Analysis the i beam subjected to three point loading or bending for different material

ANALYSIS THE I BEAM SUBJECTED TO THREE POINT

LOADING OR BENDING FOR DIFFERENT MATERIAL

ADLI ZIL IKRAM BIN ABDULLAH

SUPERVISOR DECLARATION

“I hereby declared that I have read through this thesis and in my opinion this report is

sufficient in terms of scope and quality for awarding the Degree of Bachelor Mechanical

Engineering (Design & Innovation).”

Signature : ………

Supervisor : Mr. Dr Mohd Basri bin Ali

i

ANALYSIS THE I BEAM SUBJECTED TO THREE

POINT LOADING OR BENDING FOR DIFFERENT

MATERIAL

ADLI ZIL IKRAM BIN ABDULLAH

“This report is prepared in fulfillment for awarding the Degree of Bachelor Mechanical Engineering (Design & Innovation).”

Faculty of Mechanical Engineering Universiti Teknikal Malaysia Melaka

DECLARATION

“I hereby declared that this report is a result of my own work except for the works

that have been cited clearly in the references.”

Signature : ………

Name : Adli Zil Ikram Bin Abdullah

iii

Dedicate to

My beloved mother Che Eshah Binti Hamzah

My father Abdullah Bin Muda

ACKNOWLEDGEMENT

First of all, thank to my Allah The Almighty God for giving me a bless to

complete my final year project. Also I would like to express my acknowledgement to

my former supervisor, Mr. Basri bin Ali for guiding and encouraging me to write the

best thesis. Not forgot to all member of Bachelor of Mechanical Engineering (Design

and Innovation) for giving me moral support and for being my references in order to

complete their task. My Allah blesses you all. Not to forget, my family who support

me from the bottom to the top through this year. Thank for their concern,

encouragement and understanding. Last but not list, to those who have contributed

directly or indirectly to the success of this thesis and project whom I have not

mentioned their name specifically. Without them, there will be no successful this

v

ABSTRAK

Laporan ini membincangkan tentang reka bentuk, analisis dan hubung kait

antara tegasan dan terikan rasuk I menggunakan bahan yang berbeza. Bahan yang

dipilih adalah keluli (besi), loyang dan aluminium. Ia adalah bahan umum yang

selalu digunakan dalam pembinaan struktur. Rasuk I akan dibuat mengikut dimensi

skala sebenar dengan mengecilkan nisbah dari skala sebenar iaitu 30 mm x 30 mm x

300 mm untuk dijadikan bahan eksperimen. Selain itu, laporan ini membincangkan

prosedur analitikal untuk rasuk ini. Ia merangkumi kajian sifat terikan dan

pembengkokan yang disebabkan oleh beban. Kemudian, berdasarkan data yang

diperolehi, anggaran untuk muatan maksima untuk rasuk I ini akan dibuat dengan

mengambil kira perubahan tegasan yang berlaku pada rasuk menggunakan tolok

terikan. Analisis yang dilakukan adalah berdasarkan teori dan ujikaji atau

eksperimen. Persedian untuk melakukan ujikaji ini adalah dengan membuat kajian

literatur berdasarkan elemen yang menjadi pemboleh ubah di dalam eksperimen. Ia

merangkumi kajian tentang elemen – elemen berkaitan dengan rasuk, tegasan,

terikan, pesongan dan teori serta formula yang berkaitan. Kemudian, kajian literatur

juga dibuat terhadap kajian – kajian yang telah dibuat yang berkaitan dengan kajian

ini. Ini bertujuan untuk mengkaji serta memahami konsep dan pendekatan

metodologi yang digunakan, mengkaji kelebihan dan kekurangan di dalam kajian

tersebut dan melihat hasil yang diperolehi dari kajian mereka. Untuk metodologi,

laporan ini membincangkan aspek – aspek penting untuk ujikaji seperti prosedur

ujikaji, penyediaan peralatan dan spesimen, dan permasangan alatan seperti tolok

terikan. Dalam kajian ini, keputusan yang diperolehi dalam eksperimen dan data

dibincangkan dengan terperinci. Ketepatan setiap teknik dapat ditentukan

berdasarkan analisis yg telah dibuat serta keputusan yang telah diperolehi. Perkara

yang mempengaruhi keputusan juga dapat dikenalpasti dan dibincangkan terutama

perbezaan bahan yang menjadi pemboleh ubah dimanipulasi dalam uji kaji ini.

Hubungkait antara tegasan dan terikan telah diperolehi daripada hasil kajian iaitu

tegasan berkadar terus dengan terikan yang memenuhi hukum Hooke. Keputusan

yang diperolehi dari kajian ini adalah rasuk I daripada keluli adalah lebih baik

daripada aluminium dan loyang dari segi data terikan dan pembengkokan. Keputusan

ini adalah tepat berdasarkan kajian literatur iaitu terikan dan pembengkokan berkadar

songsang dengan modulus keanjalan. Perbezaan yang sedikit diantara data yang

diperolehi dalam eksperimen dan pengiraan melalui persamaan teori membuktikan

vii

ABSTRACT

This report discussed about the shape, analysis and relationship between

stress and strain of I beam by using different types materials. Materials selected are

mild steel, brass and aluminum. It is the common materials that is used in structural.

The i beam will be made to follow the actual dimension scale by using a ratio of the

actual dimension. In addition, this report discussed an analytical procedures for the I

beam. It consist of study of stress and strain characteristics, and deflection caused by

the loads. Then, based on the data obtained, the estimation of maximum load

carrying capacity for the I beam will be made by taking into consideration the change

of stress that occurs along the beam by using the application of strain gauges. The

analysis carried out based on the theory and experiment. Preparation of the

experiment is made by doing the literature study on the related elements in this study

and experiment. It consists of elements of beams, stress, strain, deflection and related

formula and theory. Then, the literaure study is also made on the related previous

research for studying and understanding the the concept and methodology used

assess strengths and weaknesses in these studies and study the results of their thesis.

For methodolgy, this thesis discussed the important aspects for experiment such as

the procedures, materials preparation and apparatus installation. In this research, the

results of all analyze techniques and methods are compared and briefly discussed. In

this study, the results obtained in the experimental and theoretical data obtained from

Castigliano methods are compared and discussed in detail. The accuracy of each

technique can be determined based result obtained. The factor that affected the

results has been identified and discussed especially types of materials as it is the

can be determined from the finding of this thesis which is stress is directly proportional to strain which obey the Hooke’s Law. The results obtained from this

study is the I-beam of steel is better than aluminum and brass in terms of strain and

bending. The results are accurate based on the literature review as strain and

deflection is inversely proportional to the modulus of elasticity. The slightly

differences between the data obtained in the experiment and calculation by the

ix

TABLE OF CONTENT

CHAPTER CONTENT PAGE

DECLARATION II

ACKNOWLEDGEMENT III

ABSTRACT V

ABSTRAK VI

TABLE OF CONTENT VII

LIST OF TABLE X

LIST OF FIGURE XI

ANNOTATION XII

LIST OF APPENDIXES XIII

CHAPTER I INTRODUCTION

1.1 Background 1

1.2 Problem Statement 2

1.3 Objective 3

1.4 Scope of Study 4

1.6 Benefit of The Project 5

1.7 Planning and Execution 5

CHAPTER II LITERATURE REVIEW

2.1 General 6

2.2 Beam

2.2.1 Beam and Type of Beam 8

2.2.2 I Beam Element 10

2.2.3 Design Of I Beam 12

2.3 Strain Gauge

2.3.1 Type of Strain Gauge 16

2.3.2 Strain Gauge Operation 17

2.4 Mechanical Properties

2.4.1 Elastic Properties

2.4.1.1 Modulus of Elasticity 18

2.4.1.2 Modulus of Rigidity 18

2.4.1.3 Poison Ratio 19

2.4.1.4 Strain – Stress Diagram 20

2.4.2 Strength Properties

2.4.2.1 Shear Strenth 22

2.4.2.2 Bending 22

xi

2.5 Beam Teory and Methods

2.5.1 Euler–Bernoulli beam theory 26

2.5.2 Castigliano's theorem 27

2.5.3 Energy Method 28

2.5.4 Hooke’s Law 28

2.6 Previous Researches 30

CHAPTER III METHODOLOGY

3.1 Introduction 33

3.2 Experimental Procedure 36

3.3 Preparation of Material 43

3.4 Calibration of Strain Gauge 44

3.5 Beam Test 47

CHAPTER 1V RESULT 49

4.1 Introduction 49

4.2 Experimental Data 50

4.3 Force - Strain Relationship 57

4.4 Strain - Stress Relatinship 61

4.5 Force – Deflection Relatioship 68

4.6 Force – Deflection (Castigliano’s Theorem) 69

4.7 Force – Deflection (Strain Energy) 76

4.8 Strain – Deflection Relationship 83

CHAPTER V DISCUSSION 89

CHAPTER 1V CONCLUSION 91

REFERENCES 95

BIBLIOGRAPHY 99

APPENDIX A 103

APPENDIX B 104

APPENDIX C 105

xiii

LIST OF TABLE

NO CONTENT PAGE

Table 2.1 Poison Ratio for Different Materials 12

Table 2.2 Previous researchers findings 25

Table 4.1 Experimental Data for Mild Steel 42

Table 4.2 Experimental Data for Brass 43

Table 4.3 Experimental Data for Aluminium 44

Table 4.4 Average data of strain for mild steel (Experimental) 46

Table 4.5 Average data of strain for brass (Experimental) 47

Table 4.6 Average data of strain for aluminium (Experimental) 48

Table 4.7 Average data of deflection (Experimental) 49

Table 4.8 Specimen Specification 54

Table 4.9 Stress Value for Each Strain for Mild Steel 55

Table 4.10 Stress Value for Each Strain for Brass 56

Table 4.11 Stress Value for Each Strain for Aluminium 57

Table 4.12 Deflection of Each Specimen (Experimental) 62

Table 4.13 Deflection of Each Specimen (Castigliano’s Theorem) 65

Table 4.14 Percentage Error Between Experimental and Theoretical 69

Table 4.15 Deflection for Mild Steel with different support width 71

Table 4.16 Deflection for Brass with different support width 72

xv

LIST OF FIGURE

NO CONTENT PAGE

Figure 1.1 Beam Bridge or Girder Bridge Construction 2

Figure 1.2 I Beam in the Bridge Structure 2

Figure 2.1 I Beam Part 8

Figure 2.2 Stress – strain curve showing typical behaviour for non 13

ferrous alloys. Stress is shown as function of strain

Figure 2.3 Bending of I Beam 15

Figure 3.1 Project Methodology 28

Figure 3.2 Example of bend testing under a three-point bend 30

Arrangement

Figure 3.3 Basic installation of strain gauge 34

Figure 3.4 Bending stress of beam 36

Figure 3.5 Positive and negative area of i beam 37

ANNOTATION AND ABBREVIATION

UTS = Ultimate Tensile Strength

TS = Tensile Strength

Pa = Pascal Mpa = Megapascals

SMYS = Specified Minimum Yield Strength

UteM = Universiti Teknikal Malaysia Melaka

mm = Milimeter

m = Meter

kg = Kilogram

g = Gram

N = Newton

kN = Kilo Newton

xvii

LIST OF APPENDIX

BIL. TITTLE PAGE

A Poster of Seminar 1 90

B Slideshow of Presentation 1 91

C I Beam Data 92

CHAPTER 1

INTRODUCTION

1.1 BACKGROUND

A bridge is a structure that connects a gap for example river, roadway, and

valley for giving access to people and moving vehicles to places which beforehand

were not available to access in the first place. For example to cross a river and get to

the other side (Blagovest, 2004). The traffic that uses a bridge consist of people or

vehicles. There are many type of bridge depend on it purpose and use. The common

type of bridges are beam bridge, cantilever bridge, truss bridges and arch bridges.

The design are accounted depending on the the action of the bridge, the attributes of

the area area the bridge is constructed, the actual acclimated to accomplish it and the

funds accessible to body it. The failure of bridges is one of main concern

for structural engineers and contractor in trying to improve bridge design,

construction and maintenance (Blagovest, 2004). The important things is the bridge

should be designed such that it is safe, aesthetically pleasing, and conservative as it

involve the lives of people that use it when something happen to the bridge.In the

construction of pre-tensioned or post-tensioned beam bridges, a very common

problem that most contractors faced was to actuate and estimate the actual upward

deflection of beams due to prestressing (Loo, 2010). In other word, we need to able

to estimate the deflection of beam in the sturucture due to bending. From the

statements above, the objectives were stated as to design the ideal shape of I beam, to

determine the strain stress behavior using strain gauge for different materials and To

2

Stress-strain analysis of a material is restricted to confirm a large number of

its physical properties. With the information progressed through much investigation,

one can foresee how a material structure will respond when a loads are placed on it.

This can be proved when the results obained from this experiment give the desired result which same with the theorem statement. As the Castigliano’s Theorem state

that the deflection and strain is inversely proportional to Young Modulus, the results

are also give the same flow as the I Beam from mild steel give the better result inn

strain and deflection compared to brass and aluminium.

A diagnostic fix in few push elastic - plastic speculation is exhibited for the

immaculate bowing shaft under minor twisting. This fix recognizes the impacts of

both versatile distortion and plastic deformation,and gives the connection between the instant M and the arch κ verifiably (Jin and Chen, 2010). There are countless

different types of beam designs and materials in the market at the point that

composing a structure. Engineer and contractor can choose different shapes, sizes,

development materials, and development methods depend on suitability of

construction.. Settling on the best materials and shape for a specific structure could

be a muddled process. Structural designers and manufacturers have countless

different types of beam designs and materials when endeavoring to make an

structural configuration. Measuring bending stress is a main part of structural

designing. Measuring bending stress confirms what amount of burden a structure

can loads before it failed. Assembling structurally sound ventures is the main

objective of succesfull structural designing (Loo, 2010).

1.2 PROBLEM STATEMENT

Research show that many applications have limitation on the amount of

deflection that can be tolerated especially in a sturcture (Roylance, 2000). The

structure will face a collapse or failure when the the amount of deflection exceeded.

in daily life or during the accident occurs. The development of extensions is the

consequence of a blend of infrastructures in development materials, structural

shapes, what is more configuration and dissection strategies. Composite structures

were acquainted with serve as a greatly aggressive sort of connect equivalent to

regular sorts of extensions for example cement and prestressed solid scaffolds

because of their lessened weight and snappy and practical erection (Hayward et al.

1988). Therefore the prediction of deflection is important and must be studied. The

prediction of deflection is one of part of structure analysis. When deciding to analyze

the structure, engineer must know the basic part and concept of structure. In

engineering, a structre is defined as a body or assemblage of bodies that capable to

support loads. The structure elements or part are column,beam and trusses. There are

a few method of structural analysis which are elasticity method, numerical

approximation method and material strength method (Felipa, 2000). The most

popular or close with deflection tolerate are bending. There are many researchers

have been done related to subjected bending for analyzing the strain stress behavior

of the specimen. They usually use the size, design and materials as their variables.

The researches commonly focused on the bar shape because it is the basic shape.

Therefore, this report will change the shape to the I Beam shape as realize the shape

is extensively used in construction such as rail train, bridge and buildings. This report

will focused on materials as variable by use mild steel, brass and aluminum as the

main material of specimens. The choice of these three types of materials is that

because this material is often used in the construction industry.

1.3 OBJECTIVE

The aim of this study is to analysis the I beam subjected to three point

bending for different materials in term od strain stress and deflection.

The objective of this project is as follow:

4

2. To determine the strain stress behavior using strain gauge for different materials.

3. To investigate the deflection of beam between experiment and theory with by using Castigliano’s Theorem method and Strain Energy Method.

1.4 SCOPE

The scope of the study will implement a few of confinements and

specifications. Firstly is to design the ideal shape of i beam in real application. I

beam shape was selected to analyze as i beam used extensively as reinforcement to a

structure especially bridge. Then, analyze I beam based on three different materials

which are mild steel, brass and aluminium. This experiment also will use strain

gauge to measure strain for each material. The study based on experiment will

conducted at Structure and Materials Laboratory in Universiti Teknikal Malaysia

Melaka (UTeM). Lastly, the dimension of I Beam is limited to 300 mm x 30 mm x

30 mm as equipment limitation.

1.5 SUMMARY OF THE PROJECT

This project are divided into two parts which are Projek Sarjana Muda (PSM)

1 and PSM 2. PSM 1 consists of three chapters which are introduction, literature

review and methodology. Introduction discusses on the definition, objectives, scope

and problems statement related to the project. Literature review will explain in term

of fundamental, method and measurement used to gain the result. Methodology make

up of the technique used in obtaining the data of experiment. Result and discussion

will be explained in PSM 2. Result and discussion mainly explain about the result

and how the data is being analyzed after the implementation of work study. The final

chapter is conclusion and the objectives that had been determined before will be

1.6 BENEFIT OF PROJECT

There are many benefit of this project. The report can help the engineer to

estimate the suitable material for the construction. This is because the dimension of I

beam specimen is made according the ratio of the real I beam in the structural field.

Then, this report will guide the engineer in investigating the two major of beam

characteristics which are strength and stiffness. Strength describes how much load

the beam can carry where stiffness describes how much beam deflects when loaded.

So, by this researched, engineer can know how much force any structural member

can take before it will deform or break.

1.7 PLANNING AND EXECUTION

Table 1.1 : Gantt Chart of PSM 1 Research

RESEARCH ACTIVITES /TIME

SEPTEMBER OKTOBER NOVEMBER DISEMBER W 1 W 2 W 3 W 4 W 5 W 6 W 7 W 8 W 9 W 10 W 11 W 12 W 13 W 14 Title Selection Problem Statement Literature Study Design Ideal Beam shape

(for shaping process) Specimen