ARC 341 Structural Analysis II. Lecture 10: MM1.3 MM1.13

Save this PDF as:

Size: px
Start display at page:

Transcription

1 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 Solution MM1.10) Analysis & Design of Simple Structures MM1.11) Stresses on an Oblique Plane MM1.12) Stress Under General Loading Conditions

2 MM1.4) Analysis and Design The study of Mechanics of Materials aims towards: 1) Analysis of Structures: determination of stresses and deformations in structural members. 2) Design of Structures: sizing of structural members. Stress, σ, is the amount of force per unit area distributed over a cross-section (intensity of force). It can be classified as a) normal stress, b) shearing stress, and c) bearing stress. 1

3 MM1.5) Axial Loading; Normal Stress When the loading on a member is directed along its axis, we say that the member is under axial loading. Axial loading causes a stress that is perpendicular (normal) to the plane of the sections normal stress. Normal stress can be calculated by dividing the force P by the crosssectional area A. σ = In general, this formula gives the average stress over a cross-section. Why? P A 2

4 σ varies across the cross-section of a members, where it is maximum near the loading and minimum far away from the loading, but this variation is small and can be ignored at points far away from the point of loading along the axis of the member. To define σ at a given point Q of the cross-section, we should consider a small are A subjected to differential load F. The stress at point Q then is: F σ = (lim A > 0) A 3

5 MM1.6) Shearing Stress When transverse forces are applied to a members, internal forces are developed in the plane of the section to resist these forces. These internal forces are represented by shearing stress: τ P A ave = = Unlike normal stress, shearing stress cannot be assumed uniform. Why? F A 4

6 MM1.7) Bearing Stress Pins and bolts can create stresses on the members they connect along the bearing surface. The distribution of these stresses are quite complicated, so an average nominal stress called bearing stress can be computed as an approximation. Bearing stress is calculated by dividing the load by the area of the rectangle representing the projection of the pin or bolt on the plate section. Thus: σ P A b = = P td 5

7 Problem MM1.20 A 40-kN axial load is applied to a short wooden post that is supported by a concrete footing resting on undisturbed soil. Determine (a) the maximum bearing stress on the concrete footing, (b) the size of footing for which the average bearing stress in the soil is 145 kpa. 6

8 MM1.9) Method of Problem Solution Steps to solving a Mechanics Problem: 1) Clearly understand the statement of the problem. 2) Draw necessary FBD s. 3) Write equilibrium equations. 4) Solve for unknown forces. 5) Calculate stresses and deformations. 7

9 MM1.9) Numerical Accuracy The accuracy of a solution cannot exceed the (a) accuracy of given data, (b) accuracy of computations. Example: If P = 300 kn with possible error of, then the relative error is 0.13%. Thus, the solution accuracy cannot be greater than 0.13% regardless of the accuracy of computations. In engineering problems, the data are seldom known with an accuracy greater than 0.2%. 8

10 MM1.11) Stresses on an Oblique Plane Thus far, axial loads were found to cause normal stresses. And, transverse loads were found to cause shearing stresses. Why? Because stresses were determined in planes perpendicular to the axis of the member. What will happen if stresses were determined on an oblique plane? 9

11 Consider the same member subjected to an axial load P and P, but this time the stress is to be determined on an oblique plane with an angle θ. FBD shows that distributed forces on oblique section must equal P. P can be resolved to F (normal force) and V (tangential force) where: F = P cosθ V = Psinθ Divide these forces by the area of the oblique section to get normal and shearing stresses: σ = F A θ = P cosθ = A / cosθ 0 P A 0 cos 2 θ τ = V A θ = Psinθ = A / cosθ P 0 A 0 sinθ cosθ 10

12 What can we learn from the equations of stresses on an oblique plane in member under axial loading? P 2 P σ = cos θ τ = sinθ cosθ A 0 1) When θ = 0, σ = σ max and τ = 0. 2) When θ = 45 o, τ = τ max and σ = τ. The stress value in this case is P 2A 0 A 0 11

13 MM1.12) Stress Under General Loading Conditions Consider a body subjected to several loads P 1, P 2, etc. Pass a section at point Q using a plane parallel to the y-z plane. To maintain equilibrium, the sliced section must be subjected to normal force F x and shear force V x. The portion of these forces at point Q are F x and V x. V x can be further decomposed to V xy and V xz. Dividing by the area A, stresses can be defined as: σ x lim = A 0 F x A τ xy lim = A 0 V x y A τ xz lim = A 0 z A V x 12

14 Note: First subscript in σ x, τ xy, τ xz is used to indicated that the stresses under consideration are excreted on a surface perpendicular to the x-axis. The second subscript in τ τ xy, τ xz identifies the direction of the component. The normal stress σ x is positive if the corresponding arrow points in the positive x direction. τ xy, τ xz are positive if the corresponding arrows point in the positive y and z directions. If the passing section faces the negative x directions, then positive stresses will point in the negative direction. 13

15 Stress Components in 3-D: If passing planes are taken parallel to all the planes around point Q, a small cube with all the stress components can be visualized. Let each side of the cube has length a, and each face of the cube has area A. By inspection, the three equilibrium equations for the summation of forces can be satisfied. Considering one plane, the three equilibrium equations for the summation of moments can be satisfied. From this equilibrium, one concludes that τ xy = τ yx, τ yz = τ zy, τ zx = τ xz. 14

16 Other Conclusions: Only 6 components are required to define the condition of stress at a given point Q. Namely, σ x, σ y, σ z, τ xy, τ yz, τ zx. Shear can t take place in one plane only. An equal shearing stress must be excreted on another plane perpendicular to the first one. The same load condition may lead to different interpretation of the stress situation at a given point, depending on upon the orientation of the element considered. 15

17 Problem MM1.42 Members AB and BC of the truss shown are made of the same alloy. It is known that a 20-mm square bar of the same alloy has tested to failure and that an ultimate load of 120 kn was recorded. If bar AB as a cross-sectional are of 225 mm 2, determine: a) the factor of safety for bar AB b) the cross-sectional are of bar AC of it is to have the same factor of safety as bar AB. 16

18 Problem MM1.46 Two wooden members of 90 x 140 mm uniform rectangular cross section are joined by the simple glued scarf splice shown. Knowing that the maximum allowable shearing stress in the glued splice is 520 kpa, determine the largest axial load P that can be safely applied. 140 mm 90 mm 17

MECHANICS OF MATERIALS

Fifth SI Edition CHTER 1 MECHNICS OF MTERILS Ferdinand. Beer E. Russell Johnston, Jr. John T. DeWolf David F. Mazurek Introduction Concept of Stress Lecture Notes: J. Walt Oler Teas Tech University Contents

MECHANICS OF MATERIALS

Third E CHAPTER 1 Introduction MECHANICS OF MATERIALS Ferdinand P. Beer E. Russell Johnston, Jr. John T. DeWolf Lecture Notes: J. Walt Oler Texas Tech University Concept of Stress Contents Concept of Stress

MECE 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

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

[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

STRESS. 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

Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay

50 Module 4: Lecture 1 on Stress-strain relationship and Shear strength of soils Contents Stress state, Mohr s circle analysis and Pole, Principal stressspace, Stress pathsin p-q space; Mohr-Coulomb failure

Principal Stresses, Yielding Criteria, wall structures

Principal Stresses, Yielding Criteria, St i thi Stresses in thin wall structures Introduction The most general state of stress at a point may be represented by 6 components, x, y, z τ xy, τ yz, τ zx normal

Jeff 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

Chapter 1 Introduction- Concept of Stress

hapter 1 Introduction- oncept of Stress INTRODUTION Review of Statics xial Stress earing Stress Torsional Stress 14 6 ending Stress W W L Introduction 1-1 Shear Stress W W Stress and Strain L y y τ xy

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

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

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

EMA 3702 Mechanics & Materials Science (Mechanics of Materials) Chapter 6 Shearing Stress in Beams & Thin-Walled Members

EMA 3702 Mechanics & Materials Science (Mechanics of Materials) Chapter 6 Shearing Stress in Beams & Thin-Walled Members Beams Bending & Shearing EMA 3702 Mechanics & Materials Science Zhe Cheng (2018)

MECHANICS 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

Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay

51 Module 4: Lecture 2 on Stress-strain relationship and Shear strength of soils Contents Stress state, Mohr s circle analysis and Pole, Principal stressspace, Stress pathsin p-q space; Mohr-coulomb failure

Stress transformation and Mohr s circle for stresses

Stress transformation and Mohr s circle for stresses 1.1 General State of stress Consider a certain body, subjected to external force. The force F is acting on the surface over an area da of the surface.

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

Unit IV State of stress in Three Dimensions

Unit IV State of stress in Three Dimensions State of stress in Three Dimensions References Punmia B.C.,"Theory of Structures" (SMTS) Vol II, Laxmi Publishing Pvt Ltd, New Delhi 2004. Rattan.S.S., "Strength

CHAPTER 4 Stress Transformation

CHAPTER 4 Stress Transformation ANALYSIS OF STRESS For this topic, the stresses to be considered are not on the perpendicular and parallel planes only but also on other inclined planes. A P a a b b P z

Stress, Strain, Mohr s Circle

Stress, Strain, Mohr s Circle The fundamental quantities in solid mechanics are stresses and strains. In accordance with the continuum mechanics assumption, the molecular structure of materials is neglected

Mechanics of Solids I Transverse Loading Introduction o Transverse loading applied to a beam results in normal and shearing stresses in transverse sections. o Distribution of normal and shearing stresses

ME 243. Lecture 10: Combined stresses

ME 243 Mechanics of Solids Lecture 10: Combined stresses 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

COLUMNS: BUCKLING (DIFFERENT ENDS)

COLUMNS: BUCKLING (DIFFERENT ENDS) Buckling of Long Straight Columns Example 4 Slide No. 1 A simple pin-connected truss is loaded and supported as shown in Fig. 1. All members of the truss are WT10 43

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 & Free-Body Diagrams Shear Force and Bending Moments in Beams Singularity Functions Stress Cartesian Stress Components Mohr s Circle for

five Mechanics of Materials 1 ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN DR. ANNE NICHOLS SUMMER 2017 lecture

ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN DR. ANNE NICHOLS SUMMER 2017 lecture five mechanics www.carttalk.com of materials Mechanics of Materials 1 Mechanics of Materials MECHANICS MATERIALS

five Mechanics of Materials 1 ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN DR. ANNE NICHOLS SUMMER 2014 lecture

ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN DR. ANNE NICHOLS SUMMER 2014 lecture five mechanics www.carttalk.com of materials Mechanics of Materials 1 Mechanics of Materials MECHANICS MATERIALS

ES230 STRENGTH OF MATERIALS

ES230 STRENGTH OF MATERIALS Exam 1 Study Guide. Exam 1: Wednesday, February 8 th, in-class Updated 2/5/17 Purpose of this Guide: To thoroughly prepare students for the exact types of problems that will

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

7.3 Design of members subjected to combined forces

7.3 Design of members subjected to combined forces 7.3.1 General In the previous chapters of Draft IS: 800 LSM version, we have stipulated the codal provisions for determining the stress distribution in

Unit 13 Review of Simple Beam Theory

MIT - 16.0 Fall, 00 Unit 13 Review of Simple Beam Theory Readings: Review Unified Engineering notes on Beam Theory BMP 3.8, 3.9, 3.10 T & G 10-15 Paul A. Lagace, Ph.D. Professor of Aeronautics & Astronautics

Composite Structures. Indian Institute of Technology Kanpur

Mechanics of Laminated Composite Structures Nachiketa Tiwari Indian Institute of Technology Kanpur Lecture 24 Analysis of an Orthotropic Ply Lecture Overview Transformation of stresses and strains Stress

Symmetric Bending of Beams

Symmetric Bending of Beams beam is any long structural member on which loads act perpendicular to the longitudinal axis. Learning objectives Understand the theory, its limitations and its applications

ENG202 Statics Lecture 16, Section 7.1

ENG202 Statics Lecture 16, Section 7.1 Internal Forces Developed in Structural Members - Design of any structural member requires an investigation of the loading acting within the member in order to be

Mechanics of Materials

Mechanics of Materials 2. Introduction Dr. Rami Zakaria References: 1. Engineering Mechanics: Statics, R.C. Hibbeler, 12 th ed, Pearson 2. Mechanics of Materials: R.C. Hibbeler, 9 th ed, Pearson 3. Mechanics

Mechanics of Materials CIVL 3322 / MECH 3322

Mechanics of Materials CIVL 3322 / MECH 3322 2 3 4 5 6 7 8 9 10 A Quiz 11 A Quiz 12 A Quiz 13 A Quiz 14 A Quiz 15 A Quiz 16 In Statics, we spent most of our time looking at reactions at supports Two variations

3D Elasticity Theory

3D lasticity Theory Many structural analysis problems are analysed using the theory of elasticity in which Hooke s law is used to enforce proportionality between stress and strain at any deformation level.

Aluminum shell. Brass core. 40 in

PROBLEM #1 (22 points) A solid brass core is connected to a hollow rod made of aluminum. Both are attached at each end to a rigid plate as shown in Fig. 1. The moduli of aluminum and brass are EA=11,000

Name (Print) ME Mechanics of Materials Exam # 1 Date: October 5, 2016 Time: 8:00 10:00 PM

Name (Print) (Last) (First) Instructions: ME 323 - Mechanics of Materials Exam # 1 Date: October 5, 2016 Time: 8:00 10:00 PM Circle your lecturer s name and your class meeting time. Gonzalez Krousgrill

ME Statics. Structures. Chapter 4

ME 108 - Statics Structures Chapter 4 Outline Applications Simple truss Method of joints Method of section Germany Tacoma Narrows Bridge http://video.google.com/videoplay?docid=-323172185412005564&q=bruce+lee&pl=true

Entrance exam Master Course

- 1 - Guidelines for completion of test: On each page, fill in your name and your application code Each question has four answers while only one answer is correct. o Marked correct answer means 4 points

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

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

WORCESTER POLYTECHNIC INSTITUTE

WORCESTER POLYTECHNIC INSTITUTE MECHANICAL ENGINEERING DEPARTMENT STRESS ANALYSIS ES-2502, C 2012 Lecture 03: Stress 17 January 2012 General information Instructor: Cosme Furlong HL-151 (508) 831-5126

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

Smart Materials, Adaptive Structures, and Intelligent Mechanical Systems

Smart Materials, Adaptive Structures, and Intelligent Mechanical Systems Bishakh Bhattacharya & Nachiketa Tiwari Indian Institute of Technology Kanpur Lecture 19 Analysis of an Orthotropic Ply References

Review Lecture. AE1108-II: Aerospace Mechanics of Materials. Dr. Calvin Rans Dr. Sofia Teixeira De Freitas

Review Lecture AE1108-II: Aerospace Mechanics of Materials Dr. Calvin Rans Dr. Sofia Teixeira De Freitas Aerospace Structures & Materials Faculty of Aerospace Engineering Analysis of an Engineering System

ANALYSIS OF STERSSES. General State of stress at a point :

ANALYSIS OF STERSSES General State of stress at a point : Stress at a point in a material body has been defined as a force per unit area. But this definition is some what ambiguous since it depends upon

Engineering Mechanics Department of Mechanical Engineering Dr. G. Saravana Kumar Indian Institute of Technology, Guwahati

Engineering Mechanics Department of Mechanical Engineering Dr. G. Saravana Kumar Indian Institute of Technology, Guwahati Module 3 Lecture 6 Internal Forces Today, we will see analysis of structures part

ME 323 MIDTERM # 1: SOLUTION FALL SEMESTER Time allowed: 1hour

Instructions ME 2 MIDTERM # : SOLUTION FALL SEMESTER 20 Time allowed: hour. Begin each problem in the space provided on the examination sheets. If additional space is required, use the yellow paper provided.

Constitutive Equations (Linear Elasticity)

Constitutive quations (Linear lasticity) quations that characterize the physical properties of the material of a system are called constitutive equations. It is possible to find the applied stresses knowing

Tension Members. ENCE 455 Design of Steel Structures. II. Tension Members. Introduction. Introduction (cont.)

ENCE 455 Design of Steel Structures II. Tension Members C. C. Fu, Ph.D., P.E. Civil and Environmental Engineering Department University of Maryland Tension Members Following subjects are covered: Introduction

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

CHAPTER 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.

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:

MECHANICS OF MATERIALS

Third E CHAPTER 6 Shearing MECHANCS OF MATERALS Ferdinand P. Beer E. Russell Johnston, Jr. John T. DeWolf Lecture Notes: J. Walt Oler Texas Tech University Stresses in Beams and Thin- Walled Members Shearing

CHAPTER 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

Torsion of Shafts Learning objectives

Torsion of Shafts Shafts are structural members with length significantly greater than the largest cross-sectional dimension used in transmitting torque from one plane to another. Learning objectives Understand

Lecture M1 Slender (one dimensional) Structures Reading: Crandall, Dahl and Lardner 3.1, 7.2

Lecture M1 Slender (one dimensional) Structures Reading: Crandall, Dahl and Lardner 3.1, 7.2 This semester we are going to utilize the principles we learnt last semester (i.e the 3 great principles and

Example 3.7 Consider the undeformed configuration of a solid as shown in Figure 3.60.

162 3. The linear 3-D elasticity mathematical model The 3-D elasticity model is of great importance, since it is our highest order hierarchical model assuming linear elastic behavior. Therefore, it provides

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

[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

Pressure Vessels Stresses Under Combined Loads Yield Criteria for Ductile Materials and Fracture Criteria for Brittle Materials

Pressure Vessels Stresses Under Combined Loads Yield Criteria for Ductile Materials and Fracture Criteria for Brittle Materials Pressure Vessels: In the previous lectures we have discussed elements subjected

Stress Transformation Equations: u = +135 (Fig. a) s x = 80 MPa s y = 0 t xy = 45 MPa. we obtain, cos u + t xy sin 2u. s x = s x + s y.

014 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently 9 7. Determine the normal stress and shear stress acting

CIV100 Mechanics. Module 5: Internal Forces and Design. by: Jinyue Zhang. By the end of this Module you should be able to:

CIV100 Mechanics Module 5: Internal Forces and Design by: Jinyue Zhang Module Objective By the end of this Module you should be able to: Find internal forces of any structural members Understand how Shear

Solution: The moment of inertia for the cross-section is: ANS: ANS: Problem 15.6 The material of the beam in Problem

Problem 15.4 The beam consists of material with modulus of elasticity E 14x10 6 psi and is subjected to couples M 150, 000 in lb at its ends. (a) What is the resulting radius of curvature of the neutral

Continuum mechanism: Stress and strain

Continuum mechanics deals with the relation between forces (stress, σ) and deformation (strain, ε), or deformation rate (strain rate, ε). Solid materials, rigid, usually deform elastically, that is the

Module 11 Design of Joints for Special Loading. Version 2 ME, IIT Kharagpur

Module 11 Design of Joints for Special Loading Version ME, IIT Kharagpur Lesson Design of Eccentrically Loaded Welded Joints Version ME, IIT Kharagpur Instructional Objectives: At the end of this lesson,

DESIGN AND DETAILING OF COUNTERFORT RETAINING WALL

DESIGN AND DETAILING OF COUNTERFORT RETAINING WALL When the height of the retaining wall exceeds about 6 m, the thickness of the stem and heel slab works out to be sufficiently large and the design becomes

Chapter 4.1: Shear and Moment Diagram

Chapter 4.1: Shear and Moment Diagram Chapter 5: Stresses in Beams Chapter 6: Classical Methods Beam Types Generally, beams are classified according to how the beam is supported and according to crosssection

ANALYSIS OF STRAINS CONCEPT OF STRAIN

ANALYSIS OF STRAINS CONCEPT OF STRAIN Concept of strain : if a bar is subjected to a direct load, and hence a stress the bar will change in length. If the bar has an original length L and changes by an

SAULTCOLLEGE of AppliedArtsand Technology SaultSte. Marie COURSEOUTLINE

SAULTCOLLEGE of AppliedArtsand Technology SaultSte. Marie COURSEOUTLINE STRENGTH OF ~1ATERIALS MCH 103-3 revised June 1981 by W.J. Adolph ------- STRENGHT OF MATERIALS MCH 103-3 To'Cic Periods Tooic Description

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

CHAPTER 3 THE EFFECTS OF FORCES ON MATERIALS

CHAPTER THE EFFECTS OF FORCES ON MATERIALS EXERCISE 1, Page 50 1. 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

Chapter 7: Bending and Shear in Simple Beams

Chapter 7: Bending and Shear in Simple Beams Introduction A beam is a long, slender structural member that resists loads that are generally applied transverse (perpendicular) to its longitudinal axis.

BE 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)

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,

Axial Deformations. A-PDF Merger DEMO : Purchase from to remove the watermark. Introduction. Free body diagram - Revisited

A-PDF Merger DEMO : Purchase from www.a-pdf.com to remove the watermark Axial Deformations Introduction Free body diagram - Revisited Normal, shear and bearing stress Stress on inclined planes under axial

Mechanics of Earthquakes and Faulting

Mechanics of Earthquakes and Faulting www.geosc.psu.edu/courses/geosc508 Surface and body forces Tensors, Mohr circles. Theoretical strength of materials Defects Stress concentrations Griffith failure

M. Vable Mechanics of Materials: Chapter 5. Torsion of Shafts

Torsion of Shafts Shafts are structural members with length significantly greater than the largest cross-sectional dimension used in transmitting torque from one plane to another. Learning objectives Understand

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,

BTECH MECHANICAL PRINCIPLES AND APPLICATIONS. Level 3 Unit 5

BTECH MECHANICAL PRINCIPLES AND APPLICATIONS Level 3 Unit 5 FORCES AS VECTORS Vectors have a magnitude (amount) and a direction. Forces are vectors FORCES AS VECTORS (2 FORCES) Forces F1 and F2 are in

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

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

Supplement: Statically Indeterminate Trusses and Frames

: Statically Indeterminate Trusses and Frames Approximate Analysis - In this supplement, we consider an approximate method of solving statically indeterminate trusses and frames subjected to lateral loads

EMA 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 Cross-section shape Material Shaft design Non-circular

9. Stress Transformation

9.7 ABSOLUTE MAXIMUM SHEAR STRESS A pt in a body subjected to a general 3-D state of stress will have a normal stress and shear-stress components acting on each of its faces. We can develop stress-transformation

CH. 5 TRUSSES BASIC PRINCIPLES TRUSS ANALYSIS. Typical depth-to-span ratios range from 1:10 to 1:20. First: determine loads in various members

CH. 5 TRUSSES BASIC PRINCIPLES Typical depth-to-span ratios range from 1:10 to 1:20 - Flat trusses require less overall depth than pitched trusses Spans: 40-200 Spacing: 10 to 40 on center - Residential

Mechanics of Materials Primer

Mechanics of Materials rimer Notation: 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 of elasticity

1 Static Plastic Behaviour of Beams

1 Static Plastic Behaviour of Beams 1.1 Introduction Many ductile materials which are used in engineering practice have a considerable reserve capacity beyond the initial yield condition. The uniaxial

Timber and Steel Design. Lecture 11. Bolted Connections

Timber and Steel Design Lecture 11 Bolted Connections Riveted Connections Types of Joints Failure of Joints Bearing & Friction connections Truss Joints Shear and Tension on Bolt S U R A N A R E E UNIVERSITY

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.

Consider 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

1 of 7. Law of Sines: Stress = E = G. Deformation due to Temperature: Δ

NME: ES30 STRENGTH OF MTERILS FINL EXM: FRIDY, MY 1 TH 4PM TO 7PM Closed book. Calculator and writing supplies allowed. Protractor and compass allowed. 180 Minute Time Limit GIVEN FORMULE: Law of Cosines:

Equilibrium of a Particle

ME 108 - Statics Equilibrium of a Particle Chapter 3 Applications For a spool of given weight, what are the forces in cables AB and AC? Applications For a given weight of the lights, what are the forces

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

Lecture 20. ENGR-1100 Introduction to Engineering Analysis THE METHOD OF SECTIONS

ENGR-1100 Introduction to Engineering Analysis Lecture 20 THE METHOD OF SECTIONS Today s Objectives: Students will be able to determine: 1. Forces in truss members using the method of sections. In-Class