measurement project report.pdf

1

UNIVERSITI TENAGA NASIONAL

COLLEGE OF ENGINEERING

DEPARTMENT OF MECHANICAL ENGINEERING

MESB 333 ENGINEERING MEASUREMENT & LAB

FINAL REPORT

DEFLECTION OF A BEAM

GROUP NUMBER : 1

SECTION : 4A

LECTURER : MS TAN EE SANN

GROUP MEMBER :

1. THARASYAN A/L JANARTHANAN (ME 091905)

2. DARVINDER SINGH (ME 092093)

3. LEE ENG LOY (ME 091813)

4. BAVANI YUNNASOGARAM (ME 091824)

5. NG SEK KENG (ME 091910)

6. CHIA YONG NAN (ME 090840)

2

TABLE OF CONTENT

Index Title Page

1 Abstract

3

2 Objective

4

3 Theory

4

4 Procedure

7

5 Literature Review

8

6 Data and Observation

16

7 Result and Analysis

18

8 Discussion

29

9 Conclusion

32

10 Reference

32

11 Appendix

33

3

ABSTRACT

The main objective of this experiment has been achieved. The main of objective is to

measure the deflection of different materials with certain load applied on it. The deflection of

each material depends on its elasticity. Based on the tabulated data, it is known that wood draws

the highest deflection compared to other materials such as brass, steel and aluminum. One of the

reasons that other materials are said to be stronger is due to the modulus of elasticity of such

material. Modulus of elasticity was calculated and shows that it is 19200N/mm. There were

some errors occurred while conducting the experiment. Due to the error, the percentage error

calculated is more than 50%. Based on the error, it can be concluded that the instruments used

like dial gauge which has high sensitivity may have cause the readings to differ from the

theoretical values of each materials. Assumption is being made for the uncertainty for force and

deflection because the dial gauge instrument could not give 100% accuracy where the readings

does not start at 0mm. Moreover, the weight is not being placed exactly at the center of the beam

due to position of measuring device. The average reading was being taken to calculate the

uncertainty of each material.

4

Objectives

1. To investigate the relationship between load and deflection of a beam placed on two bear

affected by a concentrated load at the center.

2. To determine the modulus of elasticity of the materials.

Theory

The stress-strain behavior of brittle materials (e.g. ceramic, low toughness composite

material) is not usually ascertained by tensile tests as outline in this project. A more suitable

transverse bending test is most frequently employed, in which a rod specimen either a circular

or rectangular cross section is bent until fracture using a three- or four-point loading technique.

The assessments are conducted according to ASTM Standard C 1161, Standard Test Method

for Flexural Strength of Advanced Ceramics at Ambient Temperature.

5

Simply supported beam with central point load

For this arrangement, it can be shown that the deflection under the load

i.e. maximum deflection

EI

Wl

48

3

Where 12

3bdI

Beam compliance 3

3

4Ebd

l

W

Determination of coefficient of elasticity

6

Calculations:

Deflection formula for the load given above:

I

FLE

EI

FL

4848

33

A determination of the flexural stress yields:

4

1

LFFM

W

Mb

b

bb

Where:

= Deflection (mm.) E = Coefficient of Elasticity

L = Span(mm.) I = Inertia Factor

Mb = Moment of Flexure (Nmm) F1 = = Load occasioned by weight of load device

=2.5N

Wb = Resistance to Flexure (mm3) F = Load occasioned by additional weight (N)

b = Flexural Stress (N/mm2)

7

Set of Apparatus

i. Twist and Bend Test Machine MT 3005.

ii. 4 types of materials, brass, copper, aluminium, and wood.

iii. Dial Gauge

Procedure

i. The apparatus is set as shown in the diagram.

ii. Load is placed on the center of the beam.

iii. The dial gauge is then placed on the top of the hook that holds the load.

iv. The load is added in increasing order from 5N, 10N, 15N and 25N.

v. The readings are taken from the deflection of the dial gauge, and tabulated.

vi. The different types of materials are tested on the bending machine (wood, aluminum,

brass and copper.

8

Literature Review

2.1 Apparatus

The experiment was conducted on an apparatus that is simply designed to support at two separate

ends to enable load to be applied at the centre of the placed material to read the deflection of the

material for analysis.

2.1.1 Twist and Test Machine MT 3005

Realizing that the planned apparatus prototype in progress report 1 has the same general

concept/idea as the one in the Materials Laboratory in UNITEN, we have decided to use the

readily available instead.

MT 3005 Twist and Bend Testing Machine

9

2.1.2 MT 3005 Utilization

The MT 3005 is a very capable and versatile apparatus that can cater to several specific needs. It

combines twist and bending capabilities and can be used in laboratory exercises in conjunction

with theoretical work on twist and bending.

2.1.3 MT 3005 Specifications

Equipment Quantity

Twist and Bending Machine 1

Loading devices (0.25 Kg) 2

1 Kg weights 2

0.5 Kg weights 4

Dial Gauge 1

Rectangular cross-section steel test piece 7

Rectangular cross-section wood test piece 1

Diameter 8 mm, of resp. steel, aluminium and brass 3

End fixtures 2

Laboratory manual 1

10

2.1.4 Bending and Modulus of Elasticity

For this experiment, bending is prioritized. Through bending, the modulus of elasticity of

different materials is able to be determined. The test piece is supported at either end and load (in

a form of weights) is applied in the middle between the supports.

Example of calculation of modulus of elasticity

11

2.2 Materials

A set of materials were chosen as the test specimen for this experiment. Each of which

has 99% similarity in terms of dimensions of 375 mm x 31 mm x 6.3 mm. The following

materials were tested.

Material types: Aluminium, wood, brass & copper (top to bottom)

2.2.1 Wood

Wood is a hard, fibrous tissue found in many trees. It has been used for hundreds of

thousands of years for both fuel and as a construction material. It is an organic material, a

natural composite of cellulose fibers (which are strong in tension) embedded in

a matrix of lignin which resists compression.

The classification of wood has historically always been either hard wood; any leaf

bearing tree, and soft wood; any cone bearing tree. These terms can be confusing since some leaf

bearing trees can have very soft wood and some coniferous trees can have very hard woods. To

make this easier, below you will find a list of different tree types, classification and then

individual wood characteristics.

12

2.2.1.1 Wood Utilization

Pound for pound, wood is stronger than steel. Unlike steel, it is also resilient. This

combination of strength and resiliency gives wood the ability to absorb the shock of heavy loads

providing a greater margin of safety than many other materials.

Wood and wood-based products are the most important of all man's resources for three

main reasons. First, wood is universal. It is a raw material that can satisfy almost every

requirement or existence. It provides food for man and animals. It is one of the world's most

important sources of textile fibers. Wood is capable of producing motor fuels and lubricants. As

a building material, wood yields an astonishing variety of plywoods, plastic and wood fiber

products that can meet any engineering specification.

2.2.2 Aluminium

Aluminium (or aluminum; see spelling differences) is a chemical element in the boron

group with symbol Al and atomic number 13. It is a silvery white, soft, ductile metal. Aluminium

is the third most abundant element (after oxygen and silicon), and the most abundant metal in

the Earth's crust. It makes up about 8% by weight of the Earth's solid surface. Aluminium metal

is so chemically reactive that native specimens are rare and limited to

extreme reducing environments. Instead, it is found combined in over 270 different minerals.

The chief ore of aluminium is bauxite.

2.2.2.1 Aluminium Utilization

Aluminium is remarkable for the metal's low density and for its ability to

resist corrosion due to the phenomenon of passivation. Structural components made from

aluminium and its alloys are vital to the aerospace industry and are important in other areas of

transportation and structural materials. The most useful compounds of aluminium, at least on a

weight basis, are the oxides and sulphates.

13

2.2.3 Brass

Brass is an alloy made of copper and zinc; the proportions of zinc and copper can be

varied to create a range of brasses with varying properties. It is a sub-stitutional alloy: atoms of

the two constituents may replace each other within the same crystal structure.

By comparison, bronze is principally an alloy of copper and tin. Bronze does not

necessarily contain tin, and a variety of alloys of copper, including alloys

with arsenic, phosphorus, aluminium, manganese, and silicon, are commonly termed "bronze".

The term is applied to a variety of brasses and the distinction is largely historical, and

modern practice in museums and archaeology is increasingly to avoid both terms for historical

objects in favour of the all-embracing "copper alloy".

2.2.3.1 Brass Utilization

Brass is used for decoration for its bright gold-like appearance; for applications where

low friction is required such as locks, gears, bearings, doorknobs, ammunition casings and

valves; for plumbing and electrical applications; and extensively in brass musical instruments

such as horns and bells for its acoustic properties. It is also used in zippers. Brass is often used in

situations where it is important that sparks not be struck, as in fittings and tools around explosive

gases.

2.2.4 Copper

Copper is a chemical element with the symbol Cu (from Latin: cuprum) and atomic

number 29. It is a ductile metal with very high thermal and electrical conductivity. Pure copper is

soft and malleable; a freshly exposed surface has a reddish-orange color. It is used as a conductor

of heat and electricity, a building material, and a constituent of various metal alloys.

The metal and its alloys have been used for thousands of years. In the Roman era, copper

was principally mined on Cyprus, hence the origin of the name of the metal as yprium (metal of

Cyprus), later shortened to uprum. Its compounds are commonly encountered as copper (II)

salts, which often impart blue or green colors to minerals such as azurite and turquoise and have

been widely used historically as pigments. Architectural structures built with copper corrode to

give green verdigris (or patina). Decorative art prominently features copper, both by itself and as

part of pigments.

14

2.2.4.1 Copper Utilization

Copper is essential to all living organisms as a trace dietary mineral because it is a key

constituent of the respiratory enzyme complexcytochrome c oxidase.

In molluscs and crustacea copper is a constituent of the blood pigment hemocyanin,

which is replaced by the iron-complexed hemoglobin in fish and other vertebrates. The main

areas where copper is found in humans are liver, muscle and bone. Copper compounds are used

as bacteriostatic substances, fungicides, and wood preservatives.

15

2.3 Material Properties

Properties table including the 4 chosen materials with theoretical modulus of elasticity,

16

DATA & OBSERVATION

Task 1: Load and Deflection

Material Dimension (Length Width Height)

Wood 375 31 6.4

Aluminum 375 25 6.2

Brass 375 25 6.2

Copper 375 25 6.2

Table 1 Dimension of each material

Load

(N)

Deflection (mm)

Wood Aluminum Brass Copper

5 1.64 0.42 0.3 0.25

10 3.11 0.84 0.56 0.48

15 4.70 1.27 0.9 0.73

25 8.53 2.10 1.52 1.20

Table 2 Load and Deflection for each material

17

Task 2: Modulus of Elasticity

Material

Load,

F (N)

Moment of

Flexure, Mb

(Nmm)

Flexural

Stress

Deflection Coefficient Of Elasticity

b

(N/mm2)

(mm)

E

(N/mm2)

Eave

(N/mm2)

Wood

5 703.125 3.3225 1.64 18910.7500

19200.5

10 1171.875 5.5375 3.11 19934.9647

15 1640.625 7.7524 4.70 19786.5128

25 2578.125 12.1824 8.53 18170.4983

Aluminum

5 703.125 4.3900 0.42 26341.4343

26289.6

10 1171.875 7.3166 0.84 26341.4343

15 1640.625 10.2432 1.27 26134.0215

25 2578.125 16.0966 2.10 26341.4343

Brass

5 703.125 4.3900 0.3 36878.0081

37415.3

10 1171.875 7.3166 0.56 39512.1515

15 1640.625 10.2432 0.9 36878.0081

25 2578.125 16.0966 1.52 36392.7711

Copper

5 703.125 4.3900 0.25 44253.6097

45478.7

10 1171.875 7.3166 0.48 46097.5101

15 1640.625 10.2432 0.73 45466.0374

25 2578.125 16.0966 1.20 46097.5101

Table 3 Modulus of Elasticity

18

ANALYSIS & RESULTS

Graph 1 Deflection vs Loading

Graph 2 Theoretical vs Experimental of Coefficient of Elasticity for each material

0

1

2

3

4

5

6

7

8

9

5 10 15 25

Def

lect

ion

(m

m)

Load (N)

Graph Deflection vs Loading


0

20

40

60

80

100

120

140


Co

effi

cien

t O

f El

ast

icit

y (G

Pa

)

Material

Theoretical vs Experimental forCoefficient of Elasticity

Experrimental Theoretical

19

Calculation:

To calculate the coefficient of elasticity of steel, brass, alumunium and wood, the deflection

formula is:-

EI

FL

48

3

I

FLE

48

3

To determine the flexural stress:-

b

bb

W

M

4)( 1

LFFM b

When rectangular it is 12

3bhI and

6

2bhWb

= Deflection (mm)

L = Span (mm) = 500 mm

Mb = Moment of Flexures (Nmm)

Wb = Resistance to Flexure (mm3)

b = Flexural Stress (N/mm2)

E = Coefficient of Elasticity

I = Inertia Factor

F1 = Load occasioned by weight of Load Device (N) = 2.5 N

F = Load occasioned by additional weight (N)

20

Moment of flexure is the same for every specimen according to the load weight used.

Moment of Flexure: 4

)( 1L

FFM b

5 N NmmMb 125.7034

375)5.25(

10 N NmmMb 875.11714

375)5.210(

15 N NmmMb 625.16404

375)5.215(

25 N NmmMb 125.25784

375)5.225(

Flexural stress for wood:-

Dimension: 31 6.4 mm

322

6267.2116

4.631

6mm

bhWb

5 N 23225.36267.211

125.703

mmN

b

10 N 25375.56267.211

875.1171

mmN

b

15 N 27524.76267.211

625.1640

mmN

b

20 N 21824.126267.211

125.2578

mmN

b

21

Flexural stress for Aluminum, Brass and Copper :-

Dimension: 25 6.2 mm

322

1667.1606

2.625

6mm

bhWb

5 N 23900.41667.160

125.703

mmN

b

10 N 23166.71667.160

875.1171

mmN

b

15 N 22432.101667.160

625.1640

mmN

b

20 N 20966.161667.160

125.2578

mmN

b

Inertia Factor for Wood:

433

2053.67712

4.631

12mm

bhI

Inertia Factor for Aluminum, Brass, and Copper::

433

5167.49612

2.625

12mm

bhI

22

Modulus of Elasticity:

Wood:-

5 N GPammNI

FLE 9018.187500.18901

64.12053.17748

3755

48

233

10 N GPammNI

FLE 9350.199647.19934

11.32053.17748

37510

48

233

15 N GPammNI

FLE 7865.195128.19786

70.42053.17748

37515

48

233

25 N GPammNI

FLE 1705.184983.18170

53.82053.17748

37525

48

233

Uncertainty:

5 N ()5 = [ (

)2(

=1 )

2 ] = [(0.02)2(5)2 + (0.02)2(1.64)2]0.5 = 0.1053

10N ()10 = [ (

)2(

=1 )

2 ] = [(0.02)2(10)2 + (0.02)2(3.11)2]0.5 = 0.2095

15N ()15 = [ (

)2(

=1 )

2 ] = [(0.02)2(15)2 + (0.02)2(4.70)2]0.5 = 0.3143

25N ()25 = [ (

)2(

=1 )

2 ] = [(0.02)2(25)2 + (0.02)2(8.53)2]0.5 = 0.5283

Hence, GPaEave 2005.194

1765.187865.199350.199018.18

Hence, () = 0.1053+0.2095+0.3143+0.5283

4 = 0.2894 GPa

23

= 19.2005 0.2894

Theoretical Value = 12.5 GPa

% error = %604.531005.12

2005.195.12

% error = %2888.511005.12

)2894.02005.19(5.12

Aluminum:-

5 N GPammNI

FLE 3414.264343.26341

42.05167.49648

3755

48

233

10 N GPammNI

FLE 3414.264343.26341

84.05167.49648

37510

48

233

15 N GPammNI

FLE 1340.260215.26134

27.15167.49648

37515

48

233

25 N GPammNI

FLE 3414.264343.26341

10.25167.49648

37525

48

233

24

Uncertainty:

5 N ()5 = [ (

)2(

=1 )

2 ] = [(0.02)2(5)2 + (0.02)2(0.42)2]0.5 = 0.1005

10N ()10 = [ (

)2(

=1 )

2 ] = [(0.02)2(10)2 + (0.02)2(0.84)2]0.5 = 0.2007

15N ()15 = [ (

)2(

=1 )

2 ] = [(0.02)2(15)2 + (0.02)2(1.27)2]0.5 = 0.3010

25N ()25 = [ (

)2(

=1 )

2 ] = [(0.02)2(25)2 + (0.02)2(2.10)2]0.5 = 0.5018


3414.261340.263414.263414.26

Hence, () = 0.1005+0.2007+0.3010+0.5018

4= 0.2760

= 26.2896 0.2760

Theoretical Value = Range of 69 GPa

% error = %8991.6110069

2896.2669

% error = %4991.6110069

)2760.02896.26(69

25

Brass:-

5 N GPammNI

FLE 8780.360081.36878

3.05167.49648

3755

48

233

10 N GPammNI

FLE 5122.391515.39512

56.05167.49648

37510

48

233

15 N GPammNI

FLE 8780.360081.36878

9.05167.49648

37515

48

233

25 N GPammNI

FLE 3928.367711.36392

52.15167.49648

37525

48

233

Uncertainty:

5 N ()5 = [ (

)2(

=1 )

2 ] = [(0.02)2(5)2 + (0.02)2(0.30)2]0.5 = 0.1000

10N ()10 = [ (

)2(

=1 )

2 ] = [(0.02)2(10)2 + (0.02)2(0.56)2]0.5 =

0.2002

15N ()15 = [ (

)2(

=1 )

2 ] = [(0.02)2(15)2 + (0.02)2(0.90)2]0.5 =

0.3005

25N ()25 = [ (

)2(

=1 )

2 ] = [(0.02)2(25)2 + (0.02)2(2.10)2]0.5 =

0.5009


3928.368780.365122.398780.36

Hence, () = 0.1000+0.2002+0.3005+0.5009

4= 0.2754

26

= 37.4153 0.2754

Theoretical Value = Range of 102 to 125 GPa

% error = %3183.6310000.102

4153.3700.102

% error = %0483.6310000.102

)2754.04153.37(00.102

Copper:-

5 N GPammNI

FLE 2536.446097.44253

25.05167.49648

3755

48

233

10 N GPammNI

FLE 0975.465101.46097

48.05167.49648

37510

48

233

15 N GPammNI

FLE 4660.450374.45466

73.05167.49648

37515

48

233

25 N GPammNI

FLE 0975.465101.46097

20.15167.49648

37525

48

233

27

Uncertainty:

5 N ()5 = [ (

)2(

=1 )

2 ] = [(0.02)2(5)2 + (0.02)2(0.25)2]0.5 = 0.1000

10N ()10 = [ (

)2(

=1 )

2 ] = [(0.02)2(10)2 + (0.02)2(0.48)2]0.5 = 0.2002

15N ()15 = [ (

)2(

=1 )

2 ] = [(0.02)2(15)2 + (0.02)2(0.73)2]0.5 = 0.3003

25N ()25 = [ (

)2(

=1 )

2 ] = [(0.02)2(25)2 + (0.02)2(1.20)2]0.5 = 0.5006


0975.464660.450975.462536.44

Hence, () = 0.1000+0.2002+0.3003+0.5006

4= 0.2753

= 37.4153 0.2753

Theoretical Value = 117 GPa

% error = %1293.6110000.117

4787.4500.117

% error = %8940.6010000.117

)2753.04787.45(00.117

28

Standard Deviation:

For 5N:

=()

=1.64 + 0.42 + 0.3 + 0.25

4

= 0.6525mm

= ( )

= [(1.64 0.6525)2 + (0.42 0.6525)2 + (0.3 0.6525)2 + (0.25 0.6525)2]

4

= 0.5734

For 10N:

=()

=3.11 + 0.84 + 0.56 + 0.48

4

= 1.2475

= ( )

= [(3.11 1.2475)2 + (0.84 1.2475)2 + (0.56 1.2475)2 + (0.48 1.2475)2]

4

= 1.0836

29

Discussion

1. Why deflection occurs during the applied of the load?

In the field of engineering, deflection is understood as the degree to which a structural

element is displaced under a load. It may refer to an angle or a distance. [1] To make it

simple, when a force or a load acting towards a point of a bar, where the bar is placed in a

horizontal way, deflection will occur and can be clarified by using naked eye only. The

deflection distance of a member under a load is directly related to the slope of the deflected

shape of the member under that load and can be calculated by integrating the function that

mathematically describes the slope of the member under that load. It can normally be

calculated by using Euler or Bernoulli beam equation.

2. Why different materials will be getting different values from deflection, although the load

applied is the same?

In the graph obtained, there were four types of material used in this experiment,

wood, aluminum, brass and copper; one of the reasons to use different type of material was

to justify the theory of bending was depend on the type of material. From the result

obtained from the experiment, the material which deflection occur the most was wood.

The result is 1.64mm, 3.11mm, 4.70mm and 5.83mm. Wood is a hard, fibrous structural

tissue found in the stems and roots of trees and other woody plants. It has been used for

thousands of years for both fuel and as a construction material [1], it is an organic material.

It is a very soft type of material compared to other materials, e.g. copper. In this

experiment, copper is the strongest element. This is been proven that the deflection

obtained from the experiment is 0.25mm, 0.48mm, 0.73mm, 1.20mm. In short, it can be

concluding that the stronger the material, the better the resistant towards deflection.

30

3. The comparison of coefficient of elasticity, E.

In the Coefficients of Elasticity, E, of 4 different specimens was determined. Again

the same apparatus as in task 1 is used. After experiments are done and after calculation,

E for copper is obtained as 45478.7 GPa. This count to a percentage error of 61.12%

from the theoretical value which is 117 GPa. E for brass is found to be 37.41 GPa, with

an error of only 63.31% from theoretical value of 102 GPa. Aluminium has a theoretical

E of 69GPa, however, from the experiment, it is 26.28 GPa. The percentage error will be

61.89%. Finally E of wood was found to be 19.2GPa, an error of 53.60% from the actual

value of 12.5 GPa.

4. The uncertainty of the experiment.

In physical experiments uncertainty analysis, or experimental uncertainty

assessment, deals with assessing the uncertainty in a measurement. An experiment

designed to determine an effect, demonstrate a law, or estimate the numerical value of a

physical variable will be affected by errors due to instrumentation, methodology,

presence of confounding effects and so on. Experimental uncertainty estimates are

needed to assess the confidence in the results. [3] In this experiment, the overall

uncertainty is calculated in average of 0.09 ~ 0.1 Pa. This result means that the average

value for modulus of elastic is around 0.09 ~ 0.1 Pa from the experimental value. For

example, the modulus of elastic experimental for wood material was 19.2005 GPa and

around 0.09 ~ 0.1 Pa.

31

5. What are the errors occurred during the experiment?

No measurement can be made perfect accuracy and precision. Therefore, it is

instructive to know the various types of errors and uncertainties that are in general,

associated with measurement system. [2] There are different types of error such as

systematic error, miscellaneous type of gross errors and so on. First of all, the main error

will be the instrument error which under the category of systematic error. The testing

device which is the gauge has zero error. In other words, the measurement will never get

a correct result due to the factor. Also, errors due to faulty adjustment are one of the

factors. During the process of applying load, the equipment itself being touched

unconsciously which will affect the result. Last but not least, the parallax error is also the

reason why the results are not accurate. The way the reading being taken was not in a

correct position where it has affected the result. All this factors will explain why the

percentage error of this experiment is out of charge.

6. Calibration for the experiment.

Calibration is a comparison between measurements between known magnitude

with another device and another experiment made in as similar a way as possible with a

second device. In the experiment, three measuring gauge is in use for calibration purpose.

It is for comparing the results in order to get the accurate value. E.g. the value of

deflection of wood has been measured by three different measuring gauge. The value

difference was only 0.2 0.4mm. So, the in between results have been taken it is the

more accurate result.

32

CONCLUSION

This experiment was conducted to observe the deflection of different material when it

experiences applied load. Wood experienced the most deflection in comparison to copper which

experience the least deflection. From analyzing the results obtained copper has the highest

average modulus of elasticity which was 45478.7N/mm2 followed by brass 37415.3 N/mm2,

aluminum 26289.6 N/mm2 and finally wood 19200.5 N/mm2 in decreasing modulus of elasticity.

The experiment conducted reveals high percentage error when compared to the theoretical

modulus of elasticity of studied materials. These errors may have been caused due to reasons

such as human errors as well as instrumental errors that were discussed above; future

experiments should take extra precautions to eliminate these errors to obtain more precise data.

Uncertainty analysis carried out shows that wood has the highest uncertainty value for modulus

of elasticity with 0.289GPa followed by aluminum at 0.2760GPa, Brass 0.2754GPa and Copper

0.2753GPa in decreasing order. Hence the value of uncertainty is too small and hence does not

significantly affect the data obtained.

References

[1] http://en.wikipedia.org/wiki/Deflection_(engineering).

[2] B. C. Nakra. and K. K. Chaudhry, Instrumentation Measurement and Analysis, 3rd Ed.,

McGraw Hill Education (India) Private Limited, 2009.

[3] http://user.engineering.uiowa.edu/~cfd/pdfs/References/uncert.pdf

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Appendix

34

-p.s: Lee Eng Loy was the photographer.

measurement project report.pdf

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