2.2 - Screening and ranking for optimal selection. Outline
|
|
- Donna Madeleine Small
- 6 years ago
- Views:
Transcription
1 2 - Ashby Method Screening and ranking for optimal selection Outline Basic steps of selection 1. Translation of design requirements into a material specification 2. Screening out of materials that fail constraints 3. Ranking by ability to meet objectives: Material Indices 4. Search for supporting information for promising candidates Resources: M. F. Ashby, Materials Selection in Mechanical Design Butterworth Heinemann, 1999 Chapters 1-4 The Cambridge Material Selector (CES) software -- Granta Design, Cambridge (
2 The design process Design phase Market need Concept Embodiment Detail Tools for Design (Material needs) Data for all materials and processes, low precision Data for fewer materials or processes, higher precision Data for one material or process, highest precision Life phase Production Use Disposal Redesign Tools for life-cycle analysis Design requirements material specification Translation Design requirements Analyse: Function What does the component do? Constraints Objectives Free variables What essential conditions must be met? What is to be maximised or minimised? Which design variables are free? From which we obtain Screening criteria: go / no-go criteria (usually many) Ranking criteria: an ordering of the materials that go
3 Example: heat sink for microprocessor Step 1 -- Screening: Eliminate materials that can t do the job Constraints must operate at 200 o C be electrical insulator conduct heat well Retain materials with: 1. max service temp > 473K 2. must be good insulator 3. T-conduct. λ > 100 W/m.K Step 2 -- Ranking: Find the material that does the job best Objective minimise cost Rank materials : by price/kg Screening using a limit stage Mechanical attributes Minimum Maximum Density Mg/m 3 Young s modulus Elastic limit GPa MPa Thermal attributes Max. service temp. T-expansion 473 K W/m.K T-conductivity /K Electrical attributes Good insulator Poor insulator b Poor conductor Good conductor
4 Using CES to screen materials Selection using limits WC Steel Copper Alumina CFRP Selection using bar-charts Selection using property charts Thermal conductivity (W/m.s) Max service temperature (K) Aluminum Zinc PEEK PP PTFE Glass GFRP Fibreboard Lead Metals Polymers Ceramics Composites Metals Composites Polymers & elastomers Foams Price ($/kg) 10 Ceramics 100 Ranking: Modelling performance The steps: Identify function, constraints, objective and free variables. Write down equation for objective -- the performance equation. If the performance equation contains a free variable other than material identify the constraint that limits it. Use this constraint to eliminate the free variable in performance equation. Read off the combination of material properties that maximise performance.
5 Example 1: strong, light tie-rod Function Objective Constraints Free variables Tie-rod Minimise mass m: m = A L (1) F Area A Length L is specified Must not fail under load F Adequate fracture toughness Equation for constraint on A: F/A < σ y (2) Material choice Section area A; eliminate in (1) using (2): m = FL σ y Strong tie of length L and minimum mass L m = mass A = area L = length = density σ y = yield strength PERFORMANCE INDEX Chose materials with smallest σ y F Example 2: stiff, light beam Function Beam (solid square section). b F Objective Constraint Free variables 12 S L m = C Minimise mass, m, where: 2 m = AL = b L Stiffness of the beam S: CEI S = 3 L I is the second moment of area: 4 b I= 12 Material choice. Edge length b. Combining the equations gives: 1/ 2 5 1/ E 2 b = f( S,C,E,L ) b m = mass A = area L = length = density b = edge length S = stiffness I = second moment of area E = Youngs Modulus Chose materials with smallest L 1/ E 2
6 Materials indices FUNCTION Tie Beam Each combination of OBJECTIVE Minimum cost Function Objective Constraint Free variable CONSTRAINTS Has a characterising material index Shaft Column Mechanical, Thermal, Electrical... Minimum weight Maximum energy storage Minimum environ. impact Stiffness specified Strength specified Fatigue limit Geometry specified INDEX M = 1/ 2 E Minimise this! Demystifying material indices Material properties -- the Physicists view of materials, e.g. Cost, Density, Modulus, Strength, Endurance limit, Thermal conductivity, C m E σ y σ e T- expansion coefficient, α λ the Engineers view of materials Function Stiffness Strength Tension (tie) Bending (beam) Bending (panel) Material indices -- Objective: minimise mass /E 1/2 /E 1/3 /E /σy 2/3 /σ y 1/2 /σ y Minimise these! Many more: see Appendix B of the text
7 Materials indices FUNCTION Each combination of Function Objective Constraint Free variable Has a characterising material index OBJECTIVE Minimum cost Minimum weight Maximum energy storage Minimum environ. impact CONSTRAINTS Stiffness specified Strength specified Fatigue limit Geometry specified INDEX [ f ( E) ] M =, Minimise this! Demystifying material indices Material properties -- the Physicists view of materials, e.g. Cost, Density, Modulus, Strength, Endurance limit, Thermal conductivity, C m E σ y σ e T- expansion coefficient, α λ the Engineers view of materials Function Stiffness Strength Tension (tie) Bending (beam) Bending (panel) Material indices -- Objective: minimise mass /E 1/2 /E 1/3 /E /σy 2/3 /σ y 1/2 /σ y Minimise these! Many more: see Appendix B of the text
8 Log Index M = 1/2 E E = 2 / M 2 ( E) = 2Log( ) 2Log( M) Contours of constant M are lines of slope 2 on an E- chart Optimised selection using charts Young s modulus E, (GPa) Composites Woods C E 1 / 3 = Ceramics C E 1 / 2 = Polymers Foams Elastomers Density (Mg/m 3 ) Metals E = C 100 Selection using hard-copy charts Search region C E 1 / 2 =
9 Selection using the CES software Search region Ceramics D i am on d Tun gs ten Young s modulus (GPa) Young's Modulus (GPa ) Composites Woods C F R P P oly eth yl en e A lu m i ni um all oy s) S an ds ton e P TFE Polymers Carbon Steel Metals C E 1 / 2 = 0.1 PVC foam Foams P o lyu re tha ne Elastomers Density (Mg/m 3 ) D e nsity (M g /m ^3 ) Modulus Density chart Modulus spans 5 decades 0.01 GPa (foams) to 1000 GPa (diamond) Iso-lines E/, E 1/2 /, E 1/3 / selection for minimum weight, deflection-limited design
10 Strength Density chart Spans 5 decades 0.1 MPa (foams) to 104 MPa (diamond) Iso-lines σf/, σf2/3/, σf1/2/ selection for minimum weight, yield-limited design Fracture Toughness Density chart KIc measures resistance to crack propagation Iso-lines KIc4/3 /, KIc4/5 /, KIc2/3/, KIc1/2/ and KIc for minimum weight, fracture-limited design KIc = 20 MPa m1/2 considered minimum value for conventional design
11 Modulus Strength chart Chart is useful in selecting springs Iso-lines of normalized strength, defined as σf /E Modulus Relative Cost chart Relative cost is defined as: CR = [c/kg of material] / [c/kg of mild steel rod] Iso-lines help to maximize stiffness per unit cost
12 Strength Relative Cost chart Relative cost is defined as: C R = [c/kg of material] / [c/kg of mild steel rod] Iso-lines help to maximize strength per unit cost Basic procedure for materials selection Start with all materials Narrow choice with primary constraints Dictated by design/non-negotiable Seek subset that maximizes performance Combination of properties involved in maximization Examine performance indices
13 Primary constraints Designs impose primary constraints For example, a component must carry a load above 300 C -- this would eliminate all plastics as candidates. Components which must electrically insulate cannot be metals, and so forth. We can represent this condition by: P > P crit or P < P crit where P is a property (service temperature, for instance) and P crit is a critical value of that property, set by the design, which must be exceeded, or (in the case of cost or corrosion rate) must not be exceeded. Primary constraints
14 Performance maximizing criteria The next step is to seek, from the subset of materials which satisfy the primary constraints, those which maximize the performance of the component. We will use the same example as before -- the design of light, stiff components; the other indices are used in a similar way. Figure shows, as before, the modulus E, plotted against density, on log scales. The performance index is (tension on light-stiff tie): Taking logs, E / = C log E = log + log C is a family of straight parallel lines of slope 1, one line for each value of the constant C. Performance maximizing criteria The index for bending on light-stiff beam is: E 1/2 / = C gives another family of lines, this time with a slope of 2. The index for bending on light-stiff plate is: E 1/3 / = C gives another family of lines, this time with a slope of 3.
15 Performance maximizing criteria Performance maximizing criteria All materials which lie on a iso-line of E 1/2 / will perform equally well Lines to right are worse performers and lines to the left are better. The subset of materials with particularly good values of the index is identified by picking a line which isolates a small search region containing a reasonably small number of candidates.
16 Performance maximizing criteria The main points Design requirements are translated into a prescription for selecting a material by analysing the function of the component, the constraints must meet, and the objective of the design. Simple constraints are applied as limits on material attributes, screening out materials that can t do the job Constraints that limit objectives must be combined with the objective to identify a material index. The objective is best displayed on a material-property chart, allowing optimised selection The method allows refined selection while giving a perspective of alternatives in drawn from all classes of materials.
Materials: engineering, science, processing and design, 2nd edition Copyright (c)2010 Michael Ashby, Hugh Shercliff, David Cebon.
Modes of Loading (1) tension (a) (2) compression (b) (3) bending (c) (4) torsion (d) and combinations of them (e) Figure 4.2 1 Standard Solution to Elastic Problems Three common modes of loading: (a) tie
More informationDr. M. Medraj Mech. Eng. Dept. - Concordia University Mech321 lecture 20/2. A = x-area
Materials Selection and Design: Introduction Outline Introduction Design Requirements Exampls: - Example 1: Strong and light Tie-Rod - Example 2: Stiff & ight Tension Members - - Example 4: ight and Strong
More informationModule 2 Selection of Materials and Shapes. IIT, Bombay
Module Selection o Materials and Shapes Lecture Selection o Materials - I Instructional objectives By the end o this lecture, the student will learn (a) what is a material index and how does it help in
More informationMaterials Selection and Design Materials Selection - Practice
Materials Selection and Design Materials Selection - Practice Each material is characterized by a set of attributes that include its mechanical, thermal, electrical, optical, and chemical properties; its
More informationModule 2 Selection of Materials and Shapes. IIT, Bombay
Module Selection of Materials and Shapes Lecture 3 Selection of Materials - II Instructional objectives This is a continuation of the previous lecture. By the end of this lecture, the student will further
More informationLaboratory 4 Bending Test of Materials
Department of Materials and Metallurgical Engineering Bangladesh University of Engineering Technology, Dhaka MME 222 Materials Testing Sessional.50 Credits Laboratory 4 Bending Test of Materials. Objective
More informationMaterials Selection in Mechanical Design Michael Ashby
Materials Selection in Mechanical Design Michael Ashby Chapter 1. Introduction Mechanical components have mass, they carry loads, they conduct heat and electricity, they are exposed to wear and to corrosion,
More informationMechanics of Materials Primer
Mechanics of Materials rimer Notation: A = area (net = with holes, bearing = in contact, etc...) b = total width of material at a horizontal section d = diameter of a hole D = symbol for diameter E = modulus
More informationModule 2 Selection of Materials and Shapes. IIT, Bombay
Module Selection of Materials and Shapes Lecture 4 Case Studies - I Instructional objectives This is a continuation of the previous lecture. By the end of this lecture, the student will further learn how
More informationMATERIALES INDUSTRIALES II ( ) EJERCICIOS APLICACION CES EDUPACK SEGUNDA PARTE-2DO CUAT. 2012
MATERIALES INDUSTRIALES II ( 72.13 ) EJERCICIOS APLICACION CES EDUPACK SEGUNDA PARTE-2DO CUAT. 2012 GRUPO N 1 Case Study on a Light, Stiff, Strong Tie (Multiple constraints) 1. A tie, of length L loaded
More informationLecture 4 Honeycombs Notes, 3.054
Honeycombs-In-plane behavior Lecture 4 Honeycombs Notes, 3.054 Prismatic cells Polymer, metal, ceramic honeycombs widely available Used for sandwich structure cores, energy absorption, carriers for catalysts
More information12/8/2009. Prof. A.K.M.B. Rashid Department of MME BUET, Dhaka
Prof. A.K.M.B. Rashid Department of MME BUET, Dhaka Introduction and classes of properties Case studies showing selection of the right material for the job Deformation of material under the action of a
More informationAML 883 Properties and selection of engineering materials
AML 883 Properties and selection of engineering materials LECTURE 2. Materials choices for stiffnesslimited design Density and Modulus M P Gururajan Email: guru.courses@gmail.com Room No. MS 207/A 3 Phone:
More informationME 243. Mechanics of Solids
ME 243 Mechanics of Solids Lecture 2: Stress and Strain Ahmad Shahedi Shakil Lecturer, Dept. of Mechanical Engg, BUET E-mail: sshakil@me.buet.ac.bd, shakil6791@gmail.com Website: teacher.buet.ac.bd/sshakil
More informationUNIT I SIMPLE STRESSES AND STRAINS
Subject with Code : SM-1(15A01303) Year & Sem: II-B.Tech & I-Sem SIDDHARTH GROUP OF INSTITUTIONS :: PUTTUR Siddharth Nagar, Narayanavanam Road 517583 QUESTION BANK (DESCRIPTIVE) UNIT I SIMPLE STRESSES
More informationMassachusetts Institute of Technology Department of Aeronautics and Astronautics Cambridge, MA Problem Set 14
Massachusetts Institute of Technology Department of Aeronautics and Astronautics Cambridge, MA 02139 16.01/16.02 Unified Engineering I, II Fall 2003 Problem Set 14 Name: Due Date: 12/9/03 F18 F19 F20 M19
More informationMaterials Selection Case Study 1 Bases and Mechanical Properties. Professors: Anne Mertens and Davide Ruffoni Assistant: Tommaso Maurizi Enrici
Materials Selection Case Study 1 Bases and Mechanical Properties Professors: Anne Mertens and Davide Ruffoni Assistant: Tommaso Maurizi Enrici Thursday, October 4, 2018 Mechanical Properties Case Studies
More informationMaterials and Shape. Part 1: Materials for efficient structure. A. K. M. B. Rashid Professor, Department of MME BUET, Dhaka. Learning Objectives
MME445: Lecture 27 Materials and Shape Part 1: Materials for efficient structure A. K. M. B. Rashid Professor, Department of MME BUET, Dhaka Learning Objectives Knowledge & Understanding Understand the
More informationJohns Hopkins University What is Engineering? M. Karweit MATERIALS
Why do things break? Why are some materials stronger than others? Why is steel tough? Why is glass brittle? What is toughness? strength? brittleness? Elemental material atoms: MATERIALS A. Composition
More informationName :. Roll No. :... Invigilator s Signature :.. CS/B.TECH (CE-NEW)/SEM-3/CE-301/ SOLID MECHANICS
Name :. Roll No. :..... Invigilator s Signature :.. 2011 SOLID MECHANICS Time Allotted : 3 Hours Full Marks : 70 The figures in the margin indicate full marks. Candidates are required to give their answers
More informationMechanical properties 1 Elastic behaviour of materials
MME131: Lecture 13 Mechanical properties 1 Elastic behaviour of materials A. K. M. B. Rashid Professor, Department of MME BUET, Dhaka Today s Topics Deformation of material under the action of a mechanical
More information2.7 - Materials selection and shape. Outline. The shape factor, and shape limits. Material indices that include shape
- shy Method.7 - Materials selection and shape Outline Shape efficiency The shape factor, and shape limits Material indices that include shape Graphical ways of dealing with shape Resources: M.. shy, Materials
More informationMATERIALS. Why do things break? Why are some materials stronger than others? Why is steel tough? Why is glass brittle?
MATERIALS Why do things break? Why are some materials stronger than others? Why is steel tough? Why is glass brittle? What is toughness? strength? brittleness? Elemental material atoms: A. Composition
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 free-body diagram),
More informationME 2570 MECHANICS OF MATERIALS
ME 2570 MECHANICS OF MATERIALS Chapter III. Mechanical Properties of Materials 1 Tension and Compression Test The strength of a material depends on its ability to sustain a load without undue deformation
More informationNORMAL STRESS. The simplest form of stress is normal stress/direct stress, which is the stress perpendicular to the surface on which it acts.
NORMAL STRESS The simplest form of stress is normal stress/direct stress, which is the stress perpendicular to the surface on which it acts. σ = force/area = P/A where σ = the normal stress P = the centric
More informationOutline. Tensile-Test Specimen and Machine. Stress-Strain Curve. Review of Mechanical Properties. Mechanical Behaviour
Tensile-Test Specimen and Machine Review of Mechanical Properties Outline Tensile test True stress - true strain (flow curve) mechanical properties: - Resilience - Ductility - Toughness - Hardness A standard
More information[5] Stress and Strain
[5] Stress and Strain Page 1 of 34 [5] Stress and Strain [5.1] Internal Stress of Solids [5.2] Design of Simple Connections (will not be covered in class) [5.3] Deformation and Strain [5.4] Hooke s Law
More informationfive Mechanics of Materials 1 ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN DR. ANNE NICHOLS SUMMER 2017 lecture
ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN DR. ANNE NICHOLS SUMMER 2017 lecture five mechanics www.carttalk.com of materials Mechanics of Materials 1 Mechanics of Materials MECHANICS MATERIALS
More informationCOLUMNS: BUCKLING (DIFFERENT ENDS)
COLUMNS: BUCKLING (DIFFERENT ENDS) Buckling of Long Straight Columns Example 4 Slide No. 1 A simple pin-connected truss is loaded and supported as shown in Fig. 1. All members of the truss are WT10 43
More informationSERVICEABILITY OF BEAMS AND ONE-WAY SLABS
CHAPTER REINFORCED CONCRETE Reinforced Concrete Design A Fundamental Approach - Fifth Edition Fifth Edition SERVICEABILITY OF BEAMS AND ONE-WAY SLABS A. J. Clark School of Engineering Department of Civil
More informationHow materials work. Compression Tension Bending Torsion
Materials How materials work Compression Tension Bending Torsion Elemental material atoms: A. Composition a) Nucleus: protons (+), neutrons (0) b) Electrons (-) B. Neutral charge, i.e., # electrons = #
More informationQUESTION BANK SEMESTER: III SUBJECT NAME: MECHANICS OF SOLIDS
QUESTION BANK SEMESTER: III SUBJECT NAME: MECHANICS OF SOLIDS UNIT 1- STRESS AND STRAIN PART A (2 Marks) 1. Define longitudinal strain and lateral strain. 2. State Hooke s law. 3. Define modular ratio,
More information= 50 ksi. The maximum beam deflection Δ max is not = R B. = 30 kips. Notes for Strength of Materials, ET 200
Notes for Strength of Materials, ET 00 Steel Six Easy Steps Steel beam design is about selecting the lightest steel beam that will support the load without exceeding the bending strength or shear strength
More informationMAAE 2202 A. Come to the PASS workshop with your mock exam complete. During the workshop you can work with other students to review your work.
It is most beneficial to you to write this mock final exam UNDER EXAM CONDITIONS. This means: Complete the exam in 3 hours. Work on your own. Keep your textbook closed. Attempt every question. After the
More informationQUESTION BANK DEPARTMENT: CIVIL SEMESTER: III SUBJECT CODE: CE2201 SUBJECT NAME: MECHANICS OF SOLIDS UNIT 1- STRESS AND STRAIN PART A
DEPARTMENT: CIVIL SUBJECT CODE: CE2201 QUESTION BANK SEMESTER: III SUBJECT NAME: MECHANICS OF SOLIDS UNIT 1- STRESS AND STRAIN PART A (2 Marks) 1. Define longitudinal strain and lateral strain. 2. State
More informationTwo Tier projects for students in ME 160 class
ME 160 Introduction to Finite Element Method Spring 2016 Topics for Term Projects by Teams of 2 Students Instructor: Tai Ran Hsu, Professor, Dept. of Mechanical engineering, San Jose State University,
More informationHigh Tech High Top Hat Technicians. An Introduction to Solid Mechanics. Is that supposed to bend there?
High Tech High Top Hat Technicians An Introduction to Solid Mechanics Or Is that supposed to bend there? Why don't we fall through the floor? The power of any Spring is in the same proportion with the
More informationIntroduction to Engineering Materials ENGR2000. Dr. Coates
Introduction to Engineering Materials ENGR2 Chapter 6: Mechanical Properties of Metals Dr. Coates 6.2 Concepts of Stress and Strain tension compression shear torsion Tension Tests The specimen is deformed
More informationChapter 4 Deflection and Stiffness
Chapter 4 Deflection and Stiffness Asst. Prof. Dr. Supakit Rooppakhun Chapter Outline Deflection and Stiffness 4-1 Spring Rates 4-2 Tension, Compression, and Torsion 4-3 Deflection Due to Bending 4-4 Beam
More informationLecture 7, Foams, 3.054
Lecture 7, Foams, 3.054 Open-cell foams Stress-Strain curve: deformation and failure mechanisms Compression - 3 regimes - linear elastic - bending - stress plateau - cell collapse by buckling yielding
More information2.1 Background of Piping Stresses
2 Research Review One of the major additions to Tmin was the inclusion of analysis of a 2-Dimensional vertical piping span. The original plan from Dupont was to include several types of 2-D and 3-D vertical
More informationDESIGN OF BEAMS AND SHAFTS
DESIGN OF EAMS AND SHAFTS! asis for eam Design! Stress Variations Throughout a Prismatic eam! Design of pristmatic beams! Steel beams! Wooden beams! Design of Shaft! ombined bending! Torsion 1 asis for
More informationCES EduPack Case Studies: Thermo-Mechanical Applications
CES EduPack Case Studies: Thermo-Mechanical Applications Professor Mike Ashby Department of Engineering University of Cambridge M. F. Ashby, 2016 For reproduction guidance, see back page This case study
More informationRevision Guide for Chapter 4
Revision Guide for Chapter 4 Contents Student s Checklist Revision Notes Materials: properties and uses... 5 Materials selection charts... 5 Refraction... 8 Total internal reflection... 9 Conductors and
More informationMechanics of Solids. Mechanics Of Solids. Suraj kr. Ray Department of Civil Engineering
Mechanics Of Solids Suraj kr. Ray (surajjj2445@gmail.com) Department of Civil Engineering 1 Mechanics of Solids is a branch of applied mechanics that deals with the behaviour of solid bodies subjected
More informationIntroduction to Structural Member Properties
Introduction to Structural Member Properties Structural Member Properties Moment of Inertia (I): a mathematical property of a cross-section (measured in inches 4 or in 4 ) that gives important information
More informationMSC Elastomers Seminar Some Things About Elastomers
MSC Elastomers Seminar Some Things About Elastomers Kurt Miller, Axel Products, Inc. www.axelproducts.com Visit us at: axelproducts.com 2 Your Presenter Kurt Miller Founded Axel Products 1994 Instron Corporation,
More informationA Notes Formulas. This chapter is composed of 15 double pages which list, with commentaries, the results for:
The modeling process is a key step of conception. First, a crude modeling allows to validate (or not) the concept and identify the best combination of properties that maximize the performances. Then, a
More informationAn introduction to the possibilities of Materials Selection.
Modernization of two cycles (MA, BA) of competence-based curricula in Material Engineering according to the best experience of Bologna Process An introduction to the possibilities of Materials Selection.
More informationChapter 7. Highlights:
Chapter 7 Highlights: 1. Understand the basic concepts of engineering stress and strain, yield strength, tensile strength, Young's(elastic) modulus, ductility, toughness, resilience, true stress and true
More informationLecture 16-17, Sandwich Panel Notes, 3.054
Sandwich Panels Two stiff strong skins separated by a lightweight core Separation of skins by core increases moment of inertia, with little increase in weight Efficient for resisting bending and buckling
More informationCHAPTER 3 THE EFFECTS OF FORCES ON MATERIALS
CHAPTER THE EFFECTS OF FORCES ON MATERIALS EXERCISE 1, Page 50 1. A rectangular bar having a cross-sectional area of 80 mm has a tensile force of 0 kn applied to it. Determine the stress in the bar. Stress
More informationME 1401 FINITE ELEMENT ANALYSIS UNIT I PART -A. 2. Why polynomial type of interpolation functions is mostly used in FEM?
SHRI ANGALAMMAN COLLEGE OF ENGINEERING AND TECHNOLOGY (An ISO 9001:2008 Certified Institution) SIRUGANOOR, TIRUCHIRAPPALLI 621 105 Department of Mechanical Engineering ME 1401 FINITE ELEMENT ANALYSIS 1.
More informationComputational Analysis for Composites
Computational Analysis for Composites Professor Johann Sienz and Dr. Tony Murmu Swansea University July, 011 The topics covered include: OUTLINE Overview of composites and their applications Micromechanics
More informationAdvanced Strength of Materials Prof S. K. Maiti Mechanical Engineering Indian Institute of Technology, Bombay. Lecture 27
Advanced Strength of Materials Prof S. K. Maiti Mechanical Engineering Indian Institute of Technology, Bombay Lecture 27 Last time we considered Griffith theory of brittle fracture, where in it was considered
More informationPost Graduate Diploma in Mechanical Engineering Computational mechanics using finite element method
9210-220 Post Graduate Diploma in Mechanical Engineering Computational mechanics using finite element method You should have the following for this examination one answer book scientific calculator No
More informationMarch 24, Chapter 4. Deflection and Stiffness. Dr. Mohammad Suliman Abuhaiba, PE
Chapter 4 Deflection and Stiffness 1 2 Chapter Outline Spring Rates Tension, Compression, and Torsion Deflection Due to Bending Beam Deflection Methods Beam Deflections by Superposition Strain Energy Castigliano
More informationStrain Gages. Approximate Elastic Constants (from University Physics, Sears Zemansky, and Young, Reading, MA, Shear Modulus, (S) N/m 2
When you bend a piece of metal, the Strain Gages Approximate Elastic Constants (from University Physics, Sears Zemansky, and Young, Reading, MA, 1979 Material Young's Modulus, (E) 10 11 N/m 2 Shear Modulus,
More informationStructural Analysis I Chapter 4 - Torsion TORSION
ORSION orsional stress results from the action of torsional or twisting moments acting about the longitudinal axis of a shaft. he effect of the application of a torsional moment, combined with appropriate
More informationDETERMINATION OF EI FOR PULTRUDED GFRP SHEET PILE PANELS. Abstract
DETERMINATION OF EI FOR PULTRUDED GFRP SHEET PILE PANELS Yixin Shao, Cynthia Giroux and Zeid Bdeir McGill University Montreal, Quebec, Canada Abstract The flexural rigidity, EI, plays an especially important
More informationBending Load & Calibration Module
Bending Load & Calibration Module Objectives After completing this module, students shall be able to: 1) Conduct laboratory work to validate beam bending stress equations. 2) Develop an understanding of
More informationD : SOLID MECHANICS. Q. 1 Q. 9 carry one mark each. Q.1 Find the force (in kn) in the member BH of the truss shown.
D : SOLID MECHANICS Q. 1 Q. 9 carry one mark each. Q.1 Find the force (in kn) in the member BH of the truss shown. Q.2 Consider the forces of magnitude F acting on the sides of the regular hexagon having
More informationPart 1 is to be completed without notes, beam tables or a calculator. DO NOT turn Part 2 over until you have completed and turned in Part 1.
NAME CM 3505 Fall 06 Test 2 Part 1 is to be completed without notes, beam tables or a calculator. Part 2 is to be completed after turning in Part 1. DO NOT turn Part 2 over until you have completed and
More informationFLEXIBILITY METHOD FOR INDETERMINATE FRAMES
UNIT - I FLEXIBILITY METHOD FOR INDETERMINATE FRAMES 1. What is meant by indeterminate structures? Structures that do not satisfy the conditions of equilibrium are called indeterminate structure. These
More informationChapter kn m/kg Ans kn m/kg Ans. 187 kn m/kg Ans.
Chapter -1 From Tables A-0, A-1, A-, and A-4c, (a) UNS G1000 HR: S ut = 80 (55) MPa (kpsi), S yt = 10 (0) MPa (kpsi) Ans. (b) SAE 1050 CD: S ut = 690 (100) MPa (kpsi), S yt = 580 (84) MPa (kpsi) Ans. (c)
More information(2) Calculate the spring constant, k, for the spring. State an appropriate unit.
Q1. A manufacturer of springs tests the properties of a spring by measuring the load applied each time the extension is increased. The graph of load against extension is shown below. (a) State Hooke s
More informationFlexural properties of polymers
A2 _EN BUDAPEST UNIVERSITY OF TECHNOLOGY AND ECONOMICS FACULTY OF MECHANICAL ENGINEERING DEPARTMENT OF POLYMER ENGINEERING Flexural properties of polymers BENDING TEST OF CHECK THE VALIDITY OF NOTE ON
More informationAgricultural Science 1B Principles & Processes in Agriculture. Mike Wheatland
Agricultural Science 1B Principles & Processes in Agriculture Mike Wheatland (m.wheatland@physics.usyd.edu.au) Outline - Lectures weeks 9-12 Chapter 6: Balance in nature - description of energy balance
More informationTensile stress strain curves for different materials. Shows in figure below
Tensile stress strain curves for different materials. Shows in figure below Furthermore, the modulus of elasticity of several materials effected by increasing temperature, as is shown in Figure Asst. Lecturer
More informationExperimental Lab. Principles of Superposition
Experimental Lab Principles of Superposition Objective: The objective of this lab is to demonstrate and validate the principle of superposition using both an experimental lab and theory. For this lab you
More informationTHE DETERMINATION OF FRACTURE STRENGTH FROM ULTIMATE TENSILE AND TRANSVERSE RUPTURE STRESSES
Powder Metallurgy Progress, Vol.3 (003), No 3 119 THE DETERMINATION OF FRACTURE STRENGTH FROM ULTIMATE TENSILE AND TRANSVERSE RUPTURE STRESSES A.S. Wronski, A.Cias Abstract It is well-recognized that the
More informationThe science of elasticity
The science of elasticity In 1676 Hooke realized that 1.Every kind of solid changes shape when a mechanical force acts on it. 2.It is this change of shape which enables the solid to supply the reaction
More informationMicromechanics of recycled composites
Monday, 21 st August 2011 Micromechanics of recycled composites for material optimisation and eco-design Soraia Pimenta soraia.pimenta07@imperial.ac.uk S T Pinho, P Robinson Motivation Introduction recycled
More informationJUT!SI I I I TO BE RETURNED AT THE END OF EXAMINATION. THIS PAPER MUST NOT BE REMOVED FROM THE EXAM CENTRE. SURNAME: FIRST NAME: STUDENT NUMBER:
JUT!SI I I I TO BE RETURNED AT THE END OF EXAMINATION. THIS PAPER MUST NOT BE REMOVED FROM THE EXAM CENTRE. SURNAME: FIRST NAME: STUDENT NUMBER: COURSE: Tutor's name: Tutorial class day & time: SPRING
More informationStatics Principles. The laws of motion describe the interaction of forces acting on a body. Newton s First Law of Motion (law of inertia):
Unit 2 Review Statics Statics Principles The laws of motion describe the interaction of forces acting on a body Newton s First Law of Motion (law of inertia): An object in a state of rest or uniform motion
More information2.002 MECHANICS AND MATERIALS II Spring, Creep and Creep Fracture: Part III Creep Fracture c L. Anand
MASSACHUSETTS INSTITUTE OF TECHNOLOGY DEPARTMENT OF MECHANICAL ENGINEERING CAMBRIDGE, MA 02139 2.002 MECHANICS AND MATERIALS II Spring, 2004 Creep and Creep Fracture: Part III Creep Fracture c L. Anand
More information5. What is the moment of inertia about the x - x axis of the rectangular beam shown?
1 of 5 Continuing Education Course #274 What Every Engineer Should Know About Structures Part D - Bending Strength Of Materials NOTE: The following question was revised on 15 August 2018 1. The moment
More informationElastic Properties of Solid Materials. Notes based on those by James Irvine at
Elastic Properties of Solid Materials Notes based on those by James Irvine at www.antonine-education.co.uk Key Words Density, Elastic, Plastic, Stress, Strain, Young modulus We study how materials behave
More informationMechanics of Materials II. Chapter III. A review of the fundamental formulation of stress, strain, and deflection
Mechanics of Materials II Chapter III A review of the fundamental formulation of stress, strain, and deflection Outline Introduction Assumtions and limitations Axial loading Torsion of circular shafts
More informationMINE ROOF SUPPORT DESIGN AND ANALYSIS. Document no : Revision no : 1.0
MINE ROOF SUPPORT DESIGN AND ANALYSIS Document no : 1806-2697-23 Revision no : 1.0 DOCUMENT TITLE : MINE ROOF SUPPORT DESIGN AND ANALYSIS DOCUMENT NUMBER : 1806-2697-23 ISSUE : Issue 1.0 DATE : 7 October
More informationSingly Symmetric Combination Section Crane Girder Design Aids. Patrick C. Johnson
Singly Symmetric Combination Section Crane Girder Design Aids by Patrick C. Johnson PCJohnson@psu.edu The Pennsylvania State University Department of Civil and Environmental Engineering University Park,
More informationAssumptions: beam is initially straight, is elastically deformed by the loads, such that the slope and deflection of the elastic curve are
*12.4 SLOPE & DISPLACEMENT BY THE MOMENT-AREA METHOD Assumptions: beam is initially straight, is elastically deformed by the loads, such that the slope and deflection of the elastic curve are very small,
More informationMaterials selection The materials index
MME445: Lectue 20 Mateials selection The mateials index A. K. M. B. Rashid Pofesso, Depatment of MME BUET, Dhaka Leaning Objectives Knowledge & Undestanding Elementay knowledge of how to expess design
More informationQuestion 9.1: A steel wire of length 4.7 m and cross-sectional area 3.0 10 5 m 2 stretches by the same amount as a copper wire of length 3.5 m and cross-sectional area of 4.0 10 5 m 2 under a given load.
More informationUse Hooke s Law (as it applies in the uniaxial direction),
0.6 STRSS-STRAIN RLATIONSHIP Use the principle of superposition Use Poisson s ratio, v lateral longitudinal Use Hooke s Law (as it applies in the uniaxial direction), x x v y z, y y vx z, z z vx y Copyright
More informationClass XI Chapter 9 Mechanical Properties of Solids Physics
Book Name: NCERT Solutions Question : A steel wire of length 4.7 m and cross-sectional area 5 3.0 0 m stretches by the same 5 amount as a copper wire of length 3.5 m and cross-sectional area of 4.0 0 m
More informationME 207 Material Science I
ME 207 Material Science I Chapter 3 Properties in Tension and Compression Dr. İbrahim H. Yılmaz http://web.adanabtu.edu.tr/iyilmaz Automotive Engineering Adana Science and Technology University Introduction
More informationClass XI Physics. Ch. 9: Mechanical Properties of solids. NCERT Solutions
Downloaded from Class XI Physics Ch. 9: Mechanical Properties of solids NCERT Solutions Page 242 Question 9.1: A steel wire of length 4.7 m and cross-sectional area 3.0 10 5 m 2 stretches by the same amount
More informationChapter Objectives. Design a beam to resist both bendingand shear loads
Chapter Objectives Design a beam to resist both bendingand shear loads A Bridge Deck under Bending Action Castellated Beams Post-tensioned Concrete Beam Lateral Distortion of a Beam Due to Lateral Load
More information8 Deflectionmax. = 5WL 3 384EI
8 max. = 5WL 3 384EI 1 salesinfo@mechanicalsupport.co.nz PO Box 204336 Highbrook Auckland www.mechanicalsupport.co.nz 2 Engineering Data - s and Columns Structural Data 1. Properties properties have been
More informationUNIT-I STRESS, STRAIN. 1. A Member A B C D is subjected to loading as shown in fig determine the total elongation. Take E= 2 x10 5 N/mm 2
UNIT-I STRESS, STRAIN 1. A Member A B C D is subjected to loading as shown in fig determine the total elongation. Take E= 2 x10 5 N/mm 2 Young s modulus E= 2 x10 5 N/mm 2 Area1=900mm 2 Area2=400mm 2 Area3=625mm
More informationPES Institute of Technology
PES Institute of Technology Bangalore south campus, Bangalore-5460100 Department of Mechanical Engineering Faculty name : Madhu M Date: 29/06/2012 SEM : 3 rd A SEC Subject : MECHANICS OF MATERIALS Subject
More informationIntroduction to Properties and The Elastic Modulus
09 A. K. M. B. Rashid Professor, Department of MME BUET, Dhaka Introduction to Properties and The Elastic Modulus Topics to Cover Introduction to properties Introduction to mechanical properties The elastic
More informationε t increases from the compressioncontrolled Figure 9.15: Adjusted interaction diagram
CHAPTER NINE COLUMNS 4 b. The modified axial strength in compression is reduced to account for accidental eccentricity. The magnitude of axial force evaluated in step (a) is multiplied by 0.80 in case
More informationSample Question Paper
Scheme I Sample Question Paper Program Name : Mechanical Engineering Program Group Program Code : AE/ME/PG/PT/FG Semester : Third Course Title : Strength of Materials Marks : 70 Time: 3 Hrs. Instructions:
More informationSupplemental Material for Monolithic Multilayer Microfluidics via Sacrificial Molding of 3D- Printed Isomalt. M. K. Gelber and R.
Electronic Supplementary Material (ESI) for Lab on a Chip. This journal is The Royal Society of Chemistry 2015 Supplemental Material for Monolithic Multilayer Microfluidics via Sacrificial Molding of 3D-
More informationChapter 2. Atomic Structure
Chapter 2 Atomic Structure 2 6 (a) Aluminum foil used for storing food weighs about 0. g per square cm. How many atoms of aluminum are contained in one 6.25 cm 2 size of foil? (b) Using the densities and
More informationAppendix K Design Examples
Appendix K Design Examples Example 1 * Two-Span I-Girder Bridge Continuous for Live Loads AASHTO Type IV I girder Zero Skew (a) Bridge Deck The bridge deck reinforcement using A615 rebars is shown below.
More informationMATERIALS FOR CIVIL AND CONSTRUCTION ENGINEERS
MATERIALS FOR CIVIL AND CONSTRUCTION ENGINEERS 3 rd Edition Michael S. Mamlouk Arizona State University John P. Zaniewski West Virginia University Solution Manual FOREWORD This solution manual includes
More information