# EDEXCEL NATIONAL CERTIFICATE/DIPLOMA MECHANICAL PRINCIPLES OUTCOME 2 ENGINEERING COMPONENTS TUTORIAL 1 STRUCTURAL MEMBERS

Save this PDF as:

Size: px
Start display at page:

Download "EDEXCEL NATIONAL CERTIFICATE/DIPLOMA MECHANICAL PRINCIPLES OUTCOME 2 ENGINEERING COMPONENTS TUTORIAL 1 STRUCTURAL MEMBERS"

## Transcription

1 ENGINEERING COMPONENTS EDEXCEL NATIONAL CERTIFICATE/DIPLOMA MECHANICAL PRINCIPLES OUTCOME ENGINEERING COMPONENTS TUTORIAL 1 STRUCTURAL MEMBERS Structural members: struts and ties; direct stress and strain, dimensional changes; combined effects of direct and thermal loading, factor of safety. Compound members: series and parallel connected compound bars made up of two materials; direct stress and strain in each material, dimensional changes. Fastenings: shear stress in fastenings e.g. riveted joints, bolted joints and hinge pins subjected to single and double shearing forces You should judge your progress by completing the self assessment exercises. These may be sent for marking at a cost (see home page). On completion of this tutorial you should be able to do the following. Define structural members. Calculate direct stress and strain. Calculate changes in dimensions. Solve basic problems involving stress, strain and modulus. Explain and calculate Safety Factor. Explain and calculate stresses due to temperature changes. It is assumed that the student is already familiar with the concepts of FORCE. D.J.DUNN FREESTUDY.CO.UK 1

2 1. TYPES OF STRUCTURAL MEMBERS Engineering structures come in many forms. Here are some. STRUTS AND TIES A strut is a long thin member that is compressed and usually fails by buckling. A tie is a member that is stretched so it cannot buckle. A tie could be a rope or chain as well as a rigid length of material. Figure 1 FRAMES Struts and ties make up the members of lattice frames such as the simple one shown. The two side members are compressed and so are struts but the bottom one is stretched and could be a chain so it is a tie. Figure COLUMNS A column is a thick compression member. Struts fail due to bending but columns fail in compression. Columns are usually made of brittle material which is strong in compression such as cast iron, stone and concrete. These materials are weak in tension so it is important to ensure that bending does not produce tensile stresses in them. If the compressive stress is too big, they fail by crumbling and cracking Figure 3 D.J.DUNN FREESTUDY.CO.UK

3 BEAMS A beam is a structure, which is loaded transversely (sideways). The loads may be point loads or uniformly distributed loads (udl). The diagrams show the way that point loads and uniform loads are illustrated. Figure 4 Transverse loading causes bending and bending is a very severe form of stressing a structure. The bent beam goes into tension (stretched) on one side and compression on the other.. DIRECT STRESS σ Figure 5 When a force is applied to an elastic body, the body deforms. The way in which the body deforms depends upon the type of force applied to it. A compression force makes the body shorter. A tensile force makes the body longer. Figure 6 Tensile and compressive forces are called DIRECT FORCES. Stress is the force per unit area upon which it acts. Stress = σ = Force/Area N/m or Pascals. The symbol σ is called SIGMA NOTE ON UNITS The fundamental unit of stress is 1 N/m and this is called a Pascal. This is a small quantity in most fields of engineering so we use the multiples kpa, MPa and GPa. Areas may be calculated in mm and units of stress in N/mm are quite acceptable. Since 1 N/mm converts to N/m then it follows that the N/mm is the same as a MPa D.J.DUNN FREESTUDY.CO.UK 3

4 3. DIRECT STRAIN ε In each case, a force F produces a deformation x. In engineering we usually change this force into stress and the deformation into strain and we define these as follows. Strain is the deformation per unit of the original length Strain = ε = x/l The symbol ε is called EPSILON Strain has no units since it is a ratio of length to length. Most engineering materials do not stretch very much before they become damaged so strain values are very small figures. It is quite normal to change small numbers in to the exponent for of Engineers use the abbreviation µε (micro strain) to denote this multiple. For example a strain of could be written as 68 x 10-6 but engineers would write 68 µε. Note that when conducting a British Standard tensile test the symbols for original area are S o and for Length is L o. WORKED EXAMPLE No.1 A metal wire is.5 mm diameter and m long. A force of 1 N is applied to it and it stretches 0.3 mm. Assume the material is elastic. Determine the following. i. The stress in the wire σ. ii. The strain in the wire ε. πd π x.5 A = = = mm 4 4 F 1 σ = = =.44 N/mm A Answer (i) is hence.44 MPa x 0.3 mm ε = = = or 150 µε L 000 SELF ASSESSMENT EXERCISE No.1 1. A steel bar is 10 mm diameter and m long. It is stretched with a force of 0 kn and extends by 0. mm. Calculate the stress and strain. (Answers 54.6 MPa and 100 µε). A rod is 0.5 m long and 5 mm diameter. It is stretched 0.06 mm by a force of 3 kn. Calculate the stress and strain. (Answers 15.8 MPa and 10µε) D.J.DUNN FREESTUDY.CO.UK 4

5 4. MODULUS OF ELASTICITY E Elastic materials always spring back into shape when released. They also obey HOOKE'S LAW. This is the law of a spring which states that deformation is directly proportional to the force. F/x = stiffness = k N/m Figure 7 The stiffness is different for different materials and different sizes of the material. We may eliminate the size by using stress and strain instead of force and deformation as follows. If F and x refer to direct stress and strain then F = σa x = εl hence F x = σa εl FL and Ax σ = ε The stiffness is now in terms of stress and strain only and this constant is called the MODULUS of ELASTICITY and it has a symbol E. FL σ E = = Ax ε A graph of stress against strain will be a straight line with a gradient of E. The units of E are the same as the units of stress. 6. ULTIMATE TENSILE STRESS If a material is stretched until it breaks, the tensile stress has reached the absolute limit and this stress level is called the ultimate tensile stress. Values for different materials may be found in various sources such as the web site Matweb. WORKED EXAMPLE No. A steel tensile test specimen has a cross sectional area of 100 mm and a gauge length of 50 mm, the gradient of the elastic section is 410 x 10 3 N/mm. Determine the modulus of elasticity. The gradient gives the ratio F/A = and this may be used to find E. σ F L 3 50 E = = x = 410 x 10 x = N/mm or MPa or 05 GPa ε x A 100 D.J.DUNN FREESTUDY.CO.UK 5

6 WORKED EXAMPLE No.3 A Steel column is 3 m long and 0.4 m diameter. It carries a load of 50 MN. Given that the modulus of elasticity is 00 GPa, calculate the compressive stress and strain and determine how much the column is compressed. πd π x 0.4 A = = = 0.16 m F 50 x10 6 σ = = = x10 Pa A σ σ x10 E = so ε = = = ε E 00 x10 x ε = so x = ε L = x 3000 mm = 5.97 mm L 5. SAFETY FACTOR The stress at which a material is deemed to fail might be the ultimate stress or the yield stress. It might also be some other value based on some other criterion such as fatigue and creep. We should also bear in mind that the working stress is often higher than that predicted in the theory covered so far because of local factors such as grooves and sharp corners that raise the stress level. We will not be studying this here. The safety factor is the ratio of the maximum stress allowed and the actual stress. SF = Maximum Allowable Stress/Working Stress WORKED EXAMPLE No.4 A Steel tie rod is 0 mm diameter. It carries a load of 4 MN. Given that the maximum allowable stress is 460 MPa, calculate the safety factor. πd A = 4 π x 0. = 4 F 4 x10 σ = = A 31.4 x SF = = = 31.4 x 10 3 = 17.3 x10 6 m Pa D.J.DUNN FREESTUDY.CO.UK 6

7 SELF ASSESSMENT EXERCISE No. 1. A bar is 500 mm long and is stretched to 505 mm with a force of 50 kn. The bar is 10 mm diameter. Calculate the stress and strain. The material has remained within the elastic limit. Determine the modulus of elasticity. (Answers MPa, 0.01 and GPa.). A steel bar is stressed to 80 MPa. The modulus of elasticity is 05 GPa. The bar is 80 mm diameter and 40 mm long. Determine the following. i. The strain. ( ) ii. The force. (1.407 MN) 3. A circular metal column is to support a load of 500 Tonne and it must not compress more than 0.1 mm. The modulus of elasticity is 10 GPa. the column is m long. Calculate the cross sectional area and the diameter. (0.467 m and m) Note 1 Tonne is 1000 kg. 4. A Steel tie rod is 10 mm diameter. It carries a load of 3 MN. Given that the maximum allowable stress is 500 MPa, calculate the safety factor. (Answer 1.31) D.J.DUNN FREESTUDY.CO.UK 7

8 6. TEMPERATURE STRESSES It is not clear in the syllabus how much attention should be paid to thermal stresses and perhaps a description only would suffice. This work should be studied if you think it is required to calculate thermally induced stresses. Metals expand when heated. This can be put to good use. For example a ring may be expanded by warming it and then fitted onto a shaft and on cooling grips the shaft very tightly. Thermal expansion can also produce unwanted stresses in structures. For example, suddenly allowing hot fluid into a badly designed pipe could cause it to fracture as it tries to get longer but is prevented from doing so. COEFFICIENT OF LINEAR EXPANSION All engineering materials expand when heated and this expansion is usually equal in all directions. If a bar of material of length L has its temperature increased by θ degrees, the increase of length L is directly proportional to the original length L and to the temperature change θ. Hence L =constant x L θ The constant of proportionality is called the coefficient of linear expansion (α). L = α L θ INDUCED STRESS IN A CONSTRAINED BAR When a material is heated and not allowed to expand freely, stresses are induced which are known as "temperature stresses." Suppose the bar was allowed to expand freely by distance L and then changed back to its original length. The strain is then ε = L /L = α L θ/l = α θ Since stress/strain = modulus of elasticity (E) then the induced stress is σ = E ε = E α θ This may be a tensile stress or a compressive stress depending whether the bar was pulled back to its original length or pushed back. D.J.DUNN FREESTUDY.CO.UK 8

9 WORKED EXAMPLE No.5 A thin steel band 850 mm diameter must be expanded to fit around a disc 851 mm diameter. Calculate the temperature change needed and the stress produced in the ring. The coefficient of linear expansion is 15 x 10-6 per o C and the modulus of elasticity E is 00 GPa. Initial circumference of ring = πd = π x 850 = mm Required circumference = π x 851 = mm L = = 3.15 mm L = α L θ 3.15 = 15 x 10-6 x x θ θ = 3.15/(15 x 10-6 x ) = 78.6 Kelvin σ = Eα θ = 00 x 10 9 x 15 x 10-6 x 78.6 = 35.8 MPa. Alternatively strain ε = L/ L = 3.15/ = stress σ = Eε = 00 x 10 9 x = 35.8 MPa WORKED EXAMPLE No.6 A brass bar is 600 mm long and it is turned on a centre lathe to 100 mm diameter. It is held between the chuck jaws and a running tail stock so that it is not free to expand. During the turning process it has become heated from 0 o C to 95 o C. Calculate the thermal stress induced in the bar and the resulting thrust on the chuck and tail stock. E for brass is 90 GPa and α is 18 x 10-6 per o C. Stress induced = σ = Eα θ = 90 x 10 9 x 18 x 10-6 x (95 0) = 11.5 MPa Force = stress x cross sectional area = 11.5 x 10 6 x π x 0.1 /4 = kn WORKED EXAMPLE No.7 Determine the induced stress and thrust if the centre lathe flexed so that the bar changed length. Check your solution here. The free expansion of the bar is L = α L θ = 18 x 10-6 x 600 x (95 0) = 0.81 mm Actual change in length is 0.6 mm. Strain induced = change in length/original length = ( )/600 = Stress induced σ = E ε = 90 x 10 9 x = 31.5 MPa Force = stress x cross sectional area = 31.5 x 10 6 x π x 0.01 /4 = 47.4 kn D.J.DUNN FREESTUDY.CO.UK 9

10 SELF ASSESSMENT EXERCISE No.3 1. A steel ring is 50 mm diameter and mm thick. It must be fitted onto a shaft 50.1 mm diameter. Calculate the temperature to which it must be heated in order to fit on the shaft. The initial temperature is 0 o C and the coefficient of linear expansion is 15 x 10-6 per o C. (Answer K). A stub shaft 85. mm diameter must be shrunk to 85 mm diameter in order to insert it into a housing. By how much must the temperature be reduced? Take the coefficient of linear expansion is 1 x 10-6 per o C. (Answer K) 3. A steam pipe is 10 mm outer diameter and 100 mm inner diameter. It has a length of 30 m and passes through a wall at both ends where it is rigidly constrained. Steam at 00 o C is suddenly released into the pipe. The initial temperature of the pipe is 15 o C and the coefficient of linear expansion is 15 x 10-6 per o C. E is 00 GPa. Calculate i. the thermal stress produced. (555 MPa) ii. the force exerted by the pipe against the walls. (1.918 MN) D.J.DUNN FREESTUDY.CO.UK 10

### ENGINEERING COUNCIL CERTIFICATE LEVEL

ENGINEERING COUNCIL CERTIICATE LEVEL ENGINEERING SCIENCE C103 TUTORIAL - BASIC STUDIES O STRESS AND STRAIN You should judge your progress by completing the self assessment exercises. These may be sent

### EDEXCEL NATIONAL CERTIFICATE/DIPLOMA MECHANICAL PRINCIPLES AND APPLICATIONS NQF LEVEL 3 OUTCOME 1 - LOADING SYSTEMS TUTORIAL 3 LOADED COMPONENTS

EDEXCEL NATIONAL CERTIICATE/DIPLOMA MECHANICAL PRINCIPLES AND APPLICATIONS NQ LEVEL 3 OUTCOME 1 - LOADING SYSTEMS TUTORIAL 3 LOADED COMPONENTS 1. Be able to determine the effects of loading in static engineering

### MECHANICAL PRINCIPLES HNC/D PRELIMINARY LEVEL TUTORIAL 1 BASIC STUDIES OF STRESS AND STRAIN

MECHANICAL PRINCIPLES HNC/D PRELIMINARY LEVEL TUTORIAL 1 BASIC STUDIES O STRESS AND STRAIN This tutorial is essential for anyone studying the group of tutorials on beams. Essential pre-requisite knowledge

### EDEXCEL NATIONAL CERTIFICATE/DIPLOMA FURTHER MECHANICAL PRINCIPLES AND APPLICATIONS UNIT 11 - NQF LEVEL 3 OUTCOME 2 - STRESS AND STRAIN

EDEXCEL NATIONAL CERTIICATE/DIPLOMA URTHER MECHANICAL PRINCIPLES AND APPLICATIONS UNIT 11 - NQ LEVEL 3 OUTCOME - STRESS AND STRAIN TUTORIAL 1 - SHEAR CONTENT Be able to determine the stress in structural

### MECHANICS OF SOLIDS - BEAMS TUTORIAL 1 STRESSES IN BEAMS DUE TO BENDING. On completion of this tutorial you should be able to do the following.

MECHANICS OF SOLIDS - BEAMS TUTOIAL 1 STESSES IN BEAMS DUE TO BENDING This is the first tutorial on bending of beams designed for anyone wishing to study it at a fairly advanced level. You should judge

### MECHANICS OF SOLIDS COMPRESSION MEMBERS TUTORIAL 1 STRUTS. On completion of this tutorial you should be able to do the following.

MECHANICS OF SOLIDS COMPRESSION MEMBERS TUTORIAL 1 STRUTS You should judge your progress by completing the self assessment exercises. On completion of this tutorial you should be able to do the following.

### MECHANICS OF SOLIDS - BEAMS TUTORIAL 2 SHEAR FORCE AND BENDING MOMENTS IN BEAMS

MECHANICS OF SOLIDS - BEAMS TUTORIAL 2 SHEAR FORCE AND BENDING MOMENTS IN BEAMS This is the second tutorial on bending of beams. You should judge your progress by completing the self assessment exercises.

### Solid Mechanics. Stress. What you ll learn: Motivation

Solid Mechanics Stress What you ll learn: What is stress? Why stress is important? What are normal and shear stresses? What is strain? Hooke s law (relationship between stress and strain) Stress strain

### ENGINEERING SCIENCE H1 OUTCOME 1 - TUTORIAL 3 BENDING MOMENTS EDEXCEL HNC/D ENGINEERING SCIENCE LEVEL 4 H1 FORMERLY UNIT 21718P

ENGINEERING SCIENCE H1 OUTCOME 1 - TUTORIAL 3 BENDING MOMENTS EDEXCEL HNC/D ENGINEERING SCIENCE LEVEL 4 H1 FORMERLY UNIT 21718P This material is duplicated in the Mechanical Principles module H2 and those

### Chapter 12 Elasticity

If I have seen further than other men, it is because I stood on the shoulders of giants. Isaac Newton 12.1 The Atomic Nature of Elasticity Elasticity is that property of a body by which it experiences

### Objectives. Experimentally determine the yield strength, tensile strength, and modules of elasticity and ductility of given materials.

Lab 3 Tension Test Objectives Concepts Background Experimental Procedure Report Requirements Discussion Objectives Experimentally determine the yield strength, tensile strength, and modules of elasticity

### Properties of Matter

Mr. Patrick J Camilleri B.Ed (Hons) M.Ed Science (Sheffield) Department of Physics JC Malta Properties of Matter Basics You Should Know Elasticity. Young modulus 1. Hooke's law. Extension α tension (force

### STRESS AND DEFORMATION ANALYSIS OF LINEAR ELASTIC BARS IN TENSION

Chapter 11 STRESS AND DEFORMATION ANALYSIS OF LINEAR ELASTIC BARS IN TENSION Figure 11.1: In Chapter10, the equilibrium, kinematic and constitutive equations for a general three-dimensional solid deformable

### Stress Strain Relationships

Stress Strain Relationships Tensile Testing One basic ingredient in the study of the mechanics of deformable bodies is the resistive properties of materials. These properties relate the stresses to the

### ENGINEERING COUNCIL CERTIFICATE LEVEL ENGINEERING SCIENCE C103 TUTORIAL 3 - TORSION

ENGINEEING COUNCI CETIFICATE EVE ENGINEEING SCIENCE C10 TUTOIA - TOSION You should judge your progress by completing the self assessment exercises. These may be sent for marking or you may request copies

### Adam Zaborski handouts for Afghans

Tensile test Adam Zaborski handouts for Afghans Outline Tensile test purpose Universal testing machines and test specimens Stress-strain diagram Mild steel : proportional stage, elastic limit, yielding

### Torsion Testing. Objectives

Laboratory 4 Torsion Testing Objectives Students are required to understand the principles of torsion testing, practice their testing skills and interpreting the experimental results of the provided materials

### Simple Stresses in Machine Parts

Simple Stresses in Machine Parts n 87 C H A P T E R 4 Simple Stresses in Machine Parts 1. Introduction.. Load. 3. Stress. 4. Strain. 5. Tensile Stress and Strain. 6. Compressive Stress and Strain. 7. Young's

### MECHANICS OF SOLIDS - BEAMS TUTORIAL TUTORIAL 4 - COMPLEMENTARY SHEAR STRESS

MECHANICS OF SOLIDS - BEAMS TUTORIAL TUTORIAL 4 - COMPLEMENTARY SHEAR STRESS This the fourth and final tutorial on bending of beams. You should judge our progress b completing the self assessment exercises.

### CHAPTER 4 TENSILE TESTING

CHAPTER 4 TENSILE TESTING EXERCISE 28, Page 7 1. What is a tensile test? Make a sketch of a typical load/extension graph for a mild steel specimen to the point of fracture and mark on the sketch the following:

### Structures and Stiffness

Structures and Stiffness ENGR 10 Introduction to Engineering Ken Youssefi/Thalia Anagnos Engineering 10, SJSU 1 Wind Turbine Structure The Goal The support structure should be optimized for weight and

### Properties of Materials

CHAPTER 1 Properties of Materials INTRODUCTION Materials are the driving force behind the technological revolutions and are the key ingredients for manufacturing. Materials are everywhere around us, and

### METU DEPARTMENT OF METALLURGICAL AND MATERIALS ENGINEERING

METU DEPARTMENT OF METALLURGICAL AND MATERIALS ENGINEERING Met E 206 MATERIALS LABORATORY EXPERIMENT 1 Prof. Dr. Rıza GÜRBÜZ Res. Assist. Gül ÇEVİK (Room: B-306) INTRODUCTION TENSION TEST Mechanical testing

### MECHANICAL PRINCIPLES OUTCOME 4 MECHANICAL POWER TRANSMISSION TUTORIAL 1 SIMPLE MACHINES

MECHANICAL PRINCIPLES OUTCOME 4 MECHANICAL POWER TRANSMISSION TUTORIAL 1 SIMPLE MACHINES Simple machines: lifting devices e.g. lever systems, inclined plane, screw jack, pulley blocks, Weston differential

### COMPLEX STRESS TUTORIAL 3 COMPLEX STRESS AND STRAIN

COMPLX STRSS TUTORIAL COMPLX STRSS AND STRAIN This tutorial is not part of the decel unit mechanical Principles but covers elements of the following sllabi. o Parts of the ngineering Council eam subject

### Torsion Tests. Subjects of interest

Chapter 10 Torsion Tests Subjects of interest Introduction/Objectives Mechanical properties in torsion Torsional stresses for large plastic strains Type of torsion failures Torsion test vs.tension test

### ME 215 Engineering Materials I

ME 215 Engineering Materials I Chapter 3 Properties in Tension and Compression (Part III) Mechanical Engineering University of Gaziantep Dr. A. Tolga Bozdana www.gantep.edu.tr/~bozdana True Stress and

### B.TECH. (AEROSPACE ENGINEERING) PROGRAMME (BTAE) Term-End Examination December, 2011 BAS-010 : MACHINE DESIGN

No. of Printed Pages : 7 BAS-01.0 B.TECH. (AEROSPACE ENGINEERING) PROGRAMME (BTAE) CV CA CV C:) O Term-End Examination December, 2011 BAS-010 : MACHINE DESIGN Time : 3 hours Maximum Marks : 70 Note : (1)

### Chapter 13 - Elasticity. A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University

Chapter 13 - Elasticity PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University 2007 Chapter 13. Elasticity Photo Vol. 10 PhotoDisk/Getty BUNGEE jumping utilizes

### CHAPTER 9 :- MECHANICAL PROPERTIES OF SOLIDS ONE MARK QUESTIONS: 1. What is elasticity of a body? 2. What is plasticity? 3. Which property of a body

1 CHAPTER 9 :- MECHANICAL PROPERTIES OF SOLIDS ONE MARK QUESTIONS: 1. What is elasticity of a body? 2. What is plasticity? 3. Which property of a body is responsible for regaining original shape and size

### CHAPTER 6 MECHANICAL PROPERTIES OF METALS PROBLEM SOLUTIONS

CHAPTER 6 MECHANICAL PROPERTIES OF METALS PROBLEM SOLUTIONS Concepts of Stress and Strain 6.1 Using mechanics of materials principles (i.e., equations of mechanical equilibrium applied to a free-body diagram),

### Physics 1114: Unit 6 Homework: Answers

Physics 1114: Unit 6 Homework: Answers Problem set 1 1. A rod 4.2 m long and 0.50 cm 2 in cross-sectional area is stretched 0.20 cm under a tension of 12,000 N. a) The stress is the Force (1.2 10 4 N)

### Welcome to the first lesson of third module which is on thin-walled pressure vessels part one which is on the application of stress and strain.

Strength of Materials Prof S. K. Bhattacharya Department of Civil Engineering Indian Institute of Technology, Kharagpur Lecture -15 Application of Stress by Strain Thin-walled Pressure Vessels - I Welcome

### Sheet metal operations - Bending and related processes

Sheet metal operations - Bending and related processes R. Chandramouli Associate Dean-Research SASTRA University, Thanjavur-613 401 Table of Contents 1.Quiz-Key... Error! Bookmark not defined. 1.Bending

CH 6: Fatigue Failure Resulting from Variable Loading Some machine elements are subjected to static loads and for such elements static failure theories are used to predict failure (yielding or fracture).

### Tensile Testing. Objectives

Laboratory 1 Tensile Testing Objectives Students are required to understand the principle of a uniaxial tensile testing and gain their practices on operating the tensile testing machine. Students are able

### Stress and Deformation Analysis. Representing Stresses on a Stress Element. Representing Stresses on a Stress Element con t

Stress and Deformation Analysis Material in this lecture was taken from chapter 3 of Representing Stresses on a Stress Element One main goals of stress analysis is to determine the point within a load-carrying

### Design Analysis and Review of Stresses at a Point

Design Analysis and Review of Stresses at a Point Need for Design Analysis: To verify the design for safety of the structure and the users. To understand the results obtained in FEA, it is necessary to

### Unit 2: Science for Engineering LO4: Understand properties of materials - Force-extension graphs Instructions and answers for teachers

Unit 2: Science for Engineering LO4: Understand properties of materials - Force-extension graphs Instructions and answers for teachers These instructions should accompany the OCR resource Force-extension

### Structural Integrity Analysis

Structural Integrity Analysis 1. STRESS CONCENTRATION Igor Kokcharov 1.1 STRESSES AND CONCENTRATORS 1.1.1 Stress An applied external force F causes inner forces in the carrying structure. Inner forces

### Unit 24: Applications of Pneumatics and Hydraulics

Unit 24: Applications of Pneumatics and Hydraulics Unit code: J/601/1496 QCF level: 4 Credit value: 15 OUTCOME 2 TUTORIAL 2 HYDRAULIC AND PNEUMATIC CYLINDERS The material needed for outcome 2 is very extensive

### APPLIED PNEUMATICS AND HYDRAULICS H TUTORIAL HYDRAULIC AND PNEUMATIC CYLINDERS. This work covers part of outcome 2 of the standard Edexcel module.

APPLIED PNEUMATICS AND HYDRAULICS H TUTORIAL HYDRAULIC AND PNEUMATIC CYLINDERS This work covers part of outcome 2 of the standard Edexcel module. The material needed for outcome 2 is very extensive so

### EDEXCEL NATIONAL CERTIFICATE/DIPLOMA MECHANICAL PRINCIPLES AND APPLICATIONS NQF LEVEL 3 OUTCOME 1 - LOADING SYSTEMS

EDEXCEL NATIONAL CERTIFICATE/DIPLOMA MECHANICAL PRINCIPLES AND APPLICATIONS NQF LEVEL 3 OUTCOME 1 - LOADING SYSTEMS TUTORIAL 1 NON-CONCURRENT COPLANAR FORCE SYSTEMS 1. Be able to determine the effects

### EVERYDAY ENGINEERING EXAMPLES FOR SIMPLE CONCEPTS

EVERYDAY ENGINEERING EXAMPLES FOR SIMPLE CONCEPTS Simple Method to Calculate Young s Modulus Elasticity MECN 4600 - Mechanical Measurement and Instrumentation Dr. Omar Meza Copyright 2015 MSEIP Engineering

### OUTCOME 1 STATIC FLUID SYSTEMS TUTORIAL 1 - HYDROSTATICS

Unit 41: Fluid Mechanics Unit code: T/601/1445 QCF Level: 4 Credit value: 15 OUTCOME 1 STATIC FLUID SYSTEMS TUTORIAL 1 - HYDROSTATICS 1. Be able to determine the behavioural characteristics and parameters

### Solution for Homework #1

Solution for Homework #1 Chapter 2: Multiple Choice Questions (2.5, 2.6, 2.8, 2.11) 2.5 Which of the following bond types are classified as primary bonds (more than one)? (a) covalent bonding, (b) hydrogen

### Hardened Concrete. Lecture No. 14

Hardened Concrete Lecture No. 14 Strength of Concrete Strength of concrete is commonly considered its most valuable property, although in many practical cases, other characteristics, such as durability

### Question 6.5: A steel bar 100 mm (4.0 in.) long and having a square cross section 20 mm

14:440:407 Ch6 Question 6.3: A specimen of aluminum having a rectangular cross section 10 mm 12.7 mm (0.4 in. 0.5 in.) is pulled in tension with 35,500 N (8000 lb f ) force, producing only elastic deformation.

### MCEN 2024, Spring 2008 The week of Apr 07 HW 9 with Solutions

MCEN 2024, Spring 2008 The week of Apr 07 HW 9 with Solutions The Quiz questions based upon HW9 will open on Thursday, Apr. 11 and close on Wednesday, Apr 17 at 1:30 PM. References to A&J: Chapters 13,

### POWER SCREWS (ACME THREAD) DESIGN

POWER SCREWS (ACME THREAD) DESIGN There are at least three types of power screw threads: the square thread, the Acme thread, and the buttress thread. Of these, the square and buttress threads are the most

### MECHANICS OF SOLIDS - BEAMS TUTORIAL 3 THE DEFLECTION OF BEAMS

MECHANICS OF SOLIDS - BEAMS TUTORIAL THE DEECTION OF BEAMS This is the third tutorial on the bending of beams. You should judge your progress by completing the self assessment exercises. On completion

### Fluid Mechanics: Static s Kinematics Dynamics Fluid

Fluid Mechanics: Fluid mechanics may be defined as that branch of engineering science that deals with the behavior of fluid under the condition of rest and motion Fluid mechanics may be divided into three

### MUKAVEMET KIRILMA HİPOTEZLERİ

1 MUKAVEMET KIRILMA HİPOTEZLERİ 17. Theories of failure or yield criteria (1) Maximum shearing stress theory (2) Octahedral shearing stress theory (3) Maximum normal stress theory for brittle materials.

### MAE 20 Winter 2011 Assignment 5

MAE 20 Winter 2011 Assignment 5 6.7 For a bronze alloy, the stress at which plastic deformation begins is 275 MPa (40,000 psi), and the modulus of elasticity is 115 GPa (16.7 10 6 psi). (a) What is the

### Fig. 5 Tube Drawing Drawing Equipment

Tube drawing is very similar to bar drawing, except the beginning stock is a tube. It is used to decrease the diameter, improve surface finish and improve dimensional accuracy. A mandrel may or may not

### DESIGN OF SLABS. 3) Based on support or boundary condition: Simply supported, Cantilever slab,

DESIGN OF SLABS Dr. G. P. Chandradhara Professor of Civil Engineering S. J. College of Engineering Mysore 1. GENERAL A slab is a flat two dimensional planar structural element having thickness small compared

### Statics and Mechanics of Materials

Statics and Mechanics of Materials Chapter 4-1 Internal force, normal and shearing Stress Outlines Internal Forces - cutting plane Result of mutual attraction (or repulsion) between molecules on both

### Mechanical Properties of Metals Mechanical Properties refers to the behavior of material when external forces are applied

Mechanical Properties of Metals Mechanical Properties refers to the behavior of material when external forces are applied Stress and strain fracture or engineering point of view: allows to predict the

### 6 1. Draw the shear and moment diagrams for the shaft. The bearings at A and B exert only vertical reactions on the shaft.

06 Solutions 46060_Part1 5/27/10 3:51 PM Page 329 6 1. Draw the shear and moment diagrams for the shaft. The bearings at and exert only vertical reactions on the shaft. 250 mm 800 mm 24 kn 6 2. Draw the

### Course 1 Laboratory. Second Semester. Experiment: Young s Modulus

Course 1 Laboratory Second Semester Experiment: Young s Modulus 1 Elasticity Measurements: Young Modulus Of Brass 1 Aims of the Experiment The aim of this experiment is to measure the elastic modulus with

### Plastic Behaviour - Tensile Strength

Plastic Behaviour - Tensile Strength Transition of mechanical behaviour from elastic to plastic depends upon the material type and its condition as tested (hot-rolled, cold-rolled, heat treated, etc.).

### STRESS-STRAIN RELATIONS

STRSS-STRAIN RLATIONS Strain Strain is related to change in dimensions and shape of a material. The most elementar definition of strain is when the deformation is along one ais: change in length strain

### Unit 48: Structural Behaviour and Detailing for Construction. Chapter 13. Reinforced Concrete Beams

Chapter 13 Reinforced Concrete Beams Concrete is a material strong in its resistance to compression, but very weak indeed in tension. good concrete will safely take a stress upwards of 7 N/mm 2 in compression,

### MCE380: Measurements and Instrumentation Lab. Chapter 9: Force, Torque and Strain Measurements

MCE380: Measurements and Instrumentation Lab Chapter 9: Force, Torque and Strain Measurements Topics: Elastic Elements for Force Measurement Dynamometers and Brakes Resistance Strain Gages Holman, Ch.

### TENSILE TESTING PRACTICAL

TENSILE TESTING PRACTICAL MTK 2B- Science Of Materials Ts epo Mputsoe 215024596 Summary Material have different properties all varying form mechanical to chemical properties. Taking special interest in

### REINFORCED CONCRETE. Reinforced Concrete Design. A Fundamental Approach - Fifth Edition

CHAPTER REINFORCED CONCRETE Reinforced Concrete Design A Fundamental Approach - Fifth Edition CONCRETE Fifth Edition A. J. Clark School of Engineering Department of Civil and Environmental Engineering

### Problem P5.2: A 1 Mg container hangs from a 15 mm diameter steel cable. What is the stress in the cable?

Problem P5.: A 1 Mg container hangs from a 15 mm diameter steel cable. What is the stress in the cable? Find the cross sectional area in terms of diameter using Equation (5.1). Calculate the tensile stress

### The Suitability of CRA Lined Pipes for Flowlines Susceptible to Lateral Buckling SUT Global Pipeline Buckling Symposium, 23 24 February 2011

The Suitability of CRA Lined Pipes for Flowlines Susceptible to Lateral Buckling SUT Global Pipeline Buckling Symposium, 23 24 February 2011 Duncan Wilmot, Technical Manager, Cladtek International, Australia

### Type of Force 1 Axial (tension / compression) Shear. 3 Bending 4 Torsion 5 Images 6 Symbol (+ -)

Cause: external force P Force vs. Stress Effect: internal stress f 05 Force vs. Stress Copyright G G Schierle, 2001-05 press Esc to end, for next, for previous slide 1 Type of Force 1 Axial (tension /

### P4 Stress and Strain Dr. A.B. Zavatsky MT07 Lecture 3 Statically Indeterminate Structures

4 Stress and Strain Dr... Zavatsky MT07 ecture 3 Statically Indeterminate Structures Statically determinate structures. Statically indeterminate structures (equations of equilibrium, compatibility, and

### Mechanical properties 3 Bend test and hardness test of materials

MME131: Lecture 15 Mechanical properties 3 Bend test and hardness test of materials A. K. M. B. Rashid Professor, Department of MME BUET, Dhaka Today s Topics Bend test of brittle materials Hardness testing

### Chapter Outline. Mechanical Properties of Metals How do metals respond to external loads?

Mechanical Properties of Metals How do metals respond to external loads? Stress and Strain Tension Compression Shear Torsion Elastic deformation Plastic Deformation Yield Strength Tensile Strength Ductility

### EQUILIBRIUM AND ELASTICITY

Chapter 12: EQUILIBRIUM AND ELASTICITY 1 A net torque applied to a rigid object always tends to produce: A linear acceleration B rotational equilibrium C angular acceleration D rotational inertia E none

### Design of Steel Structures Prof. S.R.Satish Kumar and Prof. A.R.Santha Kumar

Problem 1 Design a hand operated overhead crane, which is provided in a shed, whose details are: Capacity of crane = 50 kn Longitudinal spacing of column = 6m Center to center distance of gantry girder

### Tensile Testing Laboratory

Tensile Testing Laboratory By Stephan Favilla 0723668 ME 354 AC Date of Lab Report Submission: February 11 th 2010 Date of Lab Exercise: January 28 th 2010 1 Executive Summary Tensile tests are fundamental

### Mechanical Properties

Mechanical Properties Hardness Hardness can be defined as resistance to deformation or indentation or resistance to scratch. Hardness Indentation Scratch Rebound Indentation hardness is of particular interest

### Thermal Stress & Strain. 07 Thermal Stress and Strain Copyright G G Schierle, 2001-05 press Esc to end, for next, for previous slide 3

Thermal Stress & Strain 07 Thermal Stress and Strain Copyright G G Schierle, 2001-05 press Esc to end, for next, for previous slide 3 Thermal Stress & Strain 07 Thermal Stress and Strain Copyright G G

### PROPERTIES OF MATERIALS

1 PROPERTIES OF MATERIALS 1.1 PROPERTIES OF MATERIALS Different materials possess different properties in varying degree and therefore behave in different ways under given conditions. These properties

### Structural materials Characteristics, testing, strength evaluation

Budapest University of Technology and Economics Department of Mechanics and Materials of Structures English courses General course /2013 Fundamentals of Structures BMEEPSTG201 Lecture no. 3: Structural

### Mechanical Properties and Fracture Analysis of Glass. David Dutt Chromaglass, Inc.

Mechanical Properties and Fracture Analysis of Glass David Dutt Chromaglass, Inc. IES ALC Williamsburg 2006 2 IES ALC Williamsburg 2006 3 Outline The Ideal The Practical The Reality IES ALC Williamsburg

### MATERIALS SELECTION FOR SPECIFIC USE

MATERIALS SELECTION FOR SPECIFIC USE-1 Sub-topics 1 Density What determines density and stiffness? Material properties chart Design problems LOADING 2 STRENGTH AND STIFFNESS Stress is applied to a material

### Mechanical Principles

Unit 4: Mechanical Principles Unit code: F/60/450 QCF level: 5 Credit value: 5 OUTCOME 3 POWER TRANSMISSION TUTORIAL BELT DRIVES 3 Power Transmission Belt drives: flat and v-section belts; limiting coefficient

National Aeronautics and Space Administration Lyndon B. Johnson Space Center Houston, Texas 77058 REVISION A JULY 6, 1998 REPLACES BASELINE SPACE SHUTTLE CRITERIA FOR PRELOADED BOLTS CONTENTS 1.0 INTRODUCTION..............................................

### Rolling - Introductory concepts

Rolling - Introductory concepts R. Chandramouli Associate Dean-Research SASTRA University, Thanjavur-613 401 Joint Initiative of IITs and IISc Funded by MHRD Page 1 of 8 Table of Contents 1. Rolling -

### Comparison of typical 3D printing materials [1]

Comparison of typical 3D printing materials [1] ABS Its strength, flexibility, machinability, and higher temperature resistance make it often a preferred plastic for engineers, and professional applications.

### The elements used in commercial codes can be classified in two basic categories:

CHAPTER 3 Truss Element 3.1 Introduction The single most important concept in understanding FEA, is the basic understanding of various finite elements that we employ in an analysis. Elements are used for

### The atomic packing factor is defined as the ratio of sphere volume to the total unit cell volume, or APF = V S V C. = 2(sphere volume) = 2 = V C = 4R

3.5 Show that the atomic packing factor for BCC is 0.68. The atomic packing factor is defined as the ratio of sphere volume to the total unit cell volume, or APF = V S V C Since there are two spheres associated

### Fatigue Testing. Objectives

Laboratory 8 Fatigue Testing Objectives Students are required to understand principle of fatigue testing as well as practice how to operate the fatigue testing machine in a reverse loading manner. Students

### EDEXCEL NATIONAL CERTIFICATE/DIPLOMA. PRINCIPLES AND APPLICATIONS of FLUID MECHANICS UNIT 13 NQF LEVEL 3

EDEXCEL NATIONAL CERTIFICATE/DIPLOMA PRINCIPLES AND APPLICATIONS of FLUID MECHANICS UNIT 13 NQF LEVEL 3 OUTCOME 1 - PHYSICAL PROPERTIES AND CHARACTERISTIC BEHAVIOUR OF FLUIDS TUTORIAL 1 - SURFACE TENSION

### Ideal Cable. Linear Spring - 1. Cables, Springs and Pulleys

Cables, Springs and Pulleys ME 202 Ideal Cable Neglect weight (massless) Neglect bending stiffness Force parallel to cable Force only tensile (cable taut) Neglect stretching (inextensible) 1 2 Sketch a

### Weight Measurement Technology

Kistler-Morse (KM) introduced bolt-on weight measuring systems three decades ago. These devices featured Walter Kistler s invention, the Microcell. Over the years, many improvements were made to the Microcell

### Simple stresses are expressed as the ratio of the applied force divided by the resisting. σ = Force / Area.

Simple Stresses Simple stresses are expressed as the ratio of the applied force divided by the resisting area or σ = Force / Area. It is the expression of force per unit area to structural members that

### TIE-32: Thermal loads on optical glass

PAGE 1/7 1 Introduction In some applications optical glasses have to endure thermal loads: Finishing procedures for optical elements like lenses, prisms, beam splitters and so on involve thermal processes

### Physics Final Exam Chapter 13 Review

Physics 1401 - Final Exam Chapter 13 Review 11. The coefficient of linear expansion of steel is 12 10 6 /C. A railroad track is made of individual rails of steel 1.0 km in length. By what length would

### SEISMIC RETROFITTING TECHNIQUE USING CARBON FIBERS FOR REINFORCED CONCRETE BUILDINGS

Fracture Mechanics of Concrete Structures Proceedings FRAMCOS-3 AEDIFICA TIO Publishers, D-79104 Freiburg, Germany SEISMIC RETROFITTING TECHNIQUE USING CARBON FIBERS FOR REINFORCED CONCRETE BUILDINGS H.

### Technical Note 814-TN Engineering Considerations for Temperature Change

Technical Note 814-TN Engineering Considerations for Temperature Change www.performancepipe.com Like most materials, polyethylene is affected by temperature change. However, polyethylene s response to

### Testing Anchors in Cracked Concrete

Testing Anchors in Cracked Concrete Guidance for testing laboratories: how to generate cracks BY ROLF ELIGEHAUSEN, LEE MATTIS, RICHARD WOLLMERSHAUSER, AND MATTHEW S. HOEHLER ACI Committee 355, Anchorage

### The Manitoba Water Services Board SECTION 027110 Standard Construction Specifications September 2013 Page 1 of 12

September 2013 Page 1 of 12 Part 1 General 1.1 DESCRIPTION OF WORK.1 The work shall consist of the supply and construction of a chain link fence, barb wire fences or mesh fences as shown on the Plans or