# Stress-Strain Behavior

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 Stress-Strain Behavior 6.3 A specimen of aluminum having a rectangular cross section 10 mm 1.7 mm (0.4 in. 0.5 in.) is pulled in tension with 35,500 N (8000 lb f ) force, producing only elastic deformation. Calculate the resulting strain. This problem calls for us to calculate the elastic strain that results for an aluminum specimen stressed in tension. The cross-sectional area is just (10 mm) (1.7 mm) 17 mm ( m 0.0 in. ); also, the elastic modulus for Al is given in Table 6.1 as 69 GPa (or N/m ). Combining Equations 6.1 and 6.5 and solving for the strain yields ε σ E F A 0 E 35,500 N ( m )( N/m ) 6.5 A steel bar 100 mm (4.0 in.) long and having a square cross section 0 mm (0.8 in.) on an edge is pulled in tension with a load of 89,000 N (0,000 lb f ), and experiences an elongation of 0.10 mm ( in.). Assuming that the deformation is entirely elastic, calculate the elastic modulus of the steel. This problem asks us to compute the elastic modulus of steel. For a square cross-section, A 0 b 0, where b 0 is the edge length. Combining Equations 6.1, 6., and 6.5 and solving for E, leads to F E σ ε A 0 l F b 0 l (89,000 N)( m) ( m) ( m) N/m 3 GPa ( psi)

2 6.7 For a bronze alloy, the stress at which plastic deformation begins is 75 MPa (40,000 psi), and the modulus of elasticity is 115 GPa ( psi). (a) What is the maximum load that may be applied to a specimen with a cross-sectional area of 35 mm (0.5 in. ) without plastic deformation? (b) If the original specimen length is 115 mm (4.5 in.), what is the maximum length to which it may be stretched without causing plastic deformation? (a) This portion of the problem calls for a determination of the maximum load that can be applied without plastic deformation (F y ). Taking the yield strength to be 75 MPa, and employment of Equation 6.1 leads to F y σ y A 0 ( N/m )( m ) 89,375 N (0,000 lb f ) (b) The maximum length to which the sample may be deformed without plastic deformation is determined from Equations 6. and 6.5 as l i 1 + σ E 75 MPa (115 mm) mm (4.51 in.) MPa Elastic Properties of Materials 6.15 A cylindrical specimen of aluminum having a diameter of 19 mm (0.75 in.) and length of 00 mm (8.0 in.) is deformed elastically in tension with a force of 48,800 N (11,000 lb f ). Using the data contained in Table 6.1, determine the following: (a) The amount by which this specimen will elongate in the direction of the applied stress. (b) The change in diameter of the specimen. Will the diameter increase or decrease?

3 (a) We are asked, in this portion of the problem, to determine the elongation of a cylindrical specimen of aluminum. Combining Equations 6.1, 6., and 6.5, leads to F π d 0 4 σ Eε E l Or, solving for l (and realizing that E 69 GPa, Table 6.1), yields l 4F π d 0 E (4)(48,800 N)( m) (π)( m) ( N /m ) m 0.50 mm (0.0 in.) (b) We are now called upon to determine the change in diameter, d. Using Equation 6.8 ν ε x ε z d / d 0 l / From Table 6.1, for aluminum, ν Now, solving the above expression for d yields d ν l d 0 (0.33)(0.50 mm)(19 mm) 00 mm mm ( in.) The diameter will decrease A cylindrical specimen of a hypothetical metal alloy is stressed in compression. If its original and final diameters are and 0.05 mm, respectively, and its final length is mm, compute its original length if the deformation is totally elastic. The elastic and shear moduli for this alloy are 105 GPa and 39.7 GPa, respectively.

4 This problem asks that we compute the original length of a cylindrical specimen that is stressed in compression. It is first convenient to compute the lateral strain ε x as ε x d 0.05 mm mm d mm In order to determine the longitudinal strain ε z we need Poisson's ratio, which may be computed using Equation 6.9; solving for ν yields ν E G MPa ()( MPa) Now ε z may be computed from Equation 6.8 as ε z ε x ν Now solving for using Equation 6. l i 1 + ε z mm 75.5 mm A brass alloy is known to have a yield strength of 75 MPa (40,000 psi), a tensile strength of 380 MPa (55,000 psi), and an elastic modulus of 103 GPa ( psi). A cylindrical specimen of this alloy 1.7 mm (0.50 in.) in diameter and 50 mm (10.0 in.) long is stressed in tension and found to elongate 7.6 mm (0.30 in.). On the basis of the information given, is it possible to compute the magnitude of the load that is necessary to produce this change in length? If so, calculate the load. If not, explain why. We are asked to ascertain whether or not it is possible to compute, for brass, the magnitude of the load necessary to produce an elongation of 7.6 mm (0.30 in.). It is first necessary to compute the strain at yielding from the yield strength and the elastic modulus, and then the strain experienced by the test specimen. Then, if

5 ε(test) < ε(yield) deformation is elastic, and the load may be computed using Equations 6.1 and 6.5. However, if ε(test) > ε(yield) computation of the load is not possible inasmuch as deformation is plastic and we have neither a stress-strain plot nor a mathematical expression relating plastic stress and strain. We compute these two strain values as ε(test) l 7.6 mm 50 mm 0.03 and ε(yield) σ y E 75 MPa MPa Therefore, computation of the load is not possible since ε(test) > ε(yield). Tensile Properties 6.5 Figure 6.1 shows the tensile engineering stress strain behavior for a steel alloy. (a) What is the modulus of elasticity? (b) What is the proportional limit? (c) What is the yield strength at a strain offset of 0.00? (d) What is the tensile strength? Using the stress-strain plot for a steel alloy (Figure 6.1), we are asked to determine several of its mechanical characteristics. (a) The elastic modulus is just the slope of the initial linear portion of the curve; or, from the inset and using Equation 6.10 E σ σ 1 ε ε 1 (00 0) MPa ( ) MPa 00 GPa ( psi) The value given in Table 6.1 is 07 GPa. (b) The proportional limit is the stress level at which linearity of the stress-strain curve ends, which is approximately 300 MPa (43,500 psi). (c) The 0.00 strain offset line intersects the stress-strain curve at approximately 400 MPa (58,000 psi).

6 (d) The tensile strength (the maximum on the curve) is approximately 515 MPa (74,700 psi). 6.7 A load of 85,000 N (19,100 lb f ) is applied to a cylindrical specimen of a steel alloy (displaying the stress strain behavior shown in Figure 6.1) that has a cross-sectional diameter of 15 mm (0.59 in.). (a) Will the specimen experience elastic and/or plastic deformation? Why? (b) If the original specimen length is 50 mm (10 in.), how much will it increase in length when this load is applied? This problem asks us to determine the deformation characteristics of a steel specimen, the stress-strain behavior for which is shown in Figure 6.1. (a) In order to ascertain whether the deformation is elastic or plastic, we must first compute the stress, then locate it on the stress-strain curve, and, finally, note whether this point is on the elastic or plastic region. Thus, from Equation 6.1 σ F A 0 85, 000 N π m N/m 481 MPa (69,900 psi) The 481 MPa point is beyond the linear portion of the curve, and, therefore, the deformation will be both elastic and plastic. (b) This portion of the problem asks us to compute the increase in specimen length. From the stress-strain curve, the strain at 481 MPa is approximately Thus, from Equation 6. l ε (0.0135)(50 mm) 3.4 mm (0.135 in.) 6.35 A cylindrical metal specimen having an original diameter of 1.8 mm (0.505 in.) and gauge length of mm (.000 in.) is pulled in tension until fracture occurs. The diameter at the point of fracture is 6.60 mm (0.60 in.), and the fractured gauge length is 7.14 mm (.840 in.). Calculate the ductility in terms of percent reduction in area and percent elongation.

7 This problem calls for the computation of ductility in both percent reduction in area and percent elongation. Percent reduction in area is computed using Equation 6.1 as %RA π d 0 π d f π d in which d 0 and d f are, respectively, the original and fracture cross-sectional areas. Thus, %RA 1.8 mm π 6.60 mm π 1.8 mm π % While, for percent elongation, we use Equation 6.11 as %EL l f mm mm mm 100 4% Elastic Recovery After Plastic Deformation 6.49 A cylindrical specimen of a brass alloy 7.5 mm (0.30 in.) in diameter and 90.0 mm (3.54 in.) long is pulled in tension with a force of 6000 N (1350 lb f ); the force is subsequently released. (a) Compute the final length of the specimen at this time. The tensile stress strain behavior for this alloy is shown in Figure 6.1. (b) Compute the final specimen length when the load is increased to 16,500 N (3700 lb f ) and then released. (a) In order to determine the final length of the brass specimen when the load is released, it first becomes necessary to compute the applied stress using Equation 6.1; thus

8 σ F F A 0 π d N π m 136 MPa (19,000 psi) Upon locating this point on the stress-strain curve (Figure 6.1), we note that it is in the linear, elastic region; therefore, when the load is released the specimen will return to its original length of 90 mm (3.54 in.). (b) In this portion of the problem we are asked to calculate the final length, after load release, when the load is increased to 16,500 N (3700 lb f ). Again, computing the stress σ 16,500 N π m 373 MPa (5,300 psi) The point on the stress-strain curve corresponding to this stress is in the plastic region. We are able to estimate the amount of permanent strain by drawing a straight line parallel to the linear elastic region; this line intersects the strain axis at a strain of about 0.08 which is the amount of plastic strain. The final specimen length l i may be determined from a rearranged form of Equation 6. as l i (1 + ε) (90 mm)( ) 97.0 mm (3.8 in.)

### 6.4 A cylindrical specimen of a titanium alloy having an elastic modulus of 107 GPa ( psi) and

6.4 A cylindrical specimen of a titanium alloy having an elastic modulus of 107 GPa (15.5 10 6 psi) and an original diameter of 3.8 mm (0.15 in.) will experience only elastic deformation when a tensile

### 6.37 Determine the modulus of resilience for each of the following alloys:

6.37 Determine the modulus of resilience for each of the following alloys: Yield Strength Material MPa psi Steel alloy 550 80,000 Brass alloy 350 50,750 Aluminum alloy 50 36,50 Titanium alloy 800 116,000

### Mechanical 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

### Introduction 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

Name: Date: Solid Mechanics Homework nswers Please show all of your work, including which equations you are using, and circle your final answer. Be sure to include the units in your answers. 1. The yield

### Chapter 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

### Strength of Material. Shear Strain. Dr. Attaullah Shah

Strength of Material Shear Strain Dr. Attaullah Shah Shear Strain TRIAXIAL DEFORMATION Poisson's Ratio Relationship Between E, G, and ν BIAXIAL DEFORMATION Bulk Modulus of Elasticity or Modulus of Volume

### EMA 3702 Mechanics & Materials Science (Mechanics of Materials) Chapter 2 Stress & Strain - Axial Loading

MA 3702 Mechanics & Materials Science (Mechanics of Materials) Chapter 2 Stress & Strain - Axial Loading MA 3702 Mechanics & Materials Science Zhe Cheng (2018) 2 Stress & Strain - Axial Loading Statics

### Fatigue Problems Solution

Fatigue Problems Solution Problem 1. (a) Given the values of σ m (7 MPa) and σ a (1 MPa) we are asked t o compute σ max and σ min. From Equation 1 Or, σ m σ max + σ min 7 MPa σ max + σ min 14 MPa Furthermore,

### CHAPTER 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

### Chapter 6: Mechanical Properties of Metals. Dr. Feras Fraige

Chapter 6: Mechanical Properties of Metals Dr. Feras Fraige Stress and Strain Tension Compression Shear Torsion Elastic deformation Plastic Deformation Yield Strength Tensile Strength Ductility Toughness

### TINIUS OLSEN Testing Machine Co., Inc.

Interpretation of Stress-Strain Curves and Mechanical Properties of Materials Tinius Olsen has prepared this general introduction to the interpretation of stress-strain curves for the benefit of those

### Outline. 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

### MECHANICS OF MATERIALS

Third E CHAPTER 2 Stress MECHANICS OF MATERIALS Ferdinand P. Beer E. Russell Johnston, Jr. John T. DeWolf Lecture Notes: J. Walt Oler Texas Tech University and Strain Axial Loading Contents Stress & Strain:

### UNIT 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

### CONSTITUTIVE RELATIONS FOR LINEAR ELASTIC SOLIDS

Chapter 9 CONSTITUTIV RLATIONS FOR LINAR LASTIC SOLIDS Figure 9.1: Hooke memorial window, St. Helen s, Bishopsgate, City of London 211 212 CHAPTR 9. CONSTITUTIV RLATIONS FOR LINAR LASTIC SOLIDS 9.1 Mechanical

### Outline. Organization. Stresses in Beams

Stresses in Beams B the end of this lesson, ou should be able to: Calculate the maimum stress in a beam undergoing a bending moment 1 Outline Curvature Normal Strain Normal Stress Neutral is Moment of

### Mechanics 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

### 2. Rigid bar ABC supports a weight of W = 50 kn. Bar ABC is pinned at A and supported at B by rod (1). What is the axial force in rod (1)?

IDE 110 S08 Test 1 Name: 1. Determine the internal axial forces in segments (1), (2) and (3). (a) N 1 = kn (b) N 2 = kn (c) N 3 = kn 2. Rigid bar ABC supports a weight of W = 50 kn. Bar ABC is pinned at

### MATERIALS. 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

### Lab Exercise #3: Torsion

Lab Exercise #3: Pre-lab assignment: Yes No Goals: 1. To evaluate the equations of angular displacement, shear stress, and shear strain for a shaft undergoing torsional stress. Principles: testing of round

### Date Submitted: 1/8/13 Section #4: T Instructor: Morgan DeLuca. Abstract

Lab Report #2: Poisson s Ratio Name: Sarah Brown Date Submitted: 1/8/13 Section #4: T 10-12 Instructor: Morgan DeLuca Group Members: 1. Maura Chmielowiec 2. Travis Newberry 3. Thomas Cannon Title: Poisson

### **********************************************************************

Department of Civil and Environmental Engineering School of Mining and Petroleum Engineering 3-33 Markin/CNRL Natural Resources Engineering Facility www.engineering.ualberta.ca/civil Tel: 780.492.4235

### Chapter 13 ELASTIC PROPERTIES OF MATERIALS

Physics Including Human Applications 280 Chapter 13 ELASTIC PROPERTIES OF MATERIALS GOALS When you have mastered the contents of this chapter, you will be able to achieve the following goals: Definitions

### Chapter 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)

### Task 1 - Material Testing of Bionax Pipe and Joints

Task 1 - Material Testing of Bionax Pipe and Joints Submitted to: Jeff Phillips Western Regional Engineer IPEX Management, Inc. 20460 Duncan Way Langley, BC, Canada V3A 7A3 Ph: 604-534-8631 Fax: 604-534-7616

### EMA 3702 Mechanics & Materials Science (Mechanics of Materials) Chapter 4 Pure Bending

EA 3702 echanics & aterials Science (echanics of aterials) Chapter 4 Pure Bending Pure Bending Ch 2 Aial Loading & Parallel Loading: uniform normal stress and shearing stress distribution Ch 3 Torsion:

### Laboratory 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

### 122 CHAPTER 2 Axially Loaded Numbers. Stresses on Inclined Sections

1 CHATER Aiall Loaded Numbers Stresses on Inclined Sections roblem.6-1 A steel bar of rectangular cross section (1.5 in..0 in.) carries a tensile load (see figure). The allowable stresses in tension and

### CHAPTER OBJECTIVES CHAPTER OUTLINE. 4. Axial Load

CHAPTER OBJECTIVES Determine deformation of axially loaded members Develop a method to find support reactions when it cannot be determined from euilibrium euations Analyze the effects of thermal stress

### Tuesday, February 11, Chapter 3. Load and Stress Analysis. Dr. Mohammad Suliman Abuhaiba, PE

1 Chapter 3 Load and Stress Analysis 2 Chapter Outline Equilibrium & Free-Body Diagrams Shear Force and Bending Moments in Beams Singularity Functions Stress Cartesian Stress Components Mohr s Circle for

### CSCE 155N Fall Homework Assignment 2: Stress-Strain Curve. Assigned: September 11, 2012 Due: October 02, 2012

CSCE 155N Fall 2012 Homework Assignment 2: Stress-Strain Curve Assigned: September 11, 2012 Due: October 02, 2012 Note: This assignment is to be completed individually - collaboration is strictly prohibited.

### Lecture #10: Anisotropic plasticity Crashworthiness Basics of shell elements

Lecture #10: 151-0735: Dynamic behavior of materials and structures Anisotropic plasticity Crashworthiness Basics of shell elements by Dirk Mohr ETH Zurich, Department of Mechanical and Process Engineering,

### Mechanics of Materials MENG 270 Fall 2003 Exam 3 Time allowed: 90min. Q.1(a) Q.1 (b) Q.2 Q.3 Q.4 Total

Mechanics of Materials MENG 70 Fall 00 Eam Time allowed: 90min Name. Computer No. Q.(a) Q. (b) Q. Q. Q.4 Total Problem No. (a) [5Points] An air vessel is 500 mm average diameter and 0 mm thickness, the

### MECHANICAL PROPERTIES OF SOLIDS

Chapter Nine MECHANICAL PROPERTIES OF SOLIDS MCQ I 9.1 Modulus of rigidity of ideal liquids is (a) infinity. (b) zero. (c) unity. (d) some finite small non-zero constant value. 9. The maximum load a wire

### UNIVERSITY PHYSICS I. Professor Meade Brooks, Collin College. Chapter 12: STATIC EQUILIBRIUM AND ELASTICITY

UNIVERSITY PHYSICS I Professor Meade Brooks, Collin College Chapter 12: STATIC EQUILIBRIUM AND ELASTICITY Two stilt walkers in standing position. All forces acting on each stilt walker balance out; neither

### RESEARCH PROJECT NO. 26

RESEARCH PROJECT NO. 26 DETERMINATION OF POISSON'S RATIO IN AD1 TESTING BY UNIVERSITY OF MICHIGAN REPORT PREPARED BY BELA V. KOVACS and JOHN R. KEOUGH \ MEMBER / / DUCTILE IRON \ SOCIETY Issued by the

### Please review the following statement: I certify that I have not given unauthorized aid nor have I received aid in the completion of this exam.

Group Number: Please review the following statement: I certify that I have not given unauthorized aid nor have I received aid in the completion of this exam. Signature: INSTRUCTIONS Begin each problem

### FCP Short Course. Ductile and Brittle Fracture. Stephen D. Downing. Mechanical Science and Engineering

FCP Short Course Ductile and Brittle Fracture Stephen D. Downing Mechanical Science and Engineering 001-015 University of Illinois Board of Trustees, All Rights Reserved Agenda Limit theorems Plane Stress

### ACET 406 Mid-Term Exam B

ACET 406 Mid-Term Exam B SUBJECT: ACET 406, INSTRUCTOR: Dr Antonis Michael, DATE: 24/11/09 INSTRUCTIONS You are required to answer all of the following questions within the specified time (90 minutes).you

### 1.103 CIVIL ENGINEERING MATERIALS LABORATORY (1-2-3) Dr. J.T. Germaine Spring 2004 LABORATORY ASSIGNMENT NUMBER 6

1.103 CIVIL ENGINEERING MATERIALS LABORATORY (1-2-3) Dr. J.T. Germaine MIT Spring 2004 LABORATORY ASSIGNMENT NUMBER 6 COMPRESSION TESTING AND ANISOTROPY OF WOOD Purpose: Reading: During this laboratory

### σ = Eα(T T C PROBLEM #1.1 (4 + 4 points, no partial credit)

PROBLEM #1.1 (4 + 4 points, no partial credit A thermal switch consists of a copper bar which under elevation of temperature closes a gap and closes an electrical circuit. The copper bar possesses a length

### Elastic Properties of Solids Exercises I II for one weight Exercises III and IV give the second weight

Elastic properties of solids Page 1 of 8 Elastic Properties of Solids Exercises I II for one weight Exercises III and IV give the second weight This is a rare experiment where you will get points for breaking

### Elasticity: Term Paper. Danielle Harper. University of Central Florida

Elasticity: Term Paper Danielle Harper University of Central Florida I. Abstract This research was conducted in order to experimentally test certain components of the theory of elasticity. The theory was

### Spherical Pressure Vessels

Spherical Pressure Vessels Pressure vessels are closed structures containing liquids or gases under essure. Examples include tanks, pipes, essurized cabins, etc. Shell structures : When essure vessels

### 1 Stress and Strain. Introduction

1 Stress and Strain Introduction This book is concerned with the mechanical behavior of materials. The term mechanical behavior refers to the response of materials to forces. Under load, a material may

### 3. BEAMS: STRAIN, STRESS, DEFLECTIONS

3. BEAMS: STRAIN, STRESS, DEFLECTIONS The beam, or flexural member, is frequently encountered in structures and machines, and its elementary stress analysis constitutes one of the more interesting facets

### Lecture 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

### BME 207 Introduction to Biomechanics Spring 2017

April 7, 2017 UNIVERSITY OF RHODE ISAND Department of Electrical, Computer and Biomedical Engineering BE 207 Introduction to Biomechanics Spring 2017 Homework 7 Problem 14.3 in the textbook. In addition

### ASSOCIATE DEGREE IN ENGINEERING EXAMINATIONS. SEMESTER 2 May 2013

ASSOCIATE DEGREE IN ENGINEERING EXAMINATIONS SEMESTER 2 May 2013 COURSE NAME: CODE: Mechanical Engineering Science [8 CHARACTER COURSE CODE] GROUP: AD-ENG 1 DATE: TIME: DURATION: "[EXAM DATE]" "[TIME OF

### PRELIMINARY PREDICTION OF SPECIMEN PROPERTIES CLT and 1 st order FEM analyses

OPTIMAT BLADES Page 1 of 24 PRELIMINARY PREDICTION OF SPECIMEN PROPERTIES CLT and 1 st order FEM analyses first issue Peter Joosse CHANGE RECORD Issue/revision date pages Summary of changes draft 24-10-02

### 3.032 Problem Set 2 Solutions Fall 2007 Due: Start of Lecture,

3.032 Problem Set 2 Solutions Fall 2007 Due: Start of Lecture, 09.21.07 1. In the beam considered in PS1, steel beams carried the distributed weight of the rooms above. To reduce stress on the beam, it

### ME 582 Advanced Materials Science. Chapter 2 Macromechanical Analysis of a Lamina (Part 2)

ME 582 Advanced Materials Science Chapter 2 Macromechanical Analysis of a Lamina (Part 2) Laboratory for Composite Materials Research Department of Mechanical Engineering University of South Alabama, Mobile,

### Elastic-Plastic Fracture Mechanics. Professor S. Suresh

Elastic-Plastic Fracture Mechanics Professor S. Suresh Elastic Plastic Fracture Previously, we have analyzed problems in which the plastic zone was small compared to the specimen dimensions (small scale

### The example of shafts; a) Rotating Machinery; Propeller shaft, Drive shaft b) Structural Systems; Landing gear strut, Flap drive mechanism

TORSION OBJECTIVES: This chapter starts with torsion theory in the circular cross section followed by the behaviour of torsion member. The calculation of the stress stress and the angle of twist will be

### UNIT 1 STRESS STRAIN AND DEFORMATION OF SOLIDS, STATES OF STRESS 1. Define stress. When an external force acts on a body, it undergoes deformation.

UNIT 1 STRESS STRAIN AND DEFORMATION OF SOLIDS, STATES OF STRESS 1. Define stress. When an external force acts on a body, it undergoes deformation. At the same time the body resists deformation. The magnitude

### Unified Quiz M4 May 7, 2008 M - PORTION

9:00-10: 00 (last four digits) 32-141 Unified Quiz M4 May 7, 2008 M - PORTION Put the last four digits of your MIT ID # on each page of the exam. Read all questions carefully. Do all work on that question

### ScienceDirect. Bauschinger effect during unloading of cold-rolled copper alloy sheet and its influence on springback deformation after U-bending

Available online at www.sciencedirect.com ScienceDirect Procedia Engineering 81 (2014 ) 969 974 11th International Conference on Technology of Plasticity, ICTP 2014, 19-24 October 2014, Nagoya Congress

### Basic Energy Principles in Stiffness Analysis

Basic Energy Principles in Stiffness Analysis Stress-Strain Relations The application of any theory requires knowledge of the physical properties of the material(s) comprising the structure. We are limiting

### five mechanics of materials Mechanics of Materials Mechanics of Materials Knowledge Required MECHANICS MATERIALS

RCHITECTUR STRUCTURES: FORM, BEHVIOR, ND DESIGN DR. NNE NICHOS SUMMER 2014 Mechanics o Materials MECHNICS MTERIS lecture ive mechanics o materials www.carttalk.com Mechanics o Materials 1 rchitectural

### = 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

Chapter 5 CENTRIC TENSION OR COMPRESSION ( AXIAL LOADING ) 5.1 DEFINITION A construction member is subjected to centric (axial) tension or compression if in any cross section the single distinct stress

### Example-3. Title. Description. Cylindrical Hole in an Infinite Mohr-Coulomb Medium

Example-3 Title Cylindrical Hole in an Infinite Mohr-Coulomb Medium Description The problem concerns the determination of stresses and displacements for the case of a cylindrical hole in an infinite elasto-plastic

### WPI MS4SSA Modules: What and How. Nima Rahbar and Wole Soboyejo Worcester Polytechnic Institute (WPI)

WPI Modules: What and How Nima Rahbar and Wole Soboyejo Worcester Polytechnic Institute (WPI) Initial WPI Modules: Building a Culture of S&T in Africa WPI s modules focus on complementary curricula for

### ANSYS Mechanical Basic Structural Nonlinearities

Lecture 4 Rate Independent Plasticity ANSYS Mechanical Basic Structural Nonlinearities 1 Chapter Overview The following will be covered in this Chapter: A. Background Elasticity/Plasticity B. Yield Criteria

### THEME IS FIRST OCCURANCE OF YIELDING THE LIMIT?

CIE309 : PLASTICITY THEME IS FIRST OCCURANCE OF YIELDING THE LIMIT? M M - N N + + σ = σ = + f f BENDING EXTENSION Ir J.W. Welleman page nr 0 kn Normal conditions during the life time WHAT HAPPENS DUE TO

### cos(θ)sin(θ) Alternative Exercise Correct Correct θ = 0 skiladæmi 10 Part A Part B Part C Due: 11:59pm on Wednesday, November 11, 2015

skiladæmi 10 Due: 11:59pm on Wednesday, November 11, 015 You will receive no credit for items you complete after the assignment is due Grading Policy Alternative Exercise 1115 A bar with cross sectional

### The University of Texas at Austin

r The University of Texas at Austin College of Engineering COEFFICIENT OF THERMAL EXPANSION FOR FOUR BATCH DESIGNS AND ONE SOLID GRANITE SPECIMEN by A Report Prepared for FOSTER YEOMAN LIMITED by the CENTER

### Simple Stresses and Strains

Simple Stresses and Strains CHPTER OJECTIVES In this chapter, we will learn about: Various types of (a) stresses as tensile and compressive stresses, positive and negative shear stresses, complementary

### Finite-Element Analysis of Stress Concentration in ASTM D 638 Tension Specimens

Monika G. Garrell, 1 Albert J. Shih, 2 Edgar Lara-Curzio, 3 and Ronald O. Scattergood 4 Journal of Testing and Evaluation, Vol. 31, No. 1 Paper ID JTE11402_311 Available online at: www.astm.org Finite-Element

### Lap splice length and details of column longitudinal reinforcement at plastic hinge region

Lap length and details of column longitudinal reinforcement at plastic hinge region Hong-Gun Park 1) and Chul-Goo Kim 2) 1), 2 Department of Architecture and Architectural Engineering, Seoul National University,

### AE3610 Experiments in Fluid and Solid Mechanics TRANSIENT MEASUREMENTS OF HOOP STRESSES FOR A THIN-WALL PRESSURE VESSEL

Objective AE3610 Experiments in Fluid and Solid Mechanics TRANSIENT MEASUREMENTS OF OOP STRESSES FOR A TIN-WA PRESSURE VESSE This experiment will allow you to investigate hoop and axial stress/strain relations

### MET 301 EXPERIMENT # 2 APPLICATION OF BONDED STRAIN GAGES

MET 301 EPERIMENT # 2 APPLICATION OF BONDED STRAIN GAGES 1. Objective To understand the working principle of bonded strain gauge and to study the stress and strain in a hollow cylindrical shaft under bending,

### Influence of residual stresses in the structural behavior of. tubular columns and arches. Nuno Rocha Cima Gomes

October 2014 Influence of residual stresses in the structural behavior of Abstract tubular columns and arches Nuno Rocha Cima Gomes Instituto Superior Técnico, Universidade de Lisboa, Portugal Contact:

### Flexure: Behavior and Nominal Strength of Beam Sections

4 5000 4000 (increased d ) (increased f (increased A s or f y ) c or b) Flexure: Behavior and Nominal Strength of Beam Sections Moment (kip-in.) 3000 2000 1000 0 0 (basic) (A s 0.5A s ) 0.0005 0.001 0.0015

### ENGINEERING COUNCIL CERTIFICATE LEVEL ENGINEERING SCIENCE C103 TUTORIAL 4 - STRESS AND STRAIN

NGINRING COUNCIL CRTIFICAT LVL NGINRING SCINC C03 TUTORIAL 4 - STRSS AND STRAIN This tutorial ma be skipped if ou are alread familiar with the topic You should judge our progress b completing the self

### Deflections and Strains in Cracked Shafts Due to Rotating Loads: A Numerical and Experimental Analysis

International Journal of Rotating Machinery, 9: 303 311, 2003 Copyright c Taylor & Francis Inc. ISSN: 1023-621X DOI: 10.1080/10236210390147416 Deflections and Strains in Cracked Shafts Due to Rotating

### THE ROLE OF DELAMINATION IN NOTCHED AND UNNOTCHED TENSILE STRENGTH

THE ROLE OF DELAMINATION IN NOTCHED AND UNNOTCHED TENSILE STRENGTH M. R. Wisnom University of Bristol Advanced Composites Centre for Innovation and Science University Walk, Bristol BS8 1TR, UK M.Wisnom@bristol.ac.uk

### MASSACHUSETTS INSTITUTE OF TECHNOLOGY DEPARTMENT OF MATERIALS SCIENCE AND ENGINEERING CAMBRIDGE, MASSACHUSETTS 02139

MASSACHUSES INSIUE OF ECHNOLOGY DEPARMEN OF MAERIALS SCIENCE AND ENGINEERING CAMBRIDGE, MASSACHUSES 02139 3.22 MECHANICAL PROPERIES OF MAERIALS PROBLEM SE 5 SOLUIONS 1. (Hertzber 6.2) If it takes 300 seconds

### 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

### Basic Concepts of Strain and Tilt. Evelyn Roeloffs, USGS June 2008

Basic Concepts of Strain and Tilt Evelyn Roeloffs, USGS June 2008 1 Coordinates Right-handed coordinate system, with positions along the three axes specified by x,y,z. x,y will usually be horizontal, and

### What Every Engineer Should Know About Structures

What Every Engineer Should Know About Structures Part C - Axial Strength of Materials by Professor Patrick L. Glon, P.E. This is a continuation of a series of courses in the area of study of physics called

### For more Stuffs Visit Owner: N.Rajeev. R07

Code.No: 43034 R07 SET-1 JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD II.B.TECH - I SEMESTER REGULAR EXAMINATIONS NOVEMBER, 2009 FOUNDATION OF SOLID MECHANICS (AERONAUTICAL ENGINEERING) Time: 3hours

### Brittle Deformation. Earth Structure (2 nd Edition), 2004 W.W. Norton & Co, New York Slide show by Ben van der Pluijm

Lecture 6 Brittle Deformation Earth Structure (2 nd Edition), 2004 W.W. Norton & Co, New York Slide show by Ben van der Pluijm WW Norton, unless noted otherwise Brittle deformation EarthStructure (2 nd

### Validation of the Resonalyser method: an inverse method for material identification

Validation of the Resonalyser method: an inverse method for material identification T. Lauwagie, H. Sol,. Roebben 3, W. Heylen and Y. Shi Katholieke Universiteit Leuven (KUL) Department of Mechanical ngineering

### INFLUENCE KINDS OF MATERIALS ON THE POISSON S RATIO OF WOVEN FABRICS

ISSN 1846-6168 (Print), ISSN 1848-5588 (Online) ID: TG-217816142553 Original scientific paper INFLUENCE KINDS OF MATERIALS ON THE POISSON S RATIO OF WOVEN FABRICS Željko PENAVA, Diana ŠIMIĆ PENAVA, Željko

### Written as per the revised G Scheme syllabus prescribed by the Maharashtra State Board of Technical Education (MSBTE) w.e.f. academic year

Written as per the revised G Scheme syllabus prescribed by the Maharashtra State Board of Technical Education (MSBTE) w.e.f. academic year 2012-2013 Basic Science PHYSICS irst Year Diploma Semester - I

### CHAPTER 1 ENGINEERING MECHANICS I

CHAPTER 1 ENGINEERING MECHANICS I 1.1 Verification of Lame s Theorem: If three concurrent forces are in equilibrium, Lame s theorem states that their magnitudes are proportional to the sine of the angle

### Crack Tip Plastic Zone under Mode I Loading and the Non-singular T zz -stress

Crack Tip Plastic Zone under Mode Loading and the Non-singular T -stress Yu.G. Matvienko Mechanical Engineering Research nstitute of the Russian Academy of Sciences Email: ygmatvienko@gmail.com Abstract:

### MECHANICS OF MATERIALS

CHAPTER 2 MECHANICS OF MATERIALS Ferdinand P. Beer E. Russell Johnston, Jr. John T. DeWolf David F. Mazurek Lecture Notes: J. Walt Oler Texas Tech University Stress and Strain Axial Loading 2.1 An Introduction

### Elastic moduli: Overview and characterization methods

Technical Review ITC-ME/ATCP Elastic moduli: Overview and characterization methods ATCP Physical Engineering www.atcp-ndt.com Authors: Leiliane Cristina Cossolino (Cossolino LC) and Antônio Henrique Alves

### ME111 Instructor: Peter Pinsky Class #21 November 13, 2000

Toda s Topics ME Instructor: Peter Pinsk Class # November,. Consider two designs of a lug wrench for an automobile: (a) single ended, (b) double ended. The distance between points A and B is in. and the

### Deflections and Strains in Cracked Shafts due to Rotating Loads: A Numerical and Experimental Analysis

Rotating Machinery, 10(4): 283 291, 2004 Copyright c Taylor & Francis Inc. ISSN: 1023-621X print / 1542-3034 online DOI: 10.1080/10236210490447728 Deflections and Strains in Cracked Shafts due to Rotating

### TMHL TMHL (Del I, teori; 1 p.) SOLUTION I. II.. III. Fig. 1.1

TMHL6 204-08-30 (Del I, teori; p.). Fig.. shows three cases of sharp cracks in a sheet of metal. In all three cases, the sheet is assumed to be very large in comparison with the crack. Note the different

### Unit I - Properties of Matter

Unit I - Properties of Matter Elasticity: Elastic and plastic materials Hooke s law elastic behavior of a material stress - strain diagram factors affecting elasticity. Three moduli of elasticity Poisson

### External Work. When a force F undergoes a displacement dx in the same direction i as the force, the work done is

Structure Analysis I Chapter 9 Deflection Energy Method External Work Energy Method When a force F undergoes a displacement dx in the same direction i as the force, the work done is du e = F dx If the