CHAPTER 3 THE EFFECTS OF FORCES ON MATERIALS


 Felicity Eaton
 1 years ago
 Views:
Transcription
1 CHAPTER THE EFFECTS OF FORCES ON MATERIALS EXERCISE 1, Page A rectangular bar having a crosssectional area of 80 mm has a tensile force of 0 kn applied to it. Determine the stress in the bar. Stress s force F 0 50 Pa 50 MPa area A 80. A circular section cable has a tensile force of 1 kn applied to it and the force produces a stress of 7.8 MPa in the cable. Calculate the diameter of the cable. Stress s force F area A hence, crosssectional area, A force F m stress s 7.8 Circular area π r 18. m from which, r 18. π and radius r 18. π.88 m.88 mm and diameter d r mm. A squaresectioned support of side 1 mm is loaded with a compressive force of kn. Determine the compressive stress in the support. Stress, s force F 9.44 Pa 9.44 MPa area A A bolt having a diameter of 5 mm is loaded so that the shear stress in it is 10 MPa. Determine the value of the shear force on the bolt. 58
2 Stress, s force F area A hence, force stress area stress π r 5 10 π 5 N or.5 kn 5. A split pin requires a force of 400 N to shear it. The maximum shear stress before shear occurs is 10 MPa. Determine the minimum diameter of the pin. Stress s force F area A hence, crosssectional area, A force F 400. m stress s 10 Circular area π r. m from which, r. π and radius r. π 1.00 m 1.00 mm and diameter d r mm. A tube of outside diameter 0 mm and inside diameter 40 mm is subjected to a tensile load of 0 kn. Determine the stress in the tube. Area of tube end (annulus) ( ) ( ) D d 0 40 π π mm Stress s force F Pa 8. MPa area A
3 EXERCISE, Page 5 1. A wire of length 4.5 m has a percentage strain of 0.050% when loaded with a tensile force. Determine the extension in the wire. Original length of wire 4.5 m 4500 mm and strain Strain ε extension x originallength L hence, extension x εl ( )(4500).5 mm. A metal bar.5 m long extends by 0.05 mm when a tensile load is applied to it. Determine (a) the strain, (b) the percentage strain. (a) Strain ε extension 0.05 mm 0.05 original lengh.5 mm (b) Percentage strain %. An 80 cm long bar contracts axially by 0. mm when a compressive load is applied to it. Determine the strain and the percentage strain. Strain ε contraction original lengh 0. mm mm Percentage strain % 4. A pipe has an outside diameter of 0 mm, an inside diameter of mm and length 0.0 m and it supports a compressive load of 50 kn. The pipe shortens by 0. mm when the load is applied. Determine (a) the compressive stress, (b) the compressive strain in the pipe when supporting this load. Compressive force F 50 kn N, and crosssectional area A ( D d ) π 4, 0
4 where D outside diameter 0 mm and d inside diameter mm. Hence, A π π (0 ) mm (0 ) m.5 m F N (a) Compressive stress, s 4 A.5 m 1. Pa 1. MPa (b) Contraction of pipe when loaded, x 0. mm m, and original length L 0.0 m. Hence, compressive strain, ε x (or 0.0%) L When a circular hole of diameter 40 mm is punched out of a 1.5 mm thick metal plate, the shear stress needed to cause fracture is 0 MPa. Determine (a) the minimum force to be applied to the punch, and (b) the compressive stress in the punch at this value. (a) The area of metal to be sheared, A perimeter of hole thickness of plate. Perimeter of hole πd π(40 ) 0.15 m. Hence, shear area, A m Since shear stress force area (b) Area of punch, shear force shear stress area πd π(0.040) m 4 4 Compressive stress force area N m compressive stress in the punch. ( )N kn, which is the minimum force to be applied 15.0 Pa 15.0 MPa, which is the to the punch.. A rectangular block of plastic material 400 mm long by 15 mm wide by 00 mm high has its lower face fixed to a bench and a force of 150 N is applied to the upper face and in line with it. The upper face moves 1 mm relative to the lower face. Determine (a) the shear stress, and 1
5 (b) the shear strain in the upper face, assuming the deformation is uniform. (a) Shear stress, τ force area parallel to the force Area of any face parallel to the force 400 mm 15 mm 150 N Hence, shear stress, τ 0.00m ( ) m 0.00 m 5000 Pa or 5 kpa (b) Shear strain, γ x L (or 4%)
6 EXERCISE, Page 5 1. A wire is stretched 1.5 mm by a force of 00 N. Determine the force that would stretch the wire 4 mm, assuming the elastic limit of the wire is not exceeded. Hooke's law states that extension x is proportional to force F, provided that the limit of proportionality is not exceeded, i.e. x α F or x kf where k is a constant. When x 1.5 mm, F 00 N, thus 1.5 k(00), from which, constant k When x 4 mm, then 4 kf i.e F from which, force F N Thus to stretch the wire 4 mm, a force of 800 N is required.. A rubber band extends 50 mm when a force of 00 N is applied to it. Assuming the band is within the elastic limit, determine the extension produced by a force of 0 N. Hooke's law states that extension x is proportional to force F, provided that the limit of proportionality is not exceeded, i.e. x α F or x kf where k is a constant. When x 50 mm, F 00 N, thus 50 k(00), from which, constant k When F 0 N, then x k(0) i.e. x ( 0) mm Thus, a force of 0 N stretches the wire mm.. A force of 5 kn applied to a piece of steel produces an extension of mm. Assuming the elastic limit is not exceeded, determine (a) the force required to produce an extension of.5 mm, (b) the extension when the applied force is 15 kn. From Hooke s law, extension x is proportional to force F within the limit of proportionality, i.e.
7 x α F or x kf, where k is a constant. If a force of 5 kn produces an extension of mm, then k(5), from which, constant k (a) When an extension x.5 mm, then.5 k(f), i.e F, from which, force F kn (b) When force F 15 kn, then extension x k(15) (0.08)(15) 1. mm 4. A test to determine the load/extension graph for a specimen of copper gave the following results: Load (kn) Extension (mm) Plot the load/extension graph, and from the graph determine (a) the load at an extension of 0.09 mm, and (b) the extension corresponding to a load of 1.0 kn. A graph of load/extension is shown below. (a) When the extension is 0.09 mm, the load is 19 kn 4
8 (b) When the load is 1.0 kn, the extension is mm 5. A circular section bar is.5 m long and has a diameter of 0 mm. When subjected to a compressive load of 0 kn it shortens by 0.0 mm. Determine Young's modulus of elasticity for the material of the bar. Force, F 0 kn 0000 N and crosssectional area A Stress s F MPa A m π r π.874 Bar shortens by 0.0 mm m Strain ε x L Modulus of elasticity, E stress strain GPa. A bar of thickness 0 mm and having a rectangular crosssection carries a load of 8.5 kn. Determine (a) the minimum width of the bar to limit the maximum stress to 150 MPa, (b) the modulus of elasticity of the material of the bar if the 150 mm long bar extends by 0.8 mm when carrying a load of 00 kn. (a) Force, F 8.5 kn 8500 N and crosssectional area A (0x) m, where x is the width of the rectangular bar in millimetres. Stress s F A, from which, A F 8500 N σ 150 Pa m 5.5 mm 4 Hence, 550 0x, from which, width of bar, x (b) Stress s F A MPa 7.5 mm 5.5 mm 550 mm Extension of bar 0.8 mm 5
9 Strain ε x L Modulus of elasticity, E stress strain GPa 7. A metal rod of crosssectional area 0 mm carries a maximum tensile load of 0 kn. The modulus of elasticity for the material of the rod is 00 GPa. Determine the percentage strain when the rod is carrying its maximum load. Stress s F 0000 A 0 00 MPa Modulus of elasticity, E stress strain from which, strain stress 00 9 E Hence, percentage strain, ε % 0.% 8. A metal tube 1.75 m long carries a tensile load and the maximum stress in the tube must not exceed 50 MPa. Determine the extension of the tube when loaded if the modulus of elasticity for the material is 70 GPa. Modulus of elasticity, E stress strain from which, strain, ε stress E 70 Hence, strain, ε extension x original length L from which, extension, x εl m 1.5 m 1.5 mm 9. A piece of aluminium wire is 5 m long and has a crosssectional area of 0 mm. It is subjected to increasing loads, the extension being recorded for each load applied. The results are: Load (kn) Extension (mm)
10 Draw the load/extension graph and hence determine the modulus of elasticity for the material of the wire. A graph of load/extension is shown below. E F x σ ε F A x L F L x A is the gradient of the straight line part of the load/extension graph. Gradient, F x BC 7000 N 1.4 N/m AC 5 m L Modulus of elasticity (gradient of graph) A Length of specimen, L 5 m and crosssectional area A 0 mm 0 m Hence modulus of elasticity, E ( ) GPa 7
11 . In an experiment to determine the modulus of elasticity of a sample of copper, a wire is loaded and the corresponding extension noted. The results are: Load (N) Extension (mm) Draw the load/extension graph and determine the modulus of elasticity of the sample if the mean diameter of the wire is 1. mm and its length is 4.0 m. A graph of load/extension is shown below. F x E σ ε F A x L F L x A is the gradient of the straight line part of the load/extension graph. Gradient, F x BC 10 N 8.57 N/m AC 4. m L Modulus of elasticity (gradient of graph) A 8
12 Length of specimen, L 4.0 m and crosssectional area A ( ) πd π m Hence modulus of elasticity, E ( ) GPa 9
13 EXERCISE 4, Page A steel rail may assumed to be stress free at 5 C. If the stress required to cause buckling of the rail is  50 MPa, at what temperature will the rail buckle?. It may be assumed that the rail is rigidly fixed at its ends. Take E 11 N/m and α 14 / C. Buckling stress of steel rail 50 MPa Free expansion of rail αlt αlt Hence, strain α T where T temperature rise. L 11 Stress EαT ( )( 14 ) T T.8 T Buckling stress 50 MPa.8 T from which, T C Initial temperature at which the steel rail was stressfree 5 C Hence, the temperature at which the steel rail will buckle 17.8 C + 5 C.8 C 70
14 EXERCISE 5, Page 1 1. Two layers of carbon fibre are stuck to each other, so that their fibres lie at 90 to each other, as shown below. If a tensile force of 1 kn were applied to this twolayer compound bar, determine the stresses in each. For layer 1, E 1 00 GPa and A 1 mm For layer, E 50 GPa and A A 1 mm PE1 From equation (.8) and (.9), s 1 (A E + A E ) 1 1 PE and s (A E + A E ) 1 1 PE1 s 1 (A E + A E ) ( ) ( ) Pa i.e. the stress in the steel, s MPa PE s (A E + A E ) ( ) ( ) 14.9 i.e. the stress in the concrete, s 14.9 MPa. If the compound bar of Problem 1 were subjected to a temperature rise of 5 C, what would the resulting stresses be? Assume the coefficients of linear expansion are, for layer 1, α 1 5 / C, and for layer, α 0.5 / C. 71
15 As α 1 is larger than α, the effect of a temperature rise will cause the thermal stresses in the steel to be compressive and those in the concrete to be tensile. From equation (.5), the thermal stress in the steel, ( α1 α)e1eat s 1 (A E + A E ) ( ) MPa From equation (.), the thermal stress in the concrete, σ1a1 s A From Problem 1 above: ( 4.8 ) 4.8 MPa s MPa and s MPa EXERCISE, Page XX Answers found from within the text of the chapter, pages 47 to 1. EXERCISE 7, Page XX 1. (c). (c). (a) 4. (b) 5. (c). (c) 7. (b) 8. (d) 9. (b). (c) 11. (f) 1. (h) 1. (d) 14. (b) 15. (a) 7
Mechanics of Solids. Mechanics Of Solids. Suraj kr. Ray Department of Civil Engineering
Mechanics Of Solids Suraj kr. Ray (surajjj2445@gmail.com) Department of Civil Engineering 1 Mechanics of Solids is a branch of applied mechanics that deals with the behaviour of solid bodies subjected
More informationMECE 3321 MECHANICS OF SOLIDS CHAPTER 3
MECE 3321 MECHANICS OF SOLIDS CHAPTER 3 Samantha Ramirez TENSION AND COMPRESSION TESTS Tension and compression tests are used primarily to determine the relationship between σ avg and ε avg in any material.
More information6.4 A cylindrical specimen of a titanium alloy having an elastic modulus of 107 GPa ( psi) and
6.4 A cylindrical specimen of a titanium alloy having an elastic modulus of 107 GPa (15.5 10 6 psi) and an original diameter of 3.8 mm (0.15 in.) will experience only elastic deformation when a tensile
More informationUNIT I SIMPLE STRESSES AND STRAINS
Subject with Code : SM1(15A01303) Year & Sem: IIB.Tech & ISem SIDDHARTH GROUP OF INSTITUTIONS :: PUTTUR Siddharth Nagar, Narayanavanam Road 517583 QUESTION BANK (DESCRIPTIVE) UNIT I SIMPLE STRESSES
More informationEMA 3702 Mechanics & Materials Science (Mechanics of Materials) Chapter 2 Stress & Strain  Axial Loading
MA 3702 Mechanics & Materials Science (Mechanics of Materials) Chapter 2 Stress & Strain  Axial Loading MA 3702 Mechanics & Materials Science Zhe Cheng (2018) 2 Stress & Strain  Axial Loading Statics
More informationSolid Mechanics Homework Answers
Name: Date: Solid Mechanics Homework nswers Please show all of your work, including which equations you are using, and circle your final answer. Be sure to include the units in your answers. 1. The yield
More informationStrength of Material. Shear Strain. Dr. Attaullah Shah
Strength of Material Shear Strain Dr. Attaullah Shah Shear Strain TRIAXIAL DEFORMATION Poisson's Ratio Relationship Between E, G, and ν BIAXIAL DEFORMATION Bulk Modulus of Elasticity or Modulus of Volume
More informationX has a higher value of the Young modulus. Y has a lower maximum tensile stress than X
Bulk Properties of Solids Old Exam Questions Q1. The diagram shows how the stress varies with strain for metal specimens X and Y which are different. Both specimens were stretched until they broke. Which
More informationStressStrain Behavior
StressStrain Behavior 6.3 A specimen of aluminum having a rectangular cross section 10 mm 1.7 mm (0.4 in. 0.5 in.) is pulled in tension with 35,500 N (8000 lb f ) force, producing only elastic deformation.
More informationElastic Properties of Solid Materials. Notes based on those by James Irvine at
Elastic Properties of Solid Materials Notes based on those by James Irvine at www.antonineeducation.co.uk Key Words Density, Elastic, Plastic, Stress, Strain, Young modulus We study how materials behave
More informationClass XI Chapter 9 Mechanical Properties of Solids Physics
Book Name: NCERT Solutions Question : A steel wire of length 4.7 m and crosssectional area 5 3.0 0 m stretches by the same 5 amount as a copper wire of length 3.5 m and crosssectional area of 4.0 0 m
More informationMECHANICAL PROPERTIES OF SOLIDS
Chapter Nine MECHANICAL PROPERTIES OF SOLIDS MCQ I 9.1 Modulus of rigidity of ideal liquids is (a) infinity. (b) zero. (c) unity. (d) some finite small nonzero constant value. 9. The maximum load a wire
More information1. A pure shear deformation is shown. The volume is unchanged. What is the strain tensor.
Elasticity Homework Problems 2014 Section 1. The Strain Tensor. 1. A pure shear deformation is shown. The volume is unchanged. What is the strain tensor. 2. Given a steel bar compressed with a deformation
More informationQuestion Figure shows the strainstress curve for a given material. What are (a) Young s modulus and (b) approximate yield strength for this material?
Question. A steel wire of length 4.7 m and crosssectional area 3.0 x 105 m 2 stretches by the same amount as a copper wire of length 3.5 m and crosssectional area of 4.0 x 105 m 2 under a given load.
More informationQuestion 9.1: A steel wire of length 4.7 m and crosssectional area 3.0 10 5 m 2 stretches by the same amount as a copper wire of length 3.5 m and crosssectional area of 4.0 10 5 m 2 under a given load.
More informationClass XI Physics. Ch. 9: Mechanical Properties of solids. NCERT Solutions
Downloaded from Class XI Physics Ch. 9: Mechanical Properties of solids NCERT Solutions Page 242 Question 9.1: A steel wire of length 4.7 m and crosssectional area 3.0 10 5 m 2 stretches by the same amount
More informationChapter 7. Highlights:
Chapter 7 Highlights: 1. Understand the basic concepts of engineering stress and strain, yield strength, tensile strength, Young's(elastic) modulus, ductility, toughness, resilience, true stress and true
More 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 informationQuestion 9.1: Answer. Length of the steel wire, L 1 = 4.7 m. Area of crosssection of the steel wire, A 1 = m 2
Question 9.1: A steel wire of length 4.7 m and crosssectional area 3.0 10 5 m 2 stretches by the same amount as a copper wire of length 3.5 m and crosssectional area of 4.0 10 5 m 2 under a given load.
More informationIntroduction to Engineering Materials ENGR2000. Dr. Coates
Introduction to Engineering Materials ENGR2 Chapter 6: Mechanical Properties of Metals Dr. Coates 6.2 Concepts of Stress and Strain tension compression shear torsion Tension Tests The specimen is deformed
More 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 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 informationSean Carey Tafe No Lab Report: Hounsfield Tension Test
Sean Carey Tafe No. 366851615 Lab Report: Hounsfield Tension Test August 2012 The Hounsfield Tester The Hounsfield Tester can do a variety of tests on a small testpiece. It is mostly used for tensile
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 informationSimple Stresses and Strains
Simple Stresses and Strains CHPTER OJECTIVES In this chapter, we will learn about: Various types of (a) stresses as tensile and compressive stresses, positive and negative shear stresses, complementary
More informationCHAPTER OBJECTIVES CHAPTER OUTLINE. 4. Axial Load
CHAPTER OBJECTIVES Determine deformation of axially loaded members Develop a method to find support reactions when it cannot be determined from euilibrium euations Analyze the effects of thermal stress
More informationChapter 13 ELASTIC PROPERTIES OF MATERIALS
Physics Including Human Applications 280 Chapter 13 ELASTIC PROPERTIES OF MATERIALS GOALS When you have mastered the contents of this chapter, you will be able to achieve the following goals: Definitions
More informationCHAPTER 2 COMPOUND BARS. Summary. F1 = L1 w. c L
CHAPTER 2 COMPOUND BARS Summary When a compound bar is constructed from members of different materials, lengths and areas and is subjected to an external tensile or compressive load W the load carried
More informationOnly for Reference Page 1 of 18
Only for Reference www.civilpddc2013.weebly.com Page 1 of 18 Seat No.: Enrolment No. GUJARAT TECHNOLOGICAL UNIVERSITY PDDC  SEMESTER II EXAMINATION WINTER 2013 Subject Code: X20603 Date: 26122013 Subject
More informationσ = Eα(T T C PROBLEM #1.1 (4 + 4 points, no partial credit)
PROBLEM #1.1 (4 + 4 points, no partial credit A thermal switch consists of a copper bar which under elevation of temperature closes a gap and closes an electrical circuit. The copper bar possesses a length
More 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 informationThermal stresses, Bars subjected to tension and Compression
Thermal stresses, Bars subjected to tension and Compression Compound bar: In certain application it is necessary to use a combination of elements or bars made from different materials, each material performing
More information4.MECHANICAL PROPERTIES OF MATERIALS
4.MECHANICAL PROPERTIES OF MATERIALS The diagram representing the relation between stress and strain in a given material is an important characteristic of the material. To obtain the stressstrain diagram
More informationChapter 5 CENTRIC TENSION OR COMPRESSION ( AXIAL LOADING )
Chapter 5 CENTRIC TENSION OR COMPRESSION ( AXIAL LOADING ) 5.1 DEFINITION A construction member is subjected to centric (axial) tension or compression if in any cross section the single distinct stress
More 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 informationA concrete cylinder having a a diameter of of in. mm and elasticity. Stress and Strain: Stress and Strain: 0.
2011 earson Education, Inc., Upper Saddle River, NJ. ll rights reserved. This material is protected under all copyright laws as they currently 8 1. 3 1. concrete cylinder having a a diameter of of 6.00
More 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 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 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 informationWhat Every Engineer Should Know About Structures
What Every Engineer Should Know About Structures Part C  Axial Strength of Materials by Professor Patrick L. Glon, P.E. This is a continuation of a series of courses in the area of study of physics called
More informationLab Exercise #3: Torsion
Lab Exercise #3: Prelab assignment: Yes No Goals: 1. To evaluate the equations of angular displacement, shear stress, and shear strain for a shaft undergoing torsional stress. Principles: testing of round
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 informationCHAPTER 5 Statically Determinate Plane Trusses
CHAPTER 5 Statically Determinate Plane Trusses TYPES OF ROOF TRUSS TYPES OF ROOF TRUSS ROOF TRUSS SETUP ROOF TRUSS SETUP OBJECTIVES To determine the STABILITY and DETERMINACY of plane trusses To analyse
More informationCHAPTER 5 Statically Determinate Plane Trusses TYPES OF ROOF TRUSS
CHAPTER 5 Statically Determinate Plane Trusses TYPES OF ROOF TRUSS 1 TYPES OF ROOF TRUSS ROOF TRUSS SETUP 2 ROOF TRUSS SETUP OBJECTIVES To determine the STABILITY and DETERMINACY of plane trusses To analyse
More informationChapter 12. Static Equilibrium and Elasticity
Chapter 12 Static Equilibrium and Elasticity Static Equilibrium Equilibrium implies that the object moves with both constant velocity and constant angular velocity relative to an observer in an inertial
More informationThermal physics revision questions
Thermal physics revision questions ONE SECTION OF QUESTIONS TO BE COMPLETED AND MARKED EVERY WEEK AFTER HALF TERM. Section 1: Energy 1. Define the law of conservation of energy. Energy is neither created
More informationLaboratory 4 Bending Test of Materials
Department of Materials and Metallurgical Engineering Bangladesh University of Engineering Technology, Dhaka MME 222 Materials Testing Sessional.50 Credits Laboratory 4 Bending Test of Materials. Objective
More informationOutline. Organization. Stresses in Beams
Stresses in Beams B the end of this lesson, ou should be able to: Calculate the maimum stress in a beam undergoing a bending moment 1 Outline Curvature Normal Strain Normal Stress Neutral is Moment of
More informationElasticity: Term Paper. Danielle Harper. University of Central Florida
Elasticity: Term Paper Danielle Harper University of Central Florida I. Abstract This research was conducted in order to experimentally test certain components of the theory of elasticity. The theory was
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 informationChapter 26 Elastic Properties of Materials
Chapter 26 Elastic Properties of Materials 26.1 Introduction... 1 26.2 Stress and Strain in Tension and Compression... 2 26.3 Shear Stress and Strain... 4 Example 26.1: Stretched wire... 5 26.4 Elastic
More informationMechanical properties 1 Elastic behaviour of materials
MME131: Lecture 13 Mechanical properties 1 Elastic behaviour of materials A. K. M. B. Rashid Professor, Department of MME BUET, Dhaka Today s Topics Deformation of material under the action of a mechanical
More information1 (a) On the axes of Fig. 7.1, sketch a stress against strain graph for a typical ductile material. stress. strain. Fig. 7.1 [2]
1 (a) On the axes of Fig. 7.1, sketch a stress against strain graph for a typical ductile material. stress strain Fig. 7.1 [2] (b) Circle from the list below a material that is ductile. jelly c amic gl
More informationSTRENGTH OF MATERIALS 140AU0402 UNIT 1: STRESS STRAIN DEFORMATION OF SOLIDS
UNIT 1: STRESS STRAIN DEFORMATION OF SOLIDS Rigid and Deformable bodies Strength, Stiffness and Stability Stresses; Tensile, Compressive and Shear Deformation of simple and compound bars under axial load
More informationUnit III Theory of columns. Dr.P.Venkateswara Rao, Associate Professor, Dept. of Civil Engg., SVCE, Sriperumbudir
Unit III Theory of columns 1 Unit III Theory of Columns References: Punmia B.C.,"Theory of Structures" (SMTS) Vol II, Laxmi Publishing Pvt Ltd, New Delhi 2004. Rattan.S.S., "Strength of Materials", Tata
More informationSECOND ENGINEER REG. III/2 APPLIED MECHANICS
SECOND ENGINEER REG. III/2 APPLIED MECHANICS LIST OF TOPICS Static s Friction Kinematics Dynamics Machines Strength of Materials Hydrostatics Hydrodynamics A STATICS 1 Solves problems involving forces
More informationARC 341 Structural Analysis II. Lecture 10: MM1.3 MM1.13
ARC241 Structural Analysis I Lecture 10: MM1.3 MM1.13 MM1.4) Analysis and Design MM1.5) Axial Loading; Normal Stress MM1.6) Shearing Stress MM1.7) Bearing Stress in Connections MM1.9) Method of Problem
More informationChapter 6: Mechanical Properties of Metals. Dr. Feras Fraige
Chapter 6: Mechanical Properties of Metals Dr. Feras Fraige Stress and Strain Tension Compression Shear Torsion Elastic deformation Plastic Deformation Yield Strength Tensile Strength Ductility Toughness
More 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 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 informationOutline. TensileTest Specimen and Machine. StressStrain Curve. Review of Mechanical Properties. Mechanical Behaviour
TensileTest Specimen and Machine Review of Mechanical Properties Outline Tensile test True stress  true strain (flow curve) mechanical properties:  Resilience  Ductility  Toughness  Hardness A standard
More informationCONSTITUTIVE RELATIONS FOR LINEAR ELASTIC SOLIDS
Chapter 9 CONSTITUTIV RLATIONS FOR LINAR LASTIC SOLIDS Figure 9.1: Hooke memorial window, St. Helen s, Bishopsgate, City of London 211 212 CHAPTR 9. CONSTITUTIV RLATIONS FOR LINAR LASTIC SOLIDS 9.1 Mechanical
More informationTHEME IS FIRST OCCURANCE OF YIELDING THE LIMIT?
CIE309 : PLASTICITY THEME IS FIRST OCCURANCE OF YIELDING THE LIMIT? M M  N N + + σ = σ = + f f BENDING EXTENSION Ir J.W. Welleman page nr 0 kn Normal conditions during the life time WHAT HAPPENS DUE TO
More 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 informationBME 207 Introduction to Biomechanics Spring 2017
April 7, 2017 UNIVERSITY OF RHODE ISAND Department of Electrical, Computer and Biomedical Engineering BE 207 Introduction to Biomechanics Spring 2017 Homework 7 Problem 14.3 in the textbook. In addition
More 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 informationYoung s modulus. W.E. Bailey, APAM/MSE EN1102
Young s modulus W.E. Bailey, APAM/MSE EN1102 Spring constants Remember k is the spring constant Consider two springs F = k x Figure: Thin wire (d 1 cm) W.E. Bailey, APAM/MSE EN1102 Young s modulus 2 /
More informationTension, Compression, and Shear
01Ch01.qxd 2/10/09 7:32 PM Page 1 1 ension, Compression, and Shear Normal Stress and Strain Problem 1.21 A hollow circular post ABC (see figure) supports a load P 1 7.5 kn acting at the top. A second
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 informationUniaxial Loading: Design for Strength, Stiffness, and Stress Concentrations
Uniaxial Loading: Design for Strength, Stiffness, and Stress Concentrations Lisa Hatcher This overview of design concerning uniaxial loading is meant to supplement theoretical information presented in
More information2014 MECHANICS OF MATERIALS
R10 SET  1 II. Tech I Semester Regular Examinations, March 2014 MEHNIS OF MTERILS (ivil Engineering) Time: 3 hours Max. Marks: 75 nswer any FIVE Questions ll Questions carry Equal Marks ~~~~~~~~~~~~~~~~~~~~~~~~~
More informationFIXED BEAMS IN BENDING
FIXED BEAMS IN BENDING INTRODUCTION Fixed or builtin beams are commonly used in building construction because they possess high rigidity in comparison to simply supported beams. When a simply supported
More informationStatic Equilibrium; Elasticity & Fracture
Static Equilibrium; Elasticity & Fracture The Conditions for Equilibrium Statics is concerned with the calculation of the forces acting on and within structures that are in equilibrium. An object with
More informationb between the angle bracket and the bolts and the average shear stress aver in the bolts. (Disregard friction between the bracket and the column.
1.1. A solid circular post ABC (see figure) supports a load P 1 = 11.000 N acting at the top. A second load P 2 is uniformly distributed around the shelf at B. The diameters of the upper and lower parts
More informationDetermine the resultant internal loadings acting on the cross section at C of the beam shown in Fig. 1 4a.
E X M P L E 1.1 Determine the resultant internal loadings acting on the cross section at of the beam shown in Fig. 1 a. 70 N/m m 6 m Fig. 1 Support Reactions. This problem can be solved in the most direct
More informationExperiment: Torsion Test Expected Duration: 1.25 Hours
Course: Higher Diploma in Civil Engineering Unit: Structural Analysis I Experiment: Expected Duration: 1.25 Hours Objective: 1. To determine the shear modulus of the metal specimens. 2. To determine the
More informationDesign of a fastener based on negative Poisson's ratio foam adapted from
1 Design of a fastener based on negative Poisson's ratio foam adapted from Choi, J. B. and Lakes, R. S., "Design of a fastener based on negative Poisson's ratio foam", Cellular Polymers, 10, 205212 (1991).
More informationSTRESS. Bar. ! Stress. ! Average Normal Stress in an Axially Loaded. ! Average Shear Stress. ! Allowable Stress. ! Design of Simple Connections
STRESS! Stress Evisdom! verage Normal Stress in an xially Loaded ar! verage Shear Stress! llowable Stress! Design of Simple onnections 1 Equilibrium of a Deformable ody ody Force w F R x w(s). D s y Support
More informationEpisode 228: The Young modulus
Episode 228: The Young modulus The Young modulus is often regarded as the quintessential material property, and students can learn to measure it. It is a measure of the stiffness of a material; however,
More informationA P P L I E D M E C H A N I C S I I 1. 1 I N T R O D U C T I O N
A PPLIED MECHANICS II 1. 1 INTRODUCTION T h e second aspect of the course on A pplied Mechanics deals with the internal stress and strain g e n e r a t e d by eternally applied forces. 1. STRESS AND STRAIN
More informationStresses and Strains in flexible Pavements
Stresses and Strains in flexible Pavements Multi Layered Elastic System Assumptions in Multi Layered Elastic Systems The material properties of each layer are homogeneous property at point A i is the same
More informationStructural Metals Lab 1.2. Torsion Testing of Structural Metals. Standards ASTM E143: Shear Modulus at Room Temperature
Torsion Testing of Structural Metals Standards ASTM E143: Shear Modulus at Room Temperature Purpose To determine the shear modulus of structural metals Equipment TiniusOlsen LoTorq Torsion Machine (figure
More informationContents. Concept Map
Contents 1. General Notes on Forces 2. Effects of Forces on Motion 3. Effects of Forces on Shape 4. The Turning Effect of Forces 5. The Centre of Gravity and Stability Concept Map April 2000 Forces  1
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 information**********************************************************************
Department of Civil and Environmental Engineering School of Mining and Petroleum Engineering 333 Markin/CNRL Natural Resources Engineering Facility www.engineering.ualberta.ca/civil Tel: 780.492.4235
More information122 CHAPTER 2 Axially Loaded Numbers. Stresses on Inclined Sections
1 CHATER Aiall Loaded Numbers Stresses on Inclined Sections roblem.61 A steel bar of rectangular cross section (1.5 in..0 in.) carries a tensile load (see figure). The allowable stresses in tension and
More 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 informationFailure from static loading
Failure from static loading Topics Quiz /1/07 Failures from static loading Reading Chapter 5 Homework HW 3 due /1 HW 4 due /8 What is Failure? Failure any change in a machine part which makes it unable
More informationFatigue Problems Solution
Fatigue Problems Solution Problem 1. (a) Given the values of σ m (7 MPa) and σ a (1 MPa) we are asked t o compute σ max and σ min. From Equation 1 Or, σ m σ max + σ min 7 MPa σ max + σ min 14 MPa Furthermore,
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 informationcos(θ)sin(θ) Alternative Exercise Correct Correct θ = 0 skiladæmi 10 Part A Part B Part C Due: 11:59pm on Wednesday, November 11, 2015
skiladæmi 10 Due: 11:59pm on Wednesday, November 11, 015 You will receive no credit for items you complete after the assignment is due Grading Policy Alternative Exercise 1115 A bar with cross sectional
More informationEMA 3702 Mechanics & Materials Science (Mechanics of Materials) Chapter 4 Pure Bending
EA 3702 echanics & aterials Science (echanics of aterials) Chapter 4 Pure Bending Pure Bending Ch 2 Aial Loading & Parallel Loading: uniform normal stress and shearing stress distribution Ch 3 Torsion:
More informationnot to be republished NCERT MECHANICAL PROPERTIES OF SOLIDS CHAPTER NINE
CHAPTER NINE 9.1 Introduction 9.2 Elastic behaviour of solids 9.3 Stress and strain 9.4 Hooke s law 9.5 Stressstrain curve 9.6 Elastic moduli 9.7 Applications of elastic behaviour of materials Summary
More information6.37 Determine the modulus of resilience for each of the following alloys:
6.37 Determine the modulus of resilience for each of the following alloys: Yield Strength Material MPa psi Steel alloy 550 80,000 Brass alloy 350 50,750 Aluminum alloy 50 36,50 Titanium alloy 800 116,000
More informationMATERIALS. Why do things break? Why are some materials stronger than others? Why is steel tough? Why is glass brittle?
MATERIALS Why do things break? Why are some materials stronger than others? Why is steel tough? Why is glass brittle? What is toughness? strength? brittleness? Elemental material atoms: A. Composition
More informationPRELIMINARY PREDICTION OF SPECIMEN PROPERTIES CLT and 1 st order FEM analyses
OPTIMAT BLADES Page 1 of 24 PRELIMINARY PREDICTION OF SPECIMEN PROPERTIES CLT and 1 st order FEM analyses first issue Peter Joosse CHANGE RECORD Issue/revision date pages Summary of changes draft 241002
More informationArberi Ferraj. Wentworth Institute of Technology. Design of Machine Elements MECH 420
P a g e 1 Arberi Ferraj Wentworth Institute of Technology Design of Machine Elements MECH 420 P a g e 2 1. Executive Summary A scissor car jack was designed and must be reverseengineered in order to discover
More informationEquilibrium & Elasticity
PHYS 101 Previous Exam Problems CHAPTER 12 Equilibrium & Elasticity Static equilibrium Elasticity 1. A uniform steel bar of length 3.0 m and weight 20 N rests on two supports (A and B) at its ends. A block
More information