stress and strain intro
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Queens University
MECH 215
Instrumentation and MeasurementStress and Strain
Measurement - Introduction
Darko Matovic, Winter 2006
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What we will learn about:!Wheatstone bridge
!Multiple gauges
!Compensation
Multiple Gauge UseApplications
!Measurement of torque
!Measurement of force
!Measurement of temperature
STRAIN MEASUREMENTS
!Resistance Strain Gauge
!How do we apply them?
!How do we get a signal?
!Interpreting strain signals
Examples
Single Gage Use!What is strain
!What is stress
!Poissons Ratio
!Solid Mechanics
!Stress strain link
Basics
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What is Strain?
Textbook definition: Elongation per unit length
of a member subject to an applied force.
Load
L
L
/L L =
!Strain () is non dimensional!Can be positive or negative
!Direction must be defined
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What is Stress? Textbook definition: Internal forces per unit
area. These internal forces maintain inequilibrium the applied external forces.
Load
Internal
stressLoad
Unit of stress () : Pa or psi
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Where would engineers careabout stress and strain?
Understanding the duty load carrying
components
Transducer Construction
Using a working piece under load tomeasure a third property
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Loads
Engineering design
Engineering analysis
Experimentation Measurement
Product development
Product optimization
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Load Carrying Components and
Structures
Pressure Vessels
Cranes
Shafts
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Strain Gauge Based
Transducers
Pressure Load Cells
Ex. Proving Ring
Torque transducer
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The link from Load to Strain
Stress causes strain
Cause stress
Force; Torque; Pressure; Vibrations.
We cant measure this!
We can measure this!
Is there a known relationship between stress and strain?
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The link between Stress and Strain Stress and strain are
connected. in elastic region:
xx
=
where:
strain in direction
stress in direction
Young's Modulus
x
x
x
x
E
=
=
=
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Load (Force, Torque...) Stress Strain
Resistance Change Signalforce; torque; pressure; vibrations ...
cause stress
stress causes strain
Strain creates Resistance change
Resistance change creates Signal
Link 1:
Link 2:
Link 3:
Link 4:
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F F
B
B
F axial
F
A =
Where A= area
of cross section
Link1: Load Stress
Uniaxial Extension/Compression
x
B
B
Example: A truss Uniaxial state of stress
Load is from externalforce
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Link2: Stress Strain
Uniaxial Extension/Compression
x
D
L
LD
D
=
=
F F
LLAxial Strain
Lateral Strain
xx
x
xD
E
E
=
=
x
D D/2
An axial stress willproduce both axialand
lateralstrain!Lateral Strain
Axial Strain
D
x
= =Poissons Ratio (greek nu):
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Link1: Load StressUniaxial Bending
Example: A Cantilever Beam Subject to Bending
( )( ) ( )
( ), / 2
3
/ 2 / 2
/12x h
Fx h Fx hx
I wh
= =
, / 2x h is an axial stressat the upper/lower
surface.
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Link1: Load Stress
Biaxial Stress Case
X (hoop direction)
y (axial direction)
Example: A pressure Vessel
Biaxial Stress Case
Load is from pressure
P2hoop axial
r
t
= =
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Biaxial Stress Case
Link2: Stress StrainxStresses
x
x E
=
xy
E =
y
y E
=
yx
x
v
E E
=
y xy
v
E E
=
y
x
v
E
=
Corres-
pondingstrains
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Link2: Stress
StrainBiaxial Stress Case
yx
E E
=
y x
E E
=
x
y
x
y
Rearranged, we can use our strains to figure out stresses
( )2
1
x y
x
E
+=
( )21
y x
y
E
+=