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.


 Rosaline French
 1 years ago
 Views:
Transcription
1 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 to the plane of the crosssection. 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. 10 kn 10 kn A B C D L L Shear force 10 kn Bending moment B C 10 kn B PL C Page 61
2 The above beam segment BC is subject to a pure sagging moment. The beam segment will bend into the shape shown in the following figures in which the upper surface is concave and the lower convex. It can be seen that the upper longitudinal fibres of the beam are compressed while the lower fibres are stretched. It follows that between these two extremes there is a fibre that remains unchanged in length. Thus the direct stress varies through the depth of the beam from compression in the upper fibres to tension in the lower. Clearly the direct stress is zero at the fibre which does not change in length. The surface, which contains this fibre and runs through the length of the beam, is known as the NEUTRAL SURFACE or NEUTRAL PLANE; the line of intersection of the neutral surface and any crosssection of the beam is termed the NEUTRAL AXIS. Neutral Axis: It is the axis of the crosssection of a beam at which both bending strain and bending stress are zero. The neutral axis passes through the centroid of the crosssection. Page 62
3 Deformation Geometry for a symmetrical beam in pure bending Cross sections of a beam that are plane and normal to the axis of the beam before bending remain plane and normal to the axis after bending. Page 63
4 SIMPLE THEORY OF BENDING Assumptions: 1. Beams are initially straight. 2. The material is homogenous and isotropic (i.e. its mechanical properties are the same in all directions.) 3. Stressstrain relationship is linear and elastic. 4. Young s modulus is the same in tension as in compression. 5. Sections are symmetrical about the plane of bending. 6. Sections which are plane before bending remain plane after bending. Implications of the last assumption: 1. Each section rotates during bending about a neutral axis. 2. The distribution of strain across the section is linear, with zero strain at the neutral axis. 3. The section is divided into tensile and compressive zones separated by a neutral surface. The theory gives very accurate results for stresses and deformations for most practical beams provided that deformations are small. Page 64
5 Bending Stresses in Beams Basic Assumption: Plane sections through a beam taken normal to its axis remain plane after the beam is subject to bending. Result 1: The normal strain varies along the beam depth linearly with the distance y. Result 2: (Assuming Linear Elasticity, by using Hooke s Law) The normal stress varies along the beam depth linearly with the distance y. Page 65
6 Result 3 : For the top and bottom edges of the section, one would be in tension while the other would be in compression. A plane of zero deformation and zero bending stresses (Neutral Axis plane) exists between the two. Page 66
7 Result 4 : (From considerations of equilibrium, it can be shown that :) The Neutral Axis passes through the Centroid of the section. Result 5 : The stress and strain varies linearly from zero at the Neutral Axis to their absolute maximum values at the largest value of y. Page 67
8 Result 6: The elastic Flexure formula for beam bending is as follows: The bending stress σ x at a distance y from the Neutral Axis is given by: σ x = My/I where M = Bending Moment I = Moment of inertia of the section (about its centroidal axis) and the Maximum normal stress σ max is given by: σ max = Mc/I where c = y max Use of the flexure formula The method of solving any beam stress problem involves the following steps: 1. Determine the maximum bending moment on the beam by drawing the shear and bending moment diagrams. 2. Locate the centroid of the cross section of the beam. 3. Compute the moment of inertia of the cross section with respect to its centroidal axis. 4. Compute the distance c from the centroid axis to the top or bottom of the beam, whichever is greater. 5. Compute the stress from the flexural formula, σ max = Mc/I Page 68
9 Example 1 A simply supported beam is subject a point load of 1500 N at the midspan of the beam as shown in the following figure. The cross section of the beam is a rectangular 100 mm high and 25 mm wide. Calculate the maximum stresses due to bending N Solution 1.7 m 1.7 m Step 1 The maximum bending moment occurs at the midspan of the beam. M = 750 * 1.7 = 1275 Nm Step 2 The centroid of the rectangular section is at the intersection of its two axes of symmetry. Step 3 For the rectangular section, Step 4 c = 50 mm I = 25(100) 3 /12 = 2.08 x 10 6 mm 4 Step 5 The maximum tensile and compressive stresses due to bending are: σ max, = Mc/I = 1275 x 10 3 (50)/ 2.08 x 10 6 = 30.6 N/mm 2 or 30.6 MPa Page 69
10 Example 2 A simply supported Ibeam carries a uniformly distributed load of 5 kn/m over the entire span of 6 m. The cross section of the beam is shown in the following figure. Determine the bending stresses that acts at points B and D, located at the midspan of the beam. 115 mm 115 mm 20 mm B 20 mm 300 mm D 20 mm Solution Step 1 The supported reaction = 5 * 6 / 2 = 15 kn Consider the following free body diagram. 5 kn/m H X M X 15 kn 3 m V X The bending moment occurs at the midspan of the beam. M = 15 * 3 5 * 3 * 1.5 = 22.5 knm Page 610
11 Step 2 The centroid of the Isection is at the intersection of its two axes of symmetry. Step 3 For the Isection, Moment of inertia, I = 250(340) 3 /12 2*115(300) 3 /12 = 3.01 x 10 8 mm 4 Step 4 At point B, y b = 150 mm At point D, y d = 170 mm Step 5 The compressive stress due to bending at point B is: σ b, = M y b /I = 22.5 x 10 6 * 150 / 3.01 x 10 8 = 11.2 N/mm 2 or 11.2 MPa The tensile stress due to bending at point D is: σ d, = M y d /I = 22.5 x 10 6 * 170 / 3.01 x 10 8 = 12.7 N/mm 2 or 12.7 MPa The two dimensional view of the stress distribution is shown in the following figure. B D Page 611
12 NONSYMMETRICAL SECTIONS UNDER BENDING The critical difference between the nonsymmetrical section and symmetrical section under bending is that in a nonsymmetrical section, such as a T beam or triangular shape beam, the location of the centroid is no longer obvious and is usually never at the midheight of the section. In the T beam, the centroid is located near the top flange of the member. Deformations and bending stresses in the member still vary linearly in the member and are proportional to the distance from the neutral axis of the member. This implies that the stress levels at the top and bottom of the beam are no longer equal as they typically are in symmetrical sections. The stresses are greater at the bottom of the beam than they are at the top because of the larger y distance. The two and three dimensional views of bending stress distribution in a T beam are shown in the following figures. Page 612
13 Page 613
14 SECTION MODULUS The maximum tensile and compressive stresses in the beam occur at points located farthest from the neutral axis. Let us denote by c 1 and c 2 the distances from the neutral axis to the extreme elements in the positive and negative y directions, respectively. Then the maximum normal stresses: σ 1 = M c 1 /I = M / Z 1 σ 2 = M c 2 /I = M / Z 2 in which, Z 1 = I / c 1 Z 2 = I / c 2 The quantities Z 1 are Z 2 are known as the section moduli of the cross sectional area. We see that a section modulus has dimensions of length to the third power. Stress distribution on a nonsymmetrical section Page 614
15 If the cross section is symmetric with respect to the z axis, then c 1 = c 2 = c, and the maximum tensile and compressive stresses are equal numerically: σ 1 = σ 2 = M c /I = M / Z in which Z = I / c is the section modulus. For a beam of rectangular cross section with width b and height h, the moment of inertia and section modulus are I = bh 3 /12 Z = bh 2 /6 Stress distribution on a symmetrical section Page 615
16 Example 3 A simply supported beam of span length of 8 m is subject to a uniformly distributed load of 2 kn/m over the entire span and a point load of 8 kn at 5m from the left support of the beam as shown in the following figure. Determine the maximum tensile and compressive stresses in the beam due to bending. 8 kn A 2 kn/m B C H A V A V C 5m 3m 700 mm 220 mm Cross section of the beam Page 616
17 Solution The shear force and bending moment diagrams for the beam are shown in the following figures. 8 kn A 2 kn/m C B 11 kn 13 kn 5m 3m +ve 11 A B Shear Force (kn) C A +ve B C Bending Moment (knm) Page 617
18 Method 1 : use section modulus for calculations Section modulus of the crosssectional area, Z = bh 2 /6 = 220*700 2 /6 =1.8 x 10 7 mm 3 Maximum bending tensile and compressive stresses, σ = M max / Z = 30 x 10 6 /1.8 x 10 7 = 1.67 N/mm 2 Method 2 : use moment of inertia for calculations Moment inertia of the crosssectional area, I = bh 3 /12 = 220*700 3 /12 =6.29 x 10 9 mm 4 Maximum bending tensile and compressive stresses, σ = M max c/ I = 30 x 10 6 * 350/6.29 x 10 9 = 1.67 N/mm 2 Page 618
19 Example 4 A simple supported beam with a span of 4 m supports a uniformly distribution load w. The cross section of the beam is shown in the following figure. If the allowable bending stress is 70 MPa, find the allowable uniform load w. 50 mm 50 mm 50 mm 50 mm 300 mm 225 mm Solution The maximum bending moment, M max = wl 2 /8 = w * /8 = 2 x 10 6 w Nmm Moment inertia of the beam section, I = 225*300 3 /12125*200 3 /12 = x 10 6 mm 4 The section modulus of the beam section, Z = x 10 6 /150 = x 10 6 mm 3 Page 619
20 From the bending stress formula, M max = σ Z 2 x 10 6 w = 70 * x 10 6 w = N/mm w = kn/m Example 5 A simply supported Tbeam shown in the following figure carries a uniformly distributed load of 1 kn/m over the entire span of 6 m. Calculate the maximum bending stresses induced in the beam. 120 mm Centroidal Axis 40 mm 100 mm 120 mm Page 620
21 Solution The maximum bending moment, M max = 1*6 2 /8 = 4.5 knm The moment inertia of beam, I = 120(40) 3 / *40*( ) (120) 3 / *120*(10060) 2 = 2.18 x 10 7 mm 4 The maximum tensile stress in the bottom fibre, σ = M c 2 /I = 4.5 x 10 6 *100/2.18 x 10 7 = N/mm 2 The maximum compressive stress in the top fibre, σ = M c 1 /I = 4.5 x 10 6 *60/2.18 x 10 7 = 12.4 N/mm 2 Page 621
22 Example 6 A Tbeam is loaded as shown in the following figure. Calculate the maximum bending stresses induced in the beam. 10 kn 20 kn 4 kn/m A B C D E H B VB V D 2m 2m 4m 2m 120 mm Centroidal Axis 40 mm 100 mm 120 mm Page 622
23 Solution The shear force and bending moment diagrams for the beam are shown in the following figures. 10 kn 20 kn 4 kn/m A B C D E A B C D Shear Force (kn) E 0 10 A 120 B C 8 D 0 E Bending Moment (knm) Page 623
24 The moment inertia of beam, I = 120(40) 3 / *40*( ) (120) 3 / *120*(10060) 2 = 2.18 x 10 7 mm 4 When M = 20kNm at point B, The maximum tensile stress in the top fibre, σ T = M c 1 /I = 20 x 10 6 *60/2.18 x 10 7 = 55 N/mm 2 The maximum compressive stress in the bottom fibre, σ C = M c 2 /I = 20 x 10 6 *100/2.18 x 10 7 = 91.7 N/mm 2 When M = 26.7 Nm at point C, The maximum tensile stress in the bottom fibre, σ T = M c 2 /I = 26.7 x 10 6 *100/2.18 x 10 7 = N/mm 2 The maximum compressive stress in the top fibre, σ C = M c 1 /I = 26.7 x 10 6 *60/2.18 x 10 7 = 73.5 N/mm 2 Therefore, the maximum tensile stress and compressive stress are N/mm 2 and 91.7 N/mm 2 respectively. Page 624
25 PROBLEMS for bending stress Page 625
26 Page 626
Chapter 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 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 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 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 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 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 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 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 informationUNIT III DEFLECTION OF BEAMS 1. What are the methods for finding out the slope and deflection at a section? The important methods used for finding out the slope and deflection at a section in a loaded
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 informationStress Analysis Lecture 4 ME 276 Spring Dr./ Ahmed Mohamed Nagib Elmekawy
Stress Analysis Lecture 4 ME 76 Spring 017018 Dr./ Ahmed Mohamed Nagib Elmekawy Shear and Moment Diagrams Beam Sign Convention The positive directions are as follows: The internal shear force causes a
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 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 informationChapter 3. Load and Stress Analysis
Chapter 3 Load and Stress Analysis 2 Shear Force and Bending Moments in Beams Internal shear force V & bending moment M must ensure equilibrium Fig. 3 2 Sign Conventions for Bending and Shear Fig. 3 3
More informationCIVIL 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 XX and YY of an unequal angle section 125 mm 75 mm 10 mm as shown in figure 2) Determine
More informationStresses in Curved Beam
Stresses in Curved Beam Consider a curved beam subjected to bending moment M b as shown in the figure. The distribution of stress in curved flexural member is determined by using the following assumptions:
More 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 informationCHAPTER 4. Stresses in Beams
CHAPTER 4 Stresses in Beams Problem 1. A rolled steel joint (RSJ) of section has top and bottom flanges 150 mm 5 mm and web of size 00 mm 1 mm. t is used as a simply supported beam over a span of 4 m
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 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 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 informationQUESTION BANK SEMESTER: III SUBJECT NAME: MECHANICS OF SOLIDS
QUESTION BANK SEMESTER: III SUBJECT NAME: MECHANICS OF SOLIDS UNIT 1 STRESS AND STRAIN PART A (2 Marks) 1. Define longitudinal strain and lateral strain. 2. State Hooke s law. 3. Define modular ratio,
More informationBEAM A horizontal or inclined structural member that is designed to resist forces acting to its axis is called a beam
BEM horizontal or inclined structural member that is designed to resist forces acting to its axis is called a beam INTERNL FORCES IN BEM Whether or not a beam will break, depend on the internal resistances
More informationQUESTION BANK DEPARTMENT: CIVIL SEMESTER: III SUBJECT CODE: CE2201 SUBJECT NAME: MECHANICS OF SOLIDS UNIT 1 STRESS AND STRAIN PART A
DEPARTMENT: CIVIL SUBJECT CODE: CE2201 QUESTION BANK SEMESTER: III SUBJECT NAME: MECHANICS OF SOLIDS UNIT 1 STRESS AND STRAIN PART A (2 Marks) 1. Define longitudinal strain and lateral strain. 2. State
More 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 informationKINGS COLLEGE OF ENGINEERING DEPARTMENT OF MECHANICAL ENGINEERING QUESTION BANK. Subject code/name: ME2254/STRENGTH OF MATERIALS Year/Sem:II / IV
KINGS COLLEGE OF ENGINEERING DEPARTMENT OF MECHANICAL ENGINEERING QUESTION BANK Subject code/name: ME2254/STRENGTH OF MATERIALS Year/Sem:II / IV UNIT I STRESS, STRAIN DEFORMATION OF SOLIDS PART A (2 MARKS)
More 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 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 information2. Determine the deflection at C of the beam given in fig below. Use principal of virtual work. W L/2 B A L C
CE1259, Strength of Materials UNIT I STRESS, STRAIN DEFORMATION OF SOLIDS Part A 1. Define strain energy density. 2. State Maxwell s reciprocal theorem. 3. Define proof resilience. 4. State Castigliano
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 informationPrestressed concrete = Precompression concrete Precompression stresses is applied at the place when tensile stress occur Concrete weak in tension
Prestressed concrete = Precompression concrete Precompression stresses is applied at the place when tensile stress occur Concrete weak in tension but strong in compression Steel tendon is first stressed
More informationENGINEERING COUNCIL DIPLOMA LEVEL MECHANICS OF SOLIDS D209 TUTORIAL 3  SHEAR FORCE AND BENDING MOMENTS IN BEAMS
ENGINEERING COUNCIL DIPLOMA LEVEL MECHANICS OF SOLIDS D209 TUTORIAL 3  SHEAR FORCE AND BENDING MOMENTS IN BEAMS You should judge your progress by completing the self assessment exercises. On completion
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 informationmportant nstructions 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 informationDESIGN OF BEAMS AND SHAFTS
DESIGN OF EAMS AND SHAFTS! asis for eam Design! Stress Variations Throughout a Prismatic eam! Design of pristmatic beams! Steel beams! Wooden beams! Design of Shaft! ombined bending! Torsion 1 asis for
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 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 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 informationStructural Analysis I Chapter 4  Torsion TORSION
ORSION orsional stress results from the action of torsional or twisting moments acting about the longitudinal axis of a shaft. he effect of the application of a torsional moment, combined with appropriate
More informationFIXED BEAMS IN BENDING
FIXED BEAMS IN BENDING INTRODUCTION Fixed or builtin beams are commonly used in building construction because they possess high rigidity in comparison to simply supported beams. When a simply supported
More informationThis procedure covers the determination of the moment of inertia about the neutral axis.
327 Sample Problems Problem 16.1 The moment of inertia about the neutral axis for the Tbeam shown is most nearly (A) 36 in 4 (C) 236 in 4 (B) 136 in 4 (D) 736 in 4 This procedure covers the determination
More informationName :. Roll No. :... Invigilator s Signature :.. CS/B.TECH (CENEW)/SEM3/CE301/ 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
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 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 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 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 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 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 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 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 information3 Hours/100 Marks Seat No.
*17304* 17304 14115 3 Hours/100 Marks Seat No. Instructions : (1) All questions are compulsory. (2) Illustrate your answers with neat sketches wherever necessary. (3) Figures to the right indicate full
More informationBy Dr. Mohammed Ramidh
Engineering Materials Design Lecture.6 the design of beams By Dr. Mohammed Ramidh 6.1 INTRODUCTION Finding the shear forces and bending moments is an essential step in the design of any beam. we usually
More informationCHAPTER 6: Shearing Stresses in Beams
(130) CHAPTER 6: Shearing Stresses in Beams When a beam is in pure bending, the only stress resultants are the bending moments and the only stresses are the normal stresses acting on the cross sections.
More informationSN 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
More informationME 176 Final Exam, Fall 1995
ME 176 Final Exam, Fall 1995 Saturday, December 16, 12:30 3:30 PM, 1995. Answer all questions. Please write all answers in the space provided. If you need additional space, write on the back sides. Indicate
More informationHomework No. 1 MAE/CE 459/559 John A. Gilbert, Ph.D. Fall 2004
Homework No. 1 MAE/CE 459/559 John A. Gilbert, Ph.D. 1. A beam is loaded as shown. The dimensions of the cross section appear in the insert. the figure. Draw a complete free body diagram showing an equivalent
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 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 informationMARKS DISTRIBUTION AS PER CHAPTER (QUESTION ASKED IN GTU EXAM) Name Of Chapter. Applications of. Friction. Centroid & Moment.
Introduction Fundamentals of statics Applications of fundamentals of statics Friction Centroid & Moment of inertia Simple Stresses & Strain Stresses in Beam Torsion Principle Stresses DEPARTMENT OF CIVIL
More 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 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 informationJUT!SI I I I TO BE RETURNED AT THE END OF EXAMINATION. THIS PAPER MUST NOT BE REMOVED FROM THE EXAM CENTRE. SURNAME: FIRST NAME: STUDENT NUMBER:
JUT!SI I I I TO BE RETURNED AT THE END OF EXAMINATION. THIS PAPER MUST NOT BE REMOVED FROM THE EXAM CENTRE. SURNAME: FIRST NAME: STUDENT NUMBER: COURSE: Tutor's name: Tutorial class day & time: SPRING
More informationUNIVERSITY 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
More informationUNIVERSITY OF BOLTON SCHOOL OF ENGINEERING. BEng (HONS) CIVIL ENGINEERING SEMESTER 1 EXAMINATION 2016/2017 MATHEMATICS & STRUCTURAL ANALYSIS
TW21 UNIVERSITY OF BOLTON SCHOOL OF ENGINEERING BEng (HONS) CIVIL ENGINEERING SEMESTER 1 EXAMINATION 2016/2017 MATHEMATICS & STRUCTURAL ANALYSIS MODULE NO: CIE4011 Date: Wednesday 11 th January 2017 Time:
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 informationSample 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:
More informationChapter 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
More informationChapter Objectives. Design a beam to resist both bendingand shear loads
Chapter Objectives Design a beam to resist both bendingand shear loads A Bridge Deck under Bending Action Castellated Beams Posttensioned Concrete Beam Lateral Distortion of a Beam Due to Lateral Load
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 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 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 informationR13. II B. Tech I Semester Regular Examinations, Jan MECHANICS OF SOLIDS (Com. to ME, AME, AE, MTE) PARTA
SET  1 II B. Tech I Semester Regular Examinations, Jan  2015 MECHANICS OF SOLIDS (Com. to ME, AME, AE, MTE) Time: 3 hours Max. Marks: 70 Note: 1. Question Paper consists of two parts (PartA and PartB)
More informationCHAPTER OBJECTIVES CHAPTER OUTLINE. 4. Axial Load
CHAPTER OBJECTIVES Determine deformation of axially loaded members Develop a method to find support reactions when it cannot be determined from euilibrium euations Analyze the effects of thermal stress
More 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 informationCHAPTER 5. Beam Theory
CHPTER 5. Beam Theory SangJoon Shin School of Mechanical and erospace Engineering Seoul National University ctive eroelasticity and Rotorcraft Lab. 5. The EulerBernoulli assumptions One of its dimensions
More informationPES Institute of Technology
PES Institute of Technology Bangalore south campus, Bangalore5460100 Department of Mechanical Engineering Faculty name : Madhu M Date: 29/06/2012 SEM : 3 rd A SEC Subject : MECHANICS OF MATERIALS Subject
More informationMECHANICS LAB AM 317 EXP 3 BENDING STRESS IN A BEAM
MECHANICS LAB AM 37 EXP 3 BENDING STRESS IN A BEAM I. OBJECTIVES I. To compare the experimentally determined stresses in a beam with those predicted from the simple beam theory (a.k.a. EulerBernoull beam
More informationUNITI 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
UNITI 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
More informationFlexural properties of polymers
A2 _EN BUDAPEST UNIVERSITY OF TECHNOLOGY AND ECONOMICS FACULTY OF MECHANICAL ENGINEERING DEPARTMENT OF POLYMER ENGINEERING Flexural properties of polymers BENDING TEST OF CHECK THE VALIDITY OF NOTE ON
More informationStressStrain Behavior
StressStrain Behavior 6.3 A specimen of aluminum having a rectangular cross section 10 mm 1.7 mm (0.4 in. 0.5 in.) is pulled in tension with 35,500 N (8000 lb f ) force, producing only elastic deformation.
More informationReg. 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
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 informationCIV100 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
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 informationProcedure for drawing shear force and bending moment diagram:
Procedure for drawing shear force and bending moment diagram: Preamble: The advantage of plotting a variation of shear force F and bending moment M in a beam as a function of x' measured from one end of
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 informationBE Semester I ( ) Question Bank (MECHANICS OF SOLIDS)
BE Semester I ( ) Question Bank (MECHANICS OF SOLIDS) All questions carry equal marks(10 marks) Q.1 (a) Write the SI units of following quantities and also mention whether it is scalar or vector: (i)
More information2 marks Questions and Answers
1. Define the term strain energy. A: Strain Energy of the elastic body is defined as the internal work done by the external load in deforming or straining the body. 2. Define the terms: Resilience and
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 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 informationNORMAL 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
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 informationLaboratory 4 Bending Test of Materials
Department of Materials and Metallurgical Engineering Bangladesh University of Engineering Technology, Dhaka MME 222 Materials Testing Sessional.50 Credits Laboratory 4 Bending Test of Materials. Objective
More informationDelhi Noida Bhopal Hyderabad Jaipur Lucknow Indore Pune Bhubaneswar Kolkata Patna Web: Ph:
Serial : IG1_CE_G_Concrete Structures_100818 Delhi Noida Bhopal Hyderabad Jaipur Lucknow Indore Pune Bhubaneswar Kolkata Patna Web: Email: info@madeeasy.in Ph: 011451461 CLASS TEST 01819 CIVIL ENGINEERING
More information= 50 ksi. The maximum beam deflection Δ max is not = R B. = 30 kips. Notes for Strength of Materials, ET 200
Notes for Strength of Materials, ET 00 Steel Six Easy Steps Steel beam design is about selecting the lightest steel beam that will support the load without exceeding the bending strength or shear strength
More informationEMA 3702 Mechanics & Materials Science (Mechanics of Materials) Chapter 5 Beams for Bending
MA 3702 Mechanics & Materials Science (Mechanics of Materials) Chapter 5 Beams for Bending Introduction esign of beams for mechanical or civil/structural applications Transverse loading in most cases for
More information7.3 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
More informationISHIK UNIVERSITY DEPARTMENT OF MECHATRONICS ENGINEERING
ISHIK UNIVERSITY DEPARTMENT OF MECHATRONICS ENGINEERING QUESTION BANK FOR THE MECHANICS OF MATERIALSI 1. A rod 150 cm long and of diameter 2.0 cm is subjected to an axial pull of 20 kn. If the modulus
More information