Arizona Western College Mechanical Measurement Strain Gage Lab Report helloi will upload the lab requirement along with an already written lab you can use but make sure you change every sentence completely with the same meaning also pics that weren’t taking by camera you can find them online so just change them. i think since you have an example this is very clear and i’d prefer to use but create a new one completely. The Resistance Strain Gauge

Nomenclature

Symbols

Name

σ

stress

p

Load

A

area

ε

strain

δ

defledction

E

Young Modulus of Elasticity

L

Original length

m

Suspended mass

g

Accelaration due to gravity

d

Load to gauge distabce

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The Resistance Strain Gauge

Table of Contents

Nomenclature ………………………………………………………………………………………………………………………. 1

List of tables………………………………………………………………………………………………………………………… 2

List of figures ………………………………………………………………………………………………………………………. 2

Introduction …………………………………………………………………………………………………………………………. 5

Experimental Setup ………………………………………………………………………………………………………………. 6

Results and calculations ………………………………………………………………………………………………………… 8

Results ………………………………………………………………………………………………………………………………. 10

Calculations…………………………………………………………………………………………………………………………. 9

Conclusion and recommendation ………………………………………………………………………………………….. 11

References …………………………………………………………………………………………………………………………. 12

List of tables

Table 1: Raw data of strain, voltage and deflection…………………………………………………………………. 10

List of figures

Figure 1: Metallic strain gauge ………………………………………………………………………………………………. 5

Figure 2. The Moment and shear diagram ……………………………………………………………………………….. 6

Figure 3: A Wheat stone bridge circuit ……………………………………………………………………………………. 7

Figure 4: The unstressed dummy gage for temperature compensation (Vogel, 1990). …………………… 7

Figure 5: A diagrams of a resistance strain gauge …………………………………………………………………….. 8

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The Resistance Strain Gauge

Figure 6: A strain indicator and recorder. ………………………………………………………………………………… 9

Figure 7: A graph of Voltage (mV) against deflection (inch). ……………………………………………………. 9

Figure 8: A graph of stress measurement against Voltage (calibration curve). ……………………………… 9

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The Resistance Strain Gauge

Introduction

A strain gauge is a device in which the electrical resistance varies in proportion to the amount of

strain in the device. It is a common method used to measure the amount of strain in a device. In this

lab, we are using the bonded metallic strain gauge to measure the strain. It is made of a thin wire or a

metallic foil arranged in a grid pattern that maximizes the amount of metallic wire or a foil subjected

to strain in a parallel direction (da Silva, 2002). The cross-sectional area of the grid is minimized to

reduce the effect of shear strain in the parallel direction. The grid is bonded to the backing called the

carrier attached to the test specimen. The strain that is experienced by the specimen is then

transferred to the strain gauge which respond with a linear change in electrical resistance. The

voltage across the resistance is then measured and recorded against the strain in a results table. The

figure below is a metallic strain gauge showing its parts.

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The Resistance Strain Gauge

Experimental Setup

The experiment was performed using the metallic strain gauge and a strain indicator and a beam.

The strain gauges were assembled on a specimen. The active strain gage was placed on the bottom of

the beam at mid span where the bending stress is at maximum. The digital gage was connected with

the switcher with the strain gauge on the specimen. The digital strain indicator was calibrated when

no load was on the specimen. The values of voltage was then recorded for each strain gage

measurements. An equation was derived from the experimental setup to be able to calculate the

value of strain from the deflection obtained from the experiment.

Figure 1. The Moment and shear diagram

Figure 2: A Wheat stone bridge circuit

The purpose of this bridge circuit was to measure electric resistance. It does so balancing the two

legs of the circuit where one leg is of an unknown component. The major benefit associated with this

circuit is the ability to give accurate measurement. The known resistance is adjusted till the bridge

balances insinuating that there is no current that flows across the galvanometer.

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The Resistance Strain Gauge

Figure 3: The unstressed dummy gage for temperature compensation (Vogel, 1990).

A strain gauge makes use of the physical properties of the electrical conductance and their

dependence on the geometry of conductor. When the electrical conductor is stretched such that the

elasticity limits are not exceeded, it becomes longer and narrower which makes the electrical

resistance to increase from end to end (Vaziri, 1992). Additionally, when it is compressed, it

shortens and broadens thereby decreasing the electrical resistance.

Figure 4: A diagrams of a resistance strain gauge

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The Resistance Strain Gauge

Figure 5: A strain indicator and recorder.

Equations

Equation 1

3

=

3 1

This equation expresses the stress and can be used to calculate the modulus of elasticity.

=

3

3

Equation 2

Since the beam is basically a bending beam. The amount of stress that is exerted on both the top and

bottom areas of the beam are expressed as:

= ℇ =

Equation 3

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.

The Resistance Strain Gauge

From the equation of stress (equation 2), modulus of elasticity can be expressed in terms of stress

and strain as:

=

Results and calculations

Results

Table 1: Raw data of strain, voltage and deflection

δ(in)

V(mV) Strain, σ

0

0.016

0

0.1

0.064 0.045267

0.2

0.112

0.36214

0.3

0.16 1.222222

0.4

0.208 2.897119

0.5

0.257 5.658436

0.6

0.305 9.777778

0.7

0.353 15.52675

0.8

0.401 23.17695

Page 8 of 12

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The Resistance Strain Gauge

y = 0.4817x + 0.0158

R² = 1

0.45

0.4

0.35

Voltage (mV)

0.3

0.25

0.2

0.15

0.1

0.05

0

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

deflection, δ(in)

Figure 6: A graph of Voltage (mV) against deflection (inch).

The graph is constructed using the values of measured deflection and voltage obtained from the

strain gauge. There is linear relationship between the deflection and the amount of voltage observed

in the voltmeter. The graph has a positive gradient.

Figure 7: A graph of stress measurement against Voltage (calibration curve).

The curve has a positive gradient with an equation412.31 3 − 23.401 2 + 0.9169 − 0.017. This

is the equation giving the best fit line for the data points

Calculations

=

=

Page 9 of 12

The Resistance Strain Gauge

=

= ∫ = ∫ = + = (− ) +

.

= , − = ( )

=

1

1

1 2

1

∫ = ∫ − = (

− ) + = ( 2 − )

2

=

1

∫( 2 − )

=

1 3 2

(

−

)

6

6

= 2 (3 − )

=

3

3

ℎ3

=

12

The values of I is 2.7 10−7 −1, E is 210 106 , P is 7700 / 3 , Lis the values of the measured

deflection.

Calculation of modulus of elasticity

The applied force is 1.44N

=

3

3

3

= =

3

=

=

= 2.078 10−14N/m2 and = 9.9 10−26

2.078 10−17

9.9 10−26

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= 2.10^108 Pa

The Resistance Strain Gauge

Conclusion and recommendation

A calibration curve is obtained by plotting the value of voltage and the calculated strain. A graph is

best fit giving a polynomial equation of the third order as shown in figure 1. The modulus of

elasticity obtained for the experiment is 2.10^108 Pa. The modulus of elasticity is calculated using

the values of stress and strain. The experiment was therefore successful as the intended results for

the experiment were achieved. For this lab, the procedures to setup the strain gage measurements are

not provided and this is a major recommendations for future improvements. The exact process of

performing the lab was not therefore ascertained.

Page 11 of 12

The Resistance Strain Gauge

References

Da Silva, J. G. (2002). A strain gauge tactile sensor for finger-mounted applications. IEEE

Transactions on Instrumentation and measurement, 51(1) . 18-22.

Vaziri, M. &. (1992). Etched fibers as strain gauges. Journal of lightwave technology,, 836-841.

Vogel, J. H. (1990). The automated measurement of strains from three-dimensional deformed

surfaces. JOM, 8-13.

Page 12 of 12

MECH 4400

Strain Gage Lab

Due: 10/31/18

This report will be a technical memo style lab report. The first page of the report will be

a memo that includes the date, who the report is to and from and also the subject. In paragraph

form include an experimental setup, procedure, and results. Include figures, graphs, and tables

after the narrative portion of the report. The raw data includes measured deflection and the

voltage output for each. See table 1 for measured data. The calculated result will be strain at the

strain gage location. Combine Equation 1, 2, 3 and information from the shear and moment

diagrams to formulate an equation that can be used to calculate strain based on the measured

deflection. The voltage and strain values can then be used to generate a calibration curve and

equation in excel. Finally use a known applied force to calculate the modulus of elasticity of the

test bar material.

=

3

3

Equation 1

Equation 2

Equation 3

δ (in)

V (mV)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.016

0.064

0.112

0.16

0.208

0.257

0.305

0.353

0.401

Table 1: Strain Gage Lab Measured Data

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