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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

+=