report on mech measurement strain gage

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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. 𝛿= 𝑃𝐿3 3𝐸𝐼 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 The Resistance Strain Gauge MEMO Date: 12/3/2018 To: From: Subject: Strain Gage Summary 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. Page 1 of 15 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 Page 2 of 15 The Resistance Strain Gauge Table of Contents Nomenclature ........................................................................................................................................ 2 List of tables.......................................................................................................................................... 3 List of figures ........................................................................................................................................ 3 Introduction ........................................................................................................................................... 5 Experimental Setup ............................................................................................................................... 6 Results and calculations ...................................................................................................................... 10 Results ................................................................................................................................................. 10 Calculations......................................................................................................................................... 12 Conclusion and recommendation ........................................................................................................ 14 References ........................................................................................................................................... 15 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 Page 3 of 15 The Resistance Strain Gauge Figure 6: A strain indicator and recorder. ............................................................................................. 9 Figure 7: A graph of Voltage (mV) against deflection (inch). ........................................................... 11 Figure 8: A graph of stress measurement against Voltage (calibration curve). .................................. 12 Page 4 of 15 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. Figure 1: Metallic strain gauge Page 5 of 15 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 2. The Moment and shear diagram Page 6 of 15 The Resistance Strain Gauge Figure 3: 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. Figure 4: 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 Page 7 of 15 The Resistance Strain Gauge 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 5: A diagrams of a resistance strain gauge Page 8 of 15 The Resistance Strain Gauge Figure 6: A strain indicator and recorder. Equations Equation 1 𝑃𝐿3 𝛿= 3𝐸1 This equation expresses the stress and can be used to calculate the modulus of elasticity. 𝐸= 𝑃𝐿3 3𝛿𝐼 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: 𝜎 = 𝐸ℇ = Equation 3 Page 9 of 15 𝑀. 𝐶 𝐼 The Resistance Strain Gauge From the equation of stress (equation 2), modulus of elasticity can be expressed in terms of stress and strain as: 𝐸= 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 10 of 15 𝜎 𝜀 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 7: 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. Page 11 of 15 The Resistance Strain Gauge Callibration Curve 25 y = 412.31x3 - 23.401x2 + 0.9169x - 0.017 R² = 1 20 Strain, σ 15 10 5 0 0 -5 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 Voltage (mV) Figure 8: A graph of stress measurement against Voltage (calibration curve). The curve has a positive gradient with an equation412.31𝑥 3 − 23.401𝑥 2 + 0.9169𝑥 − 0.017. This is the equation giving the best fit line for the data points Calculations 𝛿 𝜀=𝐸 Page 12 of 15 The Resistance Strain Gauge 𝛿= 𝑀𝑐 𝐼 𝑉=𝑃 𝑀 = ∫ 𝑉𝑑𝑥 = ∫ 𝑝𝑑𝑥 = 𝑃𝑋 + 𝐶= (−𝑃𝐿) + 𝐷𝑋 𝑝.𝐿 𝐿 = 𝑃, 𝑃𝑋 − 𝑃𝐿 = (𝑉) 𝛿= 1 1 1 𝑃𝑥 2 1 ∫ 𝑀𝑑𝑥 = ∫ 𝑃𝑋 − 𝑃𝐿𝑑𝑋 = ( − 𝑃𝐿𝑥) + 𝑐 = (𝑃𝑥 2 − 𝑃𝐿𝑥) 𝐸𝐼 𝐸𝐼 𝐸𝐼 2 𝐸𝐼 𝛿= 1 ∫(𝑃𝑥 2 − 𝑝𝑙𝑥)𝑑𝑥 𝐸𝐼 𝛿= 1 𝑃𝑋 3 𝑃𝐿𝑉 2 ( − ) 𝐸𝐼 6 6 𝛿 = 𝑃𝑋 2 (3𝐿 − 𝑋) 𝛿𝑚𝑎𝑥 = 𝐼= 𝑃𝐿3 3𝐸𝐼 𝑏ℎ3 12 The values of I is 2.7𝑥10−7 𝑚−1, E is 210𝑥106 𝑃𝑎, P is 7700𝐾𝑔/𝑚3 , Lis the values of the measured deflection. Calculation of modulus of elasticity The applied force is 1.44N 𝐸= 𝐸= 𝛿= 𝐸= 𝑀𝑐 𝐼 𝛿 𝑃𝐿3 = 𝜀 3𝛿𝐼 = 2.078𝑥10−14N/m2 and 𝜀 = 9.9𝑥10−26 2.078𝑋10−17 9.9𝑋10−26 Page 13 of 15 = 2.10^108 Pa 𝑃𝐿3 3𝛿𝐼 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 14 of 15 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 15 of 15
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The Resistance Strain Gauge

MEMORANDUM
Date: 09/18/2019
To:
From:
Subject: Strain Gage
Summary
This lab will perform the calculation of value of strain from the deflection obtained during
the experiment. This experiment utilized the metallic strain gauge and a strain indicator together
with a beam. The strain gauges were assembled on a certain location. The digital was associated
with the switcher with the strain measured on the specimen. The voltage values were recorded and it
would be used to calculate the strain. Evaluating the graphs outputs if the experiment is accurately
done and providing future recommendation for better accuracy of the experiment. The gauge factor,
is the change in resistance for a given value of strain (ε), as gauge factor is assumed to be equal to
the experiment.

Page 1 of 13

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

Page 2 of 13

The Resistance Strain Gauge
Table of Contents
Nomenclature ........................................................................................................................................ 2
List of tables.......................................................................................................................................... 3
List of figures ........................................................................................................................................ 3
Introduction ........................................................................................................................................... 4
Experimental Setup ............................................................................................................................... 5
Results and calculations ........................................................................................................................ 8
Results .............................................................................................................................................. 8
Calculations.................................................................................................................................... 10
Conclusion and recommendation .............................


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