MadgeTech Bridge120-100mV User manual

Application Note

Introduction to Strain and Strain Gages

• Bridge110

Here at Madgetech we are no strangers to the world of measurement and data recording. We
design and build a full line of products to meet a wide range of data logging requirements.
With the release of the Bridge110, we have introduced ourselves into the realm of strain
measurement. The intent of the Bridge110 was to make strain measurement easy and
accessible to everyone no matter what their experience level, and we feel as though we have
succeeded.

This application note was written for use in conjunction with the Bridge110. It is designed to
give the user a good working knowledge of strain and strain gages. After reading this we hope
that you feel more comfortable and confident working with strain gages.

TABLE OF CONTENTS

INTRODUCTION TO STRAIN______________________________________________________ 9
What is strain?
Why is strain important?
What is a strain gage?

HERE CAN I USE A STRAIN GAGE? ______________________________________________ 4

W

HICH STRAIN GAGE SHOULD I USE? _____________________________________________ 5

W
Considering Gage Pattern
Considering Gage Length
Considering Wire Material
Considering Backing Material
Considering Adhesives

NSTALLING A STRAIN GAGE ____________________________________________________ 9

I
Preparing the Mounting Surface
Bonding the Strain Gage

CQUIRING THE DATA __________________________ ______ See Bridge110 Application Note

A

SING THE ACQUIRED DATA ___________________________________________________ 10

U
What does the data mean?
Representing the data in Mohr’s Circle
Stress-Strain Relationships

EFERENCES _______________________________________________________________ 15

R

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INTRODUCTION TO STRAIN

What is Strain?

When forces are applied to an object they can change its size and shape. This is called
deformation. This deformation can be described by a dimensionless measurement called
strain. For most practical purposes we can define strain as follows:

Application Note

L

A

Suppose a body exists with two points within the body, A and B which are a distance L apart
from each other. Forces are applied to the body and it deforms such that A becomes A` and B
becomes B` and the distance between them becomes L`. The strain (ε) is then defined by the
limit expressed below (Eqn.1), and can be approximated by Eqn.2.

Equation 1 Equation 2

L' L−

→

→

L' L−

L

L

AB

AB

-6

m)

ε

Simple dimensional analysis shows that strain has no units (both numerator and denominator
have the same units of length). However, in practice we refer to strain as its own dimensionless
unit for convenience (e.g. ε = m/m or in/in). Typically, measured values of strain are very
small. So it is most common to refer to a value of strain in “micro-strain” (e.g. με = μm/m
where μm = 10

lim

lim

B

→:=ε

→:=

DEFORMATION

L' L−()

L' L−()

L

L

so

A`

ΔL

ΔL

ε

:=

L

L`

where

B`

ΔLL'L−( ):= L'

Why is Strain Important?

Strain is very important in the world of engineering because of its relations to other, more
important, parameters. Strain has a direct relationship to stress based on material properties.
This means that if we know the material properties and measure the strain we can calculate the
stress (which becomes very important in structural analysis). Conversely, if we apply a known
stress and measure the strain we can calculate the material properties (which is very important
in materials testing). With the advent of the strain gauge measuring strain has become
relatively easy. In addition, strain can be measured when the other parameters (e.g. stress or
material properties) cannot.

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Application Note

What is a Strain Gage?

A strain gage is simply a pattern of thin wires or foil. It works on the principle that when the
wire is put under strain (either elongated or shortened) it changes its electrical resistance
measured in Ohms. The resistance of a wire (R) is a function of three parameters, all of which
are effected by strain.

L

R ρ

The length (L) varies directly with strain (by definition). The area (A) varies inversely with strain
(due to Poisson’s Ratio*). The electrical resistivity of the material (ρ) will also vary depending
on the material of the wire. Using this formula we know how the gage’s resistance will change
with strain. We can quantify this knowledge with a value called the Gage Factor (G
sometimes called sensitivity (S).

⋅

A

)

F

dρ

ρ

G

F

12ν⋅+

+

ε

Fortunately, most of us never have to compute this as it is provided by the strain gage
manufacturer. With knowledge of the gage factor, the equation for finding strain is simplified.

ΔR

ε

G

R⋅

F

* POISSON’S RATIO

When a member is subjected to an axial tensile force not only will it elongate, but it will
also contract laterally. French scientist S.D. Poisson noticed that the ratio of these
longitudinal and lateral strains (ε
the member.

long

and ε

) was a constant, unique to the material of

lat

δ

ε

long

ε

lat

L

δ'

r

ε

−
ε

long

lat

ν

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WHERE CAN I USE A STRAIN GAGE?

Application Note

AXIAL LOADING
A member in tension or compression with a
gage mounted parallel to the axis of the
loading. Measurements can be made of to­tal deflection, applied load, and stress.

Ex. Columns, trusses, cables

BENDING BEAM
A member being bent by an applied mo­ment or by a load exerted perpendicular to
the beam. One side of the beam will be in
tension while the other in in compression.
Measurements can be made of stress, angular
and linear deflection, and applied load / mo­ment.

Ex. Leaf springs, cantilevered beams, rafters/
joists

TORSIONAL LOADING
A member in torsion with a gage mounted
to it in the direction of the strain. Strain is in
axes 45˚ to axis of torque and tangent to the
member. Measurements can be made of
stress, angular deflection, and applied
torque.

Ex. Drive shafts, torsion rods

PRESSURE DIAPHRAGM

P

A pressure vessel with a gage mounted on a
diaphragm (usually at the rear of the vessel.)
Measurements can be made of fluid pressure
inside the vessel.

Ex. Pressure transducers

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Application Note

WHICH STRAIN GAGE SHOULD I USE?

There are many different factors that come into choosing the correct strain gage for your
particular application. The first step is analyzing all the different aspects of your application.
Here are some example questions that should guide you in the right direction.

• What are you trying to measure?
◊ Localized strain or average strain?
◊ Strain in one known direction?
◊ Principal strains in a known direction?
◊ Principal strains in an unknown direction?

• Are the strain values expected to be high or low?

• Will the measured strain be mostly static or dynamic?

• Is it a high temperature application?

• Will the temperature vary much over the course of the test?

• How much space is available?

• Is the surface homogeneous?

• How much money are you willing to spend?

• How simple does the mounting process need to be?

• How critical is the accuracy of the readings?

Considering Gage Pattern

Uni-Axial strain gage should be considered if:

A single strain is to be measured and the direction is known or low cost is a priority
(several uni-axial gages can cost less than a single bi- or tri- axial gage)

Uni-Axial Strain Gage

Bi-Axial (0˚, 90˚ T-Rosette) should be considered if:

Principal strains (ε
torques)

Tri-Axial/ Three-Element (0˚-45˚-90˚ rectangular rosette, 0˚-120˚-240˚ delta rosette) should
be considered if:

0˚-45˚-90˚ Rectangular Rosette

) are to be measured and direction is KNOWN (also applicable to

1,2

Bi-Axial (0°, 90° T-Rosette) Strain Gage

0˚-120˚-240˚ Delta Rosette

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Application Note

Principal strains (ε

) are to be measured and direction is UNKNOWN

1,2

Stacked gage configuration should be considered if:

♦ There isn’t much space available for mounting

Stacked Strain Gage Configuration

♦ Localized strain is to be measured
♦ A large strain gradient exists

Planar gage configuration should be considered if:

Planar Gage Configuration

♦ Heat effects are likely to be an issue
♦ Accuracy and stability are critical

Considering Gage Length

Strain Gages are typically recommended to be 3mm to 6mm
Use a Shorter gage ( l ≤ 3mm ) if:

♦ There isn’t much space available for mounting
♦ Localized strain is to be measured (ex. Near a fillet, hole, notch etc.)
♦ As a rule l ≤ r/10, where r is the radius of the hole or fillet
♦ A large strain gradient exists
♦ Accuracy of the measurement is less critical

Use a Longer gage ( l ≥ 6mm ) if:

♦ Easier installation is a priority
♦ Heat effects are likely to be an issue
♦ Accuracy and stability are critical
♦ The surface is non-homogeneous (l ≥ 2x size of homogenuities)
♦ Low cost is a priority (5-12mm are usually cheapest)

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Considering Wire Material

There are a number of different metal alloys that are used in strain gauges. Each one has it’s
own unique properties that makes it more suitable for some specific application. On the
following page you are provided with the properties of four of the most common materials
used in foil/wire gages. In addition, the properties of common semi-conductor gages are
provided.

ONSTANTAN

C

Nickel/Copper Alloy Gage Factor ~ 2.1

♦ Most common material in gages, and therefore low cost
♦ Better suited to static strains rather than dynamic
♦ Gage factor remains nearly constant even through large deformations
♦ Exhibits self-temperature compensation
♦ Temp range -30˚C to 193˚C (though can experience a lot of drift above 65˚C)

ARMA

K

Nickel/Chromium/Iron/Aluminum Gage Factor ~ 2.0

Very similar characteristics to Constantan with these exceptions:

♦ Best suited to low temperature environments (as low as -265˚C)
♦ More stable over extended periods of strain
♦ Very difficult to solder

SO-ELASTIC

I

Iron/Nickel/Chromium/Manganese Alloy Gage Factor ~ 3.6

♦ High sensitivity
♦ High resistance
♦ Well suited for dynamic strain readings (has a good fatigue life)
♦ Does not exhibit temperature compensation
♦ Non-linear response beyond ~5000με

LATINUM BASED ALLOYS

P

Commonly alloyed with Tungsten or Iridium Gage Factor ~ 4.0 to 5.1

♦ High sensitivity
♦ Well suited to high temperature environments (in excess of 230˚C )

EMI-CONDUCTOR GAGES

S

Gage Factor ~ 70 to 135

♦ Very high sensitivity (~50x that of wire)
♦ High resistance
♦ Typically more expensive than wire
♦ Can be made smaller than wire/foil gages for lower cost
♦ More likely to drift with temperature changes
♦ Resistance doesn’t change linearly with strain (making data analysis more difficult)
♦ Typically have lower strain limits than a comparable wire gauge

Application Note

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Considering Backing Material

POLYMIDE

♦ Most common backing material, and therefore low cost
♦ Better suited to static strains rather than dynamic
♦ Capable of large elongations and is very flexible
♦ Not suitable in extreme temperature conditions

POXY

E

♦ Minimizes errors caused by the backing
♦ Brittle and require special skill to install
♦ Maximum elongation is limited

LASS FIBER ENFORCED EPOXY

G

♦ Performs well over widest temperature range (up to 400˚C)
♦ Well suited to dynamic strains and fatigue loading
♦ Maximum elongation is limited

TRIPPABLE BACKING

S

♦ Backing is removed during installation and the adhesive serves as an insulator between

the gage and the mounting surface.

♦ Best for use in extremely high temperature applications
♦ Installation requires special skill

Considering Adhesives

CYANOACRYLATE CEMENT

♦ Very common / Industry standard
♦ Fast bonding ~10min
♦ Gentle clamping required for 1-2 minutes
♦ Does not last for extended periods of time (months)

POXY

E

♦ Exhibits high bonding strength
♦ Should be used when high strains (e.g. to failure) are to be measured
♦ Required a clamping pressure (~5 to 20psi) during cure
♦ Has a long cure time, can be decreased by applying heat (~120˚C)

ERAMIC CEMENT

C

♦ Well suited to extremely high temperature applications

Application Note

INSTALLING A STRAIN GAGE

In order for your strain gage to read properly and reliably it must be installed correctly. This
means first preparing the surface to which you will be bonding the gage later. The procedures
for preparing the surface are simple and easy to follow, yet will result in consistent, strong, and
stable bonds. The procedures outlined below are generalized for most metals. More specific
surface prep instructions are available at:

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Application Note

Preparing the Mounting Surface

CLEAN SURFACE

Use a solvent (such as acetone or alcohol) to remove any grease or oils from the surface to
which the stain gage will be bonded. This is to prevent any contaminants from being driven
into the surface while performing subsequent steps. Clean an area significantly larger than
the gage (4 to 6 inches on all sides) to prevent any contaminants from the surrounding area
from being introduced into the gage area.

BRADE SURFACE

A

Remove any oxidation, paint or coating from the surface finishing the abrading with a 400
grit silicone-carbide paper to ensure a proper texture for adhesion. A cross-hatched abrasion
pattern is preferable. Be careful not to over-abrade the surface resulting in change of either
dimensions or mechanical properties.

ARK LAYOUT LINES

M

Use a clean rule and a hard pencil or pen to mark the desired position of the gage.
Perpendicular lines crossing at the center of the gage area is standard, so that they can be
lined up with reference marks on the gage.

ONDITIONING

C

Scrub the area with a solvent or marketed conditioner with a cotton-tipped applicator until
the tip no longer comes up discolored. Do not allow the conditioner to dry on the surface,
use a gauze sponge to wipe it off in a single slow stroke, then again with a clean sponge in
the opposite direction. This prevents dragging any of the contaminates back into the gage
area.

EUTRALIZING

N

(This step is optional though recommended.) Apply a proper neutralizer (for the material
you are bonding to) with a cotton tipped applicator in order to balance the pH (~7.0) of the
surface to ensure more stable bonding. Again dry the area with same technique described
above (in Conditioning).

After the surface has been prepared, do not let it stand for more than a few minutes before
bonding the gage to it. Have the gage ready and move quickly to the bonding procedure. Be
sure not to touch the surface or the gage with you fingers as the oils will decrease bond
integrity.

Bonding the Strain Gage

PREPARATION

Wash hands with soap and water. Clean the working desk area and all related tools with
solvent or degreasing agent.

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PREPARING GAGE

Carefully open the folder containing the gage. Use a tweezer, not bare hands, to grasp the
gage. Avoid touching the grid. Place on the clean working area with the bonding side down.

Application Note

RANSFERRING GAGE

T

Use a proper length, about 15 cm (6 in), of cellophane tape to pick up the strain gage and
transfer it to the gaging area of the specimen. Align the gage with the layout lines. Press one
end of the tape to the specimen, then smoothly and gently apply the whole tape and gage
into position.

PPLYING CATALYST

A

Lift one end of the tape such that the gage does not contact the gaging area and the
bonding site is exposed. Apply catalyst evenly and gently on the gage.

PPLYING ADHESIVE

A

Apply enough adhesive to provide sufficient coverage under the gage for proper adhesion.
(Determining "sufficient" might require some trial and error iterations). Place the tape and
the gage back to the specimen smoothly and gently. Immediately place thumb over the
gage and apply firm and steady pressure on the gage for at least one minute.

EMOVING TAPE

R

Leave the tape in place at least two more minutes after the thumb was removed. Peel the
tape from the specimen slowly and smoothly from one end to the other end.

**Note: Some adhesives require mixing two compounds vigorously for a sufficient time, usually 5 minutes.
Others require longer curing time up to 24 hours and/or higher temperature, usually by blowing hot air
using a heat gun or placing in an oven. Some applications require higher clamping pressure as high as
350 kPa (50 psi). Please consult with the technical notes from the vendor for the right process parameters.

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Application Note

USING DATA AQUIRED FROM A STRAIN GAGE

When a strain gage is used properly it can provide a lot of information to the user, provided
that the user has a basic understanding of stress-strain relationships. This next section is
intended to provide the reader with that knowledge.

What Does The Data Mean?

As discussed earlier, the quantity that we are actually measuring is a change in voltage. Using
Ohm’s law ( V=I x R) we can directly convert this reading into a change in resistance of the
strain gage. From this, given the gage factor, we get our reading of strain (see page 2). This
reading is the average amount of strain experienced over the length of the gage, in the
direction that the gauge is mounted. In most cases the value of strain that is important to the
user is maximum, or principal strains (ε
principal strains will be along the axis of loading (ε
mounted correctly along the principal axis, these values can be read directly from either two
separate gages or a bi-axial gage (although in the uni-axial tension case mentioned, ε
calculated easily by Poisson’s Ratio.) If the principal axis are unknown, a tri-axial strain rosette
must be used. From the three values of strain read from the rosette we can calculate both
principal strains and their direction (relative to the rosette).

Rectangular Rosette

& ε2) . For example, for a member in tension, the

1

) and perpendicular to the axis (ε2). If

1

can be

2

90

Equi-Angular Rosette

Є2

120

24

Є2

45

0

Principal

0

Mounted Axis

Principal Axis

Mounted

+θ

+θ

Є1

Є1

90

120

120

2

ε

+

()

45ε90

2

2

ε

+

()

45ε90

2

⎞

⎟
⎟

⎠

2

−

240

240

++:=

2

+−:=

9

−

9

ε0ε90+

ε

1

ε

2

θ

ε0ε

ε

ε

θ

+ε

1

ε0ε

+ε

1

2

1

atan

:=

2

2

ε0ε90+

2

ε0ε45−ε

⎛

1

⎜

atan

:=

2

⎜
⎝

+

120

240

3

+

120

240

3

3

ε

−

⋅

⎡

()

120ε240

⎢
⎢

2ε0ε

−ε

⎣

120

ε0ε45−

()

+:=

ε0ε45−

()

−:=

+

ε0ε90−

ε0ε

−ε

()

ε0ε

−ε

()

⎤
⎥

⎥

−

240

⎦

2

−

2

−

ε

()

120ε240

ε

()

120ε240

2

−

3

2

−

3

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Application Note

Representing the Data In Mohr’s Circle

Mohr’s Circle is a common graphical representation for strains and stresses. In the case of
strain we can display the values that we just calculated. Below is an example of this using
values from a rectangular strain gage. In Mohr’s circle, the X-axis is the normal strain axis, and
the Y-axis represents shear strain. The principal strains are where the circle crosses the normal
strain axis, and the average strain is at the centerpoint. One must remember when plotting
the circle that α = 2θ, thus the reason that the principal strains are shown to be 180˚ apart
while in reality we know them to be perpendicular to each other. This can be seen in the
projected axes of the strain gage as well (shown in blue). The measured values of strain are
represented by the projection on the normal strain axis of where each of the gage axes
intersects the circle.

g

max

0

ε

90

45

ε

ε

45

0

+α

ε

2

ε

1

90

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S

Application Note

Stress– Strain Relationships

As stated earlier, strain is directly related to stress based on material properties. This means
that if we know the material properties and measure the strain we can calculate the stress. In
order to relate stress and strain, we must make the assumption that they vary linearly.
However, stress and strain do not always vary linearly with one another. We can plot two
members’ stress-strain curves to demonstrate this fact. The curve in blue represents a strong
yet brittle material (e.g. cast iron), and the curve in red represents a weaker but more elastic
material (e.g. polyethylene). Each curve begins with a linear segment, this is the linearly-elastic
region. The slope of this line corresponds to the material property known as the Modulus of
Elasticity or Young’s Modulus (E). At any point in this region, if the load is removed from the
member, it will return to its original size. The end of this region is marked by the Yield
Strength of the material, beyond which any deformations are permanent and the member
eventually fails.

140

Ultimate Tensile Strength

Yield Strength

Brittle

STRES

Ultimate Tensile Strength

Yield Strength

0

070

Elastic

STRAIN

These curves are commonly generated by a testing machine (e.g. Instron) that measures load
while straining a test piece. The exact shape of the curve will vary slightly due to
inhomogenuities in the structure of the material, the speed at which it is loaded, etc. However,
the slope of the line (E) remains a constant for a given material. In order to convert strains
measured from gages we make the assumption that the material is not being stressed beyond
its linearly elastic region.

Stress (σ) can be defined in two ways, as the force exerted on a member divided by its cross­sectional area, or by the strain multiplied by the material’s Modulus of Elasticity.

F

σ

or σ Eε⋅

A

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Application Note

As a strain gage is limited to measuring strain in the plane in which it is mounted we will only
cover the two cases of uni-axial and bi-axial stresses. Formulas are given to convert the
principal strains calculated earlier into the principle stresses. The state of stress is generally
most important because it is what ultimately determines how and when the member will fail.
Yield strength, ultimate strength and fatigue life are all based on stress.

UNI-AXIAL STRESS

2

3

A single load is applied to axis 1 yielding
a single stress. The materials’ maximum
principal strain is in the direction of axis

1. Strain is experienced in the other two
axes due solely to Poisson’s Ratio.

σ1E ε1⋅

σ2σ30

1

BI-AXIAL STRESS

2

3

Two loads are applied to different
axes. They will yield two principal
strains perpendicular to each other
and two principal stresses corre­sponding to the strains (axes 1 & 2).
Strain is experienced in the third axis
due solely to Poisson’s Ratio.

σ

E

ε1νε2⋅+

⋅:=

1

1 ν

()

2

−

1

s

ν−σ1⋅

ε2ε

3

E

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σ

σ30:=

ε

3

E

ε2νε1⋅+

⋅:=

2

1 ν

1 ν−

()

2

−

ν−

ε1ε2+

⋅:=

()

Application Note

The Pressure a

Fundamentals of Machine Component Design, 3rd Edition, Robert C. Juvinall Kurt M. Marshek

Mechanics of Materials, Fourth Edition, R.C. Hibbeler

nd Strain Handbook, Vol.29, Omega Engineering Inc.

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