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Electrical resistance strain gage is awire grid on a nonconductive,flexible backing.

Precision Strain Gages Data Book , Vishay Micro-Measurements, Rev 23-Jun-05.

Soldering Tab Layout Lines

Encapsulation(Dark grey)

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Operating principle: resistance isproportional to wire length

If gage is bonded to surface, grid willdeform according to the surface strainsunder the gage

Relate m easu rable ch ang e in r es is tance to th e su rface s t rain u nd er gage

s t ra in m easu rem ent

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Gage sensitivity in one primary direction

Typically designed such that primarysensitivity is to normal strain in onedirection

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Gage Factor Relates resistance changeto length change of grid (and hence axialstrain):

R R

L L

R R

GF

Note: resistance change is pretty small typical gagefactors are approximately 2Strains well less than 1% will need to be measured.Thus resistance changes recorded by a gage will be afew percent at most. This has consequences for themanner in which the resistances are measured.

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Transverse sensitivity

Although the primary sensitivity of the gageis to strains in the primary grid direction, itshould be noted that strains perpendicular to this direction do affect the resistance.

Design featuressuch as thethickened endsnear the loopbacks helpminimize transversesensitivity

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Transverse sensitivity can becorrected for during measurement

Manufacturers supply a transverse sensitivity measurement of gages. The relationship between resistance change and strainis written to include both the axial strain a and the transversestrain t as:

y"sensitivitTransverse" :

directionrsein transveySensitivit :

directionaxialinySensitivit :

)(

ga

gt t

gt

ga

t t a ga

t gt a ga

S

S K

S

S

K S R R

S S R R

Because the relations are in terms of two unknown strain components,

independent measurement using two gages in different directions is needed

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Strain gages have negligible sensitivityto shear strain in gage axes

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We can view a strain gage as a tool tomeasure an axial strain in the direction

aligned with the grid axis.

a b

c

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Complete State of Surface Strain hasthree components

At a point on a surface, three components areneeded to fully specify the state of strain on

the plane: x

y

xyHow do w e f ind a l l three of these?

Recal l that s t ra in g ages are ins ensi t iv e to sh ear s t ra in .

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Two components are easy

a = x

c = y

x

y

How do we get xy

?

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Axial strain in an arbitrary direction on thex-y- plane, given in plane strains x, y, and xy

2

cossin2sincos 22~ xy y x x

(note the factor of in the shear term)

The strain gage can be thought of as a physical analogue of this relationship!

Gage at angle reads x~

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Add a third gage to allow completemeasurement of surface strain state

a = x

c = y

x

y

b

cossinsincos

.for Solve;,,Measure

)(cossin2sincos

)(cossin2sincos

22

2

222

222

cab xy

cba

cab

y xb

xy

xy

xy

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Strain rosette combines three gages ontoa single backing for ease of installation

Three gages are needed to fully specify theplanar state of strain at a point.

Shear strain is not measured directly, but isback-calculated from the measured axialstrains.

Images from Vishay Micro-Measurements Document Number 11191

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Rectangular Rosette: Gages = 45apart from each other

Single-Plane Stacked

Images from Vishay Micro-Measurements Document Number 11191

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Delta Rosette: All gages 120 apart

Images from Vishay Micro-Measurements Document Number 11191

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Data Acquisition: Measurement madeusing Wheatstone Bridge circuit.

Schematic of basic Wheatstone bridge(from Holman, op cit.)

Resistance change proportionalto measured voltage acrossbridge. Increases sensitivity of result Note need to balance circuitsuch that initial zero strain isrecorded Shunt calibration can be usedto simulate a given strain state(usually a maximum anticipatedvalue) by adding a knownprecision resistor in series with thegage. Then, the circuit can becalibrated to provide the correctstain measurement at thisresistance.See MAE 4284 Lab Manual

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Balancing results in zero recorded strainat initial state Strain gages are manufactured

to tight resistance tolerancesmatching resistance of internalresistors in Wheatstone bridgecircuit (typically 120 or 350 ),but during installation someprestrain may be locked in, or resistance may be added by leadwires, soldering, etc.

Balancing uses a variable

resistor in the signalconditioning circuitry to matchthe resistance of the installedgage to the resistance of theinternal resistors in theWheatstone bridge circuit.

Wheatstone bridge circuit isbalanced if resistance on each

side of the circuit is equal

Balancingresistor Strain Gage

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Shunt calibration corrects the gagefactor to account for actual performanceas-installed Addition of lead wires, solder, etc

will alter the effective gage factor of an installed gage

Shunt calibration temporarily adds aknown resistor in series with thegage to simulate the application of alarge known strain value

Gage factor in use is then adjustedfrom nominal value until the correctsimulated strain is recorded.

This corrected gage factor is thenused for subsequent testing.

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In some cases, large grids are preferred

For examp le, for c on crete m ater ia ls , w hic h a re a he terog eneou s co m bina t ion o f par t icu la tes and cem ent . A sm all gage

m ay record s t ra ins e levated by loca l ized s t ress co nc ent ra t ions . A large gr id averages th e resu l t s and can b e mo re accura te in descr ib ing th e ne t resp on se .

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Temperature Effects

CTE Mismatch Dummy Gage Gage Design: Self-Temperature

Compensation

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CTE Mismatch can cause errors in straingage measurement, reduced if gage &

test part have same CTE CTE Mismatch: If gage and structure have different

CTEs, strains will be induced in the gage uponheating that are not representative of the surface

strain in the part.

Gage m ater ials a re m ade to m atch com m on m ater ial CTEs, p rop er g age se lec t ion redu ces th is p rob lem.(e.g. In Lab we use EA-13-060-LZ- 120 gages. 13 is

the CTE in /F, which is the CTE of aluminum).

CTE: Coefficient of Thermal Expansion

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Placement Errors

Readings can be influenced by errors inplacement of gages See HW 4.

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Planar Strain Transformation

2)sin(coscossincossin

2

2cossin2cossin

2

cossin2sincos

22~~

22~

22~

xy y x

y x

xy y x y

xy y x x

2)sin(coscossincossin

cossin2cossin

cossin2sincos

2

22

22

22

~~

~

~

xy

y

x

y x

y

x

22

~~

~

~

xy

y

x

y x

y

x

T