Chapter 5 Elastic Strain, Deflection, and Stability 1. Elastic StressStrain Relationship


 Nora Bradley
 1 years ago
 Views:
Transcription
1 Chapter 5 Elastic Strain, Deflection, and Stability Elastic StressStrain Relationship A stress in the xdirection causes a strain in the xdirection by σ x also causes a strain in the ydirection & zdirection by Chapter 5 Elastic Strain, Deflection, and Stability 1
2 E Resulting Strain Each Direction Stress x y z σ x σ y σ z Chapter 5 Elastic Strain, Deflection, and Stability 2
3 Adding the columns to obtain the total strain in each direction ε x ε y ε z Shear strain γ xy, γ yz, γ zx Note: shear strain on a given plane is by the shear stresses on other planes. Generalized Hooke s Law Only elastic constants are needed for an material. G Chapter 5 Elastic Strain, Deflection, and Stability 3
4 Only two are independent elastic constant Pure shear stress Mohr s circle σ ε τ γ/2 ε 1 ε 2 from G τ/γ ε 3 γ Chapter 5 Elastic Strain, Deflection, and Stability 4
5 Example: 1. The stress that develops in the ydirection. 2. The strain in the zdirection. 3. The strain in the xdirection. 4. The stiffness E σ z / ε z in the zdireciton. Is this equal to E? ε y & σ x Chapter 5 Elastic Strain, Deflection, and Stability 5
6 1. ε y 0 σ y 2. ε z 3. ε x 4. E σ z / ε z Chapter 5 Elastic Strain, Deflection, and Stability 6
7 Volumetric Strain & Hydrostatic Stress Volume changes associated with. Shear strains cause only dv Since VLWH dv V ε v V dv ν 0. 5 ε ν > 0. 5 tensile stress decrease volume V Chapter 5 Elastic Strain, Deflection, and Stability 7
8 Hydrostatic stresses Invariant σ h σ v Volumetric strain hydrostatic stress Constant modulus B Chapter 5 Elastic Strain, Deflection, and Stability 8
9 Castigliano s Method Useful in computing elastic deflection and redundant reactions Deflection Figure 5.15 General load deflection curve for elastic range U U stored elastic energy is equal to times. du du Deflection, In general case, Chapter 5 Elastic Strain, Deflection, and Stability 9
10 Axial Loading Case U U δ U Sample problem 5.4 Chapter 5 Elastic Strain, Deflection, and Stability 10
11 Sample problem 5.4 con t. 1. M V Q M Px 2 valid only x 0 x L 2 2. U 3. U δ P Chapter 5 Elastic Strain, Deflection, and Stability 11
12 Problem 5.15 (page233) What are the angular and linear displacements of point A of Figure 5.15? Known: Figure P.15 is given. Find: Calculate the angular and linear displacements of point A. Chapter 5 Elastic Strain, Deflection, and Stability 12
13 Problem 5.19 (page 234) Figure 5.19 shows a steel shaft supported by selfaligning bearings and subjected to a uniformly distributed load. Using Castigliano s method, determine the required diameter d to limit the deflection to 0.2mm. Known: A steel shaft supported by selfaligning bearings is subjected to a uniformly distributed load. Find: Using Castigliano s Method, determine the required diameter, d, to limit the deflection to 0.2mm. Assumption: 1. The steel shaft remains in the elastic region. 2. The transverse shear deflection is negligible. Analysis: Chapter 5 Elastic Strain, Deflection, and Stability 13
14 Problem 5.23(page 235) In order to reduce the deflection of the Ibeam cantilever shown, a support is to be added at S. (a). What vertical force at S is needed to reduce the deflection at this point to zero? (b). What force is needed to cause an upward deflection at S of 5mm? (c). What can you say about the effect of these forces at S on the bending stresses at the point of beam attachment? Assumptions: 1. The beam remains elastic. 2. Transverse shear deflection is negligible. Analysis: Chapter 5 Elastic Strain, Deflection, and Stability 14
15 Redundant Reactions by Castigliano s Method Reduntant reaction: force or moment that is for equilibrium. As magnitude of a redundant reaction is varied, changes, But remains. Castigliano s theorem states that the associated with any reaction that can be varied without upsetting equilibrium. The deflection. Chapter 5 Elastic Strain, Deflection, and Stability 15
16 Sample Problem 5.9 Figure 5.22 Find: Determine the tension in the guy wire Assumption: Analysis: At point a Chapter 5 Elastic Strain, Deflection, and Stability 16
17 M Bending energy below point a 2 3 M u dy 0 2EI The horizontal deflection at point a δ 0 u F F Chapter 5 Elastic Strain, Deflection, and Stability 17
18 Euler Column Buckling Figure 5.24 B0 Q ρ cr xl, y0 Asin ρl 0 2 d y 2 dx M EI ρ 2 I Aρ S cr or S E cr Chapter 5 Elastic Strain, Deflection, and Stability 18
19 Le / p 10 S cr 0. 1 E Fig5.25 Loglog plot of Euler Eq (dimensionless, hence applies to all materials within their elastic range). Fig5.26 Euler column buckling curves illustrated for two values of E and S y. Chapter 5 Elastic Strain, Deflection, and Stability 19
20 Figure 5.27 Equivalent column lengths for various end conditions Figure 5.28 Euler and Johnson column curves illustrated for two valuses of E and S y Chapter 5 Elastic Strain, Deflection, and Stability 20
21 Secant formula for the loading, taking the into account. S cr Pcr A S y L 1+ ( ec )sec ( e 2 ) ρ ρ 4AE Where c denotes the distance from the neutral bending plane to the extreme fiber. P cr Chapter 5 Elastic Strain, Deflection, and Stability 21
22 Draft paper 1/2 Chapter 5 Elastic Strain, Deflection, and Stability 22
23 Draft paper 2/2 Chapter 5 Elastic Strain, Deflection, and Stability 23
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 informationChapter 4 Deflection and Stiffness
Chapter 4 Deflection and Stiffness Asst. Prof. Dr. Supakit Rooppakhun Chapter Outline Deflection and Stiffness 41 Spring Rates 42 Tension, Compression, and Torsion 43 Deflection Due to Bending 44 Beam
More informationChapter 2: Deflections of Structures
Chapter 2: Deflections of Structures Fig. 4.1. (Fig. 2.1.) ASTU, Dept. of C Eng., Prepared by: Melkamu E. Page 1 (2.1) (4.1) (2.2) Fig.4.2 Fig.2.2 ASTU, Dept. of C Eng., Prepared by: Melkamu E. Page 2
More informationModule 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 informationFINAL EXAMINATION. (CE1302 Mechanics of Materials)
UNIVERSITY OF CLIFORNI, ERKELEY FLL SEMESTER 001 FINL EXMINTION (CE130 Mechanics of Materials) Problem 1: (15 points) pinned bar structure is shown in Figure 1. There is an external force, W = 5000N,
More informationME Final Exam. PROBLEM NO. 4 Part A (2 points max.) M (x) y. z (neutral axis) beam crosssec+on. 20 kip ft. 0.2 ft. 10 ft. 0.1 ft.
ME 323  Final Exam Name December 15, 2015 Instructor (circle) PROEM NO. 4 Part A (2 points max.) Krousgrill 11:30AM12:20PM Ghosh 2:303:20PM Gonzalez 12:301:20PM Zhao 4:305:20PM M (x) y 20 kip ft 0.2
More information3. 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 information2 marks Questions and Answers
1. Define the term strain energy. A: Strain Energy of the elastic body is defined as the internal work done by the external load in deforming or straining the body. 2. Define the terms: Resilience and
More informationComb resonator design (2)
Lecture 6: Comb resonator design () Intro Intro. to Mechanics of Materials School of Electrical l Engineering i and Computer Science, Seoul National University Nano/Micro Systems & Controls Laboratory
More informationMECH 401 Mechanical Design Applications
MECH 40 Mechanical Design Applications Dr. M. K. O Malley Master Notes Spring 008 Dr. D. M. McStravick Rice University Design Considerations Stress Deflection Strain Stiffness Stability Often the controlling
More informationHomework No. 1 MAE/CE 459/559 John A. Gilbert, Ph.D. Fall 2004
Homework No. 1 MAE/CE 459/559 John A. Gilbert, Ph.D. 1. A beam is loaded as shown. The dimensions of the cross section appear in the insert. the figure. Draw a complete free body diagram showing an equivalent
More informationLecture Slides. Chapter 4. Deflection and Stiffness. The McGrawHill Companies 2012
Lecture Slides Chapter 4 Deflection and Stiffness The McGrawHill Companies 2012 Chapter Outline Force vs Deflection Elasticity property of a material that enables it to regain its original configuration
More informationLecture 7: The Beam Element Equations.
4.1 Beam Stiffness. A Beam: A long slender structural component generally subjected to transverse loading that produces significant bending effects as opposed to twisting or axial effects. MECH 40: Finite
More informationConsider an elastic spring as shown in the Fig.2.4. When the spring is slowly
.3 Strain Energy Consider an elastic spring as shown in the Fig..4. When the spring is slowly pulled, it deflects by a small amount u 1. When the load is removed from the spring, it goes back to the original
More informationCHAPTER 5. Beam Theory
CHPTER 5. Beam Theory SangJoon Shin School of Mechanical and erospace Engineering Seoul National University ctive eroelasticity and Rotorcraft Lab. 5. The EulerBernoulli assumptions One of its dimensions
More informationDecember 10, PROBLEM NO points max.
PROBLEM NO. 1 25 points max. PROBLEM NO. 2 25 points max. B 3A A C D A H k P L 2L Given: Consider the structure above that is made up of rod segments BC and DH, a spring of stiffness k and rigid connectors
More informationAE3160 Experimental Fluid and Solid Mechanics
AE3160 Experimental Fluid and Solid Mechanics Cantilever Beam Bending Claudio Di Leo 1 Learning Objectives 1. On Structural Mechanics: a) Mechanics of Slender Beams b) Strain Transformation Theory c) Principal
More informationD : SOLID MECHANICS. Q. 1 Q. 9 carry one mark each.
GTE 2016 Q. 1 Q. 9 carry one mark each. D : SOLID MECHNICS Q.1 single degree of freedom vibrating system has mass of 5 kg, stiffness of 500 N/m and damping coefficient of 100 Ns/m. To make the system
More information3D Elasticity Theory
3D lasticity Theory Many structural analysis problems are analysed using the theory of elasticity in which Hooke s law is used to enforce proportionality between stress and strain at any deformation level.
More informationChapter 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 informationε t increases from the compressioncontrolled Figure 9.15: Adjusted interaction diagram
CHAPTER NINE COLUMNS 4 b. The modified axial strength in compression is reduced to account for accidental eccentricity. The magnitude of axial force evaluated in step (a) is multiplied by 0.80 in case
More informationName :. Roll No. :... Invigilator s Signature :.. CS/B.TECH (CENEW)/SEM3/CE301/ SOLID MECHANICS
Name :. Roll No. :..... Invigilator s Signature :.. 2011 SOLID MECHANICS Time Allotted : 3 Hours Full Marks : 70 The figures in the margin indicate full marks. Candidates are required to give their answers
More informationExternal 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 informationReview of Strain Energy Methods and Introduction to Stiffness Matrix Methods of Structural Analysis
uke University epartment of Civil and Environmental Engineering CEE 42L. Matrix Structural Analysis Henri P. Gavin Fall, 22 Review of Strain Energy Methods and Introduction to Stiffness Matrix Methods
More informationComb Resonator Design (2)
Lecture 6: Comb Resonator Design () Intro. to Mechanics of Materials Sh School of felectrical ti lengineering i and dcomputer Science, Si Seoul National University Nano/Micro Systems & Controls Laboratory
More informationThe science of elasticity
The science of elasticity In 1676 Hooke realized that 1.Every kind of solid changes shape when a mechanical force acts on it. 2.It is this change of shape which enables the solid to supply the reaction
More information14. *14.8 CASTIGLIANO S THEOREM
*14.8 CASTIGLIANO S THEOREM Consider a body of arbitrary shape subjected to a series of n forces P 1, P 2, P n. Since external work done by forces is equal to internal strain energy stored in body, by
More informationPES Institute of Technology
PES Institute of Technology Bangalore south campus, Bangalore5460100 Department of Mechanical Engineering Faculty name : Madhu M Date: 29/06/2012 SEM : 3 rd A SEC Subject : MECHANICS OF MATERIALS Subject
More informationLab Exercise #5: Tension and Bending with Strain Gages
Lab Exercise #5: Tension and Bending with Strain Gages Prelab assignment: Yes No Goals: 1. To evaluate tension and bending stress models and Hooke s Law. a. σ = Mc/I and σ = P/A 2. To determine material
More informationUse Hooke s Law (as it applies in the uniaxial direction),
0.6 STRSSSTRAIN RLATIONSHIP Use the principle of superposition Use Poisson s ratio, v lateral longitudinal Use Hooke s Law (as it applies in the uniaxial direction), x x v y z, y y vx z, z z vx y Copyright
More informationMECHANICS OF MATERIALS
CHATR Stress MCHANICS OF MATRIALS and Strain Axial Loading Stress & Strain: Axial Loading Suitability of a structure or machine may depend on the deformations in the structure as well as the stresses induced
More informationMECHANICS 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 informationBEAM DEFLECTION THE ELASTIC CURVE
BEAM DEFLECTION Samantha Ramirez THE ELASTIC CURVE The deflection diagram of the longitudinal axis that passes through the centroid of each crosssectional area of a beam. Supports that apply a moment
More informationProblem " Â F y = 0. ) R A + 2R B + R C = 200 kn ) 2R A + 2R B = 200 kn [using symmetry R A = R C ] ) R A + R B = 100 kn
Problem 0. Three cables are attached as shown. Determine the reactions in the supports. Assume R B as redundant. Also, L AD L CD cos 60 m m. uation of uilibrium: + " Â F y 0 ) R A cos 60 + R B + R C cos
More informationUNIVERSITY OF SASKATCHEWAN ME MECHANICS OF MATERIALS I FINAL EXAM DECEMBER 13, 2008 Professor A. Dolovich
UNIVERSITY OF SASKATCHEWAN ME 313.3 MECHANICS OF MATERIALS I FINAL EXAM DECEMBER 13, 2008 Professor A. Dolovich A CLOSED BOOK EXAMINATION TIME: 3 HOURS For Marker s Use Only LAST NAME (printed): FIRST
More information2. Determine the deflection at C of the beam given in fig below. Use principal of virtual work. W L/2 B A L C
CE1259, Strength of Materials UNIT I STRESS, STRAIN DEFORMATION OF SOLIDS Part A 1. Define strain energy density. 2. State Maxwell s reciprocal theorem. 3. Define proof resilience. 4. State Castigliano
More informationCE6306 STRENGTH OF MATERIALS TWO MARK QUESTIONS WITH ANSWERS ACADEMIC YEAR
CE6306 STRENGTH OF MATERIALS TWO MARK QUESTIONS WITH ANSWERS ACADEMIC YEAR 20142015 UNIT  1 STRESS, STRAIN AND DEFORMATION OF SOLIDS PART A 1. Define tensile stress and tensile strain. The stress induced
More informationCOURSE TITLE : APPLIED MECHANICS & STRENGTH OF MATERIALS COURSE CODE : 4017 COURSE CATEGORY : A PERIODS/WEEK : 6 PERIODS/ SEMESTER : 108 CREDITS : 5
COURSE TITLE : APPLIED MECHANICS & STRENGTH OF MATERIALS COURSE CODE : 4017 COURSE CATEGORY : A PERIODS/WEEK : 6 PERIODS/ SEMESTER : 108 CREDITS : 5 TIME SCHEDULE MODULE TOPICS PERIODS 1 Simple stresses
More informationKINGS COLLEGE OF ENGINEERING DEPARTMENT OF MECHANICAL ENGINEERING QUESTION BANK. Subject code/name: ME2254/STRENGTH OF MATERIALS Year/Sem:II / IV
KINGS COLLEGE OF ENGINEERING DEPARTMENT OF MECHANICAL ENGINEERING QUESTION BANK Subject code/name: ME2254/STRENGTH OF MATERIALS Year/Sem:II / IV UNIT I STRESS, STRAIN DEFORMATION OF SOLIDS PART A (2 MARKS)
More informationFinite Element Method in Geotechnical Engineering
Finite Element Method in Geotechnical Engineering Short Course on + Dynamics Boulder, Colorado January 58, 2004 Stein Sture Professor of Civil Engineering University of Colorado at Boulder Contents Steps
More informationSTRESS STRAIN AND DEFORMATION OF SOLIDS, STATES OF STRESS
1 UNIT I 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
More informationMechanics of Materials II. Chapter III. A review of the fundamental formulation of stress, strain, and deflection
Mechanics of Materials II Chapter III A review of the fundamental formulation of stress, strain, and deflection Outline Introduction Assumtions and limitations Axial loading Torsion of circular shafts
More informationEE C245 ME C218 Introduction to MEMS Design
EE C245 ME C218 Introduction to MEMS Design Fall 2007 Prof. Clark T.C. Nguyen Dept. of Electrical Engineering & Computer Sciences University of California at Berkeley Berkeley, CA 94720 Lecture 16: Energy
More informationLecture 15 Strain and stress in beams
Spring, 2019 ME 323 Mechanics of Materials Lecture 15 Strain and stress in beams Reading assignment: 6.1 6.2 News: Instructor: Prof. Marcial Gonzalez Last modified: 1/6/19 9:42:38 PM Beam theory (@ ME
More informationJeff Brown Hope College, Department of Engineering, 27 Graves Pl., Holland, Michigan, USA UNESCO EOLSS
MECHANICS OF MATERIALS Jeff Brown Hope College, Department of Engineering, 27 Graves Pl., Holland, Michigan, USA Keywords: Solid mechanics, stress, strain, yield strength Contents 1. Introduction 2. Stress
More informationChapter 5 Structural Elements: The truss & beam elements
Institute of Structural Engineering Page 1 Chapter 5 Structural Elements: The truss & beam elements Institute of Structural Engineering Page 2 Chapter Goals Learn how to formulate the Finite Element Equations
More informationProblem d d d B C E D. 0.8d. Additional lecturebook examples 29 ME 323
Problem 9.1 Two beam segments, AC and CD, are connected together at C by a frictionless pin. Segment CD is cantilevered from a rigid support at D, and segment AC has a roller support at A. a) Determine
More informationMECHANICS OF MATERIALS
STATICS AND MECHANICS OF MATERIALS Ferdinand P. Beer E. Russell Johnston, Jr, John T. DeWolf David E Mazurek \Cawect Mc / iur/» Craw SugomcT Hilt Introduction 1 1.1 What is Mechanics? 2 1.2 Fundamental
More informationMechanical Engineering Ph.D. Preliminary Qualifying Examination Solid Mechanics February 25, 2002
student personal identification (ID) number on each sheet. Do not write your name on any sheet. #1. A homogeneous, isotropic, linear elastic bar has rectangular cross sectional area A, modulus of elasticity
More informationCritical Load columns buckling critical load
Buckling of Columns Buckling of Columns Critical Load Some member may be subjected to compressive loadings, and if these members are long enough to cause the member to deflect laterally or sideway. To
More information: APPLIED MECHANICS & STRENGTH OF MATERIALS COURSE CODE : 4021 COURSE CATEGORY : A PERIODS/ WEEK : 5 PERIODS/ SEMESTER : 75 CREDIT : 5 TIME SCHEDULE
COURSE TITLE : APPLIED MECHANICS & STRENGTH OF MATERIALS COURSE CODE : 4021 COURSE CATEGORY : A PERIODS/ WEEK : 5 PERIODS/ SEMESTER : 75 CREDIT : 5 TIME SCHEDULE MODULE TOPIC PERIODS 1 Simple stresses
More informationQUESTION BANK SEMESTER: III SUBJECT NAME: MECHANICS OF SOLIDS
QUESTION BANK SEMESTER: III SUBJECT NAME: MECHANICS OF SOLIDS UNIT 1 STRESS AND STRAIN PART A (2 Marks) 1. Define longitudinal strain and lateral strain. 2. State Hooke s law. 3. Define modular ratio,
More informationReview Lecture. AE1108II: Aerospace Mechanics of Materials. Dr. Calvin Rans Dr. Sofia Teixeira De Freitas
Review Lecture AE1108II: Aerospace Mechanics of Materials Dr. Calvin Rans Dr. Sofia Teixeira De Freitas Aerospace Structures & Materials Faculty of Aerospace Engineering Analysis of an Engineering System
More information공업역학/ 일반물리1 수강대상기계공학과 2학년
교과목명 ( 국문) 고체역학 ( 영문) Solid Mechanics 담당교수( 소속) 박주혁( 기계공학과) 학수번호/ 구분/ 학점 004510/ 전필/3(3) 1반 전화( 연구실/HP) 34083771/01062143771 강의시간/ 강의실화목9:0010:15/ 충무관106 선수과목 공업역학/ 일반물리1 수강대상기계공학과 2학년 jhpark@sejong.ac.kr
More informationELASTICITY (MDM 10203)
ELASTICITY () Lecture Module 3: Fundamental Stress and Strain University Tun Hussein Onn Malaysia Normal Stress inconstant stress distribution σ= dp da P = da A dimensional Area of σ and A σ A 3 dimensional
More information[8] Bending and Shear Loading of Beams
[8] Bending and Shear Loading of Beams Page 1 of 28 [8] Bending and Shear Loading of Beams [8.1] Bending of Beams (will not be covered in class) [8.2] Bending Strain and Stress [8.3] Shear in Straight
More informationStress Analysis Lecture 3 ME 276 Spring Dr./ Ahmed Mohamed Nagib Elmekawy
Stress Analysis Lecture 3 ME 276 Spring 20172018 Dr./ Ahmed Mohamed Nagib Elmekawy Axial Stress 2 Beam under the action of two tensile forces 3 Beam under the action of two tensile forces 4 Shear Stress
More informationCHAPTER OBJECTIVES Use various methods to determine the deflection and slope at specific pts on beams and shafts: 2. Discontinuity functions
1. Deflections of Beams and Shafts CHAPTER OBJECTIVES Use various methods to determine the deflection and slope at specific pts on beams and shafts: 1. Integration method. Discontinuity functions 3. Method
More informationLevel 7 Postgraduate Diploma in Engineering Computational mechanics using finite element method
9210203 Level 7 Postgraduate Diploma in Engineering Computational mechanics using finite element method You should have the following for this examination one answer book No additional data is attached
More informationCHAPTER THREE SYMMETRIC BENDING OF CIRCLE PLATES
CHAPTER THREE SYMMETRIC BENDING OF CIRCLE PLATES * Governing equations in beam and plate bending ** Solution by superposition 1.1 From Beam Bending to Plate Bending 1.2 Governing Equations For Symmetric
More informationNomenclature. Length of the panel between the supports. Width of the panel between the supports/ width of the beam
omenclature a b c f h Length of the panel between the supports Width of the panel between the supports/ width of the beam Sandwich beam/ panel core thickness Thickness of the panel face sheet Sandwich
More informationSymmetric 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 informationSTATICALLY 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 informationTuesday, February 11, Chapter 3. Load and Stress Analysis. Dr. Mohammad Suliman Abuhaiba, PE
1 Chapter 3 Load and Stress Analysis 2 Chapter Outline Equilibrium & FreeBody Diagrams Shear Force and Bending Moments in Beams Singularity Functions Stress Cartesian Stress Components Mohr s Circle for
More information3 2 6 Solve the initial value problem u ( t) 3. a If A has eigenvalues λ =, λ = 1 and corresponding eigenvectors 1
Math Problem a If A has eigenvalues λ =, λ = 1 and corresponding eigenvectors 1 3 6 Solve the initial value problem u ( t) = Au( t) with u (0) =. 3 1 u 1 =, u 1 3 = b True or false and why 1. if A is
More informationINTRODUCTION TO STRAIN
SIMPLE STRAIN INTRODUCTION TO STRAIN In general terms, Strain is a geometric quantity that measures the deformation of a body. There are two types of strain: normal strain: characterizes dimensional changes,
More informationENG2000 Chapter 7 Beams. ENG2000: R.I. Hornsey Beam: 1
ENG2000 Chapter 7 Beams ENG2000: R.I. Hornsey Beam: 1 Overview In this chapter, we consider the stresses and moments present in loaded beams shear stress and bending moment diagrams We will also look at
More informationChapter 8 Structural Design and Analysis. Strength and stiffness 5 types of load: Tension Compression Shear Bending Torsion
Chapter 8 Structural Design and Analysis 1 Strength and stiffness 5 types of load: Tension Compression Shear Bending Torsion Normal Stress Stress is a state when a material is loaded. For normal forces
More informationQUESTION BANK DEPARTMENT: CIVIL SEMESTER: III SUBJECT CODE: CE2201 SUBJECT NAME: MECHANICS OF SOLIDS UNIT 1 STRESS AND STRAIN PART A
DEPARTMENT: CIVIL SUBJECT CODE: CE2201 QUESTION BANK SEMESTER: III SUBJECT NAME: MECHANICS OF SOLIDS UNIT 1 STRESS AND STRAIN PART A (2 Marks) 1. Define longitudinal strain and lateral strain. 2. State
More informationFinal Exam Ship Structures Page 1 MEMORIAL UNIVERSITY OF NEWFOUNDLAND. Engineering Ship Structures
Final Exam  53  Ship Structures  16 Page 1 MEMORIA UNIVERSITY OF NEWFOUNDAND Faculty of Engineering and Applied Science Engineering 53  Ship Structures FINA EXAMINATION SONS Date: Wednesday April 13,
More informationME 323 Examination #2 April 11, 2018
ME 2 Eamination #2 April, 2 PROBLEM NO. 25 points ma. A thinwalled pressure vessel is fabricated b welding together two, openended stainlesssteel vessels along a 6 weld line. The welded vessel has an
More informationLecture 8. Stress Strain in Multidimension
Lecture 8. Stress Strain in Multidimension Module. General Field Equations General Field Equations [] Equilibrium Equations in Elastic bodies xx x y z yx zx f x 0, etc [2] Kinematics xx u x x,etc. [3]
More information2. 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 informationAircraft Stress Analysis and Structural Design Summary
Aircraft Stress Analysis and Structural Design Summary 1. Trusses 1.1 Determinacy in Truss Structures 1.1.1 Introduction to determinacy A truss structure is a structure consisting of members, connected
More informationMAAE 2202 A. Come to the PASS workshop with your mock exam complete. During the workshop you can work with other students to review your work.
It is most beneficial to you to write this mock final exam UNDER EXAM CONDITIONS. This means: Complete the exam in 3 hours. Work on your own. Keep your textbook closed. Attempt every question. After the
More informationUnit 13 Review of Simple Beam Theory
MIT  16.0 Fall, 00 Unit 13 Review of Simple Beam Theory Readings: Review Unified Engineering notes on Beam Theory BMP 3.8, 3.9, 3.10 T & G 1015 Paul A. Lagace, Ph.D. Professor of Aeronautics & Astronautics
More information1 of 12. Given: Law of Cosines: C. Law of Sines: Stress = E = G
ES230 STRENGTH OF MATERIALS FINAL EXAM: WEDNESDAY, MAY 15 TH, 4PM TO 7PM, AEC200 Closed book. Calculator and writing supplies allowed. Protractor and compass required. 180 Minute Time Limit You must have
More informationME FINITE ELEMENT ANALYSIS FORMULAS
ME 2353  FINITE ELEMENT ANALYSIS FORMULAS UNIT I FINITE ELEMENT FORMULATION OF BOUNDARY VALUE PROBLEMS 01. Global Equation for Force Vector, {F} = [K] {u} {F} = Global Force Vector [K] = Global Stiffness
More informationModule 2 Stresses in machine elements
Module 2 Stresses in machine elements Lesson 3 Strain analysis Instructional Objectives At the end of this lesson, the student should learn Normal and shear strains. 3D strain matri. Constitutive equation;
More informationExample 3.7 Consider the undeformed configuration of a solid as shown in Figure 3.60.
162 3. The linear 3D elasticity mathematical model The 3D elasticity model is of great importance, since it is our highest order hierarchical model assuming linear elastic behavior. Therefore, it provides
More information202 Index. failure, 26 field equation, 122 force, 1
Index acceleration, 12, 161 admissible function, 155 admissible stress, 32 Airy's stress function, 122, 124 d'alembert's principle, 165, 167, 177 amplitude, 171 analogy, 76 anisotropic material, 20 aperiodic
More informationR13. II B. Tech I Semester Regular Examinations, Jan MECHANICS OF SOLIDS (Com. to ME, AME, AE, MTE) PARTA
SET  1 II B. Tech I Semester Regular Examinations, Jan  2015 MECHANICS OF SOLIDS (Com. to ME, AME, AE, MTE) Time: 3 hours Max. Marks: 70 Note: 1. Question Paper consists of two parts (PartA and PartB)
More informationCombined Stresses and Mohr s Circle. General Case of Combined Stresses. General Case of Combined Stresses con t. Twodimensional stress condition
Combined Stresses and Mohr s Circle Material in this lecture was taken from chapter 4 of General Case of Combined Stresses Twodimensional stress condition General Case of Combined Stresses con t The normal
More informationM15e Bending of beams
Fakultät für Physik und Geowissenschaften Physikalisches Grundpraktikum M5e Bending of beams Tasks. Determine Young s modulus E for two metal rods of different material but of the same crosssectional form
More informationME325 EXAM I (Sample)
ME35 EXAM I (Sample) NAME: NOTE: COSED BOOK, COSED NOTES. ONY A SINGE 8.5x" ORMUA SHEET IS AOWED. ADDITIONA INORMATION IS AVAIABE ON THE AST PAGE O THIS EXAM. DO YOUR WORK ON THE EXAM ONY (NO SCRATCH PAPER
More informationBasic Equations of Elasticity
A Basic Equations of Elasticity A.1 STRESS The state of stress at any point in a loaded bo is defined completely in terms of the nine components of stress: σ xx,σ yy,σ zz,σ xy,σ yx,σ yz,σ zy,σ zx,andσ
More informationSeismic 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 informationLaboratory 4 Topic: Buckling
Laboratory 4 Topic: Buckling Objectives: To record the loaddeflection response of a clampedclamped column. To identify, from the recorded response, the collapse load of the column. Introduction: Buckling
More information7.4 The Elementary Beam Theory
7.4 The Elementary Beam Theory In this section, problems involving long and slender beams are addressed. s with pressure vessels, the geometry of the beam, and the specific type of loading which will be
More informationSTRENGTH OF MATERIALSI. Unit1. Simple stresses and strains
STRENGTH OF MATERIALSI Unit1 Simple stresses and strains 1. What is the Principle of surveying 2. Define Magnetic, True & Arbitrary Meridians. 3. Mention different types of chains 4. Differentiate between
More informationD : SOLID MECHANICS. Q. 1 Q. 9 carry one mark each. Q.1 Find the force (in kn) in the member BH of the truss shown.
D : SOLID MECHANICS Q. 1 Q. 9 carry one mark each. Q.1 Find the force (in kn) in the member BH of the truss shown. Q.2 Consider the forces of magnitude F acting on the sides of the regular hexagon having
More informationConceptual question Conceptual question 12.2
Conceptual question 12.1 rigid cap of weight W t g r A thinwalled tank (having an inner radius of r and wall thickness t) constructed of a ductile material contains a gas with a pressure of p. A rigid
More informationChapter 3. Load and Stress Analysis. Lecture Slides
Lecture Slides Chapter 3 Load and Stress Analysis 2015 by McGraw Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner.
More informationStress Analysis Lecture 4 ME 276 Spring Dr./ Ahmed Mohamed Nagib Elmekawy
Stress Analysis Lecture 4 ME 76 Spring 017018 Dr./ Ahmed Mohamed Nagib Elmekawy Shear and Moment Diagrams Beam Sign Convention The positive directions are as follows: The internal shear force causes a
More information7.5 Elastic Buckling Columns and Buckling
7.5 Elastic Buckling The initial theory of the buckling of columns was worked out by Euler in 1757, a nice example of a theory preceding the application, the application mainly being for the later invented
More informationQuestion 1. Ignore bottom surface. Solution: Design variables: X = (R, H) Objective function: maximize volume, πr 2 H OR Minimize, f(x) = πr 2 H
Question 1 (Problem 2.3 of rora s Introduction to Optimum Design): Design a beer mug, shown in fig, to hold as much beer as possible. The height and radius of the mug should be not more than 20 cm. The
More informationMaterials: engineering, science, processing and design, 2nd edition Copyright (c)2010 Michael Ashby, Hugh Shercliff, David Cebon.
Modes of Loading (1) tension (a) (2) compression (b) (3) bending (c) (4) torsion (d) and combinations of them (e) Figure 4.2 1 Standard Solution to Elastic Problems Three common modes of loading: (a) tie
More informationStress and Strain ( , 3.14) MAE 316 Strength of Mechanical Components NC State University Department of Mechanical & Aerospace Engineering
(3.83.1, 3.14) MAE 316 Strength of Mechanical Components NC State Universit Department of Mechanical & Aerospace Engineering 1 Introduction MAE 316 is a continuation of MAE 314 (solid mechanics) Review
More informationMEMS Report for Lab #3. Use of Strain Gages to Determine the Strain in Cantilever Beams
MEMS 1041 Report for Lab #3 Use of Strain Gages to Determine the Strain in Cantilever Beams Date: February 9, 2016 Lab Instructor: Robert Carey Submitted by: Derek Nichols Objective: The objective of this
More informationNCHRP FY 2004 Rotational Limits for Elastomeric Bearings. Final Report. Appendix I. John F. Stanton Charles W. Roeder Peter MackenzieHelnwein
NCHRP 1268 FY 2004 Rotational Limits for Elastomeric Bearings Final Report Appendix I John F. Stanton Charles W. Roeder Peter MackenzieHelnwein Department of Civil and Environmental Engineering University
More information