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MECH 220 MECHANICAL ENGINEERING LABORATORY I

Experiment D

Strain Measurement

OBJECTIVE

The objective of the experiment is to learn the fundamentals of measuring with strain

gages and also strain gage types and their application techniques. Calculation of the

mechanical deformations under tension, bending and torsion will be conducted. Also, the

relation between mechanical strain and electrical resistance in a strain gage will be examined.

THEORY

Stress analysis involves a determination of the stress distribution in materials of various shapes and under different loading conditions. Experimental stress analysis is performed by measuring the deformation of the material under load and inferring from this measurement the local stress occurs.

The electrical resistance strain gage is the most widely used device for strain measurement. Strain gages permit simple and reliable determination of stress and strain distribution at real components under load. The strain gage technique is thus an indispensable part of an experimental setup. Wide spread use of these devices is also consist of scales, dynamometers, pressure sensors and torque meter.

Strain gages operate on the principle that the electrical resistance of a conductor changes when it is subjected to mechanical deformation. This deformation is indicated through a measurement of the change in resistance of the element. Thus, a strain gage cannot measure stress directly; it senses the deformations on the surface of structural parts. Since stresses are related to deformations through Hookes law, results of a strain measurement can be used to predict the stresses in a specimen.

The strain gage should be mounted on the surface of the specimen of which the stress shall be determined. Normally, special bonding agents or glues are used for this purpose.

The electrical resistance strain gage in the basic form known today was first used in 1938. The discovery of the principle was made in 1856 by Lord Kelvin. He also employed the Wheatstone bridge technique to measure the resistance change.

The Wheatstone bridge circuit can be used for both static and dynamic strain gage applications. General form of the bridge is shown in Figure 1.

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Figure 1. Wheatstone bridge circuit.

There are four cases where different configurations of Wheatstone bridge apply which

are Quarter bridge (one active gage), Half bridge (one active and one dummy gage), Half

bridge (two active gages) and full bridge (four active gages). In this experiment, full bridge

circuit with four active gages will be used. The configuration of the gages differs for tension,

bending and torque setup.

The ratio of change in resistance to strain is designated as which is also known as

Strain gage constant.

= /0

Strain gages with a large factor are more sensitive than those with a small factor.

The gage factor of a gage should be given by the manufacturer.

EXPERIMENTATION

Test Set-up

The experimental setup is composed of three units for three sets of experiments.

Using strain gages, which are mounted, configured and ready to use for all units,

measurement of

a) tension or compression which is the simplest form of loading in the first unit,

b) bending in the second unit,

c) torsion in the third unit.

Figure 2 shows a picture of the experimental setup.

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Figure 2. Picture of the experimental setup.

Table 1 shows some important parameters of the test set-up that are needed in the analysis.

Table 1. Some parameters about the test set-up.

Parameter Value

Gage factor 2.05 Tension Bar Cross section 2 10 2 Strain gage element Full bridge Material Steel Cr Ni 18.8 Modulus of elasticity, 191,000 /2 Poissons ratio, 0.305 Bending Beam Length 385 Cross section 4.74 19.75 2 Section modulus 74.26 3 Modulus of elasticity 210,000 /2 Torsion Bar Length 500 Diameter 10 Section modulus 196.3 3 Shear modulus 80,000 /2

Tensile Experiment

Tensile stress is calculated from tensile force (normal force) and cross sectional

area as,

=

According to Hookes law stress and strain are linked to one another by way of the

modulus of elasticity .

=

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For experimental determination of the tensile stress, two strain gages each are fitted

to the front and back of the specimen; one strain gage is attached in longitudinal, the other

in transverse direction as shown in Figure 3.

Figure 3. Configuration of strain gages in tensile experiment.

The output signal of the measuring bridge is referenced to the feed voltage . The

sensitivity of the strain gage enables the strain to be calculated for the full bridge as

follows,

=1

2(1 + )

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Procedure

Follow the instructors step by step.

1. Fit the tension bar in the frame as shown in Figure 4 by using the holder with hook

2. Connect and switch on the measurement instrument.

3. Use offset adjuster to balance display.

4. Load bar with the set of weights supplied during the experiment.

5. Note down all the readings from the display to the data sheet.

Figure 4. Schematic of the tensile experiment setup.

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Because of weak stresses, readings are very small. Therefore, zero balancing is to be

performed with extreme care.

Bending Experiment

The stress at the surface of the bending beam can be calculated from the bending

moment and the section modulus as,

=

The section modulus for the rectangular cross section of width and height is given

as,

= 2

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For experimental determination of the bending stress, the bending beam is provided

with two strain gages each on the compression and tension sides as shown in Figure 5.

Figure 5. Configuration of strain gages in bending experiment.

The sensitivity of the strain gage enables the strain to be calculated for the full

bridge as follows,

=1

According to Hookes law, the stress being sought is obtained with the modulus of

elasticity ,

= Procedure

Follow the instructors step by step. 1. Fit the bending bar in the frame as shown in Figure 6 by using the holder with two

pins.

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2. Connect and switch on the measurement instrument.

3. Measure the distance of the slider to the strain gages.

4. Use offset adjuster to balance display.

5. Load beam with the set of weights supplied during the experiment.

6. Note down all the readings from the display to the data sheet.

Figure 6. Schematic of the bending experiment setup.

Torsion Experiment

Strain gages can also be used in measuring torsional moments. In this application the

torque in the shaft will be calculated from the shear stress measured. For experimental

determination of the torsional stress, the torsion bar is provided with four strain gages at an

angle of 45o. The strain gages are thus located in the direction of the principal normal stresses

and hence the maximum strain as shown in Figure 7.

Figure 7. Configuration of strain gages in torsion experiment.

The strain can be calculated as follows,

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=1

Whereas pure shear stress the relationship between strain and shear is,

= 2

According to Hooks law, the shear stress being sought is obtained with the shear

modulus as,

= = 2

The relationship between shear stress at the surface of the bar and torsional moment

is given as,

=

where is the section modulus of torsion bar for the circular cross section,

= 3

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The torsional moment can be calculated from,

= 2

Procedure Follow the instructors step by step.

1. Fit the torsion bar in the frame as shown in Figure 8. In doing so, place clamping end

on upper pin of holder with two pins. Support loose end of the bar with other holder.

Use the water gage to make sure the bar is horizontally aligned.

2. Connect and switch on the measurement instrument.

3. Use offset adjuster to balance display.

4. Suspend set of weights supplied during the experiment from lever arm and generate

torsional moment.

5. Note down all the readings from the display to the data sheet.

Figure 8. Schematic of the torsion experiment setup.

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Analysis For the first unit (tensile experiment), calculate the stress from measured strain for all

readings and compare these values with the theoretical correspondence. Find the percentage deviation between these values.

For the second unit (bending experiment), calculate the stress for all readings and compare these values with the theoretical correspondence. Find the percentage deviation between these values.

For the third unit (torsion experiment), calculate the stress from measured strain all readings and compare this value with the theoretical correspondence. Find the percentage deviation between these values.

Plot load versus mV/V readings for all experiment units and check if Hookes law is satisfied or not and also state weather the deformation is elastic or plastic.

CAUTION!

The experiment will be conducted in the Heat Transfer Laboratory in the Lab Building.

You will have only 40 minutes to complete the experiment.

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Name: Group No: Date:

MECH 220 MECHANICAL ENGINEERING LABORATORY I EXPERIMENT D

STRAIN MEASUREMENT Data Sheet

Table 2. Data obtained from tensile experiment.

Tensile Bending Torsion

Load Reading Load Reading Load Reading

1

2

3

4

5

6

7

8

9

10

11

12

13

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