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

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

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

Transcription

1 MA 3702 Mechanics & Materials Science (Mechanics of Materials) Chapter 2 Stress & Strain - Axial Loading

2 MA 3702 Mechanics & Materials Science Zhe Cheng (2018) 2 Stress & Strain - Axial Loading Statics vs. Mechanics of Materials Statics - Deals with un-deformable bodies (rigid bodies) Mechanics of Materials - Deals with practical, deformable bodies Need to calculate the stress and deformation (relative and absolute) of a body under various loading (stress) states Compute forces and related information (stress/strain) for certain statically indeterminate problems

3 Poisson 's Ratio When a material is subject to normal stress (e.g., tensile) in one direction, it subject to deformation in other (transverse) directions. Define Poisson s Ratio v lateral strain axial strain For isotropic material: y x z x Within elastic limit x x y z x

4 Multiaxial Loading Axial loading from more than one directions? Assumptions: ach effect is linear The deformation is small and does not change the overall condition of the body. Principle of Superposition: The combined effect (strain) = individual effect (strain)

5 Generalized Hooke's Law Normal strain along each direction (x, y, z) comes from three contributions: x y z x y z x y z x y z

6 MA 3702 Mechanics & Materials Science Zhe Cheng (2018) 2 Stress & Strain - Axial Loading Class xercise A 500 mm long, 8 mm diameter rod (i.e., cross-section area of ~50 mm 2 ) made of homogeneous rod is subject to 10 kn axial tensile load. The length increases by 0.5 mm while the diameter shrinks by 2 μm. Please calculate elastic modulus and Poisson s ratio. lastic modulus 3 P / A PL 1010 N 500mm 2 / L A 50mm 0.5mm Pa 200GPa N m 2 Poison ratio v y x mm / 8mm 0.5mm / 500mm

7 Shearing Strain (1) For general loading condition, shearing stresses are present, the angle between neighboring surfaces of cube unit will change: From a cube oblique parallelepiped

8 Shearing Strain (2) The change in angle due to shearing stress (from π/2) is defined as shearing strain xy in radians Sign convention for shearing strain: If shear causes reduction in that angle, it is positive; otherwise, negative

9 Hooke s Law for Shearing Within elastic (proportional) limit, xy G xy yz G yz xz G xz G is Shear Modulus or Modulus of Rigidity

10 Generalized Hooke s Law x y xy x x x z G xy yz G yz xz xz G Relationship between, G, and ν G y y y z z z 2 1

11 MA 3702 Mechanics & Materials Science Zhe Cheng (2018) 2 Stress & Strain - Axial Loading Class xercise A 2 inch thick 2 8 in 2 rectangular block with shear modulus G = 100 ksi is bonded between the rigid ground and one rigid top plate, as illustrated. The top plate is subjected to shear force P. Knowing the top plate moved 0.04 inch horizontally. Please calculate the average shearing strain and the shear force P. Average shearing strain arctan In case one wants to know the angle in deg, arctan in 0.02 / in 0.04 in γ P Shear force P P A G A in lb / in lb

12 Stress-Strain Distribution: Ideal vs. Actual Idealized condition: Uniform stress distribution In reality: Non-uniform distribution ave P A Local stress changes in complex way

13 Saint-Venant's Principle The stress distribution far away from the region where the load is applied is NOT related to the mode of application. Implication: for axial loading, uniform stress if it is far away from loading points MA 3702 Mechanics & Materials Science Zhe Cheng (2018) 2 Stress & Strain - Axial Loading

14 Stress Concentrations (1) Stress rises at locations where geometric discontinuity exists Stress Concentration Factor K max ave The sharper the crack tip (or smaller r), the higher K

15 Stress Concentrations (2) Stress rises at locations where geometric discontinuity exists K max ave The sharper the fillet (smaller r), the higher K The larger the dimension ratio (D/d), the higher K

16 Plastic Deformation Idealized elastoplastic behavior: After linear elastic deformation, plastic deformation is characterized by no change in stress (i.e., flat line) until fracture or rupture. y Y Rupture A

17 Stress Concentration Involving Plastic Deformation As load P increases When max < Y lastic deformation K max ave P ave A max K A When max = Y Load for yielding: When ave = Y (Ultimate) load for fracture: Yielding occurs P Y P U Y K Y A Fracture occurs (after certain deformation) A

18 Cube with unit length subject to multiaxial stress of x, y, z The total volume changes from 1 to υ: Dilation & Bulk Modulus (1) Neglecting the high order terms yields: Relative change in volume, also called dilation, e z y x e 1 From the relationships between ε i and σ i, we have z y x e 2 1 z y x 1 ) )(1 )(1 1 ( z y x

19 Dilation & Bulk Modulus (2) Dilation e 1 2 x y Special case: Hydrostatic pressure or x = y = z = -p z e 31 2 p Define as bulk modulus or modulus of compression: e p

20 Dilation & Bulk Modulus (3) Dilation e p Practically, when applying pressure, volume should shrink or dilation e should be negative must be positive Therefore, (1-2ν) > 0 0 < ν < ½ For boundary conditions ν = 0 3 e 3 p ν = ½ e 0 Incompressible solid

21 Residual Stresses After the applied load is removed, some stresses may still remain inside the material xample: solder a bar over a hole on a metal plate During cooling, metal bar gradually hardens and (tensile) stress develops within the bar, which may even exceeds yield strength!

22 MA 3702 Mechanics & Materials Science Zhe Cheng (2018) 2 Stress & Strain - Axial Loading Homework 2.0 Read text book chapter sections 2.1 to 2.7, (you may skip the sample problems) and give an honor statement confirm reading.

23 MA 3702 Mechanics & Materials Science Zhe Cheng (2018) 2 Stress & Strain - Axial Loading Homework 2.1 A plastic wire is pulled by a tensile force of 4 N, and its length increases by 1%. If the plastic has elastic modulus of 4 GPa. Please calculate (a) average normal stress in the wire and (b) the diameter of wire

24 Homework 2.2 MA 3702 Mechanics & Materials Science Zhe Cheng (2018) 2 Stress & Strain - Axial Loading The 4 mm diameter metal wire F has modulus = 200 GPa. If the maximum stress should not be higher than 250 MPa, and the elongation of the wire should be longer than 5 mm. Please calculate the maximum load P can be applied. F D 2 m F 2 m 3 m

25 MA 3702 Mechanics & Materials Science Zhe Cheng (2018) 2 Stress & Strain - Axial Loading Homework 2.3 Members CD and BC have common = psi and cross-section area of 0.75 in 2 and 0.6 in 2, respectively. For the forces shown, determine the elongation of (a) CD and (b) BC. 25 kips D 50 kips 5 ft 5 ft A C B 5 ft

26 Homework 2.4 MA 3702 Mechanics & Materials Science Zhe Cheng (2018) 2 Stress & Strain - Axial Loading A centric load of P=400 kn is applied to the composite block shown through a rigid end plate. The iron plate (G Fe =200 GPa) is sandwiched between two Cu plates (G Cu =80 GPa). Center iron plate is 40 mm thick while the outer Cu plates are 20 mm thick. All plates are 500 mm long and 100 mm wide, Calculate the normal stress in (a) the center Fe core and the outer Cu plates 400 kn 500mm 20 mm 40 mm 20 mm

27 Homework 2.5 MA 3702 Mechanics & Materials Science Zhe Cheng (2018) 2 Stress & Strain - Axial Loading A rigid bar H is supported by two steel wire of 1/16 in diameter (= psi) and a pin and bracket at H. Knowing that the wires were initially tight. Determine (a) the additional tension in each wire when a 220-lb load P is applied at. (b) The corresponding deflection (downward displacement) of point. 8 in 200 lb F G H 10 in 10 in 10 in 10 in

28 MA 3702 Mechanics & Materials Science Zhe Cheng (2018) 2 Stress & Strain - Axial Loading Homework 2.6 A tensile force of 2 kn is applied to a test steel ( = 200GPa, ν = 0.30) bar with rectangular cross-section with initial thickness of 2 mm, initial width of 10 mm, and initial length of 100 mm. Please calculate the absolute change in (a) sample length, (b) sample thickness, (c) sample width, and (d) sample cross-section area.

29 MA 3702 Mechanics & Materials Science Zhe Cheng (2018) 2 Stress & Strain - Axial Loading Homework 2.7 Two blocks of rubber with shear modulus G=10 MPa are bonded to rigid supports and a plate AB as illustrated. c = 100 mm and P = 50 kn. Calculate the minimum value for dimension a and b for the rubber blocks if the shearing stress should not exceed 1 MPa and the deflection of the plate is at least 4 mm.

30 MA 3702 Mechanics & Materials Science Zhe Cheng (2018) 2 Stress & Strain - Axial Loading Homework 2.8 Cylindrical rod CD has length of L = 50 inch and a cross-section area of 0.5 in 2. It is made of a material assumed to be elastoplastic with = psi and yield strength Y = 36 ksi. A tensile force P is applied to the rod and then completely removed to give it a permanent deformation (or set) of δ P. Calculate the maximum value of P and maximum amount deformation δ m by which the rod should be stretched if the desired value of δ P is (a) 0.1 in, (b) 0.2 in.

MECHANICS OF MATERIALS

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:

More information

Solid Mechanics Homework Answers

Solid Mechanics Homework Answers 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

More information

MECE 3321 MECHANICS OF SOLIDS CHAPTER 3

MECE 3321 MECHANICS OF SOLIDS CHAPTER 3 MECE 3321 MECHANICS OF SOLIDS CHAPTER 3 Samantha Ramirez TENSION AND COMPRESSION TESTS Tension and compression tests are used primarily to determine the relationship between σ avg and ε avg in any material.

More information

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 ( 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

More information

4.MECHANICAL PROPERTIES OF MATERIALS

4.MECHANICAL PROPERTIES OF MATERIALS 4.MECHANICAL PROPERTIES OF MATERIALS The diagram representing the relation between stress and strain in a given material is an important characteristic of the material. To obtain the stress-strain diagram

More information

Strength of Material. Shear Strain. Dr. Attaullah Shah

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

More information

Stress-Strain Behavior

Stress-Strain Behavior 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.

More information

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

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:

More information

CHAPTER 3 THE EFFECTS OF FORCES ON MATERIALS

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

More information

Class XI Chapter 9 Mechanical Properties of Solids Physics

Class 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 information

Question Figure shows the strain-stress curve for a given material. What are (a) Young s modulus and (b) approximate yield strength for this material?

Question Figure shows the strain-stress curve for a given material. What are (a) Young s modulus and (b) approximate yield strength for this material? Question. A steel wire of length 4.7 m and cross-sectional area 3.0 x 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 x 10-5 m 2 under a given load.

More information

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 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 information

Chapter 7. Highlights:

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

More information

A concrete cylinder having a a diameter of of in. mm and elasticity. Stress and Strain: Stress and Strain: 0.

A concrete cylinder having a a diameter of of in. mm and elasticity. Stress and Strain: Stress and Strain: 0. 2011 earson Education, Inc., Upper Saddle River, NJ. ll rights reserved. This material is protected under all copyright laws as they currently 8 1. 3 1. concrete cylinder having a a diameter of of 6.00

More information

UNIT I SIMPLE STRESSES AND STRAINS

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

More information

CHAPTER OBJECTIVES CHAPTER OUTLINE. 4. Axial Load

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

More information

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

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

More information

Chapter 5 CENTRIC TENSION OR COMPRESSION ( AXIAL LOADING )

Chapter 5 CENTRIC TENSION OR COMPRESSION ( AXIAL LOADING ) 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

More information

MECHANICS OF MATERIALS

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

More information

Class XI Physics. Ch. 9: Mechanical Properties of solids. NCERT Solutions

Class 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 information

Mechanics of Solids. Mechanics Of Solids. Suraj kr. Ray Department of Civil Engineering

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

More information

CONSTITUTIVE RELATIONS FOR LINEAR ELASTIC SOLIDS

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

More information

Question 9.1: Answer. Length of the steel wire, L 1 = 4.7 m. Area of cross-section of the steel wire, A 1 = m 2

Question 9.1: Answer. Length of the steel wire, L 1 = 4.7 m. Area of cross-section of the steel wire, A 1 = m 2 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 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 information

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)?

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

More information

Introduction to Engineering Materials ENGR2000. Dr. Coates

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

More information

MECE 3321 MECHANICS OF SOLIDS CHAPTER 1

MECE 3321 MECHANICS OF SOLIDS CHAPTER 1 MECE 3321 MECHANICS O SOLIDS CHAPTER 1 Samantha Ramirez, MSE WHAT IS MECHANICS O MATERIALS? Rigid Bodies Statics Dynamics Mechanics Deformable Bodies Solids/Mech. Of Materials luids 1 WHAT IS MECHANICS

More information

1. A pure shear deformation is shown. The volume is unchanged. What is the strain tensor.

1. A pure shear deformation is shown. The volume is unchanged. What is the strain tensor. Elasticity Homework Problems 2014 Section 1. The Strain Tensor. 1. A pure shear deformation is shown. The volume is unchanged. What is the strain tensor. 2. Given a steel bar compressed with a deformation

More information

Symmetric Bending of Beams

Symmetric Bending of Beams Symmetric Bending of Beams beam is any long structural member on which loads act perpendicular to the longitudinal axis. Learning objectives Understand the theory, its limitations and its applications

More information

Mechanical properties 1 Elastic behaviour of materials

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

More information

March 24, Chapter 4. Deflection and Stiffness. Dr. Mohammad Suliman Abuhaiba, PE

March 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 information

five Mechanics of Materials 1 ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN DR. ANNE NICHOLS SUMMER 2017 lecture

five 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 information

five Mechanics of Materials 1 ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN DR. ANNE NICHOLS SUMMER 2014 lecture

five Mechanics of Materials 1 ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN DR. ANNE NICHOLS SUMMER 2014 lecture ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN DR. ANNE NICHOLS SUMMER 2014 lecture five mechanics www.carttalk.com of materials Mechanics of Materials 1 Mechanics of Materials MECHANICS MATERIALS

More information

Chapter 3. Load and Stress Analysis

Chapter 3. Load and Stress Analysis Chapter 3 Load and Stress Analysis 2 Shear Force and Bending Moments in Beams Internal shear force V & bending moment M must ensure equilibrium Fig. 3 2 Sign Conventions for Bending and Shear Fig. 3 3

More information

Elastic 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 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 information

Lecture 8: Flexibility Method. Example

Lecture 8: Flexibility Method. Example ecture 8: lexibility Method Example The plane frame shown at the left has fixed supports at A and C. The frame is acted upon by the vertical load P as shown. In the analysis account for both flexural and

More information

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. 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

More information

Chapter 26 Elastic Properties of Materials

Chapter 26 Elastic Properties of Materials Chapter 26 Elastic Properties of Materials 26.1 Introduction... 1 26.2 Stress and Strain in Tension and Compression... 2 26.3 Shear Stress and Strain... 4 Example 26.1: Stretched wire... 5 26.4 Elastic

More information

MECHANICS OF MATERIALS. Prepared by Engr. John Paul Timola

MECHANICS OF MATERIALS. Prepared by Engr. John Paul Timola MECHANICS OF MATERIALS Prepared by Engr. John Paul Timola Mechanics of materials branch of mechanics that studies the internal effects of stress and strain in a solid body. stress is associated with the

More information

TRESS - STRAIN RELATIONS

TRESS - STRAIN RELATIONS TRESS - STRAIN RELATIONS Stress Strain Relations: Hook's law, states that within the elastic limits the stress is proportional to t is impossible to describe the entire stress strain curve with simple

More information

STATICALLY INDETERMINATE STRUCTURES

STATICALLY INDETERMINATE STRUCTURES STATICALLY INDETERMINATE STRUCTURES INTRODUCTION Generally the trusses are supported on (i) a hinged support and (ii) a roller support. The reaction components of a hinged support are two (in horizontal

More information

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 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

More information

ELASTICITY (MDM 10203)

ELASTICITY (MDM 10203) LASTICITY (MDM 10203) Lecture Module 5: 3D Constitutive Relations Dr. Waluyo Adi Siswanto University Tun Hussein Onn Malaysia Generalised Hooke's Law In one dimensional system: = (basic Hooke's law) Considering

More information

BME 207 Introduction to Biomechanics Spring 2017

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

More information

MECHANICAL PROPERTIES OF SOLIDS

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

More information

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

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

More information

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

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

More information

Chapter 13 ELASTIC PROPERTIES OF MATERIALS

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

More information

Due Monday, September 14 th, 12:00 midnight

Due Monday, September 14 th, 12:00 midnight Due Monday, September 14 th, 1: midnight This homework is considering the analysis of plane and space (3D) trusses as discussed in class. A list of MatLab programs that were discussed in class is provided

More information

Failure from static loading

Failure from static loading Failure from static loading Topics Quiz /1/07 Failures from static loading Reading Chapter 5 Homework HW 3 due /1 HW 4 due /8 What is Failure? Failure any change in a machine part which makes it unable

More information

Flexible Pavement Stress Analysis

Flexible Pavement Stress Analysis Flexible Pavement Stress Analysis Dr. Antonis Michael Frederick University Notes Courtesy of Dr. Christos Drakos, University of Florida Need to predict & understand stress/strain distribution within the

More information

22 Which of the following correctly defines the terms stress, strain and Young modulus? stress strain Young modulus

22 Which of the following correctly defines the terms stress, strain and Young modulus? stress strain Young modulus PhysicsndMathsTutor.com Which of the following correctly defines the terms stress, strain and Young modulus? 97/1/M/J/ stress strain Young modulus () x (area) (extension) x (original length) (stress) /

More information

ACET 406 Mid-Term Exam B

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

More information

SOLUTION (17.3) Known: A simply supported steel shaft is connected to an electric motor with a flexible coupling.

SOLUTION (17.3) Known: A simply supported steel shaft is connected to an electric motor with a flexible coupling. SOLUTION (17.3) Known: A simply supported steel shaft is connected to an electric motor with a flexible coupling. Find: Determine the value of the critical speed of rotation for the shaft. Schematic and

More information

Chapter 12. Static Equilibrium and Elasticity

Chapter 12. Static Equilibrium and Elasticity Chapter 12 Static Equilibrium and Elasticity Static Equilibrium Equilibrium implies that the object moves with both constant velocity and constant angular velocity relative to an observer in an inertial

More information

Geology 229 Engineering Geology. Lecture 5. Engineering Properties of Rocks (West, Ch. 6)

Geology 229 Engineering Geology. Lecture 5. Engineering Properties of Rocks (West, Ch. 6) Geology 229 Engineering Geology Lecture 5 Engineering Properties of Rocks (West, Ch. 6) Common mechanic properties: Density; Elastic properties: - elastic modulii Outline of this Lecture 1. Uniaxial rock

More information

BTECH MECHANICAL PRINCIPLES AND APPLICATIONS. Level 3 Unit 5

BTECH MECHANICAL PRINCIPLES AND APPLICATIONS. Level 3 Unit 5 BTECH MECHANICAL PRINCIPLES AND APPLICATIONS Level 3 Unit 5 FORCES AS VECTORS Vectors have a magnitude (amount) and a direction. Forces are vectors FORCES AS VECTORS (2 FORCES) Forces F1 and F2 are in

More information

Lecture 7, Foams, 3.054

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

More information

Spherical Pressure Vessels

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

More information

The problem of transmitting a torque or rotary motion from one plane to another is frequently encountered in machine design.

The problem of transmitting a torque or rotary motion from one plane to another is frequently encountered in machine design. CHAPER ORSION ORSION orsion refers to the twisting of a structural member when it is loaded by moments/torques that produce rotation about the longitudinal axis of the member he problem of transmitting

More information

Outline. Tensile-Test Specimen and Machine. Stress-Strain Curve. Review of Mechanical Properties. Mechanical Behaviour

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

More information

Chapter 1 Introduction- Concept of Stress

Chapter 1 Introduction- Concept of Stress hapter 1 Introduction- oncept of Stress INTRODUTION Review of Statics xial Stress earing Stress Torsional Stress 14 6 ending Stress W W L Introduction 1-1 Shear Stress W W Stress and Strain L y y τ xy

More information

CHAPTER 5 Statically Determinate Plane Trusses

CHAPTER 5 Statically Determinate Plane Trusses CHAPTER 5 Statically Determinate Plane Trusses TYPES OF ROOF TRUSS TYPES OF ROOF TRUSS ROOF TRUSS SETUP ROOF TRUSS SETUP OBJECTIVES To determine the STABILITY and DETERMINACY of plane trusses To analyse

More information

CHAPTER 5 Statically Determinate Plane Trusses TYPES OF ROOF TRUSS

CHAPTER 5 Statically Determinate Plane Trusses TYPES OF ROOF TRUSS CHAPTER 5 Statically Determinate Plane Trusses TYPES OF ROOF TRUSS 1 TYPES OF ROOF TRUSS ROOF TRUSS SETUP 2 ROOF TRUSS SETUP OBJECTIVES To determine the STABILITY and DETERMINACY of plane trusses To analyse

More information

ANSYS Mechanical Basic Structural Nonlinearities

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

More information

ARC 341 Structural Analysis II. Lecture 10: MM1.3 MM1.13

ARC 341 Structural Analysis II. Lecture 10: MM1.3 MM1.13 ARC241 Structural Analysis I Lecture 10: MM1.3 MM1.13 MM1.4) Analysis and Design MM1.5) Axial Loading; Normal Stress MM1.6) Shearing Stress MM1.7) Bearing Stress in Connections MM1.9) Method of Problem

More information

Lecture 8 Viscoelasticity and Deformation

Lecture 8 Viscoelasticity and Deformation HW#5 Due 2/13 (Friday) Lab #1 Due 2/18 (Next Wednesday) For Friday Read: pg 130 168 (rest of Chpt. 4) 1 Poisson s Ratio, μ (pg. 115) Ratio of the strain in the direction perpendicular to the applied force

More information

Seismic Pushover Analysis Using AASHTO Guide Specifications for LRFD Seismic Bridge Design

Seismic Pushover Analysis Using AASHTO Guide Specifications for LRFD Seismic Bridge Design Seismic Pushover Analysis Using AASHTO Guide Specifications for LRFD Seismic Bridge Design Elmer E. Marx, Alaska Department of Transportation and Public Facilities Michael Keever, California Department

More information

COLUMNS: BUCKLING (DIFFERENT ENDS)

COLUMNS: 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 information

Static Equilibrium; Elasticity & Fracture

Static Equilibrium; Elasticity & Fracture Static Equilibrium; Elasticity & Fracture The Conditions for Equilibrium Statics is concerned with the calculation of the forces acting on and within structures that are in equilibrium. An object with

More information

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

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

More information

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 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

More information

Chapter 5 Elastic Strain, Deflection, and Stability 1. Elastic Stress-Strain Relationship

Chapter 5 Elastic Strain, Deflection, and Stability 1. Elastic Stress-Strain Relationship Chapter 5 Elastic Strain, Deflection, and Stability Elastic Stress-Strain Relationship A stress in the x-direction causes a strain in the x-direction by σ x also causes a strain in the y-direction & z-direction

More information

THEME IS FIRST OCCURANCE OF YIELDING THE LIMIT?

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

More information

Module 4 : Deflection of Structures Lecture 4 : Strain Energy Method

Module 4 : Deflection of Structures Lecture 4 : Strain Energy Method Module 4 : Deflection of Structures Lecture 4 : Strain Energy Method Objectives In this course you will learn the following Deflection by strain energy method. Evaluation of strain energy in member under

More information

122 CHAPTER 2 Axially Loaded Numbers. Stresses on Inclined Sections

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

More information

Flexure: Behavior and Nominal Strength of Beam Sections

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

More information

Continuum mechanics V. Constitutive equations. 1. Constitutive equation: definition and basic axioms

Continuum mechanics V. Constitutive equations. 1. Constitutive equation: definition and basic axioms Continuum mechanics office Math 0.107 ales.janka@unifr.ch http://perso.unifr.ch/ales.janka/mechanics Mars 16, 2011, Université de Fribourg 1. Constitutive equation: definition and basic axioms Constitutive

More information

P.E. Civil Exam Review:

P.E. Civil Exam Review: P.E. Civil Exam Review: Structural Analysis J.P. Mohsen Email: jpm@louisville.edu Structures Determinate Indeterminate STATICALLY DETERMINATE STATICALLY INDETERMINATE Stability and Determinacy of Trusses

More information

Sean Carey Tafe No Lab Report: Hounsfield Tension Test

Sean Carey Tafe No Lab Report: Hounsfield Tension Test Sean Carey Tafe No. 366851615 Lab Report: Hounsfield Tension Test August 2012 The Hounsfield Tester The Hounsfield Tester can do a variety of tests on a small test-piece. It is mostly used for tensile

More information

Outline. Organization. Stresses in Beams

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

More information

Unified Quiz M4 May 7, 2008 M - PORTION

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

More information

Figure 1: Throwing arm dimensions

Figure 1: Throwing arm dimensions I. Overview The objective of this report is to review the design of the trebuchet model from an engineering standpoint. This study analyzes the dimensions and material selection using the COMSOL multiphisics

More information

**********************************************************************

********************************************************************** 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

More information

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? 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 information

ANALYSIS OF STRAINS CONCEPT OF STRAIN

ANALYSIS OF STRAINS CONCEPT OF STRAIN ANALYSIS OF STRAINS CONCEPT OF STRAIN Concept of strain : if a bar is subjected to a direct load, and hence a stress the bar will change in length. If the bar has an original length L and changes by an

More information

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

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

More information

The Frictional Regime

The Frictional Regime The Frictional Regime Processes in Structural Geology & Tectonics Ben van der Pluijm WW Norton+Authors, unless noted otherwise 1/25/2016 10:08 AM We Discuss The Frictional Regime Processes of Brittle Deformation

More information

BE Semester- I ( ) Question Bank (MECHANICS OF SOLIDS)

BE Semester- I ( ) Question Bank (MECHANICS OF SOLIDS) BE Semester- I ( ) Question Bank (MECHANICS OF SOLIDS) All questions carry equal marks(10 marks) Q.1 (a) Write the SI units of following quantities and also mention whether it is scalar or vector: (i)

More information

Buckling Behavior of 3D Randomly Oriented CNT Reinforced Nanocomposite Plate

Buckling Behavior of 3D Randomly Oriented CNT Reinforced Nanocomposite Plate Buckling Behavior of 3D Randomly Oriented CNT Reinforced Nanocomposite Plate Outline Introduction Representative Volume Element (RVE) Periodic Boundary Conditions on RVE Homogenization Method Analytical

More information

EE C247B ME C218 Introduction to MEMS Design Spring 2017

EE C247B ME C218 Introduction to MEMS Design Spring 2017 247B/M 28: Introduction to MMS Design Lecture 0m2: Mechanics of Materials CTN 2/6/7 Outline C247B M C28 Introduction to MMS Design Spring 207 Prof. Clark T.- Reading: Senturia, Chpt. 8 Lecture Topics:

More information

ME 202 STRENGTH OF MATERIALS SPRING 2014 HOMEWORK 4 SOLUTIONS

ME 202 STRENGTH OF MATERIALS SPRING 2014 HOMEWORK 4 SOLUTIONS ÇANKAYA UNIVERSITY MECHANICAL ENGINEERING DEPARTMENT ME 202 STRENGTH OF MATERIALS SPRING 2014 Due Date: 1 ST Lecture Hour of Week 12 (02 May 2014) Quiz Date: 3 rd Lecture Hour of Week 12 (08 May 2014)

More information

Unit M1.5 Statically Indeterminate Systems

Unit M1.5 Statically Indeterminate Systems Unit M1.5 Statically Indeterminate Systems Readings: CDL 2.1, 2.3, 2.4, 2.7 16.001/002 -- Unified Engineering Department of Aeronautics and Astronautics Massachusetts Institute of Technology LEARNING OBJECTIVES

More information

MECH 401 Mechanical Design Applications

MECH 401 Mechanical Design Applications MECH 401 Mechanical Design Applications Dr. M. O Malley Master Notes Spring 008 Dr. D. M. McStravick Rice University Updates HW 1 due Thursday (1-17-08) Last time Introduction Units Reliability engineering

More information

Elastic-Plastic Fracture Mechanics. Professor S. Suresh

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

More information

This chapter is devoted to the study of torsion and of the stresses and deformations it causes. In the jet engine shown here, the central shaft links

This chapter is devoted to the study of torsion and of the stresses and deformations it causes. In the jet engine shown here, the central shaft links his chapter is devoted to the study of torsion and of the stresses and deformations it causes. In the jet engine shown here, the central shaft links the components of the engine to develop the thrust that

More information

= 50 ksi. The maximum beam deflection Δ max is not = R B. = 30 kips. Notes for Strength of Materials, ET 200

= 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 information

Stress Transformation Equations: u = +135 (Fig. a) s x = 80 MPa s y = 0 t xy = 45 MPa. we obtain, cos u + t xy sin 2u. s x = s x + s y.

Stress Transformation Equations: u = +135 (Fig. a) s x = 80 MPa s y = 0 t xy = 45 MPa. we obtain, cos u + t xy sin 2u. s x = s x + s y. 014 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently 9 7. Determine the normal stress and shear stress acting

More information

REVIEW FOR EXAM II. Dr. Ibrahim A. Assakkaf SPRING 2002

REVIEW FOR EXAM II. Dr. Ibrahim A. Assakkaf SPRING 2002 REVIEW FOR EXM II. J. Clark School of Engineering Department of Civil and Environmental Engineering b Dr. Ibrahim. ssakkaf SPRING 00 ENES 0 Mechanics of Materials Department of Civil and Environmental

More information

3. BEAMS: STRAIN, STRESS, DEFLECTIONS

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

More information

Task 1 - Material Testing of Bionax Pipe and Joints

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

More information