Design Analysis and Review of Stresses at a Point


 Anthony Booth
 2 years ago
 Views:
Transcription
1 Design Analysis and Review of Stresses at a Point Need for Design Analysis: To verify the design for safety of the structure and the users. To understand the results obtained in FEA, it is necessary to have the theoretical knowledge of the stresses developed in various loading conditions. A detailed and comprehensive discussion of the followings can be found in: 1. Mechanical Engineering Design, 4 th edition, by Shigley and Mischke. McGraw Hill, Advanced Strength and Applied Stress Analysis, Second Edition, by Budynas. McGraw Hill, Formulas for Stress and Strain Roark and Young. McGraw Hill. 1
2 Some important terms that frequently occur in Design Analysis Uniaxial stresses Biaxial Stresses 3D Stresses Torsional Stress Bending Stress Combined Stresses Failure Theories Yield Strength Margin of safety Fatigue Stresses Impact Loading Stresses in Cylinders Normal Stress Mohr s Circle VonMises Stress Factor of safety Buckling Modal Analysis Resonance Rotating Rings 2
3 Stresses at a Point 3D Stresses y σ y τ yz τ yx τ xy τ zy τ zx τ xz σ x x σ z z 2D Stress Distribution σ y τ xy τ yx τ xy σ x σ x τ yx σ y 3
4 Principal Stresses In the above figure, the stresses at a point are given in the Cartesian coordinate (x, y, z) directions. Stresses in any direction φ (measured from the xaxis) are given by the following equation, σ = (1/2) (σ x + σ y ) + (1/2) (σ x σ y ) cos 2φ + τ xy sin 2φ Τ = (1/2) (σ x σ y ) sin 2φ + τ xy cos 2φ The normal stress σ and shearing stress Τ vary in magnitude with angle φ. When the shearing stress Τ = 0, the normal stresses become maximum and minimum in magnitude. These stresses are called principal stresses. Mohr s Circle is used to convert stresses at a point into principal stresses and the relationship is given as, σ 1 = (1/2) (σ x + σ y ) + [(1/2) (σ x σ y ) 2 + τ 2 xy] 1/2 σ 2 = (1/2) (σ x + σ y )  [(1/2) (σ x σ y ) 2 + τ 2 xy] 1/2 4
5 Uniaxial Stress Uniaxial stress occurs when a bar or a plate structure is either stretched or compressed. The resulting stress in the bar is given as, σ = F/A Where: F is the applied force, and A is the crosssection area of the bar. L F Stressstrain relations: σ = E ε F Where: E is the Young s modulus and ε is the strain. L Straindeflection relationship: ε = Change in length/original length = L/L 5
6 Biaxial Stresses When a platelike structure is loaded in its plane, there are biaxial stresses and strains, Y σ x σ x X The plate shown is loaded in the xdirection, but the strains will occur in both, x and ydirections. The plate stretches in the xdirection, but due to the poison s effect, it will shrink in the ydirection, thus creating bidirectional strains. σ Y σ x If loads are applied in both x and ydirections, the plate will have a bidirectional stress distribution. 6
7 StressStrain Relations Assuming that the x and y axes are principal directions, stresses and strains are related by the following equations: σ 1 = E (ε 1 + νε 2 )/(1 ν 2 ) ε 1 = σ 1 /E  νσ 2 /E σ 2 = E (ε 2 + νε 1 )/(1 ν 2 ) ε 2 = σ 2 /E νσ 1 /E σ 3 = 0 ε 3 = νσ 1 /E νσ 2 /E Beam in Bending Normal Stress: For a beam in pure bending, the normal stress is given as σ = Mc/I Where, I is the moment of inertia about the axis of beam rotation. Transverse Shear: The transverse shear is given as Τ = VQ/Ib Where, V is the shearing force c Q = y da y I = Moment of inertia about the bending axis b = width of the beam 7
8 If a beam is slender, the transverse shear is negligible and ignored. However, if a beam is not very slender, the transverse shear becomes significant and can t be ignored. Shear and Bending Moment Diagrams For a beam, the maximum stress occurs at the point where the bending moment is maximum. When the location of the maximum moment is not obvious, we need to draw a shear and bending moment diagram to find the magnitude and location. Sign Convention for Shear and Bending Moment Diagrams Positive Shear and moments Torsion The shearing stress in pure torsion is given as τ = Tr/J where r is the radial distance from the center of the shaft, and J is the polar moment of inertia. T r 8
9 Stress Concentration In the stress equations for axial, bending, and torsion, it is assumed that the cross section is uniform and no discontinuities exist. If there are holes, notches, fillets, change in cross section, etc., these equations cannot be used. Stresses in the irregular regions are always higher than the uniform sections as much as by a factor of 3 or more. The stress concentration factor is given as, K t = σ max /σ average Where, σ max = Maximum stress at some point σ average = Stress at the above point, calculated as if there is no stress concentration, and the area is the net area. Uniform cross section Stress concentration The stress concentration factor K t can be found in engineering handbooks and texts (see the books by Shigley, Martin, Roark and Young, etc.) 9
10 Deflections Deflection occurs when a static load is applied on a structure at rest (in equilibrium). All deflections are assumed as deformation in the structure. Rigid body motion doesn t result in stresses, and is not important in FEA, unless it is due to either buckling or warping. Buckling and warping require separate analysis, which is carried out after conduction the static analysis. 10
11 Elastic Structures All elastic structures follow the Hook s law, F = k x Most engineering structures are considered as elastic and follow the Hook s law. Tension, Compression, and Torsion Deflection for tension and compression loading is given as, δ = FL/AE The stiffness can be found by, k = F/x = (F)/ δ = (F)/(FL/AE) = AE/L Torsion Angular deflection in torsion is, θ = TL/JG The stiffness is, k = T/ θ = GJ/L 11
12 Bending Since there are numerous loading and support conditions that can be applied to a beam, the deflection equation can be found in an engineering textbook or a handbook. Shigley, Norton, and Roark and Young are good source of information. Buckling Buckling occurs in long columns that are loaded by compressive forces. A beam structure, that has several load members, should always be checked for buckling. In buckling, a structure can fail even before reaching the yield stress point, and therefore, the standard failure criteria are not valid. To check for buckling, the critical buckling load should be calculated, which will determine the maximum allowable load magnitude. Euler s formula gives the critical buckling load equation, P CR = Cπ 2 EI/L 2 C depends on the endconstraint of the part under buckling. It has the following values, 12
13 Column End Condition Recommended Value FixedFree 1/4 PinPin 1 FixedPin 1.2 FixedFixed 1.2 Some textbooks use the term Load Factor, which is similar to the Factor of Safety in stress analysis, and is defined as, LF = P cr /P applied For safety, the Load Factor (LF) must be greater than 1. Failure of Engineering Structures Generally, there are two types of engineering materials that are used in FEA: ductile and brittle. 13
14 Ductile Materials According to the ductile material failure theory, failure occurs when the VonMises stress (VMS) in the structure exceeds the yield strength of the material. The VMS is calculated from the principal stresses by the formula, σ VM = [(σ 1 ) 2 + (σ 2 ) 2  σ 1 σ 2 ] 1/2 Brittle Materials Brittle materials, such as, cast iron and concrete are governed by Modified Mohr or CoulombMohr theories. In FEA, computer is unable to distinguish between a ductile and a brittle material. Since the expected results are seldom exact answers, FEA software uses the VonMises stresses for checking failure in structures, regardless of the applicable theory for the material used. Structure Loads Generally, all loads applied in FEA are static loads. The structure is assumed to be in an equilibrium condition when the loads are applied. For other types of loads, such as, impact, vibrations, and fatigue, there are more advanced FEA software, which can handle these loads. 14
Stress and Deformation Analysis. Representing Stresses on a Stress Element. Representing Stresses on a Stress Element con t
Stress and Deformation Analysis Material in this lecture was taken from chapter 3 of Representing Stresses on a Stress Element One main goals of stress analysis is to determine the point within a loadcarrying
More informationThe elements used in commercial codes can be classified in two basic categories:
CHAPTER 3 Truss Element 3.1 Introduction The single most important concept in understanding FEA, is the basic understanding of various finite elements that we employ in an analysis. Elements are used for
More informationAnalysis of Stresses and Strains
Chapter 7 Analysis of Stresses and Strains 7.1 Introduction axial load = P / A torsional load in circular shaft = T / I p bending moment and shear force in beam = M y / I = V Q / I b in this chapter, we
More informationMECHANICS OF MATERIALS
T dition CHTR MCHNICS OF MTRIS Ferdinand. Beer. Russell Johnston, Jr. John T. DeWolf ecture Notes: J. Walt Oler Texas Tech University Stress and Strain xial oading  Contents Stress & Strain: xial oading
More informationMechanical Properties  Stresses & Strains
Mechanical Properties  Stresses & Strains Types of Deformation : Elasic Plastic Anelastic Elastic deformation is defined as instantaneous recoverable deformation Hooke's law : For tensile loading, σ =
More informationCH 6: Fatigue Failure Resulting from Variable Loading
CH 6: Fatigue Failure Resulting from Variable Loading Some machine elements are subjected to static loads and for such elements static failure theories are used to predict failure (yielding or fracture).
More informationSolid Mechanics. Stress. What you ll learn: Motivation
Solid Mechanics Stress What you ll learn: What is stress? Why stress is important? What are normal and shear stresses? What is strain? Hooke s law (relationship between stress and strain) Stress strain
More information8.2 Elastic Strain Energy
Section 8. 8. Elastic Strain Energy The strain energy stored in an elastic material upon deformation is calculated below for a number of different geometries and loading conditions. These expressions for
More informationIntroduction to Mechanical Behavior of Biological Materials
Introduction to Mechanical Behavior of Biological Materials Ozkaya and Nordin Chapter 7, pages 127151 Chapter 8, pages 173194 Outline Modes of loading Internal forces and moments Stiffness of a structure
More informationEDEXCEL NATIONAL CERTIFICATE/DIPLOMA MECHANICAL PRINCIPLES OUTCOME 2 ENGINEERING COMPONENTS TUTORIAL 1 STRUCTURAL MEMBERS
ENGINEERING COMPONENTS EDEXCEL NATIONAL CERTIFICATE/DIPLOMA MECHANICAL PRINCIPLES OUTCOME ENGINEERING COMPONENTS TUTORIAL 1 STRUCTURAL MEMBERS Structural members: struts and ties; direct stress and strain,
More informationReinforced Concrete Design SHEAR IN BEAMS
CHAPTER Reinforced Concrete Design Fifth Edition SHEAR IN BEAMS A. J. Clark School of Engineering Department of Civil and Environmental Engineering Part I Concrete Design and Analysis 4a FALL 2002 By Dr.
More informationStress Strain Relationships
Stress Strain Relationships Tensile Testing One basic ingredient in the study of the mechanics of deformable bodies is the resistive properties of materials. These properties relate the stresses to the
More informationMultiaxial Fatigue. Professor Darrell Socie. 20082014 Darrell Socie, All Rights Reserved
Multiaxial Fatigue Professor Darrell Socie 20082014 Darrell Socie, All Rights Reserved Outline Stresses around holes Crack Nucleation Crack Growth MultiaxialFatigue 20082014 Darrell Socie, All Rights
More informationChapter 2: Load, Stress and Strain
Chapter 2: Load, Stress and Strain The careful text books measure (Let all who build beware!) The load, the shock, the pressure Material can bear. So when the buckled girder Lets down the grinding span,
More informationEDEXCEL NATIONAL CERTIFICATE/DIPLOMA MECHANICAL PRINCIPLES AND APPLICATIONS NQF LEVEL 3 OUTCOME 1  LOADING SYSTEMS TUTORIAL 3 LOADED COMPONENTS
EDEXCEL NATIONAL CERTIICATE/DIPLOMA MECHANICAL PRINCIPLES AND APPLICATIONS NQ LEVEL 3 OUTCOME 1  LOADING SYSTEMS TUTORIAL 3 LOADED COMPONENTS 1. Be able to determine the effects of loading in static engineering
More informationR&DE (Engineers), DRDO. Theories of Failure. rd_mech@yahoo.co.in. Ramadas Chennamsetti
heories of Failure ummary Maximum rincial stress theory Maximum rincial strain theory Maximum strain energy theory Distortion energy theory Maximum shear stress theory Octahedral stress theory Introduction
More informationUnit 3 (Review of) Language of Stress/Strain Analysis
Unit 3 (Review of) Language of Stress/Strain Analysis Readings: B, M, P A.2, A.3, A.6 Rivello 2.1, 2.2 T & G Ch. 1 (especially 1.7) Paul A. Lagace, Ph.D. Professor of Aeronautics & Astronautics and Engineering
More informationShaft Design. Shaft Design. Shaft Design Procedure. Chapter 12
Shaft Design Chapter 1 Material taken from Mott, 003, Machine Elements in Mechanical Design Shaft Design A shaft is the component of a mechanical device that transmits rotational motion and power. It is
More informationTorsion Tests. Subjects of interest
Chapter 10 Torsion Tests Subjects of interest Introduction/Objectives Mechanical properties in torsion Torsional stresses for large plastic strains Type of torsion failures Torsion test vs.tension test
More informationChapter Outline. Mechanical Properties of Metals How do metals respond to external loads?
Mechanical Properties of Metals How do metals respond to external loads? Stress and Strain Tension Compression Shear Torsion Elastic deformation Plastic Deformation Yield Strength Tensile Strength Ductility
More informationBending Stress in Beams
93673600 Bending Stress in Beams Derive a relationship for bending stress in a beam: Basic Assumptions:. Deflections are very small with respect to the depth of the beam. Plane sections before bending
More informationMCE380: Measurements and Instrumentation Lab. Chapter 9: Force, Torque and Strain Measurements
MCE380: Measurements and Instrumentation Lab Chapter 9: Force, Torque and Strain Measurements Topics: Elastic Elements for Force Measurement Dynamometers and Brakes Resistance Strain Gages Holman, Ch.
More informationYield Criteria for Ductile Materials and Fracture Mechanics of Brittle Materials. τ xy 2σ y. σ x 3. τ yz 2σ z 3. ) 2 + ( σ 3. σ 3
Yield Criteria for Ductile Materials and Fracture Mechanics of Brittle Materials Brittle materials are materials that display Hookean behavior (linear relationship between stress and strain) and which
More informationME 215 Engineering Materials I
ME 215 Engineering Materials I Chapter 3 Properties in Tension and Compression (Part III) Mechanical Engineering University of Gaziantep Dr. A. Tolga Bozdana www.gantep.edu.tr/~bozdana True Stress and
More informationIntroduction, Method of Sections
Lecture #1 Introduction, Method of Sections Reading: 1:12 Mechanics of Materials is the study of the relationship between external, applied forces and internal effects (stress & deformation). An understanding
More informationLecture 12: Fundamental Concepts in Structural Plasticity
Lecture 12: Fundamental Concepts in Structural Plasticity Plastic properties of the material were already introduced briefly earlier in the present notes. The critical slenderness ratio of column is controlled
More informationMECHANICS OF SOLIDS COMPRESSION MEMBERS TUTORIAL 1 STRUTS. On completion of this tutorial you should be able to do the following.
MECHANICS OF SOLIDS COMPRESSION MEMBERS TUTORIAL 1 STRUTS You should judge your progress by completing the self assessment exercises. On completion of this tutorial you should be able to do the following.
More informationObjectives. Experimentally determine the yield strength, tensile strength, and modules of elasticity and ductility of given materials.
Lab 3 Tension Test Objectives Concepts Background Experimental Procedure Report Requirements Discussion Objectives Experimentally determine the yield strength, tensile strength, and modules of elasticity
More informationA beam is a structural member that is subjected primarily to transverse loads and negligible
Chapter. Design of Beams Flexure and Shear.1 Section forcedeformation response & Plastic Moment (M p ) A beam is a structural member that is subjected primarily to transverse loads and negligible axial
More informationAdam Zaborski handouts for Afghans
Tensile test Adam Zaborski handouts for Afghans Outline Tensile test purpose Universal testing machines and test specimens Stressstrain diagram Mild steel : proportional stage, elastic limit, yielding
More informationM x (a) (b) (c) Figure 2: Lateral Buckling The positions of the beam shown in Figures 2a and 2b should be considered as two possible equilibrium posit
Lateral Stability of a Slender Cantilever Beam With End Load Erik Thompson Consider the slender cantilever beam with an end load shown in Figure 1. The bending moment at any crosssection is in the xdirection.
More informationMATERIALS SELECTION FOR SPECIFIC USE
MATERIALS SELECTION FOR SPECIFIC USE1 Subtopics 1 Density What determines density and stiffness? Material properties chart Design problems LOADING 2 STRENGTH AND STIFFNESS Stress is applied to a material
More informationTorsion Testing. Objectives
Laboratory 4 Torsion Testing Objectives Students are required to understand the principles of torsion testing, practice their testing skills and interpreting the experimental results of the provided materials
More informationMechanical Properties of Metals Mechanical Properties refers to the behavior of material when external forces are applied
Mechanical Properties of Metals Mechanical Properties refers to the behavior of material when external forces are applied Stress and strain fracture or engineering point of view: allows to predict the
More informationSTRESS AND DEFORMATION ANALYSIS OF LINEAR ELASTIC BARS IN TENSION
Chapter 11 STRESS AND DEFORMATION ANALYSIS OF LINEAR ELASTIC BARS IN TENSION Figure 11.1: In Chapter10, the equilibrium, kinematic and constitutive equations for a general threedimensional solid deformable
More informationThe Basics of FEA Procedure
CHAPTER 2 The Basics of FEA Procedure 2.1 Introduction This chapter discusses the spring element, especially for the purpose of introducing various concepts involved in use of the FEA technique. A spring
More informationWelcome to the first lesson of third module which is on thinwalled pressure vessels part one which is on the application of stress and strain.
Strength of Materials Prof S. K. Bhattacharya Department of Civil Engineering Indian Institute of Technology, Kharagpur Lecture 15 Application of Stress by Strain Thinwalled Pressure Vessels  I Welcome
More informationEnd Restraint and Effective Lengths of Columns
CHAPTER Structural Steel Design LRFD Method Third Edition INTRODUCTION TO AXIALLY LOADED COMPRESSION MEMBERS A. J. Clark School of Engineering Department of Civil and Environmental Engineering Part II
More informationDESIGN OF BEAMCOLUMNS  I
13 DESIGN OF BEACOLUNS  I INTRODUCTION Columns in practice rarely experience concentric axial compression alone. Since columns are usually parts of a frame, they experience both bending moment and axial
More informationMATERIALS AND MECHANICS OF BENDING
HAPTER Reinforced oncrete Design Fifth Edition MATERIALS AND MEHANIS OF BENDING A. J. lark School of Engineering Department of ivil and Environmental Engineering Part I oncrete Design and Analysis b FALL
More informationTUTORIAL FOR RISA EDUCATIONAL
1. INTRODUCTION TUTORIAL FOR RISA EDUCATIONAL C.M. Uang and K.M. Leet The educational version of the software RISA2D, developed by RISA Technologies for the textbook Fundamentals of Structural Analysis,
More informationSEISMIC DESIGN. Various building codes consider the following categories for the analysis and design for earthquake loading:
SEISMIC DESIGN Various building codes consider the following categories for the analysis and design for earthquake loading: 1. Seismic Performance Category (SPC), varies from A to E, depending on how the
More informationModule 3. Limit State of Collapse  Flexure (Theories and Examples) Version 2 CE IIT, Kharagpur
Module 3 Limit State of Collapse  Flexure (Theories and Examples) Lesson 4 Computation of Parameters of Governing Equations Instructional Objectives: At the end of this lesson, the student should be able
More informationNonlinear analysis and formfinding in GSA Training Course
Nonlinear analysis and formfinding in GSA Training Course Nonlinear analysis and formfinding in GSA 1 of 47 Oasys Ltd Nonlinear analysis and formfinding in GSA 2 of 47 Using the GSA GsRelax Solver
More informationMohr s Circle. Academic Resource Center
Mohr s Circle Academic Resource Center Introduction The transformation equations for plane stress can be represented in graphical form by a plot known as Mohr s Circle. This graphical representation is
More informationLab for Deflection and Moment of Inertia
Deflection and Moment of Inertia Subject Area(s) Associated Unit Lesson Title Physics Wind Effects on Model Building Lab for Deflection and Moment of Inertia Grade Level (1112) Part # 2 of 3 Lesson #
More informationNew approaches in Eurocode 3 efficient global structural design
New approaches in Eurocode 3 efficient global structural design Part 1: 3D model based analysis using general beamcolumn FEM Ferenc Papp* and József Szalai ** * Associate Professor, Department of Structural
More informationENGINEERING COUNCIL CERTIFICATE LEVEL
ENGINEERING COUNCIL CERTIICATE LEVEL ENGINEERING SCIENCE C103 TUTORIAL  BASIC STUDIES O STRESS AND STRAIN You should judge your progress by completing the self assessment exercises. These may be sent
More informationInteraction between plate and column buckling
Delft, University of Technology Engineering office of Public works Rotterdam Interaction between plate and column buckling Master Thesis Name: Alex van Ham Student number: 1306138 Email: vanham.alex@gmail.com
More informationStructural Integrity Analysis
Structural Integrity Analysis 1. STRESS CONCENTRATION Igor Kokcharov 1.1 STRESSES AND CONCENTRATORS 1.1.1 Stress An applied external force F causes inner forces in the carrying structure. Inner forces
More informationDesign of reinforced concrete columns. Type of columns. Failure of reinforced concrete columns. Short column. Long column
Design of reinforced concrete columns Type of columns Failure of reinforced concrete columns Short column Column fails in concrete crushed and bursting. Outward pressure break horizontal ties and bend
More information3. AXIALLY LOADED MEMBERS
3 AXIALLY LOADED MEMBERS 31 Reading Assignment: Section 19 and Sections 81 and 82 of text Most axially loaded structural members carry some moment in addition to axial load  for this discussion, restrict
More information16. BeamandSlab Design
ENDP311 Structural Concrete Design 16. BeamandSlab Design BeamandSlab System How does the slab work? L beams and T beams Holding beam and slab together University of Western Australia School of Civil
More informationStructural Axial, Shear and Bending Moments
Structural Axial, Shear and Bending Moments Positive Internal Forces Acting Recall from mechanics of materials that the internal forces P (generic axial), V (shear) and M (moment) represent resultants
More informationUnit 6 Plane Stress and Plane Strain
Unit 6 Plane Stress and Plane Strain Readings: T & G 8, 9, 10, 11, 12, 14, 15, 16 Paul A. Lagace, Ph.D. Professor of Aeronautics & Astronautics and Engineering Systems There are many structural configurations
More informationAN EXPLANATION OF JOINT DIAGRAMS
AN EXPLANATION OF JOINT DIAGRAMS When bolted joints are subjected to external tensile loads, what forces and elastic deformation really exist? The majority of engineers in both the fastener manufacturing
More informationAnalysis of Stress CHAPTER 1 1.1 INTRODUCTION
CHAPTER 1 Analysis of Stress 1.1 INTRODUCTION The basic structure of matter is characterized by nonuniformity and discontinuity attributable to its various subdivisions: molecules, atoms, and subatomic
More informationPlaneShear Measurement with Strain Gages
MicroMeasuremeNTs Strain Gages and Instruments e TN5 Introduction Loading a specimen as shown in Figure a produces shear stresses in the material. An initially square element of the material, having
More informationMECHANICAL PRINCIPLES HNC/D PRELIMINARY LEVEL TUTORIAL 1 BASIC STUDIES OF STRESS AND STRAIN
MECHANICAL PRINCIPLES HNC/D PRELIMINARY LEVEL TUTORIAL 1 BASIC STUDIES O STRESS AND STRAIN This tutorial is essential for anyone studying the group of tutorials on beams. Essential prerequisite knowledge
More informationMechanics of Materials Summary
Mechanics of Materials Summary 1. Stresses and Strains 1.1 Normal Stress Let s consider a fixed rod. This rod has length L. Its crosssectional shape is constant and has area. Figure 1.1: rod with a normal
More informationYield and failure criteria
Theory of Plasticity lecture dam Paul Zaborski Definition Yield and failure criteria In uniaxial state of stress the point of failure or yield of material is obvious. In a simple tension tests is the yield
More informationP4 Stress and Strain Dr. A.B. Zavatsky MT07 Lecture 3 Statically Indeterminate Structures
4 Stress and Strain Dr... Zavatsky MT07 ecture 3 Statically Indeterminate Structures Statically determinate structures. Statically indeterminate structures (equations of equilibrium, compatibility, and
More informationMECHANICS OF SOLIDS  BEAMS TUTORIAL 2 SHEAR FORCE AND BENDING MOMENTS IN BEAMS
MECHANICS OF SOLIDS  BEAMS TUTORIAL 2 SHEAR FORCE AND BENDING MOMENTS IN BEAMS This is the second tutorial on bending of beams. You should judge your progress by completing the self assessment exercises.
More informationReinforced Concrete Design
FALL 2013 C C Reinforced Concrete Design CIVL 4135 ii 1 Chapter 1. Introduction 1.1. Reading Assignment Chapter 1 Sections 1.1 through 1.8 of text. 1.2. Introduction In the design and analysis of reinforced
More information1 of 79 Erik Eberhardt UBC Geological Engineering EOSC 433
Stress & Strain: A review xx yz zz zx zy xy xz yx yy xx yy zz 1 of 79 Erik Eberhardt UBC Geological Engineering EOSC 433 Disclaimer before beginning your problem assignment: Pick up and compare any set
More informationMECHANICS OF SOLIDS  BEAMS TUTORIAL TUTORIAL 4  COMPLEMENTARY SHEAR STRESS
MECHANICS OF SOLIDS  BEAMS TUTORIAL TUTORIAL 4  COMPLEMENTARY SHEAR STRESS This the fourth and final tutorial on bending of beams. You should judge our progress b completing the self assessment exercises.
More informationChapter 4: Summary and Conclusions
Chapter 4: Summary and Conclusions 4.1 Summary Three different models are presented and analyzed in this research for the purpose of studying the potential of using postbuckled or prebent elastic struts
More informationStatics and Mechanics of Materials
Statics and Mechanics of Materials Chapter 41 Internal force, normal and shearing Stress Outlines Internal Forces  cutting plane Result of mutual attraction (or repulsion) between molecules on both
More information2. Axial Force, Shear Force, Torque and Bending Moment Diagrams
2. Axial Force, Shear Force, Torque and Bending Moment Diagrams In this section, we learn how to summarize the internal actions (shear force and bending moment) that occur throughout an axial member, shaft,
More informationLecture 17. Last time we saw that the rotational analog of Newton s 2nd Law is
Lecture 17 Rotational Dynamics Rotational Kinetic Energy Stress and Strain and Springs Cutnell+Johnson: 9.49.6, 10.110.2 Rotational Dynamics (some more) Last time we saw that the rotational analog of
More informationLecture 4: Basic Review of Stress and Strain, Mechanics of Beams
MECH 466 Microelectromechanical Sstems Universit of Victoria Dept. of Mechanical Engineering Lecture 4: Basic Review of Stress and Strain, Mechanics of Beams 1 Overview Compliant Mechanisms Basics of Mechanics
More informationP4 Stress and Strain Dr. A.B. Zavatsky MT07 Lecture 4 Stresses on Inclined Sections
4 Stress and Strain Dr. A.B. Zavatsky MT07 Lecture 4 Stresses on Inclined Sections Shear stress and shear strain. Equality of shear stresses on perpendicular planes. Hooke s law in shear. Normal and shear
More informationME 343: Mechanical Design3
ME 343: Mechanical Design3 Design of Shaft (continue) Dr. Aly Mousaad Aly Department of Mechanical Engineering Faculty of Engineering, Alexandria University Objectives At the end of this lesson, we should
More informationSection 16: Neutral Axis and Parallel Axis Theorem 161
Section 16: Neutral Axis and Parallel Axis Theorem 161 Geometry of deformation We will consider the deformation of an ideal, isotropic prismatic beam the cross section is symmetric about yaxis All parts
More informationSolutions Manual. Failure, Fracture, Fatigue. An Introduction
Solutions Manual to problems in Failure, Fracture, Fatigue An Introduction by Tore Dahlberg Anders Ekberg Studentlitteratur, Lund 2002, ISBN 9144020961. This manual contains solutions to problems in
More informationBending Stress and Strain
Bending Stress and Strain DEFLECTIONS OF BEAMS When a beam with a straight longitudinal ais is loaded by lateral forces, the ais is deformed into a curve, called the deflection curve of the beam. We will
More informationLearning Module 1 Static Structural Analysis
LMST1 Learning Module 1 Static Structural Analysis What is a Learning Module? Title Page Guide A Learning Module (LM) is a structured, concise, and selfsufficient learning resource. An LM provides the
More informationLecture Slides. Chapter 10. Mechanical Springs
Lecture Slides Chapter 10 Mechanical Springs The McGrawHill Companies 2012 Chapter Outline Mechanical Springs Exert Force Provide flexibility Store or absorb energy Helical Spring Helical coil spring
More informationShear Forces and Bending Moments
Chapter 4 Shear Forces and Bending Moments 4.1 Introduction Consider a beam subjected to transverse loads as shown in figure, the deflections occur in the plane same as the loading plane, is called the
More informationApproximate Analysis of Statically Indeterminate Structures
Approximate Analysis of Statically Indeterminate Structures Every successful structure must be capable of reaching stable equilibrium under its applied loads, regardless of structural behavior. Exact analysis
More informationEDEXCEL NATIONAL CERTIFICATE/DIPLOMA MECHANICAL PRINCIPLES AND APPLICATIONS NQF LEVEL 3 OUTCOME 1  LOADING SYSTEMS
EDEXCEL NATIONAL CERTIFICATE/DIPLOMA MECHANICAL PRINCIPLES AND APPLICATIONS NQF LEVEL 3 OUTCOME 1  LOADING SYSTEMS TUTORIAL 1 NONCONCURRENT COPLANAR FORCE SYSTEMS 1. Be able to determine the effects
More informationWhen the fluid velocity is zero, called the hydrostatic condition, the pressure variation is due only to the weight of the fluid.
Fluid Statics When the fluid velocity is zero, called the hydrostatic condition, the pressure variation is due only to the weight of the fluid. Consider a small wedge of fluid at rest of size Δx, Δz, Δs
More informationσ = F / A o Chapter Outline Introduction Mechanical Properties of Metals How do metals respond to external loads?
Mechanical Properties of Metals How do metals respond to external loads? and Tension Compression Shear Torsion Elastic deformation Chapter Outline Introduction To understand and describe how materials
More informationStress: The stress in an axially loaded tension member is given by Equation (4.1) P (4.1) A
Chapter 4. TENSION MEMBER DESIGN 4.1 INTRODUCTORY CONCEPTS Stress: The stress in an axially loaded tension member is given by Equation (4.1) P f = (4.1) A where, P is the magnitude of load, and A is the
More informationBEAM THEORIES The difference between EulerBernoulli and Timoschenko
BEAM THEORIES The difference between EulerBernoulli and Timoschenko Uemuet Goerguelue Two mathematical models, namely the sheardeformable (Timoshenko) model and the shearindeformable (EulerBernoulli)
More informationShear Center in ThinWalled Beams Lab
Shear Center in ThinWalled Beams Lab Shear flow is developed in beams with thinwalled cross sections shear flow (q sx ): shear force per unit length along cross section q sx =τ sx t behaves much like
More informationProperties of Materials
CHAPTER 1 Properties of Materials INTRODUCTION Materials are the driving force behind the technological revolutions and are the key ingredients for manufacturing. Materials are everywhere around us, and
More informationChapter 12 Elasticity
If I have seen further than other men, it is because I stood on the shoulders of giants. Isaac Newton 12.1 The Atomic Nature of Elasticity Elasticity is that property of a body by which it experiences
More informationMETU DEPARTMENT OF METALLURGICAL AND MATERIALS ENGINEERING
METU DEPARTMENT OF METALLURGICAL AND MATERIALS ENGINEERING Met E 206 MATERIALS LABORATORY EXPERIMENT 1 Prof. Dr. Rıza GÜRBÜZ Res. Assist. Gül ÇEVİK (Room: B306) INTRODUCTION TENSION TEST Mechanical testing
More information3 Concepts of Stress Analysis
3 Concepts of Stress Analysis 3.1 Introduction Here the concepts of stress analysis will be stated in a finite element context. That means that the primary unknown will be the (generalized) displacements.
More informationPhysics 172H. Lecture 6 BallSpring Model of Solids, Friction. Read
Physics 172H Lecture 6 BallSpring Model of Solids, Friction Read 4.14.8 Model of solid: chemical bonds d radial force (N) 0 F linear If atoms don t move too far away from equilibrium, force looks like
More informationFatigue Failure Due to Variable Loading
Fatigue Failure Due to Variable Loading Daniel Hendrickson Department of Computer Science, Physics, and Engineering University of Michigan Flint Advisor: Olanrewaju Aluko 1. Abstract Fatigue failure in
More informationMassachusetts Institute of Technology Department of Mechanical Engineering Cambridge, MA 02139
Massachusetts Institute of Technology Department of Mechanical Engineering Cambridge, MA 02139 2.002 Mechanics and Materials II Spring 2004 Laboratory Module No. 1 Elastic behavior in tension, bending,
More informationSHAFTS: TORSION LOADING AND DEFORMATION
ECURE hird Edition SHAFS: ORSION OADING AND DEFORMAION A. J. Clark Shool of Engineering Department of Civil and Environmental Engineering 6 Chapter 3.13.5 by Dr. Ibrahim A. Assakkaf SPRING 2003 ENES 220
More informationSECTIONS
STEEL BUILDINGS, INC. Purlin Load Tables ZEE SECTIONS WWW.WHIRLWINDSTEEL.COM This page intentionally left blank. Copyright Whirlwind Steel Buildings, Inc. All Rights Reserved. Descriptions and specifications
More informationENGINEERING SCIENCE H1 OUTCOME 1  TUTORIAL 3 BENDING MOMENTS EDEXCEL HNC/D ENGINEERING SCIENCE LEVEL 4 H1 FORMERLY UNIT 21718P
ENGINEERING SCIENCE H1 OUTCOME 1  TUTORIAL 3 BENDING MOMENTS EDEXCEL HNC/D ENGINEERING SCIENCE LEVEL 4 H1 FORMERLY UNIT 21718P This material is duplicated in the Mechanical Principles module H2 and those
More informationBUCKLING OF BARS, PLATES, AND SHELLS. Virginia Polytechnic Institute and State University Biacksburg, Virginia 240610219
BUCKLING OF BARS, PLATES, AND SHELLS ROBERT M. JONES Science and Mechanics Professor Emeritus of Engineering Virginia Polytechnic Institute and State University Biacksburg, Virginia 240610219 Bull Ridge
More informationModule 2. Analysis of Statically Indeterminate Structures by the Matrix Force Method. Version 2 CE IIT, Kharagpur
Module Analysis of Statically Indeterminate Structures by the Matrix Force Method esson 11 The Force Method of Analysis: Frames Instructional Objectives After reading this chapter the student will be able
More informationNOTCHES AND THEIR EFFECTS. Ali Fatemi  University of Toledo All Rights Reserved Chapter 7 Notches and Their Effects 1
NOTCHES AND THEIR EFFECTS Ali Fatemi  University of Toledo All Rights Reserved Chapter 7 Notches and Their Effects 1 CHAPTER OUTLINE Background Stress/Strain Concentrations SN Approach for Notched Members
More informationFATIGUE CONSIDERATION IN DESIGN
FATIGUE CONSIDERATION IN DESIGN OBJECTIVES AND SCOPE In this module we will be discussing on design aspects related to fatigue failure, an important mode of failure in engineering components. Fatigue failure
More information