Lecture 4 - Strain Gages II

7/27/2019 Lecture 4 - Strain Gages II

1/36

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Department of Strength of Materialsand Structural Engineering

Experimental Mechanics ofAdvanced Materials

and Structures

Semester Fall 2013

Marco A. Prez

Lecture 4 Strain gages: instrumentation

and data analysis (Part II)


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Syllabus

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Contents Todays lecture

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Selection criteria for strain gages Types of strain gages Uniaxial and biaxial stress states Technical data The Wheatstone bridge circuit Strain measurements analysis Summary References

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Selection criteria for strain gages

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The questions that should be considered during the selectionof a type of strain gage, arise due to the variety of straingage applications and due to the conditions affecting thestrain gages during service. There is no strain gage thatfulls all requirements. For this reason numerous different

strain gages are available and are supplemented with specialtypes when required. The selection system presented hererequires the user to analyse his measurement problem. Tworequirements must be fullled:

1. The measurement task must have a clear objectiveand the details of the process and its boundaryconditions must be known.

2. The strain gage characteristicsmust be known.

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Types of strain gages

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Strain gages are available in various

shapes and sizes. Apart fromdifferent lengths of the measuringgrid there are various designs andpositions for the connections.

There is also a difference betweenlinear strain gages in single anddouble (parallel) arrangements, Xrosettes with measurement gridaxes at 90 to one another, Rrosettes with 3 measuring gridaxes arranged at certain angles toone another, strain gage chainsand numerous other special shapes.

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It is formed by a multiple strain gages withcrossinggrid axes. X rosettes (2measuringgrids whose axes intersect at 90) are used forthe investigation of biaxial stress conditions

with known principal directions. R rosettes(3measuring grids) are used for the analysis ofbiaxial stress conditions where the maindirections are unknown, both qualitatively and

quantitively. There are two basic shapes whichdiffer due to the angular interval between theirmeasuring grids: 0/45/90 and 0/60/120.With star or cross-shaped rosettes themeasuring grids are arranged over one another.


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600

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900

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In uniaxial stress state, the

maximum of the tension orcompression stresses acts inthe direction in which the forceacts. In all other directions the

stresses are smaller and followthe relationship:

Uniaxial and biaxial stress states

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In problems in experimental analysis the uniaxial stress stateis more the exception rather than the rule.

For reliable results in uniaxialtest the active direction ofthe force must be knownand the strain must be measured in

this direction. If this direction is unknown or only knownapproximately, then the measurements and their evaluationshould be carried out with the biaxial stress state withunknown principal directions.

The biaxial stress state is met far more often and itsdetermination should not be undertaken with the simplemethod used for the uniaxial stress state; this would lead tosignicant errors.


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Technical data

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Technical data

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Technical data

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Technical data

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Technical data

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Technical data

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The Wheatstonebridge can be used

for the determination of relativechanges in resistance. For strainmeasurements, R1 = R2and R3 = R4.

The Wheatstone bridge circuit

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The above equation assume that all the resistance in the

bridge change. This situation occurs for example intransducers or with test objects performing a similarfunction. In experimental stress analysis this is hardly everthe case and usually only some of the arms of the bridge

contain activestrain gages, the remainder being made up ofbridge completion resistors. Designations for the variousforms such as (a) quarter bridge, (b) half bridge, (c)double quarter or diagonal bridge and (d) full bridgeare common place.

The Wheatstone bridge circuit

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5 5 : ; =

(b)(a) (c) (d)

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The elementary loading cases normal (tensile,compressive loading), bending and torsion occur veryseldom, if at all, in a pure form. Usually the loading cases aresuperimposed to some extent whether this is desired or not.

In the following the options for the determination of pureor

combined loadings are discussed. The arrangements of thestrain gages on the object and within the Wheatstone bridgeplay a signicant role here.

Strain measurements analysis

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5 5 : ; =

Special attention should be paid to the sign

of the measured strains.

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5 5 : ; =

This s ing l e l ong i tud ina l gageconguration will respond to bendingloads but is unaffected by torsionalloads if the gage is mounted on thecentreline. Care must be taken withhow the load is applied because it willrespond to axialloads.

ForG

F = 2 and =1000

m/m:

Bending: bridge

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Because the longitudinal and thetransverse Poisson gage are inadjacent arms, the thermal effect iscompensated and the bridge output isincreasedby the factor (1+ ) as canbe proved:

For GF =2, =0.3 and =1000m/m:

Bending: bridge

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Bending: bridge

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The gage on the lower measure bendingstrains of opposite signs. Strainsproduced by axialloads and apparentstrain will be cancelled because the

two are in adjacent arms of the bridge.Moreover the output will be doubleascan be proved.

For GF = 2 and =1000m/m:!

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142

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Bending: full bridge

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This four-gage is the most popularbending beam conguration. The linearbridge output is twice that of thepreceding bridge version. Strains

produced by axialloads and apparentstrain will be cancelled because thetwo are in adjacent arms of the bridge.

For GF =2 and =1000m/m:!

SG1SG3

SG2SG4

+

-

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Axial: 2 gages in opposite arms

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Because the two gages are in oppositearms, this conguration cancelsbending strains. The output will bedouble but the thermal strain isa d d i t i v e . T h e t e m p e r a t u r ecompensation is the poorest of anyconguration shown previously.

For GF =2 and =1000m/m:! +

+

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Axial: full bridge

l

+

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SG3

SG4

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w h

This full bridge conguration withlongitudinal and Poisson gages is themost popular for axial loads. In thisconguration bendingis cancelled, the

output is increasedand it has a goodtemperaturecompensation. Note thatboth gages on a given surface are inadjacent arms.

For GF =2, =0.3 and =1000m/m:

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mV

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Torque: Full torsion bridge

+

- +

-

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TT

rIn this full bridge torsional congurationbending and axial loads are cancelled.Also it has a good temperaturecompensation. It is the most popular

design for torque measurement. However,very accurate gage orientation andplacement of all four gages is crucial forsuccess. For GF =2 and =1000m/m:!

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Summary

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In this lecture we have discussed the following topics:

The selection criteria for strain gages is based on themeasurement task (uniaxial or biaxial stress states,

space requirements, homogeneity of the straineld)

and the strain gage characteristics.

The use of the Wheatstone bridge circuit for strainmeasurements and the different congurations

for different loadingcases.

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References

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1. Recent advances in experimental mechanics by E. E. Gdoutos, 2002.2. Springer Handbook of Experimental Solid Mechanics by William N. Sharpe

Jr. (Editor), 2008.

3. Handbook on Experimental Mechanics by Albert S. Kobayashi, 1993.4. Experimental mechanics of solids by Cesar A. Sciammarella and Federico

M. Sciammarella, 2012.5. Mechanics of solids by S. S. Bhavikatti, 2010.6. An Introduction to Measurements using Strain Gages by

Karl Hoffmann, 1989.

7.

Modern experimental stress analysis by James F. Doyle,2004.

8. Modal Analysis by Jimin He and Zhi-Fang Fu, 2001.9. Harris shock and vibration handbook by Allan G. Piersol

Thomas L. Paez, 2002

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Cantilever beam test

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0

50

100

150

200

250

300

0 1 2 3 4 5 6 7

Str

ainum/m

Displacement delta (mm)

Analytical12

3wh

Iz =

Lecture 4 - Strain Gages II

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