# CHAPTER 3 THE EFFECTS OF FORCES ON MATERIALS

Save this PDF as:
Size: px
Start display at page:

## Transcription

1 CHAPTER THE EFFECTS OF FORCES ON MATERIALS EXERCISE 1, Page A rectangular bar having a cross-sectional area of 80 mm has a tensile force of 0 kn applied to it. Determine the stress in the bar. Stress 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, cross-sectional 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 square-sectioned 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, cross-sectional 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 cross-sectional 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 cross-sectional 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 cross-section 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 cross-sectional 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 cross-sectional 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 cross-sectional 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 cross-sectional 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 cross-sectional 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 stress-free 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 two-layer 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

### NORMAL STRESS. The simplest form of stress is normal stress/direct stress, which is the stress perpendicular to the surface on which it acts.

NORMAL STRESS The simplest form of stress is normal stress/direct stress, which is the stress perpendicular to the surface on which it acts. σ = force/area = P/A where σ = the normal stress P = the centric

### Direct and Shear Stress

Direct and Shear Stress 1 Direct & Shear Stress When a body is pulled by a tensile force or crushed by a compressive force, the loading is said to be direct. Direct stresses are also found to arise when

### MECE 3321 MECHANICS OF SOLIDS CHAPTER 3

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

### 6.4 A cylindrical specimen of a titanium alloy having an elastic modulus of 107 GPa ( psi) and

6.4 A cylindrical specimen of a titanium alloy having an elastic modulus of 107 GPa (15.5 10 6 psi) and an original diameter of 3.8 mm (0.15 in.) will experience only elastic deformation when a tensile

### Samantha 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

### EDEXCEL NATIONAL CERTIFICATE/DIPLOMA SCIENCE FOR TECHNICIANS OUTCOME 1 - STATIC AND DYNAMIC FORCES TUTORIAL 3 STRESS AND STRAIN

EDEXCEL NATIONAL CERTIFICATE/DIPLOMA SCIENCE FOR TECHNICIANS OUTCOME 1 - STATIC AND DYNAMIC FORCES TUTORIAL 3 STRESS AND STRAIN 1 Static and dynamic forces Forces: definitions of: matter, mass, weight,

### EDEXCEL NATIONAL CERTIFICATE/DIPLOMA MECHANICAL PRINCIPLES AND APPLICATIONS NQF LEVEL 3 OUTCOME 1 - LOADING SYSTEMS TUTORIAL 3 LOADED COMPONENTS

EDEXCEL NATIONAL CERTIICATE/DIPLOMA MECHANICAL PRINCIPLES AND APPLICATIONS NQ LEVEL 3 OUTCOME 1 - LOADING SYSTEMS TUTORIAL 3 LOADED COMPONENTS 1. Be able to determine the effects of loading in static engineering

### [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

### Strength of Materials (15CV 32)

Strength of Materials (15CV 32) Module 1 : Simple Stresses and Strains Dr. H. Ananthan, Professor, VVIET,MYSURU 8/21/2017 Introduction, Definition and concept and of stress and strain. Hooke s law, Stress-Strain

### UNIT I SIMPLE STRESSES AND STRAINS

Subject with Code : SM-1(15A01303) Year & Sem: II-B.Tech & I-Sem SIDDHARTH GROUP OF INSTITUTIONS :: PUTTUR Siddharth Nagar, Narayanavanam Road 517583 QUESTION BANK (DESCRIPTIVE) UNIT I SIMPLE STRESSES

### Simple Stresses in Machine Parts

Simple Stresses in Machine Parts 87 C H A P T E R 4 Simple Stresses in Machine Parts 1. Introduction.. Load. 3. Stress. 4. Strain. 5. Tensile Stress and Strain. 6. Compressive Stress and Strain. 7. Young's

### The University of Melbourne Engineering Mechanics

The University of Melbourne 436-291 Engineering Mechanics Tutorial Four Poisson s Ratio and Axial Loading Part A (Introductory) 1. (Problem 9-22 from Hibbeler - Statics and Mechanics of Materials) A short

### N = Shear stress / Shear strain

UNIT - I 1. What is meant by factor of safety? [A/M-15] It is the ratio between ultimate stress to the working stress. Factor of safety = Ultimate stress Permissible stress 2. Define Resilience. [A/M-15]

### PDDC 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.

### INTRODUCTION 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,

### EMA 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

### Direct (and Shear) Stress

1 Direct (and Shear) Stress 3.1 Introduction Chapter 21 introduced the concepts of stress and strain. In this chapter we shall discuss direct and shear stresses. We shall also look at how to calculate

### PES Institute of Technology

PES Institute of Technology Bangalore south campus, Bangalore-5460100 Department of Mechanical Engineering Faculty name : Madhu M Date: 29/06/2012 SEM : 3 rd A SEC Subject : MECHANICS OF MATERIALS Subject

### ME 243. Mechanics of Solids

ME 243 Mechanics of Solids Lecture 2: Stress and Strain Ahmad Shahedi Shakil Lecturer, Dept. of Mechanical Engg, BUET E-mail: sshakil@me.buet.ac.bd, shakil6791@gmail.com Website: teacher.buet.ac.bd/sshakil

### Strength of Material. Shear Strain. Dr. Attaullah Shah

Strength of Material Shear Strain Dr. Attaullah Shah Shear Strain TRIAXIAL DEFORMATION Poisson's Ratio Relationship Between E, G, and ν BIAXIAL DEFORMATION Bulk Modulus of Elasticity or Modulus of Volume

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

### QUESTION 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,

### Stress-Strain Behavior

Stress-Strain Behavior 6.3 A specimen of aluminum having a rectangular cross section 10 mm 1.7 mm (0.4 in. 0.5 in.) is pulled in tension with 35,500 N (8000 lb f ) force, producing only elastic deformation.

### Name :. Roll No. :... Invigilator s Signature :.. CS/B.TECH (CE-NEW)/SEM-3/CE-301/ 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

### X 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

### Solid Mechanics Chapter 1: Tension, Compression and Shear

Solid Mechanics Chapter 1: Tension, Compression and Shear Dr. Imran Latif Department of Civil and Environmental Engineering College of Engineering University of Nizwa (UoN) 1 Why do we study Mechanics

### STRESS, STRAIN AND DEFORMATION OF SOLIDS

VELAMMAL COLLEGE OF ENGINEERING AND TECHNOLOGY, MADURAI 625009 DEPARTMENT OF CIVIL ENGINEERING CE8301 STRENGTH OF MATERIALS I -------------------------------------------------------------------------------------------------------------------------------

### ME 2570 MECHANICS OF MATERIALS

ME 2570 MECHANICS OF MATERIALS Chapter III. Mechanical Properties of Materials 1 Tension and Compression Test The strength of a material depends on its ability to sustain a load without undue deformation

### R13. II B. Tech I Semester Regular Examinations, Jan MECHANICS OF SOLIDS (Com. to ME, AME, AE, MTE) PART-A

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 (Part-A and Part-B)

### Chapter Two: Mechanical Properties of materials

Chapter Two: Mechanical Properties of materials Time : 16 Hours An important consideration in the choice of a material is the way it behave when subjected to force. The mechanical properties of a material

### Mechanical 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

### STANDARD SAMPLE. Reduced section " Diameter. Diameter. 2" Gauge length. Radius

MATERIAL PROPERTIES TENSILE MEASUREMENT F l l 0 A 0 F STANDARD SAMPLE Reduced section 2 " 1 4 0.505" Diameter 3 4 " Diameter 2" Gauge length 3 8 " Radius TYPICAL APPARATUS Load cell Extensometer Specimen

### Elastic Properties of Solid Materials. Notes based on those by James Irvine at

Elastic Properties of Solid Materials Notes based on those by James Irvine at www.antonine-education.co.uk Key Words Density, Elastic, Plastic, Stress, Strain, Young modulus We study how materials behave

### Chapter 4-b Axially Loaded Members

CIVL 222 STRENGTH OF MATERIALS Chapter 4-b Axially Loaded Members AXIAL LOADED MEMBERS Today s Objectives: Students will be able to: a) Determine the elastic deformation of axially loaded member b) Apply

### CIVIL DEPARTMENT MECHANICS OF STRUCTURES- ASSIGNMENT NO 1. Brach: CE YEAR:

MECHANICS OF STRUCTURES- ASSIGNMENT NO 1 SEMESTER: V 1) Find the least moment of Inertia about the centroidal axes X-X and Y-Y of an unequal angle section 125 mm 75 mm 10 mm as shown in figure 2) Determine

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

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

### QUESTION 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

### 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.

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

### Purpose 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 in-class Updated 3/3/17 Purpose of this Guide: To thoroughly prepare students for the exact types of problems that will be on

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

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

### INTRODUCTION (Cont..)

INTRODUCTION Name : Mohamad Redhwan Abd Aziz Post : Lecturer @ DEAN CENTER OF HND STUDIES Subject : Solid Mechanics Code : BME 2033 Room : CENTER OF HND STUDIES OFFICE H/P No. : 019-2579663 W/SITE : Http://tatiuc.edu.my/redhwan

### Unit I Stress and Strain

Unit I Stress and Strain Stress and strain at a point Tension, Compression, Shear Stress Hooke s Law Relationship among elastic constants Stress Strain Diagram for Mild Steel, TOR steel, Concrete Ultimate

### Stress Strain Elasticity Modulus Young s Modulus Shear Modulus Bulk Modulus. Case study

Stress Strain Elasticity Modulus Young s Modulus Shear Modulus Bulk Modulus Case study 2 In field of Physics, it explains how an object deforms under an applied force Real rigid bodies are elastic we can

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

Question. A steel wire of length 4.7 m and cross-sectional area 3.0 x 10-5 m 2 stretches by the same amount as a copper wire of length 3.5 m and cross-sectional area of 4.0 x 10-5 m 2 under a given load.

### MECHANICAL PROPERTIES OF SOLIDS

Chapter Nine MECHANICAL PROPERTIES OF SOLIDS MCQ I 9.1 Modulus of rigidity of ideal liquids is (a) infinity. (b) zero. (c) unity. (d) some finite small non-zero constant value. 9. The maximum load a wire

### and F NAME: ME rd Sample Final Exam PROBLEM 1 (25 points) Prob. 1 questions are all or nothing. PROBLEM 1A. (5 points)

ME 270 3 rd Sample inal Exam PROBLEM 1 (25 points) Prob. 1 questions are all or nothing. PROBLEM 1A. (5 points) IND: In your own words, please state Newton s Laws: 1 st Law = 2 nd Law = 3 rd Law = PROBLEM

### ISHIK UNIVERSITY DEPARTMENT OF MECHATRONICS ENGINEERING

ISHIK UNIVERSITY DEPARTMENT OF MECHATRONICS ENGINEERING QUESTION BANK FOR THE MECHANICS OF MATERIALS-I 1. A rod 150 cm long and of diameter 2.0 cm is subjected to an axial pull of 20 kn. If the modulus

### PURE 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 cross-section of a beam is to induce a state of stress across that section. These stresses are known as bending stresses and they act normally

Question 9.1: A steel wire of length 4.7 m and cross-sectional area 3.0 10 5 m 2 stretches by the same amount as a copper wire of length 3.5 m and cross-sectional area of 4.0 10 5 m 2 under a given load.

### Class XI Chapter 9 Mechanical Properties of Solids Physics

Book Name: NCERT Solutions Question : A steel wire of length 4.7 m and cross-sectional area 5 3.0 0 m stretches by the same 5 amount as a copper wire of length 3.5 m and cross-sectional area of 4.0 0 m

### MAAE 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

### Semester: BE 3 rd Subject :Mechanics of Solids ( ) Year: Faculty: Mr. Rohan S. Kariya. Tutorial 1

Semester: BE 3 rd Subject :Mechanics of Solids (2130003) Year: 2018-19 Faculty: Mr. Rohan S. Kariya Class: MA Tutorial 1 1 Define force and explain different type of force system with figures. 2 Explain

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

Downloaded from Class XI Physics Ch. 9: Mechanical Properties of solids NCERT Solutions Page 242 Question 9.1: A steel wire of length 4.7 m and cross-sectional area 3.0 10 5 m 2 stretches by the same amount

### 2. Rigid bar ABC supports a weight of W = 50 kn. Bar ABC is pinned at A and supported at B by rod (1). What is the axial force in rod (1)?

IDE 110 S08 Test 1 Name: 1. Determine the internal axial forces in segments (1), (2) and (3). (a) N 1 = kn (b) N 2 = kn (c) N 3 = kn 2. Rigid bar ABC supports a weight of W = 50 kn. Bar ABC is pinned at

### Chapter 7. Highlights:

Chapter 7 Highlights: 1. Understand the basic concepts of engineering stress and strain, yield strength, tensile strength, Young's(elastic) modulus, ductility, toughness, resilience, true stress and true

### Stress Analysis Lecture 3 ME 276 Spring Dr./ Ahmed Mohamed Nagib Elmekawy

Stress Analysis Lecture 3 ME 276 Spring 2017-2018 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

### Sample Question Paper

Scheme I Sample Question Paper Program Name : Mechanical Engineering Program Group Program Code : AE/ME/PG/PT/FG Semester : Third Course Title : Strength of Materials Marks : 70 Time: 3 Hrs. Instructions:

PURWANCHAL UNIVERSITY III SEMESTER FINAL EXAMINATION-2002 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

### Engineering 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

### Course: US01CPHY01 UNIT 1 ELASTICITY I Introduction:

Course: US0CPHY0 UNIT ELASTICITY I Introduction: If the distance between any two points in a body remains invariable, the body is said to be a rigid body. In practice it is not possible to have a perfectly

### STRENGTH OF MATERIALS-I. Unit-1. Simple stresses and strains

STRENGTH OF MATERIALS-I Unit-1 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

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

Question 9.1: A steel wire of length 4.7 m and cross-sectional area 3.0 10 5 m 2 stretches by the same amount as a copper wire of length 3.5 m and cross-sectional area of 4.0 10 5 m 2 under a given load.

### Introduction to Engineering Materials ENGR2000. Dr. Coates

Introduction to Engineering Materials ENGR2 Chapter 6: Mechanical Properties of Metals Dr. Coates 6.2 Concepts of Stress and Strain tension compression shear torsion Tension Tests The specimen is deformed

### (2) Calculate the spring constant, k, for the spring. State an appropriate unit.

Q1. A manufacturer of springs tests the properties of a spring by measuring the load applied each time the extension is increased. The graph of load against extension is shown below. (a) State Hooke s

### IDE 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

### UNIT-I STRESS, STRAIN. 1. A Member A B C D is subjected to loading as shown in fig determine the total elongation. Take E= 2 x10 5 N/mm 2

UNIT-I STRESS, STRAIN 1. A Member A B C D is subjected to loading as shown in fig determine the total elongation. Take E= 2 x10 5 N/mm 2 Young s modulus E= 2 x10 5 N/mm 2 Area1=900mm 2 Area2=400mm 2 Area3=625mm

### Mechanics 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

### MECHANICS OF MATERIALS

Third E CHAPTER 2 Stress MECHANICS OF MATERIALS Ferdinand P. Beer E. Russell Johnston, Jr. John T. DeWolf Lecture Notes: J. Walt Oler Texas Tech University and Strain Axial Loading Contents Stress & Strain:

### SRI CHANDRASEKHARENDRA SARASWATHI VISWA MAHAVIDHYALAYA

SRI CHANDRASEKHARENDRA SARASWATHI VISWA MAHAVIDHYALAYA (Declared as Deemed-to-be University under Section 3 of the UGC Act, 1956, Vide notification No.F.9.9/92-U-3 dated 26 th May 1993 of the Govt. of

### KINGS 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)

### Torsion 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

### UNIVERSITY 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

### Sean Carey Tafe No Lab Report: Hounsfield Tension Test

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

### The 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

### Elasticity. A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University Modified by M.

Elasticity A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University Modified by M. Lepore Elasticity Photo Vol. 10 PhotoDisk/Getty BUNGEE jumping utilizes

### Reg. No. : Question Paper Code : B.Arch. DEGREE EXAMINATION, APRIL/MAY Second Semester AR 6201 MECHANICS OF STRUCTURES I

WK 4 Reg. No. : Question Paper Code : 71387 B.Arch. DEGREE EXAMINATION, APRIL/MAY 2017. Second Semester AR 6201 MECHANICS OF STRUCTURES I (Regulations 2013) Time : Three hours Maximum : 100 marks Answer

### Module 2 Stresses in machine elements. Version 2 ME, IIT Kharagpur

Module Stresses in machine elements Lesson Compound stresses in machine parts Instructional Objectives t the end of this lesson, the student should be able to understand Elements of force system at a beam

### Question 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

### Advanced 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

### CHAPTER 6 MECHANICAL PROPERTIES OF METALS PROBLEM SOLUTIONS

CHAPTER 6 MECHANICAL PROPERTIES OF METALS PROBLEM SOLUTIONS Concepts of Stress and Strain 6.1 Using mechanics of materials principles (i.e., equations of mechanical equilibrium applied to a free-body diagram),

### Mechanical 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

### NAME: 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.

### Theory at a Glance (for IES, GATE, PSU)

1. Stress and Strain Theory at a Glance (for IES, GATE, PSU) 1.1 Stress () When a material is subjected to an external force, a resisting force is set up within the component. The internal resistance force

### Part 1 is to be completed without notes, beam tables or a calculator. DO NOT turn Part 2 over until you have completed and turned in Part 1.

NAME CM 3505 Fall 06 Test 2 Part 1 is to be completed without notes, beam tables or a calculator. Part 2 is to be completed after turning in Part 1. DO NOT turn Part 2 over until you have completed and

### (1) Brass, an alloy of copper and zinc, consists of 70% by volume of copper and 30% by volume of zinc.

PhysicsAndMathsTutor.com 1 Q1. (a) Define the density of a material....... (1) (b) Brass, an alloy of copper and zinc, consists of 70% by volume of copper and 30% by volume of zinc. density of copper =

### MATERIALS FOR CIVIL AND CONSTRUCTION ENGINEERS

MATERIALS FOR CIVIL AND CONSTRUCTION ENGINEERS 3 rd Edition Michael S. Mamlouk Arizona State University John P. Zaniewski West Virginia University Solution Manual FOREWORD This solution manual includes

### ME Final Exam. PROBLEM NO. 4 Part A (2 points max.) M (x) y. z (neutral axis) beam cross-sec+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 11:30AM-12:20PM Ghosh 2:30-3:20PM Gonzalez 12:30-1:20PM Zhao 4:30-5:20PM M (x) y 20 kip ft 0.2

### 2012 MECHANICS OF SOLIDS

R10 SET - 1 II B.Tech II Semester, Regular Examinations, April 2012 MECHANICS OF SOLIDS (Com. to ME, AME, MM) Time: 3 hours Max. Marks: 75 Answer any FIVE Questions All Questions carry Equal Marks ~~~~~~~~~~~~~~~~~~~~~~

mportant nstructions to examiners: ) The answers should be examined by key words and not as word-to-word as given in the model answer scheme. ) The model answer and the answer written by candidate may

### Structural 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

### 13 Solid materials Exam practice questions

Pages 206-209 Exam practice questions 1 a) The toughest material has the largest area beneath the curve the answer is C. b) The strongest material has the greatest breaking stress the answer is B. c) A

### Which expression gives the elastic energy stored in the stretched wire?

1 wire of length L and cross-sectional area is stretched a distance e by a tensile force. The Young modulus of the material of the wire is E. Which expression gives the elastic energy stored in the stretched

### , causing the length to increase to l 1 R U M. L Q P l 2 l 1

1 1 Which of the following correctly defines the terms stress, strain and oung modulus? stress strain oung modulus (force) x (area) (extension) x (original length) (stress) / (strain) (force) x (area)

### 9 MECHANICAL PROPERTIES OF SOLIDS

9 MECHANICAL PROPERTIES OF SOLIDS Deforming force Deforming force is the force which changes the shape or size of a body. Restoring force Restoring force is the internal force developed inside the body

### 18.Define the term modulus of resilience. May/June Define Principal Stress. 20. Define Hydrostatic Pressure.

CE6306 STREGNTH OF MATERIALS Question Bank Unit-I STRESS, STRAIN, DEFORMATION OF SOLIDS PART-A 1. Define Poison s Ratio May/June 2009 2. What is thermal stress? May/June 2009 3. Estimate the load carried

### SN QUESTION YEAR MARK 1. State and prove the relationship between shearing stress and rate of change of bending moment at a section in a loaded beam.

ALPHA COLLEGE OF ENGINEERING AND TECHNOLOGY DEPARTMENT OF MECHANICAL ENGINEERING MECHANICS OF SOLIDS (21000) ASSIGNMENT 1 SIMPLE STRESSES AND STRAINS SN QUESTION YEAR MARK 1 State and prove the relationship

### Problem " 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