MAE 170

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MAE 170 Experimental Techniques Lecture 8 Strain
measurement Nov. 15, 2004
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Announcements

• In-lab final Nov. 30-Dec. 3
• Written final
• Monday, Dec. 6 from 7-10 pm
• Make up labs for Veterans Day (Thurs. Nov. 11)
• Monday and Tues., Nov. 22 and 23 all day
• Wed., Nov. 24 in morning only

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Format of in-lab final

• Time 1 hour total during regular lab hours
• Electrical circuits (black box)
• e.g. op-amps, filters
• Experimental
• LabView practical
• Simple data acquisition and VI programming

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Format of written final exam

• Same format as mid-term
• Multiple choice, true/false
• Between 40-50 questions
• You have all 3 hours to complete the exam

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Goals of this experiment

• Measurement of strain and force
• Understanding the principles and use of strain
  gauges

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Objectives

• Using an aluminum alloy (2024-T4) cantilever beam
• Determine the spring constant (k)
• Determine the elastic modulus (E)
• Determine Poissons ratio (n)

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Principle of experiment
Strain due to cantilever deflection is sensed
electrically, through a strain gauge The strain
gauge is the unknown resistor in a Wheatstone
bridge configuration
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Concepts

• Hookes Law
• Relates stress and strain
• Gauge factor for a strain gauge (G.F.)
• Mechanics of beam bending

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Hookes Law

• Stress (s) is proportional to strain (e)
• s E e
• E elastic modulus

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Poissons ratio (n)

• For a 3-dimensional solid, we have to consider
  the strain the transverse direction
• Most materials n 0.3-0.5

transverse
longitudinal
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In this experiment, strain due to bending is
sensed resistively
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Strain gauges
A length change causes a resistance change, which
is measured by a strain gauge
R resistance r resistivity L length A area
Change of resistance
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Strain gauges

See lab manual for geometry
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Gauge Factor (G.F.)
The G.F. is proportional to the inverse of the
longitudinal strain multiplied by the change in
resistivity
The G.F. relates a change in resistance to
strain For most elements, G.F. ranges from
2.0-4.0 e.g., constantan 2.0, nichrome 2.2
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Wheatstone bridge
The change in resistance is measured by a
Wheatstone bridge
Adjust R3 so that VAB 0 (VA VB 0) VA - Vi
VB - Vi i1R1 i3R3 i2R2i3Rx
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An unbalanced Wheatstone bridge
Rx is the STRAIN GAUGE, generally VAB ? 0
Rx changes due to strain ?VAB changes
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A strain gauge
Made of Cu-Ni or Nichrome alloys
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Strain rosette
A strain rosette can be used to measure the
general state of strain at a point.
For your experiments, you will use a 45 strain
rosette
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A 45 strain rosette
SG 4
Free end
SG 3
SG 1
SG 2
SG 5
Strain Rosette configuration
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Experiment Part 1
Measure the resistance of the strain gauges
before and after loading
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Experiment part 1

• Example for strain gauge 2
• In longitudinal direction
• Unloaded resistance 126.29
• Loaded with around 340 gms, change is lt 1
• In transverse direction
• Unloaded resistance is 131.32
• Loaded with around 350 gm, change is ltlt 1

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Experiment Part 2
D E F L E C T I O N
Add weights and measure deflection (x), from
graph of force vs displacement determine k, F
kx from k 3EI/L3 find E I is moment of
inertia, I bh3/12
End View
h
b
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Experiment Part 2

• Deflection is measured by a yardstick

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Experiment Part 3
dV G.F.?Vo(1/4)
Plot dV (change in voltage across Wheatstone
Bridge) vs mass and comment on shape (positive or
negative)
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Experiment Part 3

• Take off all the weights and get 0 volts from the
  strain gauge
• The strain is proportional to the mass, as given
  in the previous equation
• Either positive or negative dV for compression or
  tension

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Experiment Part 4
Determine the G.F. for strain gauge 3
Calculate strain, ? , from theory ?max
xhF/(2EI) - for each load measure dV - plot dV
vs ?maxV(1/4) and find best fit slope G.F.

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To do before the experiment

• Understand the terms stress, strain, Poissons
  ratio, gauge factor
• Review principle of Wheatstone bridges
• Review the experimental procedure