E when it is super-
imposed on E. Therefore to measure E independently it is necessary that E should be blocked from
the output. In these applications it is possible to block D.C. voltage E

Rm is large
in comparison to RbRg/(Rb Rg) then voltage across Rm will be

(8.11)

Since the E component of the potentiometer output E E is constant with time (i.e. w 0) thus

for the measurement of dynamic strain signal.

the Wheatstone bridge circuit with four arms with resistances R1, R , R3, and R4, subjected to input
voltage V. Voltage between A and C points
 If R1 R3 R R4 these output voltage, E 0, a null balance is achieved. It is this feature of null
balance which permits the Wheatstone bridge circuit to be employed for static and dynamic strain
measurements both.
Now let us assume that all resistances change to , respec-
tively, and taking R1 R3 R R4, the voltage output will be

Neglecting second order terms

where ratio

Let us consider
R1 Rg gauge resistance
and

then

This expression shows that voltage output E is proportional to strain. The voltage output can be
calibrated in terms of strain. This type of circuit is known as direct readout circuit.
In static strain measurement it is possible to employ a null-balance bridge, where the resistance
of one or more arms in the bridge is changed to match the effect of change in resistance of the strain
gauge and the voltage output E becomes zero. Null balance system is more accurate than the direct
readout bridge and requires less expensive equipment for its operation.
helical potentiometer
is placed across the bridge from the point B and D. The centre tap of potentiometer is connected to
point C. Strain gauges may be placed in any or all arms of the bridge.
Let us consider a single strain gauge. A voltage measuring instrument with a high sensitivity near
the null point is placed between the points B and D. Initial null balance is established, i.e. R1R3 R R4
and R5 R6 , G reads zero.
 Now the gauge is subjected to strain , and R1 changes to R1 R1. The slide wire or potentiometer
is adjusted making R5 R6 until the bridge is balanced again.
R5 R6 and this potentiometer adjustment is calibrated in terms of the strain to which the strain
gauge R1 is subjected. The mechanical movement of the potentiometer serves as the means of readout.
For this bridge, expression (6) can be written as

Since

but for null balance bridge,

So,

because R1 Rg

(8.14)

This equation can be used to determine strain directly if

Problem 8.7 For a strain gauge with the following characteristics, calculate Se, V and Rb in a
potentiometer circuit.
Rg , Sg Ig

Solution:

where

or r

Ballast resistor, Rb rRg 1080

Input voltage, V Ig (Rb Rg)
where Ig gauge current 0.030 amp.
V 1080) 0.030 36 V
 SC

6.48 V/unit strain 6.48 V/ strain

Problem 8.8 A cantilever beam fabricated from a circular rod is employed as a load cell to measure
the load P as shown in Figure 8.30. Show that two active strain gauges can be employed in a potenti-
ometer circuit to measure the load P while cancelling out the signal due to twisting moment T.

Solution: If the two gauges R1 and R are mounted on the top and bottom of the rod, at a distance of
l from the load point P, then
(i) bending moment M Pl acts on the gauges in addition to the twisting moment T.
(ii) due to M, gauge R1 will be subjected to tensile strain and gauge R will be subjected to
compressive strain, – . Then

and

(iii) Due to twisting moment T, there will be shear stress at surface of the rod. Strain gauges do not
respond to shear stress.

Voltage output, where

(Figure 8.31)

or

Strain is directly proportional to voltage output E.

Problem 8.9

Rg

Pg 0.05 W
Sg
Solution: In this problem, resistances R1 R4 and R R3.

Power through the gauge,

Voltage,

Now,
 because Sg

Circuit sensitivity

V/ strain

Problem 8.10 Design a parallel balance Wheatstone bridge with the capability of measuring strain in
increments of 1 gauge having Sg

Solution: For the null balance bridge, strain can be directly measured in terms of R5 if

(Figure 8.33)

Say the range of the instrument is m/m, which is usually the range for a commercial strain
indicator.
Then

or

Say R5 50R

To increase circuit sensitivity let us take

R5 50 54000 54 k
R5 for 1 m/m strain

R5 1 6
51 54000
.

8.7 For a strain with the following characteristics, compute SC, and Rb in a potentiometer circuit.
Rg 350 , Sg Ig 60 mA

80
Ans. [33.6 V/ strain, 105 V, 1400
8.8 A cantilever beam fabricated from a circular rod is employed as a torque cell to measure the
torque T as shown in Figure 8.34. Show that two active strain gauges can be employed in a
potentiometer circuit to measure T while cancelling out the signal due to load P.
Ans. [Two strain gauges at
8.9 Determine the circuit sensitivity for the bridge arrangement as shown in Figure 8.35.
Ans. [Ig Sg Rg if R1 and R4
8.10 Design a parallel balance Wheatstone bridge circuit with the capability of measuring strains over
a range of gauge having Sg
instrument.
Electrical resistance strain gauge suffer from several limitations as follows:
(a
(b
(c) Output signal from the gauge is very small.
(d
Therefore there was necessity of a strain gauge with one single straight element, high initial resis-
doped with impurities to provide positive or negative type gauge factor have been developed, in
which gauge factor varies from 50 to 175 depending upon the concentration of impurity atoms which
varies from 1016 to 10 atoms/cm3 of crystal. Single crystal of germanium or silicon is grown in

are piezoresistive
element in the gauge.
The resistivity of a single crystal semiconductor with impurity concentrations is given by

where resistivity,
e electron charge depending upon the type of impurity,
N number of charge carriers, depending on concentration of impurity atoms, and
mobility of charge carrier, depending on strain and relative direction of strain with
respect to crystal axis.
Strain sensitivity of an alloy is

For metallic conductor, the contribution of is very small, but for semiconductors the effects

of term 175, depending upon the type and concentration of impurity. So,
the gauge factor of semiconductor strain gauge is about 100 times the gauge factor of metallic-alloy
strain gauge.
Boron is used as a trace impurity in producing P (positive) gauge factor type gauge and Arsenic
used to produce N (negative gauge factor) type strain gauge.
Resistivity of P-type silicon gauge is of the order of 500 .m while resistivity of constantan alloy
 The effect of temperature on sensitivity SA
diminished as the concentration impurity atoms increase from 1016 atoms/cm3 to 10 atoms/cm3
leads are attached at ends to eliminate any corrosion due to environmental attack.
Temperative compensation of a single element P-type semiconductor strain gauge is not possible.
Therefore for temperature compensation during read out period another N-type semiconductor strain
gauge is used.

advantage of high gauge factor.

There are dual-element gauge, with one P-type and another N-type element available commercially
so that they can form one half of a Wheatstone bridge circuit.

-
portional to the stress along the axis in which the gauge is mounted on the specimen. There are two types
of stress gauge, i.e. (i) direct stress gauge and (ii) shear stress gauge.

x-axis, at an
unknown angle from the axis of principal stress p1. There
are two parts of the grid, i.e. top and bottom grid..
Strain along top grid

strain along the lower grid

Adding the two expressions

–a a 1
( 1–

From the Mohr’s strain circle

xx yy 1

xx
– yy
( 1–
Putting these values
– – xx yy
( xx
– yy

xx yy
( xx
– yy
) (cos – sin )

xx
cos yy
sin )
[ xx yy
tan
If the gauge is made with
tan v,
where v is Poisson’s ratio.
Then

But

when E is Young’s modulus.

Putting the value of , we get

or

So, the gauge reading gives and multiplied

by gives the value of direct stress .

xx

If the principal directions are known then a single

gauge mounted at angle tan–1 with respect to axis
of, p1, gives the reading which is proportional to principal
stress p1 as shown in Figure 8.38.

Plane Shear Gauge

Consider two strain gauge A and B, mounted at
to axis x
strains,
 or

Shear strain is proportional to the difference of strain readings, i.e. This shows that shear
strain can be measured by the differences of readings from two-element rectangular rosette shear stress
xy xy
G. (shear modulus)

1. What is the diameter of strain sensing wire 6. Observation made in three directions from
in a wire grid gauge? a three-element rectangular rosette are
800 cm/cm –400 cm/cm, and
(c) 0.15 mm (d) None of these –860 cm/cm. Direction A is along
x-axis. What is the strain ?
possesses maximum strain sensitivity (a) 800 cm/cm (b) –400 cm/cm
(a) Constantan (c) –860 cm/cm (d) None of these
(b) Isoelastic 7. In a potentiometer circuit, ratio of ballast re-
(c) Karma
(d) All have equal strain sensitivity
3. Which of the following adhesive takes mini- (b) 80
mum time for setting (c) 75 (d) None of these
(a) Cellulose nitrate (b) Phenolic 8. Power through the gauge is 0.05 W, its
(c) Epoxy (d) Cynocrylate , what is the gauge
4. If are principal strains, E and v are current?
elastic constants, what is the value of princi-
pal stress p1? (c) 0.0004 amp (d) None of these

(a) (b) the direction of orientation of top and bot-

tom grid along axis of gauge?
(c) (d) None of these (a) 17° (b) 30°
(d) None of these
5. Recorded apparent strains are
10. What is the angle of mounting two strain
strains, strain, if K 0.01, cross-
gauge elements about x-axis, if plane shear
sensitivity factor, what is the value of true
gauge is to be Obtained?
strain ?
(a) 30°
strain
(c) 45° (d) None of these
strain (d) None of these
 8.1 Enumerate the optimum characteristics of a strain gauge.
8.2 What is the effect of end loop on the sensitivity of a strain gauge.
8.3 Compare the merits and demerits of Advance alloy and isoelastic alloy as strain sensing ele-
ment.
8.4 What is a thin foil gauge? What are its advantages over wire grid gauge? How cross-sensitivity
factor is reduced in thin foil gauge.
8.5 What is a dual element temperature compensated strain gauge?
8.6 What are the adhesives used to install strain gauge on a sample? Which is the most appropriate
adhesive?
8.7 Discuss the effect of following parameters on the behaviour of electrical resistance strain gauge

8.8 What is zero drift? How it is accounted for?

8.9
8.10 What are four element rectangular rosette and four element T-delta rosette? What is the advan-
tage of extra strain gauge element?
8.11 What is cross-sensitivity factor? How it is accounted for in strain readings?
8.12 Compare the merits and demerits of Wheatstone bridge circuit over potentiometer circuit.
8.13 Derive expression for circuit sensitivity of potentiometer circuit.
8.14 What is a semiconductor strain gauge? What are its merits over electrical resistance wire grid
gauge?
8.15 What is a stress gauge? How single gauge can be used a stress gauge? By what arrangement we
get a plane shear stress gauge?