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


 Jessica Bailey
 2 years ago
 Views:
Transcription
1 Course 1 Laboratory Second Semester Experiment: Young s Modulus 1
2 Elasticity Measurements: Young Modulus Of Brass 1 Aims of the Experiment The aim of this experiment is to measure the elastic modulus with as high precision as possible. You will also find this experiment a valuable practice of error analysis and to planning an experiment. Skills Checklist At the end of the experiment, you should have mastered and understood the following main features: Basic error analysis Use of error analysis in planning experiments Selection of appropriate measuring instruments Measurements of quantities to the appropriate degree of accuracy. Introduction This experiment uses the bending of a beam under an applied load to measure the Young modulus of brass. Concentrate on the experimental setup, measurements and error estimates, rather than on the detailed theory of the experiment. You should, however, know what the Young modulus is, and how it enters into a bending situation. or the experimental setup shown in igure 1, the Young modulus is given by Mg ac gac E = = 4 x bd 4mbd (1) where a and c are as in igure 1, b and d are the breadth and depth of the beam respectively, x is the vertical deflection or elevation of the centre of the beam when a mass M is suspended, and m is the average value of x/m, found from the slope of the graph of x plotted against M. Shallow grooves have been cut in the upper surface of the bar to hold the knife edges from which the load is suspended. The centre of the bar is marked, and scribed lines show suitable positions for the supporting knifeedges. Please do not make any other marks on the bar. 4 Experiments 4.1 Preliminary Measurements (0 min) Before proceeding with accurate measurements, measure quickly the displacement x for one or two values of M to obtain a rough value for m = x/m. Make estimates or rough measurements of a, b, c, and d. Calculate the Young modulus from equation 1; you should get a value near Nm Main Measurements ( hr 0 min) Mount the dial gauge with its pin resting on the midpoint of the bar and record the zero ½Mg a Pillar c Mg Stirrup Knife Edge igure 1 Experimental arrangement x a ½Mg
3 reading. Hang the mass holder from the midpoint of the bar passing through the lower ends of the stirrups which hang from the beam. Measure the resulting vertical deflection x. Take a series of measurements of x for masses M up to 6 kg. Then take readings while the bar is unloaded to check for reproducibility. What should you do if the readings do not reproduce exactly? Check the positions of the knife edges frequently, and that they remain square. Plot a graph of x against M on mm graph paper whilst you are taking the results, not afterwards: this will enable you to spot "rogue" results immediately they arise, and you can check them at once. Use the Mathcad least squares fitting spreadsheet to find the best value of m and its error. You will find that the experimental points do not all lie exactly on the straight line. To investigate these deviations, measure the deflection x for a mass of about  kg. Make several measurements at this mass, unloading and replacing the mass between each reading. Use Excel to calculate the mean value of x, and to estimate the standard deviation of the observations about the mean, σ(x), NOT the standard deviation (standard error) of the mean, u(x). Since each point on the graph was obtained by measuring one value of x for each value of M, so the error in x for any one of these points should be the error in x when only one reading of x is made, and this is σ(x). Put errors bars equal to ±σ(x) on each point of your graph. About / of the error bars should intersect the bestfit straight line; is this true for your results? What can you say if all the error bars intersect the line? What can you say if only a few of the error bars intersect the line? What is your value of χ and how does that relate to the above observations? Another (very rough) check on your results can be made. The computer will give a value for the error in m, σ(m). However, assuming that the error in M is negligible, and that there are p points on your graph, then the fractional error in m, σ(m)/m, is roughly 1/ p times the fractional error in x, σ(x)/x. Use both methods to estimate σ(m); the two values should agree to within a factor of or so. The checks described above are examples of consistency checks. If the different methods do not agree, then something is wrong somewhere. Unfortunately, agreement does not guarantee that nothing is wrong! 4. Completing the Experiment (1 hr) The object of this part is to use the theory of propagation of errors as an aid in planning the rest of the experiment, and then to use these results in measuring the remaining variables to an appropriate accuracy using an appropriate instrument which you have selected on the basis of your results. The fractional error in E in terms of the fractional errors in m, a, b, c and d is σ( E) σ( m) σ( a) σ( b) σ( c) σ( d ) E = m + a + b + c + d () or maximum efficiency the percent errors in m, a, b, c², and d should be equal, i.e. the five terms on the RHS of eq. () should be the same. But you have a value for one of these terms! So knowing the percent error in m, use equation () to estimate the errors σ(a) etc. you want in a, b, c, and d. What error in E would you expect to get at the end of the experiment? Given that the resolution of a wood rule is 1mm, that of a good steel rule is 0.1mm, that of Vernier callipers is 0.0 mm and that of a micrometer screw gauge is 0.001mm (1µm),
4 select the appropriate instrument to make accurate measurements of a, b, c, and d Make accurate measurements of a, b, c, and d, and find the errors in these values. The following points should be noted. 1. Make and record repeated measurements. Use Excel to analyse your results. The errors you want here are the standard errors of the means, NOT the standard deviations. The estimates of errors that you have made before are targets, and it may not be possible to reach them with the equipment you have available. Do not try to better any target unless you can improve on all of them with little effort! Calculate the error in c² and d from the errors in c and d.. When measuring b and d, check the beam for uniformity. Does it matter if the beam is nonuniform outside the supports?. When you use a micrometer, use the ratchet mechanism to tighten the jaws; do not twist the main barrel. Unless you are a skilled operator, using the barrel will give erratic results, and you may damage the object being measured if it is squashed too fiercely. Remember it is possible to read a micrometer to 0.1 of the smallest graduation on its barrel. 4. Use equation (1) to calculate the Young modulus of the brass. Use equation () to find the error in your value of E, using the actual errors you have just found, not the target estimates from the earlier work! 5 Discussion 1. The beam provided is made of brass. Compare your results with values of E for brass given in books of tables. Take the experimental uncertainty in your value of E into account.. Sketch a bent beam and mark the regions of tensile and compressive strains. Show the stresses producing these strains; do they form a couple? Use your sketch to explain why bending a beam allows the measurement of the tensile Young modulus.. Consider the advantages and disadvantages of this method compared with the direct stretching of the beam or a wire of the same material. Can you think of any other ways of measuring the Young modulus? 4. What are the main sources of error in E? Is the limit to your accuracy variation due to e.g. nonuniformity or to the precision of your measuring equipment? Is it feasible, bearing in mind the time and equipment available, to reduce these errors? Is it really essential to reduce the errors? 5. Equation (1) relates the elevation per unit mass x/m to the lengths a and c. It is clear that x/m=0 for a=0 or c=0, and therefore for a beam of fixed length (c+a) there must be a value of c for which x/m is a maximum. If you have time, show that this is achieved when c=4a. Why should you choose c and a to satisfy this relation? Does it matter if c is not exactly equal to 4a? 6 References Newman.H., Searle V.H.L., Arnold, London) The General Properties of Matter, 5th edition, (Edward 4
5 Sprackling M.T., Liquids and Solids, (Routledge and Kegan Paul, London) Appendix 1 These notes summarise the general forms of the response of a solid body to applied forces. urther details can be found in Sprackling, chapter, or Newman and Searle, chapter Elastic Moduli The moduli of elasticity of a material are measures of its resistance to a change of size or shape under the influence of a set of applied forces. The applied forces constitute stresses, expressed as a force per unit area, and the resulting deformation is described as a strain, which is the ratio of the change in some dimension to an original dimension. If the strain returns to zero when the stress is removed, the deformation is said to be elastic. In many materials for small elastic strains, the deformation obeys Hooke's law which states that the stress is proportional to the strain. The constant of proportionality is the elastic modulus, so that Modulus = stress/strain Area A ϕ Crosssectional area A igure Shear modulus and Young modulus Materials can be deformed in several different ways, corresponding to different moduli of elasticity. or isotropic materials (i.e. those whose properties are the same in all directions) there are three moduli of particular importance. 1. The bulk modulus, K, corresponds to a change of volume without change of shape. This applies to deformation under a uniform hydrostatic pressure, The stress is the pressure p, and the strain is the change in volume δv (negative because increase in pressure produces a decrease in volume) divided by the initial volume V. The bulk modulus is given by K = p/(δv/v).. The shear modulus, n, also known as the modulus of rigidity, corresponds to a change of shape at constant volume. The stress is the tangential force acting over a surface of area A divided by A, and the strain is represented by the angle of shear, φ. The modulus is given by n = (/A)/φ.. Young modulus, E, is used when a change in length of a sample is produced when a tensile or compressive stress is applied, with no external forces applied to the side surfaces of the specimen. The stress is the tensile force divided by the crosssectional area of the sample, and the strain is the change in length δl divided by the original length l, The modulus is given by E = (/A)/(δl/l). At the same time, there is also a contraction or expansion at right angles to the tensile or compressive stress. The ratio of the magnitude of this transverse strain to the principal strain is called the Poisson ratio, σ. l δl 5
6 These various moduli are related by the equations K = E { ( 1 σ) } and E n = { ( 1+ σ )}. All types of elastic deformation of isotropic media can be described in terms of any two of these moduli. Note however that an elastic modulus only has meaning if Hooke's law is obeyed; the ratio stress/strain is not constant for a nonlinear material, even if it is perfectly elastic. 7. Theory of A Bending Beam When a beam is bent into an arc of radius R, the material in one part of the beam is stretched and under tension, and the material in another part is under compression. These tensile and compressive strains are produced by related stresses, which combine to form a couple called the bending moment G. R and G are obviously related to each other, and a little thought should convince you that the Young modulus of the material, E, and the shape of the bar are also involved. The full theory of the elastic bending of a beam or cantilever is given in Newman and Searle (section 5.9). There it is shown (eq. 5.1) that E is given by E GR = (A1) I where I, called the second moment of area, is the factor that takes account of the shape of the bar. (Newman and Searle use the symbol Y for the Young Modulus. They call the second moment of area I the geometrical moment of inertia, and they use the combination Ak² for this.) In this experiment, the bending moment is constant along the length AB of the beam, and its value is G = 1 Mga (A) rom the geometry of a circle, it can be shown that the radius R is related to the elevation x of the midpoint by provided that x is much smaller than R R c = (A) 8 x or a rectangular beam of thickness d and width b, the second moment of area I about its neutral axis is d / bd I = b y d y = 1 d / Substituting expressions (), () and (4) into (1) gives an expression for the Young modulus in terms of easily measurable quantities: (A4) Mgac gac E = = (A5) 4xbd 4bd m where m is the average value of x/m. This is equation (1) of the main text. 6
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
More informationExperiment 3 Modulus of Elasticity
Related topics Young s modulus, modulus of elasticity, stress, deformation, Poisson s ratio, Hooke s Law. Principle and task A flat bar is supported at two points. It is bent by the action a force acting
More informationMATERIALS SELECTION FOR SPECIFIC USE
MATERIALS SELECTION FOR SPECIFIC USE1 Subtopics 1 Density What determines density and stiffness? Material properties chart Design problems LOADING 2 STRENGTH AND STIFFNESS Stress is applied to a material
More informationLaboratory Weeks 9 10 Theory of Pure Elastic Bending
Laboratory Weeks 9 10 Theory of Pure Elastic Bending Objective To show the use of the Sagital method for finding the Radius of Curvature of a beam, to prove the theory of bending, and find the elastic
More informationMECHANICS 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.
More informationMENG 302L Lab 4: Modulus of Elasticity and Poisson s Ratio
MENG 302L Lab 4: Modulus of Elasticity and Poisson s Ratio Introduction: In Lab 4 we will measure the two fundamental elastic constants relating stress to strain: Modulus of Elasticity and Poisson s Ratio.
More informationStress 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 loadcarrying
More informationMECHANICS OF MATERIALS
2009 The McGrawHill Companies, Inc. All rights reserved. Fifth SI Edition CHAPTER 4 MECHANICS OF MATERIALS Ferdinand P. Beer E. Russell Johnston, Jr. John T. DeWolf David F. Mazurek Pure Bending Lecture
More informationCHAPTER 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
More informationBending Beam. Louisiana State University. Joshua Board
Bending Beam Louisiana State University Joshua Board Table of Contents: Table of Figures:... 4 Purpose... 5 Introduction... 5 Apparatus and Test Procedures... 11 Summary of Data... 14 Discussion of Results...
More informationChapter 4 Strain and Material Relations
CIVL 222 STRENGTH OF MATERIALS Chapter 4 Strain and Material Relations Terminology 1. Displacement 2. Deformation 3. Strain 4. Average Axial Strain 5. Shearing Strain 6. Poisson s Ratio 7. Mechanical Properties
More informationProblem 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
More informationThere are three principle ways a load can be applied:
MATERIALS SCIENCE Concepts of Stress and Strains Stressstrain test is used to determine the mechanical behavior by applying a static load uniformly over a cross section or a surface of a member. The test
More informationMECHANICAL 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 prerequisite knowledge
More informationTorsion 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
More informationStructures 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
More informationChapter 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
More informationENGINEERING 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
More informationSTRESSSTRAIN RELATIONS
STRSSSTRAIN 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
More informationStrength of materials Lab. Manual. Production Engineering
1 Strength of materials Lab. Manual Production Engineering 2 Strength of materials lab. manual Contents S.No. Title Pg.no 1. Rockwell Hardness test 3 2. Brinell hardness test. 5 3. Impact test 8 4. Tension
More informationENGINEERING 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
More informationPin jointed structures are often used because they are simple to design, relatively inexpensive to make, easy to construct, and easy to modify.
4. FORCES in PIN JOINTED STRUCTURES Pin jointed structures are often used because they are simple to design, relatively inexpensive to make, easy to construct, and easy to modify. They can be fixed structures
More informationSTRENGTH OF MATERIALS LABORATORY
STRENGTH OF MATERIALS LABORATORY 1. TESTING OF MATERIALS IN TORSION OBJECTIVE To apply an increasing torque to straight cylindrical specimens of material, to observe the deformation of the specimens, and
More informationStressStrain Relationship
(Strength of Materials) Dave Morgan StressStrain Relationship p. 1/21 The tension test: StressStrain Relationship p. 2/21 The tension test: Is a common standardised test that can
More informationMECHANICS 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.
More informationKINGS COLLEGE OF ENGINEERING DEPARTMENT OF MECHANICAL ENGINEERING QUESTION BANK. UNIT I STRESS STRAIN DEFORMATION OF SOLIDS PART A (2 Marks)
KINGS COLLEGE OF ENGINEERING DEPARTMENT OF MECHANICAL ENGINEERING QUESTION BANK SUB CODE/NAME: CE1259 STRENGTH OF MATERIALS YEAR/SEM: II / IV 1. What is Hooke s Law? 2. What are the Elastic Constants?
More information8.2 Elastic Strain Energy
Section 8. 8. Elastic Strain Energy The strain energy stored in an elastic material upon deformation is calculated below for a number of different geometries and loading conditions. These expressions for
More informationReinforced Concrete Design SHEAR IN BEAMS
CHAPTER Reinforced Concrete Design Fifth Edition SHEAR IN BEAMS A. J. Clark School of Engineering Department of Civil and Environmental Engineering Part I Concrete Design and Analysis 4a FALL 2002 By Dr.
More informationσ = F / A o Chapter Outline Introduction Mechanical Properties of Metals How do metals respond to external loads?
Mechanical Properties of Metals How do metals respond to external loads? and Tension Compression Shear Torsion Elastic deformation Chapter Outline Introduction To understand and describe how materials
More informationEQUILIBRIUM 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
More informationStresses in Beam (Basic Topics)
Chapter 5 Stresses in Beam (Basic Topics) 5.1 Introduction Beam : loads acting transversely to the longitudinal axis the loads create shear forces and bending moments, stresses and strains due to V and
More informationCH 4: Deflection and Stiffness
CH 4: Deflection and Stiffness Stress analyses are done to ensure that machine elements will not fail due to stress levels exceeding the allowable values. However, since we are dealing with deformable
More informationRigid pavement design
Chapter 29 Rigid pavement design 29.1 Overview As the name implies, rigid pavements are rigid i.e, they do not flex much under loading like flexible pavements. They are constructed using cement concrete.
More informationMECHANICS 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
More informationMechanics of Materials StressStrain Curve for Mild Steel
StressStrain Curve for Mild Steel 131 Definitions 132a Hooke s Law Shear Modulus: Stress: Strain: Poisson s Ratio: Normal stress or strain = " to the surface Shear stress = to the surface Definitions
More informationWelcome to the first lesson of third module which is on thinwalled 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 Thinwalled Pressure Vessels  I Welcome
More informationEDEXCEL 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
More informationSolid 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
More informationPhysical Measurements
Name: Date: PC1141 Physics I Physical Measurements 5 Laboratory Worksheet Part A: Density Determination Instrument Least count Estimated fraction Meter stick Vernier caliper Micrometer caliper Mass balance
More information10 Space Truss and Space Frame Analysis
10 Space Truss and Space Frame Analysis 10.1 Introduction One dimensional models can be very accurate and very cost effective in the proper applications. For example, a hollow tube may require many thousands
More informationChapter 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
More informationSAMPLE OF THE STUDY MATERIAL PART OF CHAPTER 1 STRESS AND STRAIN
SAMPLE OF THE STUDY MATERIAL PART OF CHAPTER 1 STRESS AND STRAIN 1.1 Stress & Strain Stress is the internal resistance offered by the body per unit area. Stress is represented as force per unit area. Typical
More information1.103 CIVIL ENGINEERING MATERIALS LABORATORY (123) Dr. J.T. Germaine Spring 2004 TENSILE TESTING AND STRESS STRAIN PROPERTIES OF STEEL
1.103 CIVIL ENGINEERING MATERIALS LABORATORY (123) Dr. J.T. Germaine MIT Spring 2004 Purpose: LABORATORY ASSIGNMENT NUMBER 2 TENSILE TESTING AND STRESS STRAIN PROPERTIES OF STEEL You will learn about:
More informationStrength of Materials
FE Review Strength of Materials Problem Statements Copyright 2008 C. F. Zorowski NC State E490 Mechanics of Solids 110 KN 90 KN 13.5 KN A 3 = 4.5x103 m 2 A 2 = 2x103 m 2 A 1 = 5x104 m 2 1. A circular
More informationMCEN 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,
More informationMECHANICS OF MATERIALS Plastic Deformations of Members With a Single Plane of Symmetry
Plastic Deformations of Members With a Single Plane of Smmetr Full plastic deformation of a beam with onl a vertical plane of smmetr. The neutral axis cannot be assumed to pass through the section centroid.
More informationStrength of Materials
Strength of Materials 1. Strain is defined as the ratio of (a) change in volume to original volume (b) change in length to original length (c) change in crosssectional area to original crosssectional
More informationStatics and Mechanics of Materials
Statics and Mechanics of Materials Chapter 4 Stress, Strain and Deformation: Axial Loading Objectives: Learn and understand the concepts of internal forces, stresses, and strains Learn and understand the
More informationLab for Deflection and Moment of Inertia
Deflection and Moment of Inertia Subject Area(s) Associated Unit Lesson Title Physics Wind Effects on Model Building Lab for Deflection and Moment of Inertia Grade Level (1112) Part # 2 of 3 Lesson #
More informationMCE380: 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.
More informationQuestion 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.
More informationFigure 12 1 Short columns fail due to material failure
12 Buckling Analysis 12.1 Introduction There are two major categories leading to the sudden failure of a mechanical component: material failure and structural instability, which is often called buckling.
More informationStress 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
More informationIdeal 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
More informationRotational Motion. Symbol Units Symbol Units Position x (m) θ (rad) (m/s) " = d# Source of Parameter Symbol Units Parameter Symbol Units
Introduction Rotational Motion There are many similarities between straightline motion (translation) in one dimension and angular motion (rotation) of a rigid object that is spinning around some rotation
More informationEDEXCEL NATIONAL CERTIFICATE/DIPLOMA MECHANICAL PRINCIPLES OUTCOME 2 ENGINEERING COMPONENTS TUTORIAL 1 STRUCTURAL MEMBERS
ENGINEERING COMPONENTS EDEXCEL NATIONAL CERTIFICATE/DIPLOMA MECHANICAL PRINCIPLES OUTCOME ENGINEERING COMPONENTS TUTORIAL 1 STRUCTURAL MEMBERS Structural members: struts and ties; direct stress and strain,
More informationME 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
More information1.1 To determine the effect the slenderness ratio has on the load carrying capacity of pin ended columns.
I. OBJECTIVES 1.1 To determine the effect the slenderness ratio has on the load carrying capacity of pin ended columns. 1. To observe short, intermediate and long column behavior under the application
More informationSHM Simple Harmonic Motion revised June 16, 2012
SHM Simple Harmonic Motion revised June 16, 01 Learning Objectives: During this lab, you will 1. communicate scientific results in writing.. estimate the uncertainty in a quantity that is calculated from
More informationDeflections. Question: What are Structural Deflections?
Question: What are Structural Deflections? Answer: The deformations or movements of a structure and its components, such as beams and trusses, from their original positions. It is as important for the
More informationPLASTIC DEFORMATION AND STRESSSTRAIN CURVES
PLASTIC DEFORMATION AND STRESSSTRAIN CURVES Introduction Background Unit: Plastic Deformation and StressStrain Curves In the last unit we studied the elastic response of materials to externally applied
More informationUnit 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,
More informationMECHANICAL PROPERTIES OF MATERIALS. IE114 Materials Science and General Chemistry Lecture6
MECHANICAL PROPERTIES OF MATERIALS IE114 Materials Science and General Chemistry Lecture6 Overview 1) ELASTIC DEFORMATION  Elastic Behavior  Anelasticity  Elastic Properties of Materials 2) PLASTIC
More informationYOUNG S MODULUS. Introduction
Introduction In this experiment, we study the elasticity of some solid materials by measuring their Young s modulus. A highly useful optical method is also introduced for the measurement of a very small
More informationSTUDY THE EFFECT OF THE VARIATION OF LAYER'S THICKNESS ON THE BENDING CHARACTERISTICS OF THE COMPOSITE BEAM
STUDY THE EFFECT OF THE VARIATION OF LAYER'S THICKNESS ON THE BENDING CHARACTERISTICS OF THE COMPOSITE BEAM Assist. Lecturer Manal Hameed Jasem AlMustansiriya University/College of Eng./Mech. Eng. Depart.
More informationMechanics of Materials
Mechanics of Materials Notation: a = acceleration A = area (net = with holes, bearing = in contact, etc...) ASD = allowable stress design d = diameter of a hole = calculus symbol for differentiation e
More informationCHAPTER MECHANICS OF MATERIALS
CHPTER 4 Pure MECHNCS OF MTERLS Bending Pure Bending Pure Bending Other Loading Tpes Smmetric Member in Pure Bending Bending Deformations Strain Due to Bending Stress Due to Bending Beam Section Properties
More informationIntroduction to Mechanical Behavior of Biological Materials
Introduction to Mechanical Behavior of Biological Materials Ozkaya and Nordin Chapter 7, pages 127151 Chapter 8, pages 173194 Outline Modes of loading Internal forces and moments Stiffness of a structure
More informationChapter 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
More informationMeasurement of Length, Mass, Volume and Density
Measurement of Length, Mass, Volume and Density Experimental Objective The objective of this experiment is to acquaint you with basic scientific conventions for measuring physical quantities. You will
More informationValidation of Simulation Results Through Use of DIC Techniques
Validation of Simulation Results Through Use of DIC Techniques Brian Croop and Daniel Roy, DatapointLabs + technical center for materials a DatapointLabs affiliate Materials Testing Data Infrastructure
More informationThe following sketches show the plans of the two cases of oneway slabs. The spanning direction in each case is shown by the double headed arrow.
9.2 Oneway Slabs This section covers the following topics. Introduction Analysis and Design 9.2.1 Introduction Slabs are an important structural component where prestressing is applied. With increase
More informationMUKAVEMET 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.
More informationMAE 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
More informationMETU 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: B306) INTRODUCTION TENSION TEST Mechanical testing
More informationCHAPTER 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 freebody diagram),
More informationP4 Stress and Strain Dr. A.B. Zavatsky MT07 Lecture 4 Stresses on Inclined Sections
4 Stress and Strain Dr. A.B. Zavatsky MT07 Lecture 4 Stresses on Inclined Sections Shear stress and shear strain. Equality of shear stresses on perpendicular planes. Hooke s law in shear. Normal and shear
More informationMechanical properties laboratory practice guide 2015
Mechanical properties laboratory practice guide 215 Hardness test methods Hardness is resistance of material to plastic deformation caused by indentation. 1. Brinell Hardness Test [1] Dr. J. A. Brinell
More informationStress Calculation Basics and Examples
Stress Calculation Basics and Examples Miskolc University During solidification and cooling stresses appear in the casting. This can be caused: by the shrinkage of the casting, by the formation of temperature
More informationR A = R B = = 3.6 kn. ΣF y = 3.6 V = 0 V = 3.6 kn. A similar calculation for any section through the beam at 3.7 < x < 7.
ENDNG STRESSES & SHER STRESSES N EMS (SSGNMENT SOLUTONS) Question 1: 89 mm 3 mm Parallam beam has a length of 7.4 m and supports a concentrated load of 7.2 kn, as illustrated below. Draw shear force and
More informationME 105 Mechanical Engineering Laboratory Spring Quarter Tensile Test
ME 105 Mechanical Engineering Lab Page 1 ME 105 Mechanical Engineering Laboratory Spring Quarter 2003 3. Tensile Test Introduction In this lab, you will study the deformation and fracture characteristics
More informationAdam Zaborski handouts for Afghans
Tensile test Adam Zaborski handouts for Afghans Outline Tensile test purpose Universal testing machines and test specimens Stressstrain diagram Mild steel : proportional stage, elastic limit, yielding
More informationStrength of Materials Prof: S.K.Bhattacharya Dept of Civil Engineering, IIT, Kharagpur Lecture no 29 Stresses in Beams IV
Strength of Materials Prof: S.K.Bhattacharya Dept of Civil Engineering, IIT, Kharagpur Lecture no 29 Stresses in Beams IV Welcome to the fourth lesson of the sixth module on Stresses in Beams part 4.
More informationStretching Rubber Bands Understanding Hooke's Law
Stretching Rubber Bands Understanding Hooke's Law Experimental Writeup Introduction The reason that we can see rubber bands stretch when we pull on them, but pulling as hard as you can on your table will
More informationPOWER 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
More informationEML 5526 FEA Project 1 Alexander, Dylan. Project 1 Finite Element Analysis and Design of a Plane Truss
Problem Statement: Project 1 Finite Element Analysis and Design of a Plane Truss The plane truss in Figure 1 is analyzed using finite element analysis (FEA) for three load cases: A) Axial load: 10,000
More informationWorked Examples of mathematics used in Civil Engineering
Worked Examples of mathematics used in Civil Engineering Worked Example 1: Stage 1 Engineering Surveying (CIV_1010) Tutorial  Transition curves and vertical curves. Worked Example 1 draws from CCEA Advanced
More informationMECHANICS 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.
More informationPHYS2212 LAB Coulomb s Law and the Force between Charged Plates
PHYS2212 LAB Coulomb s Law and the Force between Charged Plates Objectives To investigate the electrostatic force between charged metal plates and determine the electric permittivity of free space, ε
More informationPC1221 Fundamentals of Physics I Inertia Wheel
PC1221 Fundamentals of Physics I Inertia Wheel 1 Purpose Determination of the angular acceleration of the inertial wheel as a function of the applied torque Determination of the moment of inertia I of
More informationCE Mechanics of Materials Lab. Louisiana State University. Laboratory Report No. 1. Hardness Test. Joshua Board
CE 3410 Mechanics of Materials Lab Louisiana State University Laboratory Report No. 1 Hardness Test by Joshua Board Table of Contents Purpose:... 3 Introduction:... 3 Apparatus and Test Procedures:...
More information11 Vibration Analysis
11 Vibration Analysis 11.1 Introduction A spring and a mass interact with one another to form a system that resonates at their characteristic natural frequency. If energy is applied to a spring mass system,
More informationCitation Journal of Constructional Steel Research, 2014, v. 96, p
Title The Art of Coupon Tests Author(s) Huang, Y; Young, B Citation Journal of Constructional Steel Research, 014, v. 96, p. 159175 Issued Date 014 URL http://hdl.handle.net/107/00516 Rights NOTICE: this
More informationMeasurement of Density
PC1221 Fundamentals of Physics I Measurement of Density 1 Purpose Determine the mass, length, inner and outer diameters of a hollow cylinder of unknown metal. Calculate the density of the hollow cylinder.
More informationAnalysis of Stress and Strain
07Ch07.qd 9/7/08 1:18 PM Page 571 7 Analsis of Stress and Strain Plane Stress Problem 7.1 An element in plane stress is subjected to stresses s 4750 psi, s 100 psi, and t 950 psi, as shown in the figure.
More informationDetermination of g using a spring
INTRODUCTION UNIVERSITY OF SURREY DEPARTMENT OF PHYSICS Level 1 Laboratory: Introduction Experiment Determination of g using a spring This experiment is designed to get you confident in using the quantitative
More informationWMH group Germany. QuALität. NTS Beam System
WMH group Germany. QuALität. NTS Beam System Profile overview For detailed dimensions, please see the enclosed 1:1 die drawings. NTS 23x16 l die No. 41735 G=19,82 kg/m NTS 23x16 s die No. 41738 G=29,74
More informationComparison 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.
More informationProperties 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
More informationStructural 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
More information