Chapter 3. Load and Stress Analysis. Lecture Slides


 Ira Hart
 4 years ago
 Views:
Transcription
1 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. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.
2 Chapter Outline 31 Equilibrium and FreeBody Diagrams 32 Shear Force and Bending Moments in Beams 33 Singularity Functions 34 Stress 35 Cartesian Stress Components 36 Mohr s Circle for Plane Stress 37 General ThreeDimensional Stress 38 Elastic Strain 39 Uniformly Distributed Stresses 310 Normal Stresses for Beams in Bending 311 Shear Stresses for Beams in Bending 312 Torsion 313 Stress Concentration 314 Stresses in Pressurized Cylinders 315 Stresses in Rotating Rings 316 Press and Shrink Fits 317 Temperature Effects 318 Curved Beams in Bending 319 Contact Stresses 320 Summary
3 Equilibrium and FreeBody Diagrams Equilibrium A system with zero acceleration is said to be in equilibrium, if that system is motionless or, at most, has constant velocity. FreeBody Diagram Freebody diagrams help simplifying the analysis of a very complex structure or machine by successively isolating each element and then studying and analyzing it.
4 Example 31
5 Solution Example 31
6 Example 31 Input shaft Output shaft Gear box
7 Example 31
8 Example 31
9 Example 31
10 Shear Force and Bending Moments in Beams Cut beam at any location x 1 Internal shear force V and bending moment M must ensure equilibrium Sign Conventions
11 Shear Force and Bending Moments in Beams Distributed Load on Beam Distributed load q(x) called load intensity Units of force per unit length Relationships between Load, Shear, and Bending The change in shear force from A to B is equal to the area of the loading diagram between x A and x B. The change in moment from A to B is equal to the area of the shearforce diagram between x A and x B.
12 Example 32 Shear Force and Bending Moments in Beams
13 Example 33 Shear Force and Bending Moments in Beams
14 Cartesian Stress Component Normal stress is normal to a surface, designated by Shear stress is tangent to a surface, designated by Stress element Represents stress at a point Coordinate directions are arbitrary Choosing coordinates which result in zero shear stress will produce principal stresses
15 PlaneStress Transformation Equations Cutting plane stress element at an arbitrary angle and balancing stresses gives planestress transformation equations
16 Principal Stresses for Plane Stress Principal stresses Principal directions (zero shear stresses) Maximum shear stresses
17 Maximum Shear Stress There are always three principal stresses. One is zero for plane stress. There are always three extremevalue shear stresses. The maximum shear stress is always the greatest of these three If principal stresses are ordered so that 1 > 2 > 3, then max = 1/3
18 Mohr s Circle Diagram Parametric relationship between and (with 2 as parameter) Relationship is a circle with center at C = (, ) = [( x + y )/2, 0 ] R x 2 y 2 2 xy
19 Example 34
20 xy orientation Example 34 Principal stress orientation Max shear orientation
21 General ThreeDimensional Stress All stress elements are actually 3D. Plane stress elements simply have one surface with zero stresses. For cases where there is no stressfree surface, the principal stresses are found from the roots of the cubic equation
22 General ThreeDimensional Stress Always three extreme shear values Maximum Shear Stress is the largest Principal stresses are usually ordered such that 1 > 2 > 3, in which case max = 1/3
23 Homework
24 Homework (a) 8 7 C 0.5 MPa CD 7.5 MPa 2 R MPa MPa Mpa p 2 6 R 9.60 MPa tan cw cw s
25 Homework (b) 9 6 C 1.5 MPa CD 7.5 MPa 2 R MPa MPa MPa p tan 10.9 cw R MPa ccw s
26 Homework (c) 12 4 C 4 MPa CD 8 MPa 2 R MPa MPa MPa 1 8 p 2 7 R MPa tan 69.4 ccw ccw s
27 Homework (d) 6 5 C 0.5 MPa CD 5.5 MPa 2 R MPa MPa MPa p tan ccw R 9.71 MPa cw s
28 Elastic Strain Hooke s law E is Young s modulus, or modulus of elasticity Tension in on direction produces negative strain (contraction) in a perpendicular direction. For axial stress in x direction, The constant of proportionality is Poisson s ratio See Table A5 for values for common materials.
29 Elastic Strain For a stress element undergoing x, y, and z, simultaneously, Hooke s law for shear: Shear strain G is the change in a right angle of a stress element when subjected to pure shear stress. G is the shear modulus of elasticity or modulus of rigidity. For a linear, isotropic, homogeneous material,
30 Uniformly Distributed Stresses Uniformly distributed stress distribution is often assumed for pure tension, pure compression, or pure shear. For tension and compression, For direct shear (no bending present),
31 Normal Stresses for Beams in Bending Straight beam in positive bending x axis is neutral axis xz plane is neutral plane Neutral axis is coincident with the centroidal axis of the cross section Bending stress varies linearly with distance from neutral axis, y I is the secondarea moment about the z axis
32 Normal Stresses for Beams in Bending Maximum bending stress is where y is greatest. c is the magnitude of the greatest y Z = I/c is the section modulus
33 Normal Stresses for Beams in Bending Pure bending (though effects of axial, torsional, and shear loads are often assumed to have minimal effect on bending stress) Material is isotropic and homogeneous Material obeys Hooke s law Beam is initially straight with constant cross section Beam has axis of symmetry in the plane of bending Proportions are such that failure is by bending rather than crushing, wrinkling, or sidewise buckling Plane cross sections remain plane during bending
34 Example 35 Dimensions in mm
35 Example 35
36 Example 35
37 Example 35
38 Example 35
39 TwoPlane Bending Consider bending in both xyplane and xzplane Cross sections with one or two planes of symmetry only For solid circular cross section, the maximum bending stress is
40 Example 36
41 Example 36
42 Example 36 Answer Answer
43 Example 36
44 Shear Stress for Beams in Bending
45 Shear Stress for Beams in Bending Transverse shear stress is always accompanied with bending stress.
46 Transverse Shear Stress in a Rectangular Beam
47 Maximum Values of Transverse Shear Stress
48 Significance of Transverse Shear Compared to Bending Example: Cantilever beam, rectangular cross section Maximum shear stress, including bending stress (My/I) and transverse shear stress (VQ/Ib),
49 Significance of Transverse Shear Compared to Bending Critical stress element (largest max ) will always be either Due to bending, on the outer surface (y/c=1), where the transverse shear is zero Or due to transverse shear at the neutral axis (y/c=0), where the bending is zero Transition happens at some critical value of L/h Valid for any cross section that does not increase in width farther away from the neutral axis. Includes round and rectangular solids, but not I beams and channels
50 Example 37
51 Example 37
52 Example 37
53 Example 37
54 Example 37
55 Example 37
56 Torsion Torque vector a moment vector collinear with axis of a mechanical element A bar subjected to a torque vector is said to be in torsion Angle of twist, in radians, for a solid round bar
57 Torsion For round bar in torsion, torsional shear stress is proportional to the radius r Maximum torsional shear stress is at the outer surface
58 Assumption for Torsion Equations Torsional Equations are only applicable for the following conditions Pure torque Remote from any discontinuities or point of application of torque Material obeys Hooke s law Adjacent cross sections originally plane and parallel remain plane and parallel Radial lines remain straight Depends on axisymmetry, so does not hold true for noncircular cross sections Consequently, only applicable for round cross sections
59 Torsional Shear in Rectangular Section Shear stress does not vary linearly with radial distance for rectangular cross section Shear stress is zero at the corners Maximum shear stress is at the middle of the longest side For rectangular b x c bar, where b is longest side
60 Power, Speed, and Torque Power equals torque times speed A convenient conversion with speed in rpm where H = power, W n = angular velocity, revolutions per minute
61 Power, Speed, and Torque In U.S. Customary units, with unit conversion built in
62 Example 38
63 Example 38 T A = T 2 = 0.13 knm M A = 1.3k (0.125) = 0.66 knm F = 1.3 kn T c = 1.3k (0.038) = 0.05 knm F = 1.3 kn M 2 = T 1 = 0.05kNm F = 1.3 kn T 1 = 0.05kNm F = 1.3 kn M 1 = 1.3k (0.1) =0.13 knm T 2 = M 1 = 0.13 knm
64 Example 38
65 Example 38 F = 1.3 kn T c = 1.3k (0.038) = 0.05 knm T 1 = 0.05kNm F = 1.3 kn M 1 = 1.3k (0.1) =0.13 knm
66 Example 38
67 Example 38
68 Example 38
69 Example 38
70 Example 39
71 Example 39
72 Example 39
73 Example 39
74 Example 39
75 Example 39
76 Closed ThinWalled Tubes Wall thickness t << tube radius r (r/t > 10) Product of shear stress times wall thickness is constant Shear stress is inversely proportional to wall thickness Total torque T is Shear flow (q) ( q t constant) A m is the area enclosed by the section median line Fig. 3 25
77 Solving for shear stress Closed ThinWalled Tubes Angular twist (radians) per unit length L m is the length of the section median line
78 Example 3 10 Fig. 3 26
79 Example 3 10
80 Example 3 11 Solution
81 Open ThinWalled Sections When the median wall line is not closed, the section is said to be an open section Some common open thinwalled sections Fig Torsional shear stress where T = Torque, L = length of median line, c = wall thickness, G = shear modulus, and 1 = angle of twist per unit length
82 Open ThinWalled Sections Shear stress is inversely proportional to c 2 Angle of twist is inversely proportional to c 3 For small wall thickness, stress and twist can become quite large Example: Compare thin round tube with and without slit Ratio of wall thickness to outside diameter of 0.1 Stress with slit is 12.3 times greater Twist with slit is 61.5 times greater
83 Example 312
84 Example 312
85 Example 312
86 Stress Concentration Localized increase of stress near discontinuities K t is Theoretical (Geometric) Stress Concentration Factor
87 Theoretical Stress Concentration Factor Graphs available for standard configurations See Appendix A15 and A16 for common examples Many more in Peterson s StressConcentration Factors Note the trend for higher Kt at sharper discontinuity radius, and at greater disruption
88 Example 313
89 Example 313
90 Example 313
91 Example 313
92 Contact Stress Two bodies with curved surfaces pressed together Point or line contact changes to area contact Stresses developed are threedimensional Called contact stresses or Hertzian stresses Common examples Wheel rolling on rail Mating gear teeth Rolling bearings
93 Spherical Contact Stress Two solid spheres of diameters d 1 and d 2 are pressed together with force F Circular area of contact of radius a Pressure distribution is hemispherical Maximum pressure at the center of contact area
94 Spherical Contact Stress Maximum stresses on the z axis Principal stresses From Mohr s circle, maximum shear stress is
95 Cylindrical Contact Stress Two right circular cylinders with length l and diameters d 1 and d 2 Area of contact is a narrow rectangle of width 2b and length l Pressure distribution is elliptical Halfwidth b Maximum pressure
96 Cylindrical Contact Stress Maximum stresses on z axis
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 & FreeBody Diagrams Shear Force and Bending Moments in Beams Singularity Functions Stress Cartesian Stress Components Mohr s Circle for
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 informationUNIT 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 informationAdvanced Structural Analysis EGF Section Properties and Bending
Advanced Structural Analysis EGF316 3. Section Properties and Bending 3.1 Loads in beams When we analyse beams, we need to consider various types of loads acting on them, for example, axial forces, shear
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 informationMechanical Design in Optical Engineering
Torsion Torsion: Torsion refers to the twisting of a structural member that is loaded by couples (torque) that produce rotation about the member s longitudinal axis. In other words, the member is loaded
More information(48) CHAPTER 3: TORSION
(48) CHAPTER 3: TORSION Introduction: In this chapter structural members and machine parts that are in torsion will be considered. More specifically, you will analyze the stresses and strains in members
More informationCHAPTER 6 BENDING Part 1
Ishik University / Sulaimani Civil Engineering Department Mechanics of Materials CE 211 CHAPTER 6 BENDING Part 11 CHAPTER 6 Bending Outlines of this chapter: 6.1. Chapter Objectives 6.2. Shear and
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 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 information6. Bending CHAPTER OBJECTIVES
CHAPTER OBJECTIVES Determine stress in members caused by bending Discuss how to establish shear and moment diagrams for a beam or shaft Determine largest shear and moment in a member, and specify where
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 informationTorsion of shafts with circular symmetry
orsion of shafts with circular symmetry Introduction Consider a uniform bar which is subject to a torque, eg through the action of two forces F separated by distance d, hence Fd orsion is the resultant
More informationQUESTION BANK SEMESTER: III SUBJECT NAME: MECHANICS OF SOLIDS
QUESTION BANK SEMESTER: III SUBJECT NAME: MECHANICS OF SOLIDS UNIT 1 STRESS AND STRAIN PART A (2 Marks) 1. Define longitudinal strain and lateral strain. 2. State Hooke s law. 3. Define modular ratio,
More information: 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 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 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 informationStructural Analysis I Chapter 4  Torsion TORSION
ORSION orsional stress results from the action of torsional or twisting moments acting about the longitudinal axis of a shaft. he effect of the application of a torsional moment, combined with appropriate
More 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 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 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 informationNAME: Given Formulae: Law of Cosines: Law of Sines:
NME: Given Formulae: Law of Cosines: EXM 3 PST PROBLEMS (LESSONS 21 TO 28) 100 points Thursday, November 16, 2017, 7pm to 9:30, Room 200 You are allowed to use a calculator and drawing equipment, only.
More informationChapter 5: Torsion. 1. Torsional Deformation of a Circular Shaft 2. The Torsion Formula 3. Power Transmission 4. Angle of Twist CHAPTER OBJECTIVES
CHAPTER OBJECTIVES Chapter 5: Torsion Discuss effects of applying torsional loading to a long straight member (shaft or tube) Determine stress distribution within the member under torsional load Determine
More information[5] Stress and Strain
[5] Stress and Strain Page 1 of 34 [5] Stress and Strain [5.1] Internal Stress of Solids [5.2] Design of Simple Connections (will not be covered in class) [5.3] Deformation and Strain [5.4] Hooke s Law
More 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 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 informationPURE BENDING. If a simply supported beam carries two point loads of 10 kn as shown in the following figure, pure bending occurs at segment BC.
BENDING STRESS The effect of a bending moment applied to a crosssection of a beam is to induce a state of stress across that section. These stresses are known as bending stresses and they act normally
More informationChapter 5 Torsion STRUCTURAL MECHANICS: CE203. Notes are based on Mechanics of Materials: by R. C. Hibbeler, 7th Edition, Pearson
STRUCTURAL MECHANICS: CE203 Chapter 5 Torsion Notes are based on Mechanics of Materials: by R. C. Hibbeler, 7th Edition, Pearson Dr B. Achour & Dr Eng. K. Elkashif Civil Engineering Department, University
More informationEMA 3702 Mechanics & Materials Science (Mechanics of Materials) Chapter 3 Torsion
EMA 3702 Mechanics & Materials Science (Mechanics of Materials) Chapter 3 Torsion Introduction Stress and strain in components subjected to torque T Circular Crosssection shape Material Shaft design Noncircular
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 informationMECHANICS OF MATERIALS
2009 The McGrawHill Companies, Inc. All rights reserved. Fifth SI Edition CHAPTER 3 MECHANICS OF MATERIALS Ferdinand P. Beer E. Russell Johnston, Jr. John T. DeWolf David F. Mazurek Torsion Lecture Notes:
More informationMECH 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 (11708) Last time Introduction Units Reliability engineering
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 informationSub. Code:
Important Instructions to examiners: ) The answers should be examined by key words and not as wordtoword as given in the model answer scheme. ) The model answer and the answer written by candidate may
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 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 informationMechanics of Materials Primer
Mechanics of Materials rimer Notation: A = area (net = with holes, bearing = in contact, etc...) b = total width of material at a horizontal section d = diameter of a hole D = symbol for diameter E = modulus
More 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 information2. (a) Explain different types of wing structures. (b) Explain the advantages and disadvantages of different materials used for aircraft
Code No: 07A62102 R07 Set No. 2 III B.Tech II Semester Regular/Supplementary Examinations,May 2010 Aerospace Vehicle Structures II Aeronautical Engineering Time: 3 hours Max Marks: 80 Answer any FIVE
More information3 Hours/100 Marks Seat No.
*17304* 17304 14115 3 Hours/100 Marks Seat No. Instructions : (1) All questions are compulsory. (2) Illustrate your answers with neat sketches wherever necessary. (3) Figures to the right indicate full
More informationUNIT I Thin plate theory, Structural Instability:
UNIT I Thin plate theory, Structural Instability: Analysis of thin rectangular plates subject to bending, twisting, distributed transverse load, combined bending and inplane loading Thin plates having
More informationCOURSE TITLE : THEORY OF STRUCTURES I COURSE CODE : 3013 COURSE CATEGORY : B PERIODS/WEEK : 6 PERIODS/SEMESTER: 90 CREDITS : 6
COURSE TITLE : THEORY OF STRUCTURES I COURSE CODE : 0 COURSE CATEGORY : B PERIODS/WEEK : 6 PERIODS/SEMESTER: 90 CREDITS : 6 TIME SCHEDULE Module Topics Period Moment of forces Support reactions Centre
More informationDownloaded from Downloaded from / 1
PURWANCHAL UNIVERSITY III SEMESTER FINAL EXAMINATION2002 LEVEL : B. E. (Civil) SUBJECT: BEG256CI, Strength of Material Full Marks: 80 TIME: 03:00 hrs Pass marks: 32 Candidates are required to give their
More informationMarch 24, Chapter 4. Deflection and Stiffness. Dr. Mohammad Suliman Abuhaiba, PE
Chapter 4 Deflection and Stiffness 1 2 Chapter Outline Spring Rates Tension, Compression, and Torsion Deflection Due to Bending Beam Deflection Methods Beam Deflections by Superposition Strain Energy Castigliano
More information[7] Torsion. [7.1] Torsion. [7.2] Statically Indeterminate Torsion. [7] Torsion Page 1 of 21
[7] Torsion Page 1 of 21 [7] Torsion [7.1] Torsion [7.2] Statically Indeterminate Torsion [7] Torsion Page 2 of 21 [7.1] Torsion SHEAR STRAIN DUE TO TORSION 1) A shaft with a circular cross section is
More information4. SHAFTS. A shaft is an element used to transmit power and torque, and it can support
4. SHAFTS A shaft is an element used to transmit power and torque, and it can support reverse bending (fatigue). Most shafts have circular cross sections, either solid or tubular. The difference between
More informationCHAPTER 4: BENDING OF BEAMS
(74) CHAPTER 4: BENDING OF BEAMS This chapter will be devoted to the analysis of prismatic members subjected to equal and opposite couples M and M' acting in the same longitudinal plane. Such members are
More informationCE 221: MECHANICS OF SOLIDS I CHAPTER 1: STRESS. Dr. Krisada Chaiyasarn Department of Civil Engineering, Faculty of Engineering Thammasat university
CE 221: MECHANICS OF SOLIDS I CHAPTER 1: STRESS By Dr. Krisada Chaiyasarn Department of Civil Engineering, Faculty of Engineering Thammasat university Agenda Introduction to your lecturer Introduction
More informationMECHANICS OF MATERIALS
GE SI CHAPTER 3 MECHANICS OF MATERIALS Ferdinand P. Beer E. Russell Johnston, Jr. John T. DeWolf David F. Mazurek Torsion Lecture Notes: J. Walt Oler Texas Tech University Torsional Loads on Circular Shafts
More information7.6 Stress in symmetrical elastic beam transmitting both shear force and bending moment
7.6 Stress in symmetrical elastic beam transmitting both shear force and bending moment à It is more difficult to obtain an exact solution to this problem since the presence of the shear force means that
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 informationStresses in Curved Beam
Stresses in Curved Beam Consider a curved beam subjected to bending moment M b as shown in the figure. The distribution of stress in curved flexural member is determined by using the following assumptions:
More informationPDDC 1 st Semester Civil Engineering Department Assignments of Mechanics of Solids [ ] Introduction, Fundamentals of Statics
Page1 PDDC 1 st Semester Civil Engineering Department Assignments of Mechanics of Solids [2910601] Introduction, Fundamentals of Statics 1. Differentiate between Scalar and Vector quantity. Write S.I.
More informationCIVL222 STRENGTH OF MATERIALS. Chapter 6. Torsion
CIVL222 STRENGTH OF MATERIALS Chapter 6 Torsion Definition Torque is a moment that tends to twist a member about its longitudinal axis. Slender members subjected to a twisting load are said to be in torsion.
More informationVYSOKÁ ŠKOLA BÁŇSKÁ TECHNICKÁ UNIVERZITA OSTRAVA
VYSOKÁ ŠKOLA BÁŇSKÁ TECHNICKÁ UNIVERZITA OSTRAVA FAKULTA METALURGIE A MATERIÁLOVÉHO INŽENÝRSTVÍ APPLIED MECHANICS Study Support Leo Václavek Ostrava 2015 Title:Applied Mechanics Code: Author: doc. Ing.
More informationPERIYAR CENTENARY POLYTECHNIC COLLEGE PERIYAR NAGAR  VALLAM THANJAVUR. DEPARTMENT OF MECHANICAL ENGINEERING QUESTION BANK
PERIYAR CENTENARY POLYTECHNIC COLLEGE PERIYAR NAGAR  VALLAM  613 403  THANJAVUR. DEPARTMENT OF MECHANICAL ENGINEERING QUESTION BANK Sub : Strength of Materials Year / Sem: II / III Sub Code : MEB 310
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 informationDEPARTMENT OF MECHANICAL ENIGINEERING, UNIVERSITY OF ENGINEERING & TECHNOLOGY LAHORE (KSK CAMPUS).
DEPARTMENT OF MECHANICAL ENIGINEERING, UNIVERSITY OF ENGINEERING & TECHNOLOGY LAHORE (KSK CAMPUS). Lab Director: Coordinating Staff: Mr. Muhammad Farooq (Lecturer) Mr. Liaquat Qureshi (Lab Supervisor)
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 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 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 informationINSTITUTE OF AERONAUTICAL ENGINEERING (Autonomous) Dundigal, Hyderabad
INSTITUTE OF AERONAUTICAL ENGINEERING (Autonomous) Dundigal, Hyderabad 00 04 CIVIL ENGINEERING QUESTION BANK Course Name : STRENGTH OF MATERIALS II Course Code : A404 Class : II B. Tech II Semester Section
More informationtwenty one concrete construction: shear & deflection ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN DR. ANNE NICHOLS SUMMER 2014 lecture
ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN DR. ANNE NICHOLS SUMMER 2014 lecture twenty one concrete construction: Copyright Kirk Martini shear & deflection Concrete Shear 1 Shear in Concrete
More informationUnit Workbook 1 Level 4 ENG U8 Mechanical Principles 2018 UniCourse Ltd. All Rights Reserved. Sample
Pearson BTEC Levels 4 Higher Nationals in Engineering (RQF) Unit 8: Mechanical Principles Unit Workbook 1 in a series of 4 for this unit Learning Outcome 1 Static Mechanical Systems Page 1 of 23 1.1 Shafts
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 informationThe 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 informationStrength of Materials II (Mechanics of Materials) (SI Units) Dr. Ashraf Alfeehan
Strength of Materials II (Mechanics of Materials) (SI Units) Dr. Ashraf Alfeehan 20172018 Mechanics of Material II Text Books Mechanics of Materials, 10th edition (SI version), by: R. C. Hibbeler, 2017
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 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 information8. Combined Loadings
CHAPTER OBJECTIVES qanalyze the stress developed in thinwalled pressure vessels qreview the stress analysis developed in previous chapters regarding axial load, torsion, bending and shear qdiscuss the
More informationSamantha Ramirez, MSE. Stress. The intensity of the internal force acting on a specific plane (area) passing through a point. F 2
Samantha Ramirez, MSE Stress The intensity of the internal force acting on a specific plane (area) passing through a point. Δ ΔA Δ z Δ 1 2 ΔA Δ x Δ y ΔA is an infinitesimal size area with a uniform force
More informationMechanical Properties of Materials
Mechanical Properties of Materials Strains Material Model Stresses Learning objectives Understand the qualitative and quantitative description of mechanical properties of materials. Learn the logic of
More informationEngineering Science OUTCOME 1  TUTORIAL 4 COLUMNS
Unit 2: Unit code: QCF Level: Credit value: 15 Engineering Science L/601/10 OUTCOME 1  TUTORIAL COLUMNS 1. Be able to determine the behavioural characteristics of elements of static engineering systems
More informationStructural Dynamics Lecture Eleven: Dynamic Response of MDOF Systems: (Chapter 11) By: H. Ahmadian
Structural Dynamics Lecture Eleven: Dynamic Response of MDOF Systems: (Chapter 11) By: H. Ahmadian ahmadian@iust.ac.ir Dynamic Response of MDOF Systems: ModeSuperposition Method ModeSuperposition Method:
More informationOUTCOME 1  TUTORIAL 3 BENDING MOMENTS. You should judge your progress by completing the self assessment exercises. CONTENTS
Unit 2: Unit code: QCF Level: 4 Credit value: 15 Engineering Science L/601/1404 OUTCOME 1  TUTORIAL 3 BENDING MOMENTS 1. Be able to determine the behavioural characteristics of elements of static engineering
More informationIDE 110 Mechanics of Materials Spring 2006 Final Examination FOR GRADING ONLY
Spring 2006 Final Examination STUDENT S NAME (please print) STUDENT S SIGNATURE STUDENT NUMBER IDE 110 CLASS SECTION INSTRUCTOR S NAME Do not turn this page until instructed to start. Write your name on
More informationMembers Subjected to Torsional Loads
Members Subjected to Torsional Loads Torsion of circular shafts Definition of Torsion: Consider a shaft rigidly clamped at one end and twisted at the other end by a torque T = F.d applied in a plane perpendicular
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 informationMECE 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 informationMECH 344/X Machine Element Design
1 MECH 344/X Machine Element Design Time: M 14:4517:30 Lecture 2 Contents of today's lecture Introduction to Static Stresses Axial, Shear and Torsional Loading Bending in Straight and Curved Beams Transverse
More information4. BEAMS: CURVED, COMPOSITE, UNSYMMETRICAL
4. BEMS: CURVED, COMPOSITE, UNSYMMETRICL Discussions of beams in bending are usually limited to beams with at least one longitudinal plane of symmetry with the load applied in the plane of symmetry or
More informationMARKS DISTRIBUTION AS PER CHAPTER (QUESTION ASKED IN GTU EXAM) Name Of Chapter. Applications of. Friction. Centroid & Moment.
Introduction Fundamentals of statics Applications of fundamentals of statics Friction Centroid & Moment of inertia Simple Stresses & Strain Stresses in Beam Torsion Principle Stresses DEPARTMENT OF CIVIL
More informationTorsion Stresses in Tubes and Rods
Torsion Stresses in Tubes and Rods This initial analysis is valid only for a restricted range of problem for which the assumptions are: Rod is initially straight. Rod twists without bending. Material is
More informationMECHANICS 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 information18.Define the term modulus of resilience. May/June Define Principal Stress. 20. Define Hydrostatic Pressure.
CE6306 STREGNTH OF MATERIALS Question Bank UnitI STRESS, STRAIN, DEFORMATION OF SOLIDS PARTA 1. Define Poison s Ratio May/June 2009 2. What is thermal stress? May/June 2009 3. Estimate the load carried
More informationPROBLEM 3.3 ( )(45 10 ) T 5.17 kn m. A c c. 2 J c, (2)( ) 2 ( ) mm ( )
0 mm PROEM..4 m 45 mm (a) Determine the torque that causes a maximum shearing stress of 45 MPa in the hollow cylindrical steel shaft shown. Determine the maximum shearing stress caused by the same torque
More informationPhysical Science and Engineering. Course Information. Course Number: ME 100
Physical Science and Engineering Course Number: ME 100 Course Title: Course Information Basic Principles of Mechanics Academic Semester: Fall Academic Year: 20162017 Semester Start Date: 8/21/2016 Semester
More informationCHAPTER 6: Shearing Stresses in Beams
(130) CHAPTER 6: Shearing Stresses in Beams When a beam is in pure bending, the only stress resultants are the bending moments and the only stresses are the normal stresses acting on the cross sections.
More information2. Polar moment of inertia As stated above, the polar second moment of area, J is defined as. Sample copy
GATE PATHSHALA  91. Polar moment of inertia As stated above, the polar second moment of area, is defined as z π r dr 0 R r π R π D For a solid shaft π (6) QP 0 π d Solid shaft π d Hollow shaft, " ( do
More informationBE 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 informationPurpose of this Guide: To thoroughly prepare students for the exact types of problems that will be on Exam 3.
ES230 STRENGTH OF MTERILS Exam 3 Study Guide Exam 3: Wednesday, March 8 th inclass Updated 3/3/17 Purpose of this Guide: To thoroughly prepare students for the exact types of problems that will be on
More informationSRI CHANDRASEKHARENDRA SARASWATHI VISWA MAHAVIDHYALAYA
SRI CHANDRASEKHARENDRA SARASWATHI VISWA MAHAVIDHYALAYA (Declared as Deemedtobe University under Section 3 of the UGC Act, 1956, Vide notification No.F.9.9/92U3 dated 26 th May 1993 of the Govt. of
More informationStrength of Materials Prof. S.K.Bhattacharya Dept. of Civil Engineering, I.I.T., Kharagpur Lecture No.26 Stresses in BeamsI
Strength of Materials Prof. S.K.Bhattacharya Dept. of Civil Engineering, I.I.T., Kharagpur Lecture No.26 Stresses in BeamsI Welcome to the first lesson of the 6th module which is on Stresses in Beams
More informationMAHALAKSHMI ENGINEERING COLLEGE
MAHALAKSHMI ENGINEERING COLLEGE TIRUCHIRAALLI  6113. QUESTION WITH ANSWERS DEARTMENT : CIVIL SEMESTER: V SUB.CODE/ NAME: CE 5 / Strength of Materials UNIT 3 COULMNS ART  A ( marks) 1. Define columns
More information(Refer Slide Time: 01:00 01:01)
Strength of Materials Prof: S.K.Bhattacharya Department of Civil Engineering Indian institute of Technology Kharagpur Lecture no 27 Lecture Title: Stresses in Beams II Welcome to the second lesson of
More informationLECTURE 13 Strength of a Bar in Pure Bending
V. DEMENKO MECHNCS OF MTERLS 015 1 LECTURE 13 Strength of a Bar in Pure Bending Bending is a tpe of loading under which bending moments and also shear forces occur at cross sections of a rod. f the bending
More informationThe example of shafts; a) Rotating Machinery; Propeller shaft, Drive shaft b) Structural Systems; Landing gear strut, Flap drive mechanism
TORSION OBJECTIVES: This chapter starts with torsion theory in the circular cross section followed by the behaviour of torsion member. The calculation of the stress stress and the angle of twist will be
More informationIntroduction to Aerospace Engineering
Introduction to Aerospace Engineering Lecture slides Challenge the future 1 Aircraft & spacecraft loads Translating loads to stresses Faculty of Aerospace Engineering 29112011 Delft University of Technology
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 informationMechanics of Solids notes
Mechanics of Solids notes 1 UNIT II Pure Bending Loading restrictions: As we are aware of the fact internal reactions developed on any crosssection of a beam may consists of a resultant normal force,
More information