UAA School of Engineering

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Strain Gage Theory

• UAA School of Engineering
• CE 334 - Properties of Materials
• Lecture 18

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What are Strain Gages?

• One of several devices that can be used to obtain
  strains directly.
• A small device that can be attached directly to
  the item for which strain data is required.
• The device measures strain at the surface of an
  structural element.
• A strain gage is a small wire grid whose
  electrical resistance changes as it strains.

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Basic Principle

• Professor William Thomson (Lord Kelvin) was the
  first to discover the relationship between
  electrical resistance of wires and induced
  strains.
• Strains imposed by tensile stresses cause an
  increase in electrical resistance.
• Strains imposed by compressive
• stresses cause a decrease in
• electrical resistance.

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Uses of Strain Gages

• Valuable tool for use by stress analysts.
• Analyze new designs (prototypes)
• Trouble shooting and correcting old designs.
• Service load analysis
• Theoretical investigations
• Control systems.

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Wheatstone Bridge

• Wheatstone bridge (an electrical circuit devised
  by Sir Charles Wheatstone) is most commonly used
  to determine the change of electric resistant.
• R1 is the active gage and is placed at the
  location where strain is to be measured.
• R2 is a dummy gage.
• R4 is a precision variable resistor.
• Galvanometer is calibrated to read in strain
  units.

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Measurement of Change in Resistance

• Resistance changes are small. On the order of
  thousandths of an ohm.
• Bridge is balance when Ig0
• I1R1 I2R2 and
• I1 I4, I2 I3, I1R4 I2R3
• or I1/I2R2/R1,
• I1/I2R3/R4, R2/R1 R3/R4
• ? R1 (R2/R3)R4

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Gage Factor

• The gage factor, K, of a strain gage relates the
  change in resistance(?R) to the change in
  length(?L). This is constant for a given strain
  gage.
• K (?R/R)/(?L/L) (?R/R)/?.
• Rearrange the terms to get ? (?R/R)/K
• Once installed, we read the change in resistance
  (?R) and use the above equation to determine the
  strain (?).

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Points to be considered in selecting a resistance
alloy

• Gage Factor (The higher the better)
• Resistance (The higher the better)
• The effect of temperature
• Relationship between the change in resistance and
  strain (should be linear)
• Wire size (small so as to be weaker than adhesive)

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Temperature Compensation
Temperature Compensation

• Reasons
• The resistance of the wires changes with
  temperature.
• If the temperature coefficient of the strain gage
  differs from that of the specimen, there are some
  temperature effects in the readings.
• Temperature effects are compensated for by
  attaching the dummy gage R2 to the specimen in
  such a way that it is not strained.
• R1/R4 R2/R3 at the balance condition.
• if R1 R2 and ?R1 ?R2 then (R1?R1)/R4
  (R2?R2)/R3

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Temperature Compensation and Doubling output on a
Bending Member
Temperature Compensation

• Attach the two active
• gages on opposite sides.
• The circuit not only
• compensates for temperature
• but also doubles the
• sensitivity.
• Because with R1 in
• compression and R2 in
• tension, the resistant changes
• of opposite signs in effect
• add together.

R1
R2
R4
R3
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Poisson Arrangement
Temperature Compensation

• Temperature compensation only.
• Attach both gages to same side but at one
  perpendicular to the direction of stress.
• Need to know Poissons Ratio to compensate for
  strain in the dummy gage.

R1
R2
R4
R3
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Filtering Bending Forces
P

• R1 and R1 are used as the active gages on
  opposite sides.
• The strain in R1gtRaxial, in R1ltRaxial.
• The circuit adds their results and divides by
  two. Errors are canceled out.
• It gives the true axial strain irrespective of
  any bending.

e
R1
R2
R1
R2
R4
R3
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Placement on Shaft in Torsion

• All four gages used.
• Output is quadrupled.
• Temperature is compensated.
• Gages are measuring the principle strains.

R1
R2
R3
R4
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Multi-element Strain Gages

• Multi-element strain gages have 2 or more strain
  gages built into them.
• The orientation of the gages relative to each
  other is fixed.
• Using Mohrs Circle for strain, the magnitude and
  direction of the principle stresses can be
  computed.

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45E Rosette

• For the 45 deg rosette, the magnitudes of
  principle stresses
• can be determined from basic strain
  relationships

?a
?b
?c
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60E Rosette

• The principle stresses and strains can be
  determine from basic relationships.
• Advantage of the Rosettes is that they make it
  possible to determine the magnitude and direction
  of principle stresses when the direction is not
  obvious or changes with loading.

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Specialty Gages

• There are a myriad of specialty gages that have
  been developed for special applications.
• Gages may vary in types of materials used or in
  configuration to meet the demands of special
  situations.
• High heat, moist environments, and large strains
  are examples of situations that require special
  gages.

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Advantages of Strain Gages

• Ease of Installation
• Relatively high accuracy
• Adjustable sensitivity
• Remote indication
• Very short gage length
• Response to dynamic strain.

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Strain Gage Testing of a Cantilever
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Strain Gage Testing of a Cantilever

• Objectives
• 1. Assist in acquiring strain gage measurements
  from a cantilever beam.
• 2. Determine the stresses in a cantilever from
  the strain gage measurements.
• 3. Compare the results with the theoretical
  predictions based on ES-331, the Mechanics of
  Materials course.

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Strain Gage Testing
Have fun!