Stresses in Curved Beam


 Alfred Stone
 1 years ago
 Views:
Transcription
1 Stresses in Curved Beam Consider a curved beam subjected to bending moment M b as shown in the figure. The distribution of stress in curved flexural member is determined by using the following assumptions: i) The material of the beam is perfectly homogeneous [i.e., same material throughout] and isotropic [i.e., equal elastic properties in all directions] ii) The cross section has an axis of symmetry in a plane along the length of the beam. iii) The material of the beam obeys Hooke's law. iv) The transverse sections which are plane before bending remain plane after bending also. v) Each layer of the beam is free to expand or contract, independent of the layer above or below it. vi) The Young's modulus is same both in tension and compression. Derivation for stresses in curved beam Nomenclature used in curved beam C i =Distance from neutral axis to inner radius of curved beam C o =Distance from neutral axis to outer radius of curved beam C 1 =Distance from centroidal axis to inner radius of curved beam C 2 = Distance from centroidal axis to outer radius of curved beam F = Applied load or Force A = Area of cross section L = Distance from force to centroidal axis at critical section σ d = Direct stress σ bi = Bending stress at the inner fiber σ bo = Bending stress at the outer fiber σ ri = Combined stress at the inner fiber σ ro = Combined stress at the outer fiber
2 F CA NA c 1 c 2 c i co e F F M b F M b r i r n C L rc r o Stresses in curved beam M b = Applied Bending Moment r i = Inner radius of curved beam r o = Outer radius of curved beam r c = Radius of centroidal axis r n = Radius of neutral axis C L = Center of curvature In the above figure the lines 'ab' and 'cd' represent two such planes before bending. i.e., when there are no stresses induced. When a bending moment 'Mb' is applied to the beam the plane cd rotates with respect to 'ab' through an angle 'dθ' to the position 'fg' and the outer fibers are shortened while the inner fibers are elongated. The original length of a strip at a distance 'y' from the neutral axis is (y + rn)θ. It is shortened by the amount ydθ and the stress in this fiber is, σ = E.e Where σ = stress, e = strain and E = Young's Modulus
3 We know, stress σ = E.e We know, stress e Ѳ Ѳ i.e., σ = E θ θ... (i) Since the fiber is shortened, the stress induced in this fiber is compressive stress and hence negative sign. The load on the strip having thickness dy and cross sectional area da is 'df' i.e., df = σda = θ θ da From the condition of equilibrium, the summation of forces over the whole crosssection is zero and the summation of the moments due to these forces is equal to the applied bending moment. Let M b = Applied Bending Moment r i = Inner radius of curved beam r o = Outer radius of curved beam
4 r c = Radius of centroidal axis r n = Radius of neutral axis C L = Centre line of curvature Summation of forces over the whole cross section i.e. df 0 θ θ =0 As θ θ is not equal to zero, = 0... (ii) The neutral axis radius 'rn' can be determined from the above equation. If the moments are taken about the neutral axis, M b = ydf Substituting the value of df, we get M b = θ θ da = θ θ y da = θ θ yda 0 Since yda represents the statical moment of area, it may be replaced by A.e., the product of total area A and the distance 'e' from the centroidal axis to the neutral axis.
5 M b = θ θ A.e... (iii) From equation (i) θ = σ θ Substituting in equation (iii) M b = σ. A. e. σ =... (iv) This is the general equation for the stress in a fiber at a distance 'y' from neutral axis. At the outer fiber, y = c o Bending stress at the outer fiber σ bo i.e., σ bo = ( rn + co = ro)... (v) Where co = Distance from neutral axis to outer fiber. It is compressive stress and hence negative sign. At the inner fiber, y = ci Bending stress at the inner fiber σ bi = i.e., σ bi = ( rn ci = ri)... (vi) Where ci = Distance from neutral axis to inner fiber. It is tensile stress and hence positive sign.
6 Difference between a straight beam and a curved beam Sl.no straight beam curved beam 1 In Straight beams the neutral In case of curved beams the axis of the section coincides neutral axis of the section is with its centroidal axis and the shifted towards the center of stress distribution in the beam curvature of the beam causing is linear. a nonlinear stress distribution.
7 2 3 Neutral axis and centroidal Neutral axis is shifted axis coincides towards the least centre of curvature Location of the neutral axis By considering a rectangular cross section
8 Centroidal and Neutral Axis of Typical Section of Curved Beams
9
10 Why stress concentration occur at inner side or concave side of curved beam Consider the elements of the curved beam lying between two axial planes ab and cd separated by angle θ. Let fg is the final position of the plane cd having rotated through an angle dθ about neutral axis. Consider two fibers symmetrically located on either side of the neutral axis. Deformation in both the fibers is same and equal to ydθ.
11 Since length of inner element is smaller than outer element, the strain induced and stress developed are higher for inner element than outer element as shown. Thus stress concentration occur at inner side or concave side of curved beam The actual magnitude of stress in the curved beam would be influenced by magnitude of curvature However, for a general comparison the stress distribution for the same section and same bending moment for the straight beam and the curved beam are shown in figure. It is observed that the neutral axis shifts inwards for the curved beam. This results in stress to be zero at this position, rather than at the centre of gravity. In cases where holes and discontinuities are provided in the beam, they should be preferably placed at the neutral axis, rather than that at the centroidal axis. This results in a better stress distribution. Example: For numerical analysis, consider the depth of the section ass twice the inner radius.
12 For a straight beam: Inner most fiber: Outer most fiber: For curved beam: h=2r i e = r c  r n = h 0.910h = h c o = r o  r n = h 0.910h = 0590h c i = r n  r i = 0.910h  = 0.410h
13 Comparing the stresses at the inner most fiber based on (1) and (3), we observe that the stress at the inner most fiber in this case is: σ bci = 1.522σ BSi Thus the stress at the inner most fiber for this case is times greater than that for a straight beam. From the stress distribution it is observed that the maximum stress in a curved beam is higher than the straight beam. Comparing the stresses at the outer most fiber based on (2) and (4), we observe that the stress at the outer most fiber in this case is: σ bco = 1.522σ BSi Thus the stress at the inner most fiber for this case is times that for a straight beam. The curvatures thus introduce a non linear stress distribution. This is due to the change in force flow lines, resulting in stress concentration on the inner side. To achieve a better stress distribution, section where the centroidal axis is the shifted towards the insides must be chosen, this tends to equalize the stress variation on the inside and outside fibers for a curved beam. Such sections are trapeziums, non symmetrical I section, and T sections. It should be noted that these sections should always be placed in a manner such that the centroidal axis is inwards. Problem no.1 Plot the stress distribution about section AB of the hook as shown in figure. Given data: r i = 50mm r o = 150mm F = 22X10 3 N b = 20mm h = = 100mm A = bh = 20X100 = 2000mm 2
Chapter 3. Load and Stress Analysis
Chapter 3 Load and Stress Analysis 2 Shear Force and Bending Moments in Beams Internal shear force V & bending moment M must ensure equilibrium Fig. 3 2 Sign Conventions for Bending and Shear Fig. 3 3
More informationPURE BENDING. If a simply supported beam carries two point loads of 10 kn as shown in the following figure, pure bending occurs at segment BC.
BENDING STRESS The effect of a bending moment applied to a crosssection of a beam is to induce a state of stress across that section. These stresses are known as bending stresses and they act normally
More informationLecture 15 Strain and stress in beams
Spring, 2019 ME 323 Mechanics of Materials Lecture 15 Strain and stress in beams Reading assignment: 6.1 6.2 News: Instructor: Prof. Marcial Gonzalez Last modified: 1/6/19 9:42:38 PM Beam theory (@ ME
More informationMechanics of Solids notes
Mechanics of Solids notes 1 UNIT II Pure Bending Loading restrictions: As we are aware of the fact internal reactions developed on any crosssection of a beam may consists of a resultant normal force,
More informationCHAPTER 6 BENDING Part 1
Ishik University / Sulaimani Civil Engineering Department Mechanics of Materials CE 211 CHAPTER 6 BENDING Part 11 CHAPTER 6 Bending Outlines of this chapter: 6.1. Chapter Objectives 6.2. Shear and
More informationSimulation of Geometrical CrossSection for Practical Purposes
Simulation of Geometrical CrossSection for Practical Purposes Bhasker R.S. 1, Prasad R. K. 2, Kumar V. 3, Prasad P. 4 123 Department of Mechanical Engineering, R.D. Engineering College, Ghaziabad, UP,
More informationAdvanced Structural Analysis EGF Section Properties and Bending
Advanced Structural Analysis EGF316 3. Section Properties and Bending 3.1 Loads in beams When we analyse beams, we need to consider various types of loads acting on them, for example, axial forces, shear
More informationConsider an elastic spring as shown in the Fig.2.4. When the spring is slowly
.3 Strain Energy Consider an elastic spring as shown in the Fig..4. When the spring is slowly pulled, it deflects by a small amount u 1. When the load is removed from the spring, it goes back to the original
More informationMechanics in Energy Resources Engineering  Chapter 5 Stresses in Beams (Basic topics)
Week 7, 14 March Mechanics in Energy Resources Engineering  Chapter 5 Stresses in Beams (Basic topics) KiBok Min, PhD Assistant Professor Energy Resources Engineering i Seoul National University Shear
More information6. Bending CHAPTER OBJECTIVES
CHAPTER OBJECTIVES Determine stress in members caused by bending Discuss how to establish shear and moment diagrams for a beam or shaft Determine largest shear and moment in a member, and specify where
More information[8] Bending and Shear Loading of Beams
[8] Bending and Shear Loading of Beams Page 1 of 28 [8] Bending and Shear Loading of Beams [8.1] Bending of Beams (will not be covered in class) [8.2] Bending Strain and Stress [8.3] Shear in Straight
More informationCHAPTER THREE SYMMETRIC BENDING OF CIRCLE PLATES
CHAPTER THREE SYMMETRIC BENDING OF CIRCLE PLATES * Governing equations in beam and plate bending ** Solution by superposition 1.1 From Beam Bending to Plate Bending 1.2 Governing Equations For Symmetric
More information4. BEAMS: CURVED, COMPOSITE, UNSYMMETRICAL
4. BEMS: CURVED, COMPOSITE, UNSYMMETRICL Discussions of beams in bending are usually limited to beams with at least one longitudinal plane of symmetry with the load applied in the plane of symmetry or
More informationMechanics of Structure
S.Y. Diploma : Sem. III [CE/CS/CR/CV] Mechanics of Structure Time: Hrs.] Prelim Question Paper Solution [Marks : 70 Q.1(a) Attempt any SIX of the following. [1] Q.1(a) Define moment of Inertia. State MI
More information3. BEAMS: STRAIN, STRESS, DEFLECTIONS
3. BEAMS: STRAIN, STRESS, DEFLECTIONS The beam, or flexural member, is frequently encountered in structures and machines, and its elementary stress analysis constitutes one of the more interesting facets
More informationSolution: The moment of inertia for the crosssection 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
More informationBeam Bending Stresses and Shear Stress
Beam Bending Stresses and Shear Stress Notation: A = name or area Aweb = area o the web o a wide lange section b = width o a rectangle = total width o material at a horizontal section c = largest distance
More informationSTRESS STRAIN AND DEFORMATION OF SOLIDS, STATES OF STRESS
1 UNIT I STRESS STRAIN AND DEFORMATION OF SOLIDS, STATES OF STRESS 1. Define: Stress When an external force acts on a body, it undergoes deformation. At the same time the body resists deformation. The
More 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 informationSub. Code:
Important Instructions to examiners: ) The answers should be examined by key words and not as wordtoword as given in the model answer scheme. ) The model answer and the answer written by candidate may
More informationChapter 3. Load and Stress Analysis. Lecture Slides
Lecture Slides Chapter 3 Load and Stress Analysis 2015 by McGraw Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner.
More informationENG2000 Chapter 7 Beams. ENG2000: R.I. Hornsey Beam: 1
ENG2000 Chapter 7 Beams ENG2000: R.I. Hornsey Beam: 1 Overview In this chapter, we consider the stresses and moments present in loaded beams shear stress and bending moment diagrams We will also look at
More informationSTRENGTH OF MATERIALSI. Unit1. Simple stresses and strains
STRENGTH OF MATERIALSI Unit1 Simple stresses and strains 1. What is the Principle of surveying 2. Define Magnetic, True & Arbitrary Meridians. 3. Mention different types of chains 4. Differentiate between
More informationNATIONAL PROGRAM ON TECHNOLOGY ENHANCED LEARNING (NPTEL) IIT MADRAS Offshore structures under special environmental loads including fireresistance
Week Eight: Advanced structural analyses Tutorial Eight Part A: Objective questions (5 marks) 1. theorem is used to derive deflection of curved beams with small initial curvature (Castigliano's theorem)
More informationChapter Objectives. Copyright 2011 Pearson Education South Asia Pte Ltd
Chapter Objectives To generalize the procedure by formulating equations that can be plotted so that they describe the internal shear and moment throughout a member. To use the relations between distributed
More informationMechanical Engineering Ph.D. Preliminary Qualifying Examination Solid Mechanics February 25, 2002
student personal identification (ID) number on each sheet. Do not write your name on any sheet. #1. A homogeneous, isotropic, linear elastic bar has rectangular cross sectional area A, modulus of elasticity
More informationSymmetric Bending of Beams
Symmetric Bending of Beams beam is any long structural member on which loads act perpendicular to the longitudinal axis. Learning objectives Understand the theory, its limitations and its applications
More informationCHAPTER 4: BENDING OF BEAMS
(74) CHAPTER 4: BENDING OF BEAMS This chapter will be devoted to the analysis of prismatic members subjected to equal and opposite couples M and M' acting in the same longitudinal plane. Such members are
More information7.4 The Elementary Beam Theory
7.4 The Elementary Beam Theory In this section, problems involving long and slender beams are addressed. s with pressure vessels, the geometry of the beam, and the specific type of loading which will be
More informationMECE 3321: Mechanics of Solids Chapter 6
MECE 3321: Mechanics of Solids Chapter 6 Samantha Ramirez Beams Beams are long straight members that carry loads perpendicular to their longitudinal axis Beams are classified by the way they are supported
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 informationLecture 5: Pure bending of beams
Lecture 5: Pure bending of beams Each end of an initiall straight, uniform beam is subjected to equal and opposite couples. The moment of the couples is denoted b (units of FL. t is shown in solid mechanics
More informationStrength of Materials Prof. S.K.Bhattacharya Dept. of Civil Engineering, I.I.T., Kharagpur Lecture No.26 Stresses in BeamsI
Strength of Materials Prof. S.K.Bhattacharya Dept. of Civil Engineering, I.I.T., Kharagpur Lecture No.26 Stresses in BeamsI Welcome to the first lesson of the 6th module which is on Stresses in Beams
More informationMechanics of Materials II. Chapter III. A review of the fundamental formulation of stress, strain, and deflection
Mechanics of Materials II Chapter III A review of the fundamental formulation of stress, strain, and deflection Outline Introduction Assumtions and limitations Axial loading Torsion of circular shafts
More information(Refer Slide Time: 01:00 01:01)
Strength of Materials Prof: S.K.Bhattacharya Department of Civil Engineering Indian institute of Technology Kharagpur Lecture no 27 Lecture Title: Stresses in Beams II Welcome to the second lesson of
More 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 informationComb resonator design (2)
Lecture 6: Comb resonator design () Intro Intro. to Mechanics of Materials School of Electrical l Engineering i and Computer Science, Seoul National University Nano/Micro Systems & Controls Laboratory
More informationMechanics 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
More informationMECHANICS OF MATERIALS. Analysis of Beams for Bending
MECHANICS OF MATERIALS Analysis of Beams for Bending By NUR FARHAYU ARIFFIN Faculty of Civil Engineering & Earth Resources Chapter Description Expected Outcomes Define the elastic deformation of an axially
More informationStrength of Materials Prof. Dr. Suraj Prakash Harsha Mechanical and Industrial Engineering Department Indian Institute of Technology, Roorkee
Strength of Materials Prof. Dr. Suraj Prakash Harsha Mechanical and Industrial Engineering Department Indian Institute of Technology, Roorkee Lecture  28 Hi, this is Dr. S. P. Harsha from Mechanical and
More informationSamantha Ramirez, MSE
Samantha Ramirez, MSE Centroids The centroid of an area refers to the point that defines the geometric center for the area. In cases where the area has an axis of symmetry, the centroid will lie along
More information1 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
More informationLECTURE 13 Strength of a Bar in Pure Bending
V. DEMENKO MECHNCS OF MTERLS 015 1 LECTURE 13 Strength of a Bar in Pure Bending Bending is a tpe of loading under which bending moments and also shear forces occur at cross sections of a rod. f the bending
More informationMechanics of Materials Primer
Mechanics of Materials rimer Notation: A = area (net = with holes, bearing = in contact, etc...) b = total width of material at a horizontal section d = diameter of a hole D = symbol for diameter E = modulus
More informationPDDC 1 st Semester Civil Engineering Department Assignments of Mechanics of Solids [ ] Introduction, Fundamentals of Statics
Page1 PDDC 1 st Semester Civil Engineering Department Assignments of Mechanics of Solids [2910601] Introduction, Fundamentals of Statics 1. Differentiate between Scalar and Vector quantity. Write S.I.
More informationChapter 6: CrossSectional Properties of Structural Members
Chapter 6: CrossSectional Properties of Structural Members Introduction Beam design requires the knowledge of the following. Material strengths (allowable stresses) Critical shear and moment values Cross
More informationME Final Exam. PROBLEM NO. 4 Part A (2 points max.) M (x) y. z (neutral axis) beam crosssec+on. 20 kip ft. 0.2 ft. 10 ft. 0.1 ft.
ME 323  Final Exam Name December 15, 2015 Instructor (circle) PROEM NO. 4 Part A (2 points max.) Krousgrill 11:30AM12:20PM Ghosh 2:303:20PM Gonzalez 12:301:20PM Zhao 4:305:20PM M (x) y 20 kip ft 0.2
More informationBEAM DEFLECTION THE ELASTIC CURVE
BEAM DEFLECTION Samantha Ramirez THE ELASTIC CURVE The deflection diagram of the longitudinal axis that passes through the centroid of each crosssectional area of a beam. Supports that apply a moment
More informationLab Exercise #5: Tension and Bending with Strain Gages
Lab Exercise #5: Tension and Bending with Strain Gages Prelab assignment: Yes No Goals: 1. To evaluate tension and bending stress models and Hooke s Law. a. σ = Mc/I and σ = P/A 2. To determine material
More informationROTATING RING. Volume of small element = Rdθbt if weight density of ring = ρ weight of small element = ρrbtdθ. Figure 1 Rotating ring
ROTATIONAL STRESSES INTRODUCTION High centrifugal forces are developed in machine components rotating at a high angular speed of the order of 100 to 500 revolutions per second (rps). High centrifugal force
More informationCHAPTER OBJECTIVES Use various methods to determine the deflection and slope at specific pts on beams and shafts: 2. Discontinuity functions
1. Deflections of Beams and Shafts CHAPTER OBJECTIVES Use various methods to determine the deflection and slope at specific pts on beams and shafts: 1. Integration method. Discontinuity functions 3. Method
More 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 information7 TRANSVERSE SHEAR transverse shear stress longitudinal shear stresses
7 TRANSVERSE SHEAR Before we develop a relationship that describes the shearstress distribution over the cross section of a beam, we will make some preliminary remarks regarding the way shear acts within
More informationProperties of Sections
ARCH 314 Structures I Test Primer Questions Dr.Ing. Peter von Buelow Properties of Sections 1. Select all that apply to the characteristics of the Center of Gravity: A) 1. The point about which the body
More informationPurpose of this Guide: To thoroughly prepare students for the exact types of problems that will be on Exam 3.
ES230 STRENGTH OF MTERILS Exam 3 Study Guide Exam 3: Wednesday, March 8 th inclass Updated 3/3/17 Purpose of this Guide: To thoroughly prepare students for the exact types of problems that will be on
More informationComb Resonator Design (2)
Lecture 6: Comb Resonator Design () Intro. to Mechanics of Materials Sh School of felectrical ti lengineering i and dcomputer Science, Si Seoul National University Nano/Micro Systems & Controls Laboratory
More informationDEPARTMENT OF CIVIL ENGINEERING
KINGS COLLEGE OF ENGINEERING DEPARTMENT OF CIVIL ENGINEERING SUBJECT: CE 2252 STRENGTH OF MATERIALS UNIT: I ENERGY METHODS 1. Define: Strain Energy When an elastic body is under the action of external
More informationUnit Workbook 1 Level 4 ENG U8 Mechanical Principles 2018 UniCourse Ltd. All Rights Reserved. Sample
Pearson BTEC Levels 4 Higher Nationals in Engineering (RQF) Unit 8: Mechanical Principles Unit Workbook 1 in a series of 4 for this unit Learning Outcome 1 Static Mechanical Systems Page 1 of 23 1.1 Shafts
More 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 informationPart 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
More informationMECHANICS OF MATERIALS Sample Problem 4.2
Sample Problem 4. SOLUTON: Based on the cross section geometry, calculate the location of the section centroid and moment of inertia. ya ( + Y Ad ) A A castiron machine part is acted upon by a knm couple.
More informationBending Stress. Sign convention. Centroid of an area
Bending Stress Sign convention The positive shear force and bending moments are as shown in the figure. Centroid of an area Figure 40: Sign convention followed. If the area can be divided into n parts
More informationUNSYMMETRICAL BENDING
UNSYMMETRICAL BENDING The general bending stress equation for elastic, homogeneous beams is given as (II.1) where Mx and My are the bending moments about the x and y centroidal axes, respectively. Ix and
More informationUNIT I Thin plate theory, Structural Instability:
UNIT I Thin plate theory, Structural Instability: Analysis of thin rectangular plates subject to bending, twisting, distributed transverse load, combined bending and inplane loading Thin plates having
More informationExample 3.7 Consider the undeformed configuration of a solid as shown in Figure 3.60.
162 3. The linear 3D elasticity mathematical model The 3D elasticity model is of great importance, since it is our highest order hierarchical model assuming linear elastic behavior. Therefore, it provides
More information7.6 Stress in symmetrical elastic beam transmitting both shear force and bending moment
7.6 Stress in symmetrical elastic beam transmitting both shear force and bending moment à It is more difficult to obtain an exact solution to this problem since the presence of the shear force means that
More informationCE6306 STRENGTH OF MATERIALS TWO MARK QUESTIONS WITH ANSWERS ACADEMIC YEAR
CE6306 STRENGTH OF MATERIALS TWO MARK QUESTIONS WITH ANSWERS ACADEMIC YEAR 20142015 UNIT  1 STRESS, STRAIN AND DEFORMATION OF SOLIDS PART A 1. Define tensile stress and tensile strain. The stress induced
More informationFlexure: Behavior and Nominal Strength of Beam Sections
4 5000 4000 (increased d ) (increased f (increased A s or f y ) c or b) Flexure: Behavior and Nominal Strength of Beam Sections Moment (kipin.) 3000 2000 1000 0 0 (basic) (A s 0.5A s ) 0.0005 0.001 0.0015
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 informationSamantha Ramirez, MSE. Stress. The intensity of the internal force acting on a specific plane (area) passing through a point. F 2
Samantha Ramirez, MSE Stress The intensity of the internal force acting on a specific plane (area) passing through a point. Δ ΔA Δ z Δ 1 2 ΔA Δ x Δ y ΔA is an infinitesimal size area with a uniform force
More information3D Elasticity Theory
3D lasticity Theory Many structural analysis problems are analysed using the theory of elasticity in which Hooke s law is used to enforce proportionality between stress and strain at any deformation level.
More informationChapter 4 Deflection and Stiffness
Chapter 4 Deflection and Stiffness Asst. Prof. Dr. Supakit Rooppakhun Chapter Outline Deflection and Stiffness 41 Spring Rates 42 Tension, Compression, and Torsion 43 Deflection Due to Bending 44 Beam
More informationProblem d d d B C E D. 0.8d. Additional lecturebook examples 29 ME 323
Problem 9.1 Two beam segments, AC and CD, are connected together at C by a frictionless pin. Segment CD is cantilevered from a rigid support at D, and segment AC has a roller support at A. a) Determine
More informationSEMM Mechanics PhD Preliminary Exam Spring Consider a twodimensional rigid motion, whose displacement field is given by
SEMM Mechanics PhD Preliminary Exam Spring 2014 1. Consider a twodimensional rigid motion, whose displacement field is given by u(x) = [cos(β)x 1 + sin(β)x 2 X 1 ]e 1 + [ sin(β)x 1 + cos(β)x 2 X 2 ]e
More informationPERIYAR CENTENARY POLYTECHNIC COLLEGE PERIYAR NAGAR  VALLAM THANJAVUR. DEPARTMENT OF MECHANICAL ENGINEERING QUESTION BANK
PERIYAR CENTENARY POLYTECHNIC COLLEGE PERIYAR NAGAR  VALLAM  613 403  THANJAVUR. DEPARTMENT OF MECHANICAL ENGINEERING QUESTION BANK Sub : Strength of Materials Year / Sem: II / III Sub Code : MEB 310
More informationBasic Energy Principles in Stiffness Analysis
Basic Energy Principles in Stiffness Analysis StressStrain Relations The application of any theory requires knowledge of the physical properties of the material(s) comprising the structure. We are limiting
More informationOUTCOME 1  TUTORIAL 3 BENDING MOMENTS. You should judge your progress by completing the self assessment exercises. CONTENTS
Unit 2: Unit code: QCF Level: 4 Credit value: 15 Engineering Science L/601/1404 OUTCOME 1  TUTORIAL 3 BENDING MOMENTS 1. Be able to determine the behavioural characteristics of elements of static engineering
More information: APPLIED MECHANICS & STRENGTH OF MATERIALS COURSE CODE : 4021 COURSE CATEGORY : A PERIODS/ WEEK : 5 PERIODS/ SEMESTER : 75 CREDIT : 5 TIME SCHEDULE
COURSE TITLE : APPLIED MECHANICS & STRENGTH OF MATERIALS COURSE CODE : 4021 COURSE CATEGORY : A PERIODS/ WEEK : 5 PERIODS/ SEMESTER : 75 CREDIT : 5 TIME SCHEDULE MODULE TOPIC PERIODS 1 Simple stresses
More informationSTRESSES WITHIN CURVED LAMINATED BEAMS OF DOUGLASFIR
UNITED STATES DEPARTMENT OF AGRICULTURE. FOREST SERVICE  FOREST PRODUCTS LABORATORY  MADISON, WIS. STRESSES WITHIN CURVED LAMINATED BEAMS OF DOUGLASFIR NOVEMBER 1963 FPL020 STRESSES WITHIN CURVED LAMINATED
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 informationName (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
More informationCOURSE TITLE : THEORY OF STRUCTURES I COURSE CODE : 3013 COURSE CATEGORY : B PERIODS/WEEK : 6 PERIODS/SEMESTER: 90 CREDITS : 6
COURSE TITLE : THEORY OF STRUCTURES I COURSE CODE : 0 COURSE CATEGORY : B PERIODS/WEEK : 6 PERIODS/SEMESTER: 90 CREDITS : 6 TIME SCHEDULE Module Topics Period Moment of forces Support reactions Centre
More information14. *14.8 CASTIGLIANO S THEOREM
*14.8 CASTIGLIANO S THEOREM Consider a body of arbitrary shape subjected to a series of n forces P 1, P 2, P n. Since external work done by forces is equal to internal strain energy stored in body, by
More informationDESIGN AND APPLICATION
III. 3.1 INTRODUCTION. From the foregoing sections on contact theory and material properties we can make a list of what properties an ideal contact material would possess. (1) High electrical conductivity
More informationMechanical Design in Optical Engineering
OPTI Buckling Buckling and Stability: As we learned in the previous lectures, structures may fail in a variety of ways, depending on the materials, load and support conditions. We had two primary concerns:
More informationDECLARATION. Supervised by: Prof Stephen Mutuli
DECLARATION The work presented in this project is the original work, which to the best of our knowledge has never been produced and presented elsewhere for academic purposes... EYSIMGOBANAY K. J F18/1857/006
More informationMECHANICS OF MATERIALS
GE SI CHAPTER 3 MECHANICS OF MATERIALS Ferdinand P. Beer E. Russell Johnston, Jr. John T. DeWolf David F. Mazurek Torsion Lecture Notes: J. Walt Oler Texas Tech University Torsional Loads on Circular Shafts
More informationInitial Stress Calculations
Initial Stress Calculations The following are the initial hand stress calculations conducted during the early stages of the design process. Therefore, some of the material properties as well as dimensions
More informationME311 Machine Design
ME311 Machine Design Lecture : Materials; Stress & Strain; Power Transmission W Dornfeld 13Sep018 airfield University School of Engineering StressStrain Curve for Ductile Material Ultimate Tensile racture
More informationMechanics 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 informationAERO 214. Lab II. Measurement of elastic moduli using bending of beams and torsion of bars
AERO 214 Lab II. Measurement of elastic moduli using bending of beams and torsion of bars BENDING EXPERIMENT Introduction Flexural properties of materials are of interest to engineers in many different
More informationCH. 4 BEAMS & COLUMNS
CH. 4 BEAMS & COLUMNS BEAMS Beams Basic theory of bending: internal resisting moment at any point in a beam must equal the bending moments produced by the external loads on the beam Rx = Cc + Tt  If the
More informationStrength of Materials Prof: S.K.Bhattacharya Dept of Civil Engineering, IIT, Kharagpur Lecture no 28 Stresses in Beams III
Strength of Materials Prof: S.K.Bhattacharya Dept of Civil Engineering, IIT, Kharagpur Lecture no 28 Stresses in Beams III Welcome to the 3 rd lesson of the 6 th module which is on Stresses in Beams part
More informationSolution: The strain in the bar is: ANS: E =6.37 GPa Poison s ration for the material is:
Problem 10.4 A prismatic bar with length L 6m and a circular cross section with diameter D 0.0 m is subjected to 0kN compressive forces at its ends. The length and diameter of the deformed bar are measured
More informationChapter 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
More informationSAULTCOLLEGE of AppliedArtsand Technology SaultSte. Marie COURSEOUTLINE
SAULTCOLLEGE of AppliedArtsand Technology SaultSte. Marie COURSEOUTLINE STRENGTH OF ~1ATERIALS MCH 1033 revised June 1981 by W.J. Adolph  STRENGHT OF MATERIALS MCH 1033 To'Cic Periods Tooic Description
More informationMECHANICS OF MATERIALS
2009 The McGrawHill Companies, Inc. All rights reserved. Fifth SI Edition CHAPTER 3 MECHANICS OF MATERIALS Ferdinand P. Beer E. Russell Johnston, Jr. John T. DeWolf David F. Mazurek Torsion Lecture Notes:
More informationSTANDARD 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
More information2012 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 ~~~~~~~~~~~~~~~~~~~~~~
More information