Strain Guage Technique

8/8/2019 Strain Guage Technique

1/10

MMEE22111144 -- 11 SSttrraaiinn

GGaauuggee TTeecchhnniiqquuee

by

Lin Shaodun

Student ID: A0066078X

Sub Group: Lab 2B

Date: 19th

Mar 2010


2/10

1

TABLE OF CONTENTS

OBJECTIVES 1

INTRODUCTION 1

EXPERIMENTAL PROCEDURES 2

SAMPLE CALCULATIONS 3

RESULTS (TABLES & GRAPHS) 7

DISCUSSION 11

CONCLUSION 15


3/10

2

OBJECTIVES

The objectives of this experiment are:

To practice using strain gauge rosette and strain meter to measure strain ofaluminum cantilever beam under a point load at its free end.

To study the static behavior of aluminum cantilever beam subjects to bendingmoment.

To have a better understanding on two dimensional strain transformationequations.

INTRODUCTION

DESCRIPTION OF EQUIPMENT.

(1)Strain Measurement Equipment.A commonly used instrument for strain measurement is a strain meter and its

circuit is based on the principle of a Wheatstone bridge. For most applications

strain gauges are connected using the quarter bridge configuration. This bridge

arrangement contains one active strain gauge in the circuit as shown in Fig. 1.

The meter readings record the strain of one active gauge.

Strain gauges can also be connected using the half bridge configuration. This

bridge arrangement contains two active gauges in the circuit as shown in Fig. 2.

The meter readings in this case record the total strains of two active gauges. The

half bridge configuration is often used in the measurement of bending strain.

(2)Strain Indicator (Fig 3) and Balancing Unit (Fig 4)

P-

P+

R R

RActiveGauge

M

P-

P+

R R

ActiveGauge

M

ActiveGauge

Fig 1: Quarter Bridge Configuration Fig 2: Half Bridge Configuration

Fig 3: Strain Indicator Fig 4: Balancing Unit (use Channel 10 only)


4/10

3

(3)Cantilever Test Rig (Fig 5) and Strain Gauge Locations (Fig 6)

EXPERIMENTAL PROCEDURES

1. The given average dimensions of the Aluminum beam as follow: Width (b) =25.60mm, Thickness (t) = 6.06mm and Length (L) = 0.300m.

2. Zero the dial indicator before measurement of end deflection YL. Connect thestrain gauges which measuring the surface strains at locations A (Fig 7) to SB-10Balancing Unit channel 10 using quarter bridge configuration. Adjust the channel

10 VR until the Strain indicator reading is zero.

Cantilever Test Rig

Dial Indicator (0.01mm)

Aluminum Test Specimen

Weights (0.25 Kg x 6)

Strain Gauge A

Strain Gauge Rosette

Fig 5: Cantilever Test Rig

Fig 7: Strain Gauge Locations

Fig 6: Strain Gauge Locations


5/10

4

3. Load the weight onto the hanger at the end of aluminum beam with 0.25Kgincrement, record the deflection YL and the strain readings A at each stage, untilthe total weight reaches 1.50Kg.

4. Unload the weight at 0.25Kg decrement, record the corresponding beamdeflection YL and the strain gauge reading

A during unloading.

5. Repeat above steps 3~5 for strain gauge e, f, andg (Fig 7), record the straingauge reading for each loading and unloading stages.

6. Connect the strain gauges measuring the surface axial strain at locations A and B(Fig 7)to the strain meter using half-bridge configuration. Load and unload the

beam and at 0.25 increment following similar steps as above described and

record the strain reading AB.

SAMPLE CALCULATIONS

A) CALCULATION OF THEORETICAL STRAIN AT POINT A, A

|

B) CALCULATION OF THEORETICAL DEFLECTION OF BEAM YL

|

C) CALCULATION OF PRINCIPAL STRAIN 1 AND 2

( )

( )

[ ]

( )

( )

[

]


6/10

5

RESULTS (TABLES & GRAPHS)

A. TABLES

P inKg

YL (mm) TheoreticalStrainLoading Unloading Average Loading Unloading Average

0.25 0.68 0.70 0.69 33 33 33 33.5

0.50 1.37 1.44 1.41 66 68 67.5 67.1

0.75 2.10 2.18 2.14 99 102 100.5 100.6

1.00 2.81 2.86 2.84 135 135 135 134.2

1.25 3.53 3.57 3.55 169 170 169.5 167.7

1.50 4.27 4.27 202 202 201.2

P inKg

Loading Unloading Average Loading Unloading Average Loading Unloading Average

0.25 48 48 48 19 18 18.5 -13 -14 -13.5

0.50 95 99 97 38 37 37.5 -30 -31 -30.5

0.75 147 149 148 56 56 56 -46 -47 -46.5

1.00 195 199 197 74 75 74.5 -61 -63 -62

1.25 245 247 246 92 92 92 -77 -78 -77.5

1.50 295 295 113 113 -93 -93

P inKg

Loading Unloading Average0.25 64 68 66 48.0

0.50 132 138 135 97.1

0.75 200 206 203 148.1

1.00 266 270 268 197.2

1.25 336 339 337 246.2

1.50 402 402 295.4


7/10

6

B. GRAPHSi. P against YL

ii. P against A

iii. P against AB


8/10

7

iv. P against e

v. P against 1

b) Fit the best straight line through the above experimental results and obtain theslope for each line.

i. Slope for the P against YL = 0.3497 Kg/mmii. Slope for the P against A = 0.0074 Kg/Strain

iii. Slope for the P against AB = 0.0037 Kg/Strainiv. Slope for the P against e = 0.0051 Kg/Strainv. Slope for the P against 1= 0.0050 Kg/Strain


9/10

8

c) From the graph of a(i) and Eq. (1), compute the Young's modulus of the material.

DISCUSSION

d) Obtain the ratio of the slopes of a(ii) and a(iii) for the beam. Comment on thevalues obtained.

From the above graph:

Slope for the P againstA = 0.0074 Kg/Strain

Slope for the P againstAB = 0.0037 Kg/Strain

The ratio of both graphs is 1:2. This shows that the half bridge configuration

output is twice of the quarter bridge configuration. This is obvious as in a

quarter-bridge configuration, transducer A located at the top of the beam is

measuring the tension strain of the beam, while in a half-bridge

configuration, the strain output is the sum ofA andB hence the strain shows

in the meter is twice ofA.

e)

Plot the theoretical P vs.A on the same graph as a(ii) and comment on the

results.


10/10

9

From the above graph we can see the two trend lines are almost the same.

This shows that the experimental data are very close to theoretical data. The

slight variations are due to experimental errors like:

Instable strain meter The weight of the hanger at the end of beam is not considered. Strain gauge mounting position tolerance, etc. Also, when calculating the theoretical values, we assume the Youngs

Modulus is 70Gpa, this might not be the exact property of the test specimen.

f) Compare the slopes of a(iv) and a(v) and comment on the results.From the above graph:

Slope for the P againste = 0.0051 Kg/Strain

Slope for the P against1 = 0.0050 Kg/Strain

Slope of Graph (iv) and Graph (v) are almost the same. This means the

maximum principle strain value and direction is the same as the normal

strain at 0 direction when the beam is subjected pure bending stress. The

slight different might due to the strain gauge rosette was not mounted at

exact0 direction or other measurement error.

g) Have you used the values ofA, e , f and g for unloading in your calculations?Why?

Yes, we take values ofA, e , f andg during unloading of each load P. It is

important to make the experiment result more accurate as we can double

confirm the material is loaded within elastic limit, when the material is

applied load under elastic limit, the stress-strain curve will be linear, which

means the loading curve should be the same as unloading curve in theory. By

taking the average values of the strain of both loading and unloading, we can

minimize the measurement errors as well.

CONCLUSION

All the objectives of this experiment is achieved, the experimental data is very close

to theoretical data. I have familiarized the use of the strain meter and the quarter and

half bridge configurations. I also have better understanding of behavior of cantilever

beam subjects to pure bending stress.

Documents

Strain Guage Technique