Measurement Project Report.pdf

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) 1

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

2

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/mm². 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.

3

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.”

4

Simply supported beam with central point load

For this arrangement, it can be shown that the deflection under the load i.e. maximum deflection 

Wl 3 48 EI

bd 3 Where I  12 Beam compliance

 l3  W 4Ebd 3

Determination of coefficient of elasticity

5

Calculations:

Deflection formula for the load given above:



FL3 48 EI

E

FL3 48 I

A determination of the flexural stress yields:

b 

Mb Wb

M b  F  F1 

L 4

Where:  =

Deflection (mm.)

E = Coefficient of Elasticity

L =

Span(mm.)

I =

Mb =

Moment of Flexure (Nmm)

F1 = Load occasioned = by weight of load device

Inertia Factor

=2.5N Wb = Resistance to Flexure (mm3) F = Load occasioned by additional weight (N) b =

Flexural Stress (N/mm2)

6

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.

7

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

8

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 Twist and Bending Machine Loading devices (0.25 Kg) 1 Kg weights 0.5 Kg weights Dial Gauge Rectangular cross-section steel test piece Rectangular cross-section wood test piece Diameter 8 mm, of resp. steel, aluminium and brass End fixtures Laboratory manual

Quantity 1 2 2 4 1 7 1 3 2 1

9

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

10

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.

11

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 plywood’s, 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.

12

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 сyprium (metal of Cyprus), later shortened to сuprum. 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.

13

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.

14

2.3

Material Properties

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

15

DATA & OBSERVATION

Task 1: Load and Deflection

Dimension (Length × Width × Height)

Material Wood

375𝑚𝑚 × 31𝑚𝑚 × 6.4𝑚𝑚

Aluminum

375𝑚𝑚 × 25𝑚𝑚 × 6.2𝑚𝑚

Brass

375𝑚𝑚 × 25𝑚𝑚 × 6.2𝑚𝑚

Copper

375𝑚𝑚 × 25𝑚𝑚 × 6.2𝑚𝑚 Table 1 Dimension of each material

Load

Deflection (mm)

(N)

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

16

Task 2: Modulus of Elasticity

Material

Wood

Aluminum

Brass

Copper

Moment of

Flexural

Deflection

Coefficient Of Elasticity

Load,

Flexure, Mb

Stress

F (N)

(Nmm)

σb

δ

E

Eave

(N/mm2)

(mm)

(N/mm2)

(N/mm2)

5

703.125

3.3225

1.64

18910.7500

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

5

703.125

4.3900

0.42

26341.4343

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

5

703.125

4.3900

0.3

36878.0081

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

5

703.125

4.3900

0.25

44253.6097

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

19200.5

26289.6

37415.3

45478.7

Table 3 Modulus of Elasticity

17

ANALYSIS & RESULTS

Deflection (mm)

Graph Deflection vs Loading 9 8 7 6 5 4 3 2 1 0 5

10

15

25

Load (N) Wood

Aluminum

Brass

Copper

Graph 1 Deflection vs Loading

Coefficient Of Elasticity (GPa)

Theoretical vs Experimental for Coefficient of Elasticity 140 120

100 80 60

40 20 0 Wood

Aluminum

Brass

Copper

Material Experrimental

Theoretical

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

18

Calculation: To calculate the coefficient of elasticity of steel, brass, alumunium and wood, the deflection formula is:-



FL3 48 EI

E

FL3 48 I

To determine the flexural stress:-

b 

When rectangular it is

Mb Wb

bh3 I 12

M b  ( F  F1 )

and

L 4

bh 2 Wb  6

δ = Deflection (mm) L = Span (mm) = 500 mm Mb = Moment of Flexures (Nmm) Wb = Resistance to Flexure (mm3) σb = 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)

19

Moment of flexure is the same for every specimen according to the load weight used. Moment of Flexure: M b  ( F  F1 )

L 4

5 N  M b  (5  2.5)

375  703.125 Nmm 4

10 N  M b  (10  2.5)

375  1171 .875 Nmm 4

15 N  M b  (15  2.5)

375  1640 .625 Nmm 4

25 N  M b  (25  2.5)

375  2578 .125 Nmm 4

Flexural stress for wood:Dimension: 31 × 6.4 mm

bh2 31 6.4 2 Wb    211.6267 mm3 6 6

5 N  b 

703.125  3.3225 N mm2 211.6267

10 N   b 

1171 .875  5.5375 N mm2 211.6267

15 N   b 

1640 .625  7.7524 N mm2 211.6267

20 N   b 

2578 .125  12.1824 N mm2 211.6267

20

Flexural stress for Aluminum, Brass and Copper :Dimension: 25 × 6.2 mm

Wb 

bh2 25  6.2 2   160.1667 mm3 6 6

5 N  b 

703.125  4.3900 N mm2 160.1667

10 N   b 

1171 .875  7.3166 N mm2 160.1667

15 N   b 

1640 .625  10.2432 N mm2 160.1667

20 N   b 

2578 .125  16.0966 N mm2 160.1667

Inertia Factor for Wood:

bh3 31 6.43 I   677.2053mm4 12 12 Inertia Factor for Aluminum, Brass, and Copper::

bh3 25  6.23 I   496.5167 mm4 12 12

21

Modulus of Elasticity: Wood:-

FL3 5  375 3 5N  E   18901 .7500 N mm2  18.9018GPa 48 I 48 177.2053 1.64 10 N  E 

FL3 10  3753   19934 .9647 N mm2  19.9350GPa 48I 48  177.2053  3.11

15 N  E 

FL3 15  375 3   19786 .5128 N mm2  19.7865GPa 48 I 48  177.2053  4.70

25 N  E 

FL3 25  3753   18170 .4983 N mm2  18.1705GPa 48I 48  177.2053  8.53

Uncertainty: 𝑑𝑦

5 N  (𝑈)5𝑁 = ± [ ∑𝑛𝑖=1(𝑑𝑥 )2 (𝑌𝑥𝑖 )2 ] = [(0.02)2 (5)2 + (0.02)2 (1.64)2 ]0.5 = 0.1053 𝐺𝑃𝑎 𝑑𝑦

10N (𝑈)10𝑁 = ± [ ∑𝑛𝑖=1(𝑑𝑥 )2 (𝑌𝑥𝑖 )2 ] = [(0.02)2 (10)2 + (0.02)2 (3.11)2 ]0.5 = 0.2095 𝐺𝑃𝑎 𝑑𝑦

15N (𝑈)15𝑁 = ± [ ∑𝑛𝑖=1(𝑑𝑥 )2 (𝑌𝑥𝑖 )2 ] = [(0.02)2 (15)2 + (0.02)2 (4.70)2 ]0.5 = 0.3143 𝐺𝑃𝑎 𝑑𝑦

25N (𝑈)25𝑁 = ± [ ∑𝑛𝑖=1(𝑑𝑥 )2 (𝑌𝑥𝑖 )2 ] = [(0.02)2 (25)2 + (0.02)2 (8.53)2 ]0.5 = 0.5283 𝐺𝑃𝑎

Hence, Eave 

18.9018  19.9350  19.7865  18.1765  19.2005GPa 4

Hence, (𝑈)𝑜𝑣𝑒𝑟𝑎𝑙𝑙 =

0.1053+0.2095+0.3143+0.5283 4

= 0.2894 GPa

22

∴ 𝐸 = 19.2005 𝐺𝑃𝑎 ± 0.2894 𝐺𝑃𝑎

Theoretical Value = 12.5 GPa

% error =

% error =

12.5  19.2005  100  53.604% 12.5

12.5  (19.2005  0.2894 ) 12.5

 100  51.2888 %

Aluminum:5N  E

FL3 5  375 3   26341 .4343 N mm2  26.3414GPa 48 I 48  496.5167  0.42

10 N  E 

FL3 10  375 3   26341 .4343 N mm2  26.3414GPa 48I 48  496.5167  0.84

15 N  E 

FL3 15  375 3   26134 .0215 N mm2  26.1340GPa 48 I 48  496.5167  1.27

FL3 25  375 3 25 N  E    26341 .4343 N mm2  26.3414GPa 48I 48  496.5167  2.10

23

Uncertainty:

𝑑𝑦

5 N  (𝑈)5𝑁 = ± [ ∑𝑛𝑖=1( )2 (𝑌𝑥𝑖 )2 ] = [(0.02)2 (5)2 + (0.02)2 (0.42)2 ]0.5 = 0.1005 𝐺𝑃𝑎 𝑑𝑥 𝑑𝑦

10N (𝑈)10𝑁 = ± [ ∑𝑛𝑖=1(𝑑𝑥 )2 (𝑌𝑥𝑖 )2 ] = [(0.02)2 (10)2 + (0.02)2 (0.84)2 ]0.5 = 0.2007 𝐺𝑃𝑎 𝑑𝑦

15N (𝑈)15𝑁 = ± [ ∑𝑛𝑖=1(𝑑𝑥 )2 (𝑌𝑥𝑖 )2 ] = [(0.02)2 (15)2 + (0.02)2 (1.27)2 ]0.5 = 0.3010 𝐺𝑃𝑎 𝑑𝑦

25N (𝑈)25𝑁 = ± [ ∑𝑛𝑖=1(𝑑𝑥 )2 (𝑌𝑥𝑖 )2 ] = [(0.02)2 (25)2 + (0.02)2 (2.10)2 ]0.5 = 0.5018 𝐺𝑃𝑎

Hence, Eave 

26.3414  26.3414  26.1340  26.3414  26.2896GPa 4

Hence, (𝑈)𝑜𝑣𝑒𝑟𝑎𝑙𝑙 =

0.1005+0.2007+0.3010+0.5018 4

= 0.2760 𝐺𝑃𝑎

∴ 𝐸 = 26.2896 𝐺𝑃𝑎 ± 0.2760 𝐺𝑃𝑎

Theoretical Value = Range of 69 GPa

% error =

% error =

69  26.2896  100  61.8991 % 69 69  (26.2896  0.2760 ) 69

 100  61.4991 %

24

Brass:5N  E

FL3 5  375 3   36878 .0081N mm2  36.8780GPa 48 I 48  496.5167  0.3

10 N  E 

FL3 10  375 3   39512 .1515 N mm2  39.5122GPa 48I 48  496.5167  0.56

15 N  E 

FL3 15  3753   36878 .0081 N mm2  36.8780GPa 48I 48  496.5167  0.9

25 N  E 

FL3 25  375 3   36392 .7711 N mm2  36.3928GPa 48I 48  496.5167  1.52

Uncertainty: 𝑑𝑦

5 N  (𝑈)5𝑁 = ± [ ∑𝑛𝑖=1(𝑑𝑥 )2 (𝑌𝑥𝑖 )2 ] = [(0.02)2 (5)2 + (0.02)2 (0.30)2 ]0.5 = 0.1000 𝐺𝑃𝑎 𝑑𝑦

10N (𝑈)10𝑁 = ± [ ∑𝑛𝑖=1(𝑑𝑥 )2 (𝑌𝑥𝑖 )2 ] = [(0.02)2 (10)2 + (0.02)2 (0.56)2 ]0.5 = 0.2002 𝐺𝑃𝑎 𝑑𝑦

15N (𝑈)15𝑁 = ± [ ∑𝑛𝑖=1(𝑑𝑥 )2 (𝑌𝑥𝑖 )2 ] = [(0.02)2 (15)2 + (0.02)2 (0.90)2 ]0.5 = 0.3005 𝐺𝑃𝑎 𝑑𝑦

25N (𝑈)25𝑁 = ± [ ∑𝑛𝑖=1(𝑑𝑥 )2 (𝑌𝑥𝑖 )2 ] = [(0.02)2 (25)2 + (0.02)2 (2.10)2 ]0.5 = 0.5009 𝐺𝑃𝑎

Hence, Eave 

36.8780  39.5122  36.8780  36.3928  37.4153GPa 4

Hence, (𝑈)𝑜𝑣𝑒𝑟𝑎𝑙𝑙 =

0.1000+0.2002+0.3005+0.5009 4

= 0.2754 𝐺𝑃𝑎

25

∴ 𝐸 = 37.4153 𝐺𝑃𝑎 ± 0.2754 𝐺𝑃𝑎

Theoretical Value = Range of 102 to 125 GPa

% error =

% error =

102 .00  37.4153 102 .00

 100  63.3183 %

102.00  (37.4153  0.2754 ) 102.00

 100  63.0483 %

Copper:5N  E

FL3 5  375 3   44253 .6097 N mm2  44.2536GPa 48 I 48  496.5167  0.25

10 N  E 

FL3 10  375 3   46097 .5101 N mm2  46.0975GPa 48 I 48  496.5167  0.48

15 N  E 

FL3 15  375 3   45466 .0374 N mm2  45.4660GPa 48I 48  496.5167  0.73

25 N  E 

FL3 25  375 3   46097 .5101 N mm2  46.0975GPa 48I 48  496.5167  1.20

26

Uncertainty: 𝑑𝑦

5 N  (𝑈)5𝑁 = ± [ ∑𝑛𝑖=1(𝑑𝑥 )2 (𝑌𝑥𝑖 )2 ] = [(0.02)2 (5)2 + (0.02)2 (0.25)2 ]0.5 = 0.1000 𝐺𝑃𝑎 𝑑𝑦

10N (𝑈)10𝑁 = ± [ ∑𝑛𝑖=1( )2 (𝑌𝑥𝑖 )2 ] = [(0.02)2 (10)2 + (0.02)2 (0.48)2 ]0.5 = 0.2002 𝐺𝑃𝑎 𝑑𝑥 𝑑𝑦

15N (𝑈)15𝑁 = ± [ ∑𝑛𝑖=1(𝑑𝑥 )2 (𝑌𝑥𝑖 )2 ] = [(0.02)2 (15)2 + (0.02)2 (0.73)2 ]0.5 = 0.3003 𝐺𝑃𝑎 𝑑𝑦

25N (𝑈)25𝑁 = ± [ ∑𝑛𝑖=1(𝑑𝑥 )2 (𝑌𝑥𝑖 )2 ] = [(0.02)2 (25)2 + (0.02)2 (1.20)2 ]0.5 = 0.5006 𝐺𝑃𝑎

Hence, Eave 

44.2536  46.0975  45.4660  46.0975  45.4787 GPa 4

Hence, (𝑈)𝑜𝑣𝑒𝑟𝑎𝑙𝑙 =

0.1000+0.2002+0.3003+0.5006 4

= 0.2753 𝐺𝑃𝑎

∴ 𝐸 = 37.4153 𝐺𝑃𝑎 ± 0.2753 𝐺𝑃𝑎

Theoretical Value = 117 GPa

% error =

% error =

117.00  45.4787  100  61.1293 % 117.00

117 .00  (45.4787  0.2753) 117 .00

 100  60.8940 %

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Standard Deviation: For 5N: 𝑥̅ =

∑(𝑥𝑖 ) ∑𝑛

𝑥̅ =

1.64 + 0.42 + 0.3 + 0.25 4

𝑥̅ = 0.6525mm

𝑆𝐷𝐸 = √

𝜀(𝑥𝑖 − 𝑥̅ ) 𝑁

𝑆𝐷𝐸 = √

[(1.64 − 0.6525)2 + (0.42 − 0.6525)2 + (0.3 − 0.6525)2 + (0.25 − 0.6525)2 ] 4

𝑆𝐷𝐸 = 0.5734𝑚𝑚

For 10N: 𝑥̅ =

∑(𝑥𝑖 ) ∑𝑛

𝑥̅ =

3.11 + 0.84 + 0.56 + 0.48 4

𝑥̅ = 1.2475𝑚𝑚

𝑆𝐷𝐸 = √

𝜀(𝑥𝑖 − 𝑥̅ ) 𝑁

𝑆𝐷𝐸 = √

[(3.11 − 1.2475)2 + (0.84 − 1.2475)2 + (0.56 − 1.2475)2 + (0.48 − 1.2475)2 ] 4

𝑆𝐷𝐸 = 1.0836𝑚𝑚

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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.

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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.

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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.

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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

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

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