strain gages for stress analysis.ppt

8/16/2019 STRAIN GAGES FOR STRESS ANALYSIS.ppt

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When external forces are applied to a stationary

object, stress and strain are the result. Stress is

defined as the object's internal resisting forces,

and strain is defined as the displacement anddeformation that occur. For a uniform distribution

of internal resisting forces, stress can be

calculated (Figure 2-1 by di!iding the force (F

applied by the unit area ("#



$ Strain is defined as the amount of deformationper unit length of an object %hen a load isapplied. Strain is calculated by di!iding the total

deformation of the original length by the originallength (&#

$

ypical !alues for strain are less than .)inch*inch and are often expressed in micro-strainunits#

$



$ Strain may be compressi!e or tensile and

is typically measured by strain gages. +t

%as &ord el!in %ho first reported in 1)

that metallic conductors subjected to

mechanical strain exhibit a change in their

electrical resistance. his phenomenon

%as first put to practical use in the 1/0s.



Figure 2-1# efinitions of Stress Strain



$ Fundamentally, all strain gages are designed tocon!ert mechanical motion into an electronicsignal. " change in capacitance, inductance, or

resistance is proportional to the strainexperienced by the sensor. +f a %ire is heldunder tension, it gets slightly longer and itscross-sectional area is reduced. his changes itsresistance (3 in proportion to the strainsensiti!ity (S of the %ire's resistance. 4hen astrain is introduced, the strain sensiti!ity, %hichis also called the gage factor (5F, is gi!en by#



$ he ideal strain gage %ould change resistance only due to thedeformations of the surface to %hich the sensor is attached.6o%e!er, in real applications, temperature, material properties, theadhesi!e that bonds the gage to the surface, and the stability of themetal all affect the detected resistance. 7ecause most materials donot ha!e the same properties in all directions, a 8no%ledge of theaxial strain alone is insufficient for a complete analysis. 9oisson,bending, and torsional strains also need to be measured. :achre;uires a different strain gage arrangement.Shearing strain considers the angular distortion of an object under

stress. +magine that a hori<ontal force is acting on the top rightcorner of a thic8 boo8 on a table, forcing the boo8 to become

some%hat trape<oidal (Figure 2-2. he shearing strain in this casecan be expressed as the angular change in radians bet%een the!ertical y-axis and the ne% position. he shearing strain is thetangent of this angle.



$ Poisson strain expresses both the thinningand elongation that occurs in a strainedbar (Figure 2-0. 9oisson strain is defined

as the negati!e ratio of the strain in thetra!erse direction (caused by thecontraction of the bar's diameter to thestrain in the longitudinal direction. "s thelength increases and the cross sectionalarea decreases, the electrical resistance ofthe %ire also rises.



Figure 2-0# 9oisson Strain



$ Bending strain, or moment strain, is calculated by determining therelationship bet%een the force and the amount of bending %hichresults from it. "lthough not as commonly detected as the othertypes of strain, torsional strain is measured %hen the strainproduced by t%isting is of interest. orsional strain is calculated bydi!iding the torsional stress by the torsional modulus of elasticity.

$ Sensor Designshe deformation of an object can be measured by mechanical,optical, acoustical, pneumatic, and electrical means. he earlieststrain gages %ere mechanical de!ices that measured strain bymeasuring the change in length and comparing it to the originallength of the object. For example, the extension meter

(extensiometer uses a series of le!ers to amplify strain to areadable !alue. +n general, ho%e!er, mechanical de!ices tend topro!ide lo% resolutions, and are bul8y and difficult to use.



$ >ptical sensors are sensiti!e and accurate, but aredelicate and not !ery popular in industrial applications.hey use interference fringes produced by optical flats tomeasure strain. >ptical sensors operate best underlaboratory conditions.he most %idely used characteristic that !aries in

proportion to strain is electrical resistance. "lthoughcapacitance and inductance-based strain gages ha!ebeen constructed, these de!ices' sensiti!ity to !ibration,their mounting re;uirements, and circuit complexity ha!e

limited their application. he photoelectric gage uses alight beam, t%o fine gratings, and a photocell detector togenerate an electrical current that is proportional to strain.he gage length of these de!ices can be as short as 1*1inch, but they are costly and delicate.



$ he first bonded, metallic %ire-type strain gage %asde!eloped in 1/0. he metallic foil-type strain gageconsists of a grid of %ire filament (a resistor ofapproximately .1 in. (.2) mm thic8ness, bondeddirectly to the strained surface by a thin layer of epoxyresin (Figure 2-=". 4hen a load is applied to thesurface, the resulting change in surface length iscommunicated to the resistor and the correspondingstrain is measured in terms of the electrical resistance ofthe foil %ire, %hich !aries linearly %ith strain. he foil

diaphragm and the adhesi!e bonding agent must %or8together in transmitting the strain, %hile the adhesi!emust also ser!e as an electrical insulator bet%een thefoil grid and the surface.



$ 4hen selecting a strain gage, one must consider not only the straincharacteristics of the sensor, but also its stability and temperaturesensiti!ity. ?nfortunately, the most desirable strain gage materialsare also sensiti!e to temperature !ariations and tend to changeresistance as they age. For tests of short duration, this may not be aserious concern, but for continuous industrial measurement, onemust include temperature and drift compensation.:ach strain gage %ire material has its characteristic gage factor,

resistance, temperature coefficient of gage factor, thermal coefficientof resisti!ity, and stability. ypical materials include @onstantan(copper-nic8el alloy, Aichrome B (nic8el-chrome alloy, platinumalloys (usually tungsten, +soelastic (nic8el-iron alloy, or arma-type

alloy %ires (nic8el-chrome alloy, foils, or semiconductor materials.he most popular alloys used for strain gages are copper-nic8elalloys and nic8el-chromium alloys.



$ +n the mid-1/)s, scientists at 7ell &aboratories disco!ered thepie<oresisti!e characteristics of germanium and silicon. "lthough thematerials exhibited substantial nonlinearity and temperature sensiti!ity, theyhad gage factors more than fifty times, and sensiti!ity more than a 1times, that of metallic %ire or foil strain gages. Silicon %afers are also moreelastic than metallic ones. "fter being strained, they return more readily to

their original shapes. "round 1/C, the first semiconductor (silicon strain gages %ere de!elopedfor the automoti!e industry. "s opposed to other types of strain gages,semiconductor strain gages depend on the pie<oresisti!e effects of silicon orgermanium and measure the change in resistance %ith stress as opposed tostrain. he semiconductor bonded strain gage is a %afer %ith the resistanceelement diffused into a substrate of silicon. he %afer element usually is notpro!ided %ith a bac8ing, and bonding it to the strained surface re;uiresgreat care as only a thin layer of epoxy is used to attach it (Figure 2-=7.he si<e is much smaller and the cost much lo%er than for a metallic foilsensor. he same epoxies that are used to attach foil gages also are usedto bond semiconductor gages.



$ 4hile the higher unit resistance and sensiti!ity of semiconductor%afer sensors are definite ad!antages, their greater sensiti!ity totemperature !ariations and tendency to drift are disad!antages incomparison to metallic foil sensors. "nother disad!antage ofsemiconductor strain gages is that the resistance-to-strainrelationship is nonlinear, !arying 1-2D from a straight-linee;uation. 4ith computer-controlled instrumentation, theselimitations can be o!ercome through soft%are compensation. " further impro!ement is the thin-film strain gage that eliminatesthe need for adhesi!e bonding (Figure 2-=@. he gage is producedby first depositing an electrical insulation (typically a ceramic ontothe stressed metal surface, and then depositing the strain gage onto

this insulation layer. Bacuum deposition or sputtering techni;ues areused to bond the materials molecularly.



$ 7ecause the thin-film gage is molecularly bonded to thespecimen, the installation is much more stable and theresistance !alues experience less drift. "notherad!antage is that the stressed force detector can be ametallic diaphragm or beam %ith a deposited layer of

ceramic insulation.iffused semiconductor strain gages represent a further

impro!ement in strain gage technology because theyeliminate the need for bonding agents. 7y eliminatingbonding agents, errors due to creep and hysteresis also

are eliminated. he diffused semiconductor strain gageuses photolithography mas8ing techni;ues and solid-state diffusion of boron to molecularly bond the resistanceelements. :lectrical leads are directly attached to thepattern (Figure 2-=.



$ he diffused gage is limited to moderate-temperatureapplications and re;uires temperature compensation.iffused semiconductors often are used as sensingelements in pressure transducers. hey are small,

inexpensi!e, accurate and repeatable, pro!ide a %idepressure range, and generate a strong output signal.heir limitations include sensiti!ity to ambienttemperature !ariations, %hich can be compensated for inintelligent transmitter designs.

+n summary, the ideal strain gage is small in si<e andmass, lo% in cost, easily attached, and highly sensiti!e tostrain but insensiti!e to ambient or process temperature!ariations.



Figure 2-)# 7onded 3esistance

Strain 5age @onstruction



$ Bonded Resistance Gageshe bonded semiconductor strain gage %as schematically describedin Figures 2-=" and 2-=7. hese de!ices represent a popularmethod of measuring strain. he gage consists of a grid of !ery finemetallic %ire, foil, or semiconductor material bonded to the strainedsurface or carrier matrix by a thin insulated layer of epoxy (Figure 2-

). 4hen the carrier matrix is strained, the strain is transmitted to thegrid material through the adhesi!e. he !ariations in the electricalresistance of the grid are measured as an indication of strain. hegrid shape is designed to pro!ide maximum gage resistance %hile8eeping both the length and %idth of the gage to a minimum.7onded resistance strain gages ha!e a good reputation. hey are

relati!ely inexpensi!e, can achie!e o!erall accuracy of better than E*-.1D, are a!ailable in a short gage length, are only moderatelyaffected by temperature changes, ha!e small physical si<e and lo%mass, and are highly sensiti!e. 7onded resistance strain gages canbe used to measure both static and dynamic strain.



ypical metal-foil strain gages.



$ +n bonding strain gage elements to a strained surface, it is important thatthe gage experience the same strain as the object. 4ith an adhesi!ematerial inserted bet%een the sensors and the strained surface, theinstallation is sensiti!e to creep due to degradation of the bond, temperatureinfluences, and hysteresis caused by thermoelastic strain. 7ecause manyglues and epoxy resins are prone to creep, it is important to use resinsdesigned specifically for strain gages.he bonded resistance strain gage is suitable for a %ide !ariety of

en!ironmental conditions. +t can measure strain in jet engine turbinesoperating at !ery high temperatures and in cryogenic fluid applications attemperatures as lo% as -=)2F (-2/@. +t has lo% mass and si<e, highsensiti!ity, and is suitable for static and dynamic applications. Foil elementsare a!ailable %ith unit resistances from 12 to ), ohms. 5age lengthsfrom . in. to = in. are a!ailable commercially. he three primary

considerations in gage selection are# operating temperature, the nature ofthe strain to be detected, and stability re;uirements. +n addition, selectingthe right carrier material, grid alloy, adhesi!e, and protecti!e coating %illguarantee the success of the application.



$ Measuring Circuits+n order to measure strain %ith a bonded resistancestrain gage, it must be connected to an electric circuitthat is capable of measuring the minute changes inresistance corresponding to strain. Strain gagetransducers usually employ four strain gage elementselectrically connected to form a 4heatstone bridgecircuit (Figure 2-. " 4heatstone bridge is a di!ided bridge circuit used forthe measurement of static or dynamic electrical

resistance. he output !oltage of the 4heatstone bridgeis expressed in milli!olts output per !olt input. he4heatstone circuit is also %ell suited for temperaturecompensation.



Figure 2-# 4heatstone 7ridge

@ircuit Schematic



$ +n Figure 2-, if 31, 32, 30, and 3= are e;ual, and a!oltage, B+A, is applied bet%een points " and @, then theoutput bet%een points 7 and %ill sho% no potentialdifference. 6o%e!er, if 3= is changed to some !alue%hich does not e;ual 31, 32, and 30, the bridge %illbecome unbalanced and a !oltage %ill exist at the outputterminals. +n a so-called 5-bridge configuration, the!ariable strain sensor has resistance 3g, %hile the otherarms are fixed !alue resistors.he sensor, ho%e!er, can occupy one, t%o, or four

arms of the bridge, depending on the application. hetotal strain, or output !oltage of the circuit (B>? ise;ui!alent to the difference bet%een the !oltage dropacross 31 and 3=, or 3g. his can also be %ritten as#



$ For more detail, see Figure 2-. he bridge isconsidered balanced %hen 31*32 G 3g*30 and,therefore, B>? e;uals <ero. "ny small change in the resistance of thesensing grid %ill thro% the bridge out of balance,ma8ing it suitable for the detection of strain.4hen the bridge is set up so that 3g is the onlyacti!e strain gage, a small change in 3g %ill

result in an output !oltage from the bridge. +f thegage factor is 5F, the strain measurement isrelated to the change in 3g as follo%s#



$ he number of acti!e strain gages that shouldbe connected to the bridge depends on theapplication. For example, it may be useful toconnect gages that are on opposite sides of a

beam, one in compression and the other intension. +n this arrangement, one can effecti!elydouble the bridge output for the same strain. +ninstallations %here all of the arms are connectedto strain gages, temperature compensation isautomatic, as resistance change due totemperature !ariations %ill be the same for allarms of the bridge.



$ +n a four-element 4heatstone bridge, usually t%o gages are %iredin compression and t%o in tension. For example, if 31 and 30 are intension (positi!e and 32 and 3= are in compression (negati!e,then the output %ill be proportional to the sum of all the strainsmeasured separately. For gages located on adjacent legs, thebridge becomes unbalanced in proportion to the difference in strain.

For gages on opposite legs, the bridge balances in proportion to thesum of the strains. 4hether bending strain, axial strain, shear strain,or torsional strain is being measured, the strain gage arrangement%ill determine the relationship bet%een the output and the type ofstrain being measured. "s sho%n in Figure 2-, if a positi!e tensilestrain occurs on gages 32 and 30, and a negati!e strain is

experienced by gages 31 and 3=, the total output, B>?, %ould befour times the resistance of a single gage.



Figure 2-C# @he!ron 7ridge @ircuit

Schematic



$ The Chevron Bridgehe @he!ron bridge is illustrated in Figure 2-C. +t is amultiple channel arrangement that ser!es to compensatefor the changes in bridge-arm resistances by periodically

s%itching them. 6ere, the four channel positions areused to s%itch the digital !oltmeter (BH bet%een 5-bridge (one acti!e gage and 6-bridge (t%o acti!e gagesconfigurations. he BH measurement de!ice al%aysshares the po%er supply and an internal 6-bridge. his

arrangement is most popular for strain measurements onrotating machines, %here it can reduce the number ofslip rings re;uired.



Figure 2-# Four-4ire >hm @ircuit

Schematic



$ Four-Wire Ohm Circuit "lthough the 4heatstone bridge is one of the most popular methodsof measuring electrical resistance, other methods can also be used.he main ad!antage of a four-%ire ohm circuit is that the lead %iresdo not affect the measurement because the !oltage is detecteddirectly across the strain gage element.

" four-%ire ohm circuit installation might consist of a !oltmeter, acurrent source, and four lead resistors, 31, in series %ith a gageresistor, 3g (Figure 2-. he !oltmeter is connected to the ohmssense terminals of the BH, and the current source is connected tothe ohms source terminals of the BH. o measure the !alue ofstrain, a lo% current flo% (typically one milliampere is supplied to

the circuit. 4hile the !oltmeter measures the !oltage drop across3g, the absolute resistance !alue is computed by the multimeterfrom the !alues of current and !oltage.



$ he measurement is usually done by first measuring the !alue of gageresistance in an unstrained condition and then ma8ing a secondmeasurement %ith strain applied. he difference in the measured gageresistances di!ided by the unstrained resistance gi!es a fractional !alue ofthe strain. his !alue is used %ith the gage factor (5F to calculate strain.he four-%ire circuit is also suitable for automatic !oltage offset

compensation. he !oltage is first measured %hen there is no current flo%.his measured !alue is then subtracted from the !oltage reading %hencurrent is flo%ing. he resulting !oltage difference is then used to computethe gage resistance. 7ecause of their sensiti!ity, four-%ire strain gages aretypically used to measure lo% fre;uency dynamic strains. 4hen measuringhigher fre;uency strains, the bridge output needs to be amplified. he samecircuit also can be used %ith a semiconductor strain-gage sensor and highspeed digital !oltmeter. +f the BH sensiti!ity is 1 micro!olts, the current

source is .== milliamperes, the strain-gage element resistance is 0) ohmsand its gage factor is 1, the resolution of the measurement %ill be microstrains.



Figure 2-/# @onstant @urrent @ircuit

Schematic



$ Constant Current Circuit3esistance can be measured by exciting the bridge %ith either aconstant !oltage or a constant current source. 7ecause 3 G B*+, ifeither B or + is held constant, the other %ill !ary %ith the resistance.7oth methods can be used.4hile there is no theoretical ad!antage to using a constant current

source (Figure 2-/ as compared to a constant !oltage, in somecases the bridge output %ill be more linear in a constant currentsystem. "lso, if a constant current source is used, it eliminates theneed to sense the !oltage at the bridgeI therefore, only t%o %iresneed to be connected to the strain gage element.he constant current circuit is most effecti!e %hen dynamic strain is

being measured. his is because, if a dynamic force is causing achange in the resistance of the strain gage (3g, one %ould measurethe time !arying component of the output (B>?, %hereas slo%lychanging effects such as changes in lead resistance due totemperature !ariations %ould be rejected. ?sing this configuration,temperature drifts become nearly negligible.



$ Application !nstallationhe output of a strain gage circuit is a !ery lo%-le!el!oltage signal re;uiring a sensiti!ity of 1 micro!olts orbetter. he lo% le!el of the signal ma8es it particularlysusceptible to un%anted noise from other electrical

de!ices. @apaciti!e coupling caused by the lead %ires'running too close to "@ po%er cables or ground currentsare potential error sources in strain measurement. >thererror sources may include magnetically induced !oltages%hen the lead %ires pass through !ariable magnetic

fields, parasitic (un%anted contact resistances of lead%ires, insulation failure, and thermocouple effects at the junction of dissimilar metals. he sum of suchinterferences can result in significant signal degradation.



$ ShieldingHost electric interference and noise problems can besol!ed by shielding and guarding. " shield around themeasurement lead %ires %ill intercept interferences andmay also reduce any errors caused by insulation

degradation. Shielding also %ill guard the measurementfrom capaciti!e coupling. +f the measurement leads arerouted near electromagnetic interference sources suchas transformers, t%isting the leads %ill minimi<e signaldegradation due to magnetic induction. 7y t%isting the

%ire, the flux-induced current is in!erted and the areasthat the flux crosses cancel out. For industrial processapplications, t%isted and shielded lead %ires are usedalmost %ithout exception.



$ Guarding5uarding the instrumentation itself is just as important as shieldingthe %ires. " guard is a sheet-metal box surrounding the analogcircuitry and is connected to the shield. +f ground currents flo%through the strain-gage element or its lead %ires, a 4heatstonebridge circuit cannot distinguish them from the flo% generated by the

current source. 5uarding guarantees that terminals of electricalcomponents are at the same potential, %hich thereby pre!entsextraneous current flo%s.@onnecting a guard lead bet%een the test specimen and the

negati!e terminal of the po%er supply pro!ides an additional currentpath around the measuring circuit. 7y placing a guard lead path in

the path of an error-producing current, all of the elements in!ol!ed(i.e., floating po%er supply, strain gage, all other measuringe;uipment %ill be at the same potential as the test specimen. 7yusing t%isted and shielded lead %ires and integrating BHs %ithguarding, common mode noise error can !irtually be eliminated.



Figure 2-1# "lternati!e &ead-4ire @onfigurations



$ "ead-Wire #$$ectsStrain gages are sometimes mounted at a distance from themeasuring e;uipment. his increases the possibility of errors due totemperature !ariations, lead desensiti<ation, and lead-%ireresistance changes. +n a t%o-%ire installation (Figure 2-1", thet%o leads are in series %ith the strain-gage element, and any

change in the lead-%ire resistance (31 %ill be indistinguishablefrom changes in the resistance of the strain gage (3g.o correct for lead-%ire effects, an additional, third lead can be

introduced to the top arm of the bridge, as sho%n in Figure 2-17. +nthis configuration, %ire @ acts as a sense lead %ith no currentflo%ing in it, and %ires " and 7 are in opposite legs of the bridge.

his is the minimum acceptable method of %iring strain gages to abridge to cancel at least part of the effect of extension %ire errors.



$ heoretically, if the lead %ires to the sensor ha!e the same nominalresistance, the same temperature coefficient, and are maintained atthe same temperature, full compensation is obtained. +n reality,%ires are manufactured to a tolerance of about 1D, and three-%ireinstallation does not completely eliminate t%o-%ire errors, but it doesreduce them by an order of magnitude. +f further impro!ement is

desired, four-%ire and offset-compensated installations (Figures 2-1@ and 2-1 should be considered.+n t%o-%ire installations, the error introduced by lead-%ire

resistance is a function of the resistance ratio 31*3g. he lead erroris usually not significant if the lead-%ire resistance (31 is small incomparison to the gage resistance (3g, but if the lead-%ire

resistance exceeds .1D of the nominal gage resistance, thissource of error becomes significant. herefore, in industrialapplications, lead-%ire lengths should be minimi<ed or eliminated bylocating the transmitter directly at the sensor.



Figure 2-11# 5age-Factor

emperature ependence



$ Temperature and the Gage Factor Strain-sensing materials, such as copper, change their internal structure athigh temperatures. emperature can alter not only the properties of a straingage element, but also can alter the properties of the base material to %hichthe strain gage is attached. ifferences in expansion coefficients bet%eenthe gage and base materials may cause dimensional changes in the sensorelement.

:xpansion or contraction of the strain-gage element and*or the basematerial introduces errors that are difficult to correct. For example, a changein the resisti!ity or in the temperature coefficient of resistance of the straingage element changes the <ero reference used to calibrate the unit.he gage factor is the strain sensiti!ity of the sensor. he manufacturer

should al%ays supply data on the temperature sensiti!ity of the gage factor.Figure 2-11 sho%s the !ariation in gage factors of the !arious strain gage

materials as a function of operating temperature. @opper-nic8el alloys suchas "d!ance ha!e gage factors that are relati!ely sensiti!e to operatingtemperature !ariations, ma8ing them the most popular choice for straingage materials.

Figure 2-12# "pparent Strain



Figure 2 12# "pparent StrainBariation

%ith emperature



$ Apparent Strain "pparent strain is any change in gage resistance that is not causedby the strain on the force element. "pparent strain is the result of theinteraction of the thermal coefficient of the strain gage and thedifference in expansion bet%een the gage and the test specimen.he !ariation in the apparent strain of !arious strain-gage materials

as a function of operating temperature is sho%n in Figure 2-12. +naddition to the temperature effects, apparent strain also can changebecause of aging and instability of the metal and the bonding agent.@ompensation for apparent strain is necessary if the temperature

!aries %hile the strain is being measured. +n most applications, theamount of error depends on the alloy used, the accuracy re;uired,and the amount of the temperature !ariation. +f the operatingtemperature of the gage and the apparent strain characteristics are8no%n, compensation is possible.



$ Sta%ilit& Considerations+t is desirable that the strain-gage measurement system be stableand not drift %ith time. +n calibrated instruments, the passage of timeal%ays causes some drift and loss of calibration. he stability ofbonded strain-gage transducers is inferior to that of diffused strain-gage elements. 6ysteresis and creeping caused by imperfect

bonding is one of the fundamental causes of instability, particularly inhigh operating temperature en!ironments.7efore mounting strain-gage elements, it should be established that

the stressed force detector itself is uniform and homogeneous,because any surface deformities %ill result in instability errors. +norder to remo!e any residual stresses in the force detectors, theyshould be carefully annealed, hardened, and stress-relie!ed usingtemperature aging. " transducer that uses force-detector springs,diaphragms, or bello%s should also be pro!ided %ith mechanicalisolation. his %ill protect the sensor element from external stressescaused either by the strain of mounting or by the attaching of electricconduits to the transducer.



$ +f stable sensors are used, such as deposited thin-filmelement types, and if the force-detector structure is %elldesigned, balancing and compensation resistors %ill besufficient for periodic recalibration of the unit. he most

stable sensors are made from platinum or other lo%-temperature coefficient materials. +t is also important thatthe transducer be operated %ithin its design limits.>ther%ise, permanent calibration shifts can result.:xposing the transducer to temperatures outside its

operating limits can also degrade performance. Similarly,the transducer should be protected from !ibration,acceleration, and shoc8.

Fi 2 10 St i 5



Figure 2-10# Strain 5age

+nstallation "lternati!es



$ Transducer DesignsStrain gages are used to measure displacement, force, load, pressure,tor;ue or %eight. Hodern strain-gage transducers usually employ a grid offour strain elements electrically connected to form a 4heatstone bridgemeasuring circuit.he strain-gage sensor is one of the most %idely used means of load,

%eight, and force detection. +n Figure 2-10", a !ertical beam is subjected to

a force acting on the !ertical axis. "s the force is applied, the supportcolumn experiences elastic deformation and changes the electricalresistance of each strain gage. 7y the use of a 4heatstone bridge, the!alue of the load can be measured. &oad cells are popular %eighingelements for tan8s and silos and ha!e pro!en accurate in many other%eighing applications.

Strain gages may be bonded to cantile!er springs to measure the force of

bending (Figure 2-107. he strain gages mounted on the top of the beamexperience tension, %hile the strain gages on the bottom experiencecompression. he transducers are %ired in a 4heatstone circuit and areused to determine the amount of force applied to the beam.



$ Strain-gage elements also are used %idely in the design of industrialpressure transmitters. Figure 2-10@ sho%s a bello%s type pressuresensor in %hich the reference pressure is sealed inside the bello%son the right, %hile the other bello%s is exposed to the processpressure. 4hen there is a difference bet%een the t%o pressures, thestrain detector elements bonded to the cantile!er beam measure the

resulting compressi!e or tensile forces. " diaphragm-type pressure transducer is created %hen four straingages are attached to a diaphragm (Figure 2-10. 4hen theprocess pressure is applied to the diaphragm, the t%o central gageelements are subjected to tension, %hile the t%o gages at the edgesare subjected to compression. he corresponding changes inresistance are a measure of the process pressure. 4hen all of thestrain gages are subjected to the same temperature, such as in thisdesign, errors due to operating temperature !ariations are reduced.



$ !nstallation Diagnostics "ll strain gage installations should be chec8ed using the follo%ing steps#

$ 1. Heasure the base resistance of the unstrained strain gage after it ismounted, but before %iring is connected.

2. @hec8 for surface contamination by measuring the isolation resistancebet%een the gage grid and the stressed force detector specimen using anohmmeter, if the specimen is conducti!e. his should be done beforeconnecting the lead %ires to the instrumentation. +f the isolation resistance isunder ) megaohms, contamination is li8ely.

0. @hec8 for extraneous induced !oltages in the circuit by reading the!oltage %hen the po%er supply to the bridge is disconnected. 7ridge output!oltage readings for each strain-gage channel should be nearly <ero.

=. @onnect the excitation po%er supply to the bridge and ensure both the

correct !oltage le!el and its stability.). @hec8 the strain gage bond by applying pressure to the gage. he

reading should be unaffected.

strain gages for stress analysis.ppt

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