Experimental Stress Analysis Experimental Stress Analysis

log = log + log − log − 2log ……………………………. (2)

Unit1: Electrical Resistance Strain Gauges When the wire is strained axially, each of the variables in eq (2) may change. Differentiate eq (2)
The strain gauges:
While there are several methods of measuring strain, the most common is with a strain gauge, a
= + −2 ……………………….( )
device whose electrical resistance varies in proportion to the amount of strain in the device.
The metallic strain gauge consists of a very fine wire or, more commonly, metallic foil arranged This can be written as
in a grid pattern. The grid pattern maximizes the amount of metallic wire or foil subject to strain ⁄ ⁄ ⁄
= +1−2
in the parallel direction (Figure 2).The cross sectional area of the grid is minimized to reduce the ⁄ ⁄ ⁄
effect of shear strain and Poisson Strain. The grid is bonded to a thin backing, called the carrier,
which is attached directly to the test specimen. Therefore, the strain experienced by the test This can be written as
specimen is transferred directly to the strain gauge, which responds with a linear change in ⁄ ⁄
= + (1 + 2 )
electrical resistance. ∈ ∈
Strain gauges are used to measure the strain and to determine material stress in specimen, nature ∈ = strain in the wire
∈ ⁄
and amount of forces acting on the specimen etc. strain gauge can only perform its task properly =∈ =− = poisons ratio
⁄
if the strain to be measured is transferred faultlessly and free of loss.
This may be rewritten as
Application of strain gauges: =
⁄
= (1 + 2 ) +
⁄
…………………. (3)
 Experimental study of stress in transport vehicles. ∈
Where is the sensitivity of the metallic alloy used in the conducer and is defined as the
 Experimental analysis of stress in structures and machines, apartments, building, pressure
resistance change per unit of initial resistance divided by the applied strain.
vessel, bridges, dams, towers etc.
Eq (3) shows that the strain sensitivity of any alloy is due to two factors, namely the change in
 Experimental verification of theoretical analysis.
the dimension of the conductor, as expressed by the term(1 + 2 ), and change in specific
 Design and development of machines and structures.
( ⁄ )
 Assist failure analysis. resistance, as represented by . Experimental results show that varies from about -12.1 to
 As a sensing element in transducer for measurement of forces, load, pressure, 6.1 for metallic alloys. Since most metal materials have the Poisson's ratio around 0.25 to 0.35,
displacement, torque etc the (1 + 2 ), term in the strain sensitivity factor is expected to be 1.5 to 1.7.
Strain Sensitivity in the Metallic Alloys The value of the strain sensitivity will depend upon the degree of cold-working imparted to
the conductor in its formation, the impurities in the alloy, and the range of strain over which the
Lord Kelvin noted that the resistance of a wire increases with increasing strain and decreases
with decreasing strain. The question then arises as to whether this change in resistance is due to measurement of is made.
the dimensional change in the wire under strain or to the change in resistivity of the wire with The sensitivity factors of common strain gauge materials are listed in the following table.
strain. It is possible to answer this question by performing a very simple analysis and comparing
the results with experimental data which have been compiled on the characteristics of certain Many of the electrical resistance strain gauges produced today are fabricated from the copper-
wire alloys. The analysis proceeds in the following manner: nickel alloy know as advance. Although the sensitivity factor S is usually provided by the strain
The resistance R of a uniform conductor with a length L, cross sectional area A, and specific gauge vendors, engineers still need to choose the right gauge wire materials for their
resistance ′ ′ is given by applications.

= = … … … … … … … … … … … … … … . . (1)
is area of cross section of wire,A
Hence D is a sectional dimension and c is proportionality constant. For example, c=1 and for
square and circular cross-section respectively.
Taking log on both side of eq (1)

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Experimental Stress Analysis Experimental Stress Analysis

compensation.
Material Sensitivity (S)
- It has almost constant sensitivity across a wide range of strain.

Platinum (Pt 100%) 6.1 - Annealed Constantan can even be used in the plastic region
with strain > 5%.

Nickel (Ni 100%) -12.1 But,

- The resistance of Constantan drifts continuously when the
Silver (Ag 100%) 2.9 temperature rises above 65 ºC (150 ºF), which may become
troublesome for strain measurements over a long period of
time or in high temperature.
Copper (Cu 100%) 2.6
• Isoelastic alloy is suitable for dynamic strain measurement in vibration and impact.
- It has higher sensitivity (3.6 vs. 2.1 in Constantan), which
Isoelastic (Fe 55.5%, Ni 36% Cr
3.6 improves the signal to noise ratio.
8%, Mn 0.5%) *
- It has higher resistance such that most Isoelastic strain gauges
have resistance of 350W compared to 120 W in common
Constantan / Advance / Copel Constantan strain gauges, which also increases the strain
2.1
(Ni 45%, Cu 55%) * sensitivity.
- It has better fatigue properties among strain gauge materials.
Nichrome V (Ni 80%, Cr 20%) But,
2.1
* - Isoelastic does not have self-temperature-compensation
property unlike Constantan or Karma.
Karma (Ni 74%, Cr 20%, Al - It is too sensitive to changes in temperature, so that it is not
2.0
3%, Fe 3%) * suitable for measurements which last a long period of time
with temperature fluctuations.

Alloy 479(Pt 92%, W 8%) 4.0 - Sensitivity reduces from 3.1 to 2.5 when strain exceed 7,500 µ.
• Karma alloy has similar overall properties to Constantan.
• Constantan (Advance, Copel alloy) is the oldest and most widely used strain gauge - It has effective self-temperature-compensation property from -
materials. 73 to 260 ºC (-100 to 500 ºF).
- It has a high enough electric resistivity (r = 0.49 mW·m) to - It has higher cyclic strain resistance than Constantan.
achieve a proper resistance for a small gauge length.
But,
- It has a relatively low temperature induced strain in the
- It is more difficult to solder.
temperature range of -30 to 193 ºC (-20 to 380 ºF). This
material is thus considered to have self-temperature-

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• Nichrome V, Armour D, and the Platinum based alloys are used for high temperature
environment (> 230ºC; 450°F) or for other special purposes. 1. Unbounded Wire Strain Gauges:

Gauge construction
In the electrical resistance strain gauges the displacement or strain is measured as a
function of the resistance change produced by the displacement in the gauging circuit. An
ideal strain gauge should have the following basic characteristics:
1. The gauge should be of extremely small size so as to adequately estimate strain at
a point.
2. The gauge should be of significant mass to permit the recording of dynamic
strains.
3. The gauge should b easy to attach to the member being analyzed and easy to
handle.
4. The strain sensitivity and accuracy of the gauge should be sufficiently high.
5. The gauge should be unaffected by temperature, vibration, humidity or other
ambient conditions.
6. The calibration constant for the gauge should be stable over a wide range of
temperature and time.
7. The gauge should be capable of indicating both static and dynamic strains. The basic mechanism of unbounded stain gauge is illustrated in fig.
8. It should be possible to read the gauge either on location or remotely.
9. The gauge should exhibit linear response to strain.  Component parts A and B are both rigid frames; however, frames A is fixed
10. The gauge and the associated equipment should be available at a reasonable cost. and frame B is permitted to move in the direction indicated in the fig.
11. The gauge should be suitable for use as a sensing element or other transducer  In moving frame B, if the initial tension in wire 2-6 and 3-7 is increased, then
system. the initial tension in wires 1-5 and 4-8 is reduced.
 These wires, which are fabricated from a strain sensitive material, represent
four individual strain gauges.
It is theoretically possible to measure strain with, say, a single length of wire as the  The movement of the frame B produces two positive changes in resistance
sensing element of the strain gauge. However, circuit requirements necessary to prevent and two negative changes.
overloading the power supply and the need to minimize gauge current place a lower limit  These four individual elements are connected in an appropriate fashion to a
on the gauge resistance of approximately 100Ω. For eg , with a strain gauge fabricated Wheatstone bridge circuit so that the resistance changes are added and the net
from wire 0.0001 in. in diameter with a resistance of 25 Ω/in. , it is clear that a 100 Ω output of the bridge is proportional to 4∆R/R.
gauge would require a single length of wire 4 in. in long. Since this gauge length is often  Output voltages on the bridge are of the order of 40 mV full scale for an
undesirable, it is normally shortened considerably by forming a zigzag pattern with the excitation voltage of 14 volts.
wire at the expense of gauge width and induced cross sensitivity. Applications:
Construction details of four major classes, and the applications and advantages of each a) Used in transducer application because of its excellent stability.
class will be discussed. b) In rare occasion it is used in direct stress analysis because it is difficult to use than
the bonded wire or foil strain gauge.
c) Transducers to measure acceleration, pressure, and force are commercially

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available with unbounded strain gauges employed as the sensing element.

2. Bonded wire strain gauges:
3. Metal Foil Strain Gauges:

 The foil type of strain gauges has a foil grid made up of thin strain sensitive foil.
 The width of the foil is very large as compared to the thickness (microns) so that
larger area of the gauge is for cementing.
 Currently the gauges are so thin (about 150μin. ) that they are often referred to
as metal-film gauges. It is significant but proprietary developments have been
 The bonded metallic type of strain gauge consists of a strain sensitive made in highly refined photo-etching process used to form the grid
conductor (wire) mounted on a small piece of paper or plastic backing. configurations.
 In us this gauge is cemented to the surface of the structural member to be  The result of these manufacturing improvements is a gauge which has better
tested. tolerances on both the gauge factor and the initial resistance.
 The wire grid may be & flat type or wrap-around.  The metal film or foil gauges are usually mounted on a thin epoxy carrier which
 In the flat type after attaching the lead wires to the ends of the grids, a second is approximately 0.001 in. thick and extremely flexible.
piece of paper is cemented over the wire as cover.  It is mounted on to a specimen with a suitable adhesive to give a strain-
 In the wrap-around type, the wire is wound around a cylindrical core in the measuring gauge in intimate contact with the surface of the specimen.
form of a close wound helix. This core is then flattened & cemented between  The metal-film strain gauges are available in gauge lengths ranging from 1/64 to
layers of paper for the purpose of protection and insulation. 1 in. and which range from 60 to 1,000 Ω.
 Formerly only wrap-around gauges were available, but generally flat grid
gauges are preferred as they are superior to wrap-around gauge in terms of 4. Weld able Strain Gauges:
hysteresis, creep, elevated temperature, performance, stability & current
carrying capacity.
 The two layer of wire and three layer of paper result in a gauge which is
approximately 0.006in. thick. The backing material which carry the wire grid,
protect it from damage.

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 Weld able strain gauges are easy to install in minutes in any environment compared to  For short-time tests using thin paper gauges, curing at room temperature for several
bonded type strain gauge. hours may sufficient. The curing time for wrap around gauges is 5 to 10 times longer
 The weld able strain gauge consists of a strain sensitive element, the nickel Chromium or than for flat-grid gauges.
platinum Tungsten, housed within a small diameter stainless steel tube.  In case of long term test stability is an important requirement; a ten day room
 The strain element is insulated from the tube with highly compacted ceramic insulation. temperature cure may be required. This time can be reduced to day or two day by
 This gauge is subsequently spot welded to structure under test and provides bonding to circulating air at about 55 oC over the gauge installation.
transfer the strain.  As nitro-Cellulose cement is hydroscopic, the cured gauge should be immediately
 The test specimen which is put into tension or compression, the stress is transmitted protected by a moisture resistance coating. This will ensure electrical and
through the weld to mounting flange and in to strain tube. These gauges can be used for dimensional stability of the gauge installation.
static or dynamic applications.
 The wire inside the case is reduced in diameter by an etching process; hence the
minimum gauge resistance is obtained with very small-diameter high resistance wire b) Epoxy cement:
rather than by forming a grid of larger-diameter wire.
 At present these weld able gauges are available with resistance ranging from 60 to 240 Ω
and length of 9/16 to 1 5/32 in. they are suitable for use in the range from -390 to 7500 F.  Two types of epoxy cements-room-temperature epoxies and thermosetting epoxies-
are commonly used.
 Both types have two constituents a monometer and a hardening agent. Mixing of a
Adhesives: monomer with the hardening agent induces polymerization.
 Room temperature epoxies use amine-type hardening agent while thermosetting
The bondable strain gauges are attached to the test specimen by some form of cement or
epoxies require anhydride type of hardening agent.
adhesives. A number of bonding cements are available which require various detailed techniques
 In case of room temperature epoxy polymerization takes place at room temperature
for their use. The following are the desirable characteristics of the bonding cements:
or at a temperature slightly above room temperature.
 High mechanical strength  Thermosetting epoxies need at a curing temperature in excess of 120oC for several
 High creep resistance hours for complete polymerization
 High dielectric strength  Organic fillers in moderate quantities are added to improve the adhesive strength and
 Minimum temperature resistance to reduce the coefficient o expansion of the epoxy.

Good adherence giving shear strength of 10.5 to 14N/mm2  A clamping pressure of 35 to 140 kPa during the curing period ensures a thin
 Minimum moisture absorption adhesive layer or bond line in case of epoxy cements.
 Ease of application.  Epoxy cements resists moisture and chemicals and are useful for test temperatures in
 Low setting time. the range -230oC to 300 oC.

a) Nitro-Cellulose cement: c) Cyanoacrylate Cement:

 Nitro-Cellulose cement is commonly used to mount paper-backed gauges.  Cyanoacrylate cement cures rapidly at room temperature.
 Since these cements contain a very large fraction of solvent (about 85%), the bonded  It is an excellent general-purpose adhesive for laboratory and short-term field
gauge should be cured to remove all the solvents by evaporation. applications.
 The curing time varies with the percentage of solvent, relative humidity, curing  It is compatible with most of the test materials and strain gauge backing materials.
temperature and also the purpose for which the gauge is used.  A firm thumb pressure for about a minute is sufficient to induce polymerization at
room temperature.

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 A strain gauge bonded with this adhesive can be used approximately 10 min after
bonding.
 When protected with coating like microcrystalline wax or silicone rubber, the life of (1) Select strain gauge:
the strain gauge bonded with this adhesive can be extended to 1 or 2 years.
Select the strain gauge model and gauge
 The typical operative temperature range for this adhesive is -75 o to 65oC.
length which meets the requirements of
the measuring object and purpose.
d) Phenolic Adhesives:

 Phenolics are single component thermosetting adhesives requiring curing at an

elevated temperature of 120o to 175oC for fairly long period.
 In most applications these adhesives have been replaced by epoxy-phenolic
adhesives. (2) Remove dust and paint:
 However, phenolic adhesives are still attractive for transducer applications as they
Using a sand cloth (#200 to 300), polish
provide long-term stability under load.
the strain-gauge bonding site over a
 In short time tests phenolic bonded gauges can be used upto a temperature of 260 oC.
wider area than the strain-gauge size.
Wipe off paint, rust and plating, if any,
with a grinder or sand blast before
e) Ceramic cements:
polishing.

 Ceramic cements are used for bonding high temperature strain gauges.
 One such cement consists of ceramic powders such as silica or alumina combined (3) Decide bonding position:
with a phosphoric acid.
 These powders are mixed with a solvent to form a liquid mixture. A bush is used to Using pencils or a marking-off pin, mark
apply a thin layer of this liquid mixture to the test surface. the measuring site in the strain direction.
 The gauge installation is cured at 300oC and used over a temperature range of -235 o When using a marking-off pin, take care
to 500 oC. not to deeply scratch the strain-gauge
 Flame spayed adhesives can be used over a wide temperature range of -235 o to bonding surface.
800oC.
 They are hygroscopic and have poor insulation resistance at high temperatures.
 Gauge bonded this way function satisfactorily in vacuum and in a nuclear-radiation
environment.

Mounting Technique:
The strain-gauge bonding method differs depending on the type of the strain gauge, the
applied adhesive and operating environment. Here, for the purpose of strain measurement at
normal temperatures in a room, we show how to bond a typical lead wire-equipped KFG
gauge to a mild steel specimen using CC-33A quick-curing cyanoacrylate adhesive.

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(4) Remove grease from bonding surface and clean: (7) Press strain gauge:

Using an industrial tissue paper Cover the strain gauge with the
(SILBON paper) dipped in acetone, accessory polyethylene sheet and press it
clean the strain-gauge bonding site. over the sheet with a thumb. Quickly
Strongly wipe the surface in a single perform steps (5) to (7) as a series of
direction to collect dust and then remove actions. Once the strain gauge is placed
by wiping in the same direction. A on the bonding site, do not lift it to
reciprocal wiping cause dust to move adjust the position. The adhesive
back and forth and does not ensure strength will be extremely lowered.
cleaning.

(5) Apply adhesive: (8) Complete bonding work:

Ascertain the back and front of the strain After pressing the strain gauge with a
gauge. Apply a drop of CC- 33A thumb for one minute or so, remove the
adhesive to the back of the strain gauge. polyethylene sheet and make sure the
Do not spread the adhesive. If spreading strain gauge is securely bonded. The
occurs, curing is adversely accelerated, above steps complete the bonding work.
thereby lowering the adhesive strength. However, good measurement results are
available after60 minutes of complete
curing of the adhesive.
(6) Bond strain gauge to measuring site:

After applying a drop of the adhesive, Gauge Sensitivity and Gauge Factor:
put the strain gauge on the measuring
site while lining up the center marks The strain sensitivity of a single uniform length of a conductor was previously defined as
with the marking-off lines. ⁄ ∆ ⁄
= ≈ … … … … … . . (1)
∈ ∈
Here ∈ is a uniform strain along the conductor and in the direction of the conductor. This
sensitivity is a function of the alloy employed to fabricate the conductor. Whenever the
conductor, say a wire, is wound into a strain-gauge grid, however, certain effects take place
which alter to a certain degree this value of sensitivity assigned to the gauge. The change is
introduced by the end loops, which are at right angles to the straight portion of the grid. If the
gauge is in a biaxial strain field, the loops will register a resistance change proportional to the
cross strain.

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Sample preparation:
Axial strain sensitivity: The wire or a foil type strain gauge is mounted on a specimen with an adhesive which serves the
∆ ⁄ vital function of transmitting the strain from the specimen to the gauge sensing element without
|| = ∈
When ∈ = 0 distortion. While employing the adhesive, it is essential that the surface of the specimen be
In this case the gauge is directed along the x axis, and the state of strain is such that ∈ = 0 properly prepared and absolutely clean. Any paint or oxide film on the surface of the specimen is
removed by sanding. The surface is then thoroughly degreased by scrubbing it with acetone. At
Normal strain sensitivity: 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
= ∈
When ∈ = 0 temperature for a suitable length of time to ensure complete cure.
Here the gauge is again directed along the x axis, and the state of strain uniaxial with the strain The curing process is quite complicated since adhesive expands because of heat, experience a
acting normal to the axis of the gauge. reduction in volume due to polymerization, exhibits a contraction upon cooling, and many a
times indicates a posture shrinkage. Since the adhesive is sufficiently strong to control the
Gauge factor:
deformation of the strain sensitive element in the gauge, any residual stress set up in the adhesive
∆ ⁄ will influence the output from the strain gauge.
= = When ∈ = −0.285 ∈
∈

This definition gives the sensitivity provided by the manufacturer of the gauge and indicates the
calibration procedure. A gauge is mounted parallel to the x axis, and the specimen is subjected to Adhesives:
a uniaxial stress . This uniaxial stress gives rise to the biaxial state of surface strain defined Cellulose nitrate: it consists of 85% solvent and 15% solids; therefore an appreciable amount of
above. The sensitivity determined in this calibration process is called the gauge factor, which is solvent is to be removed by evaporation. By placing a strain gauge component in an air
used as the scaling factor to convert resistance change to strain. If the gauge factor is used to circulating oven at 130 F, the time required for curing is appreciably shortened and complete
convert resistance change to strain in any strain field other than the one in which was cure can be affected in a day or two. Once the gauge is completely dried, it must be immediately
determined, an error will result. It is possible to correct any error resulting from the cross water proofed otherwise the cellulose nitrate cement will began to absorb moisture from the
sensitivity of the gauge; however, the development of the correction procedure requires one atmosphere and it will expand. This expansion can materially influence the gauge reading if the
further definition, namely, the cross sensitivity factor K. readout period is long.
Cross sensitivity factor: Phonelic cement: it is cure by a combination of pressure and heat over a given interval of time.
∆ ⁄ Phonelic, a combination of pheonol and formaldehyde during curing, release water as a by-
∈
K= = ∆ ⁄
product and it is necessary that this water be removed and any porosity produced as a result of
||
∈ the formation of water vapors must be avoided. Curing at 180 F for 12 hour at 7 to 14 kg/cm2
It is possible to determine the cross-sensitivity factor K for a flat grid gauge from geometric pressure will be accomplishing this task.
consideration alone. Epoxy cement: it consists of a monometer and a hardening agent which induces polymerization.
It is a thermosetting plastic and exhibits higher bond strength.
Parameters Influencing the Behavior of Strain Gauge:
The amount of hardener added to the monometer is extremely important because the heat
Electrical resistance strain gauges are manufactured with a gauge factor accurate to ± 0.5% and a distortion temperatures and residual stress produced during polymerization can be materially
resistance accurate to about ± 0.2%. But during experimental analysis, several parameters can influenced by a slight variation from the specific value. a filler material such as aluminum oxide
influence the behavior of the gauge and affect its accuracy. The successful application of 5% to 10% by weight is often beneficial since it improves the bond strength and reduces
electrical resistance strain gauges demands a thorough knowledge of all these parameters such as temperature coefficient of expansion of epoxy.
adhesive, strain cycles, heat dissipation, time, humidity, moisture, hydrostatic pressure, etc.

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Cynoacrylate cement: it is quite unusual in that it requires neither heat nor catalyst to induce The temperature variation can significantly influence the output of strain gauges, particularly of
polymerization. The minute trace of water or any other weak bases on the surface of the those which are not temperature compensated. The temperature of the gauge is of course
component are sufficient to trigger the process of polymerization. The shelf life of this adhesive influenced by the ambient temperature variations and by power dissipation in the gauge in the
is very short, i.e. 2 to 3 months only. It must be stored at low temperature at 35-45oF. form of heat when it is connected into a Wheatstone bridge or a potentiometer circuit. The
Ceramic cement: it consists of a blend of finely ground ceramic powder such as alumina and dissipated heat depends upon voltage applied to the gauge and the gauge resistance.
silica combined with phosphoric acid. This blend is mixed with a solvent such as isopropyl P, power dissipated= =
alcohol and an organic binder to form a liquid mixture. A precoat of ceramic cement is applied
on specimen and fired so as to form a thin layer of insulation between gauge grid and specimen. Where P= power in watts, W,
A second layer of ceramic cement is than applied to bond the gauge element. I= gauge current, Amperes, A,
R=gauge resistance, ohms, and
Strain cycles: V=voltage across the gauge in volts.
When a strain gauge is subjected to strain cycles, then for the first few cycles, the gauge sensing There are number of factors such as gauge size, gauge configuration, material of specimen, type
element is often cold worked and hysteresis and zero shift effects are evident. The cold working of adhesive, etc. which govern the heat dissipation.
induces resistivity changes in the gauge alloy and due to hysteresis, the gauge output deviates
from a linear relationship with the applied strain. Power density, = =

The hysteresis and zero shifts reduce to very normal values if the gauge is cycled five to six Power densities which can be tolerated by a gauge are strongly related to the specimen which
times before it is used to record the strain. This strain cycling stabilizes the gauge and improved serves as the heat sink. For thin steel sections, power densities 0.0015 to 0.003 W/mm2 are
the accuracy of the strain measuring system to a considerable extent. allowable. In other words for a strain gauge of 120 Ω resistance, 10mm gauge length, the current
After many thousands or millions of cycles, the gauge begins to fail in fatigue and incorrect should be limited to 20-30mA.
readings are obtained. In general, foil gauge is more satisfactory than wire type gauge for fatigue
applications because foil gauges withstand a large number of cycles before failure. For wire
Moisture and Humidity:
gauges, the point of failure usually is located at the joint between the heavy lead wire and the
fine strain sensitive wire. To avoid this failure, gauges with duel loads are employed. Failure in The gauges or the bonding adhesive may absorb water. The moisture decreases the gauge to
the case of a foil gauge is not abrupt. Instead, a crack usually initiates in the foil near the solder ground resistance, degrades the strength and rigidity of the bond, and thus reduces the
terminal on the tab and slowly propagates across the width of the conductor until the circuit effectiveness of the adhesive. Moreover, the presence of water in the adhesive cause’s
opens. electrolysis when current passes through the gauge and gauge filament gets ended. This can
cause dimensional changes which appear as false strain values. Another effect when moisture
connections forms high resistance connected in parallel with the gauge. To prevent this, gauges
Cross – sensitivity: should be bonded in dry condition or suitable electrically insulating water repellent, such as a
Because a strain gauge has width as well as length, a small proportion of the resistance element silicone rubber compound.
lies at right angles to the major axis of the gauge, at the points where the conductor reverses
direction at the ends of the gauge. So as well as responding to strain in the direction of its major
Hydrostatic pressure:
axis, the gauge will also be somewhat responsive to any strain there may be at right angles to
major axis. In applications like pressure vessels, the normal pressure will produce a small change in
resistance of the gauge due to change in resistivity co-efficient due to pressure. The bubbles in
the adhesive cannot be tolerated because the hydrostatic pressure will force the sensing element
Heat dissipation: into any void beneath the gauge and erroneous resistance changes will be recorded.

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Dummy gauge required for temperature compensation should not be placed in the pressure
vessel but it should be mounted on a small block of material from which the pressure vessel is
fabricated.

Magnetic field:
If a strain gauge is installed on or near electrical equipment producing relatively high magnetic
fields then output from the gauge is affected in many ways. When the gauge is in motion it may
cut flux lines and current will be generated affecting the gauge output. Isoelastic alloy is
magnetostrictive, i.e. the dimensions of the alloy change in relation to the strength of the
magnetic field. If a gauge fabricated from this alloy is employed in proximity to magnetic field,
significant errors can result.

Time:
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 readout period, all the factors which can influence the behavior of the strain
gauge get an opportunity to do so and the error developed due to each of the factors can be When the resistances in the circuit are R1 and R2 the open-circuit voltage E across AB is
considerable.
= ∙ = ∙ ……………….. (1)

Where m= ⁄ and V is the excitation voltage. If resistance R and R change by incremental

Potentiometer circuit: amounts ∆R and ∆R respectively,
∆
The potentiometer circuit is well suited for dynamic strain measurements. An attractive feature E+∆E= ∙ ∆ ∆
……………… (2)
of this circuit is its extreme simplicity. The increment of the open-circuit voltage ∆E of the
From (1) - (2)
potentiometer circuit can be derived as follows:
∆
∆E= ∙ ∆ ∆
− ………… (a)

On simplification
∆ ∆
( )
∆E= ∆ ∆ ∙ …………….. (3)

or
∆ ∆
∆E= ( )
− (1 − )…….. (4)

Where nonlinear term is

=1− ∆ ∆ ………………. (5)

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The error due to nonlinearity of the circuit can be estimated with R as the resistance due to a Constant Current Potentiometer Circuits:
strain gauge, R as a resistor of fixed resistance and ∆R as the change in the resistance of the
gauge due to a strain∈, The potentiometer circuit described in the previous sections has a constant voltage source. In
such circuits the error due to nonlinear effects is significant if the change in the resistance ∆ ⁄
=1− ∆ ….. (6)
∙ is large. As semiconductor gauges have a very large gauge factor, about 50 to 70 times that of
metallic strain gauges, the change in their resistance ∆ ⁄ is large even at relative low strain
=1− ………….. (7) levels. Hence constant voltage potentiometer circuit is not well-suited for use with
∈
semiconductor gauges. Special constant current circuits have been developed for use with
It is seen that the nonlinear term is dependent on the magnitude of strain∈, gauge factor F and the semiconductor gauges.
ratio m= ⁄ . Hence in most strain measurements, the nonlinearity term can be neglected
and ∆E can be determined from
∆ ∆
∆E = ( )
− …….. (8)

However, if high accuracy in strain measurement is required or large strains are to be measured,
the output signal determined through eq (8) can be corrected for the error due to nonlinearity.

The output signal per unit strain or the circuit sensitivity of the potentiometer circuit is given (a) Constant current potentiometer circuit:
by
∆ ∆ ∆
= = − …… (9)
∈ ∈( )

With an active strain gauge R and fixed-ballast resistorR ,

∆
= ∙( )
∙ = ∙ ∙( )
……… (10)
∈

Thus the circuit sensitivity of the potentiometer circuit is dependent on the voltage V and ratio
m= ⁄ . The sensitivity is limited by the maximum power that can dissipated by the
gauge without unfavorable effects on its performance. As power dissipated in the gauge is equal
to .By Ohm’s law relationship between V and I is given by
= (1 + )…….. (11)
Substituting this value of V in eq 10
= ∙ ∙( ………………. (12)
) A constant current potentiometer circuit is shown in fig above. Hence the current supplied by
the source remains constant while the resistance R changes from R to R+∆ .the open-circuit
Thus as in the case of the Wheatstone bridge circuit, the circuit sensitivity of the potentiometer
voltage across AB is
circuit is dependent on ⁄(1 + ) and ∙ . The term ⁄(1 + ) is depend on the
E = (R)……(1)
design of the circuit or on the ratio ⁄ .the term ∙ is entirely depend on the
characteristic of the strain gauge it may be noted that the circuit sensitivity, in practice is quite When resistance R changes to R+∆ , the output voltage is
low; it is often of the order 5 to 10μV per micro strain. E + ∆ = (R + ∆ )………..(2)

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Hence the change in output voltage ∆ corresponding to the change in resistance ∆ is, from
eq 1 and 2
∆
∆ = ∙∆ = ∙ ∙ …………..(3)

If = is the resistance of a strain gauge with gauge factor F, and ∆ is the change in
resistance corresponding to strain ε,
∆ = ε…………(4)
It is seen from eq 3 and 4 that the relationship between the output voltage ∆ and the change
in resistance ∆ or strain ε is linear. The circuit sensitivity is
= ….. (5)
By increasing the gauge current to the maximum value dictated by power-dissipation
considerations, the circuit sensitivity can be maximized. Thus
= = ∙ …………(6) In a double-constant-current potentiometer circuit two constant-current genetrators are used
as shown in fig . the terminals C and D of the circuit are earthed. The output voltage is
Where the power dissipation in the strain gauge = . Thus by proper selection of the
mesured across points A and B. with currents I1 and I2 passing through the resistance R1 and
strain gauge, i.e. proper choice of gauge with appropriate P, F and , the desired circuit
R2 respectively, the potentials at points A and B are
sensitivity can be achieved.
= = ……………. (1)
As in a constant –voltage potentiometer circuit, an R-C filter is required to eliminate the
static component E in the output signalE + ∆ . Thus the simple constant current The output voltage across AB is then
potentiometer circuit is only suitable for dynamic strain measurements. = − = − ………………… (2)
However through the use of a double-constant-current potentiometer circuit, both static and If the circuit is balanced initially, i.e. E=0, then
dynamic strain can be measured. In such a circuit temperature compensation can be effected
− =0 = …………….. (3)
through the use of an additional dummy/ active gauge.
Let the resistances and change by ∆ and ∆ respectively. The output voltage across
AB is given by
(b) Double constant current potentiometer circuit: ( )− ( ) ……. (4)
+∆ = +∆ +∆
In an initially balaced circuit, E=0 and = . Substituteing these in eq.(4)
∆ ∆
∆ = ∆ − ∆ = −

∆ ∆
∆ = − ……..(5)

A study of eq 5 shows that the output voltage ∆ varies linearly with changes ∆ and ∆
of resistance and respectively, i.e., = = . The output voltage ∆ will be given
by
∆
∆ = = ∈……..(6)

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The circuit sensitivity with gauge current set equal to the limiting value correspronding to
the strain gauge used is
= ∆ ⁄∈ = = ∙ ……..(7)

Where the power dissipation in the strain gauge is = . Thus the circuit sensitivity
with one active gauge in the double-constant-current potentiometer circuit is the same as for
a constant –current potentiometer circuit.
When the both the gauges placed in positions of resistance and are active and the
strains in these gagues are equal but of opposite sign, the output voltage ∆ is from eq (5)
∆
∆ =2 =2 ∙ ∈…………(8)

The corresponding circuit sensitivity is

=2 =2 ∙ …….(9)
Thus when both gauges are active, the circuit sensitivity is doubled.
The main feature of the double constant current potentiometer circuit are:
I. It is well-suited for use with semicondutor gauges as the output voltage ∆ varies The voltage drop VAB across R1 is
linearly with the resistance change ∆ ⁄ .
V =i R = ∙ R ………………(a)
II. It is suitable for measurement of both static and dynamic strains.
III. Temprature compensation can be achived through the use of additional dummy/ Similarly, the voltage drop V across R4 is
active gauges.
IV. The circuit is suittable for use with transducers using multiple gagues. V =i R = ∙ R ………………..(b)
V. As in conventional potentiometer circuit the circuit can be grounded, a relatively high
The potential differnce between B and D, V , is
signal-to-noise ratio can be achived.
VI. The constant current source should be of high quality.this reqirement increases the V =V −V = E…………………….(c)
cost of this rather simple circuit. On substituteing of eq (a) and (b) in (c), we get
Wheatstone bridge: E=V
R
−
R
R +R R +R
A dc wheatstone bridge consisting of four resistance arms with a battery and a meter is
shown in fig below. In this bridge the resistance shown in each of the four arms of the bridge E=V ( )( )
………………..(1)
can represent a strain gauge. A voltage V is applied to the bridge.some mesureing
instruments such as galvonometer is used to measure the output of the bridge. The condetion for balance is that the voltage E should be zero, i.e. the numerator in eq 1
should be zero
The reqirements for balance, i.e. zero potential difference E between points B and D can be
determined as follows: R R = R R ………(2)

= ……(2a)

Or

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= ……..(2b) A general expression for ∆E can be derived in a similar manner for the case where all the
four resistances R , R , R , R change by incremental amounts ∆R , ∆R , ∆R ,∆R
Eq (2a) and (2b) gives the condetion for the wheatstone bridge to balance-the ratio of respectively. This expression is given below
resistance of any two adjacent arms of the bridge must be equal to the ratio of the resistance ∆ ∆ ∆ ∆
∆E = V∙ − + − (1 − η)……………..(4)
of the remaining two arms taken in the same order. ( )

Then change the resistance R by an amount ∆R . As the bridge willl then be unbalanced, a Where
voltage ∆E will be prodused between B and D which can be measured with a suitable meter.
(1 − η) = ………………………..(4a)
An expression for ∆E is derived as follows: ∆ ∆ ∆ ∆

As the bridge is initially balanced, from eq.2b

It is seen from eq 4 and also from eq 3 that the relationship between the output ∆E and
R R
= change in resistance ΔR ⁄R , ΔR ⁄R etc. is nonlinear.the nonlinear term η has to be
R R
neglected in order to obtain linear relations for one and four active gauges as follows.
when the bridge is unbalanced due to R changing from R to R + ∆R , the voltage ∆E ∆
across B and D is form eq 1 ∆E = ( )
V∙ ……(5a)
( ∆ )
∆E = V …..(3a) ∆ ∆ ∆ ∆
( ∆ )( ) ∆E = ( )
V∙ − + − ……(5)
Divideing both numrator and denominator on the R.H.S. of Eq. (3a) by R R and noting that
The sensitivity of the wheat stone bridge may be defined as the out of balance voltage, ∆E
R R = R R , we get
produced by unit strain.from eq 5, the brige sensitivity S is
∆
∆ ∆ ∆ ∆
∆E = V ∙ ∆ S =( )
∙ − + − …………..(6)

∆ in multiple gauge circuit with n strain gauges (n can be 1,2,3 or 4), the strain gauge are
∆E = V ∙ ……..(3b) usually so connected that their outputs add up. Hence one can write
∆
∆ ∆ ∆ ∆ ∆
− + − =k ….(6a)
Substituteing in Eq(3b) R ⁄R = R ⁄R = and simplifying the denominator on the R.H.S
of Eq.(3b), we get Where k is termed as the bridge factor. & substituteing eq 5 in eq 6a, we get
∆ ∆ ∆ ∆ ∆
∆E = V ∙ ……………..(3c)
− + − = kFϵ ….(6b)
∆ ⁄
( )
( )
Substituteing eq 6b in 6 gives
∆
∆E = ( V∙ (1 − η)….(3)
) S =( )
∙ V ∙ k ∙ F….(8)
Where
it may be noted that this eq is applicable in case where the bridge voltage V is fixed and
(1 − η) = …………..(3d) is independent of the gauge current. It is also seen that the bridge sensitivity is dependent on:
∆
(1) The magnitude of the bridge voltage, V,
(1 − η) is the nonlinearity factor in the expression for ∆E. (2) The gauge factor, F,
(3) The bridge factor, k or the number of active arms employed, and
(4) The ratio of the resistances, m or R ⁄R .

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