# CHAPTER THREE SYMMETRIC BENDING OF CIRCLE PLATES

Size: px
Start display at page:

## Transcription

1 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 Bending of Circular Plates, Some Typical Solutions 1.3 Solution by Superposition

2 1.1 FROM BEAM BENDING TO PLATE BENDING The similarity between the beam bending and plate bending (loads, deformation, basic assumption etc)

3 The governing equations for beam bending

4

5 The results are based on the following assumptions (they apply also to plates) (1) An unloaded beam is straight, and b and t are constant. (for plate, it is flat and t is const.) (2) The material is homogeneous, isotropic and linearly elastic. (3) Loading: distributed lateral force q, shear force and bending moments on the beam ends (or plate edges). Forces are z-parallel and moment vectors are z-perpendicular (4) The only stresses of significance are axial stress σ x in a beam, and xyparallel stresses σ x, σ y, τ xy in a plate. Each z = constant layer is assumed to be uniaxially stressed in a beam and biaxially stressed in a plate. (5) Transverse shear forces (Q in a beam, Q x and Q y in a plate) exist, but transverse shear strains are very small, so that line AB (CD) neutral axis (neutral surface) before and after loading. (6) w is small and, the z-direction deflection w of the neutral surface describes all about the deformation state.

6 Plate Bending Equations in X-Y-Z Coordinates

7 The displacement w = w(x,y) The strain-displacement relations are The equation for w(x,y) is When w = w(x) beam bending equation (before)

8 A simple case of plate bending ---- bending into a cylindrical surface FIGURE (a) Moments M x = -2c 1 D bend the central portion of the plate to a cylindrical surface. (b) Deformation of a cross section if edges y = ±b/2 are free. (c) Deformation of a cross section if b and t are of comparable size, as with a beam.

9 (1) In this case, the displacement field is w = w(x) = c 1 x 2 (c 1 is a constant) (2) The associated bending and twisting moments are This means that if edge moment M x is applied, moment M y will automatically arise due to Poisson effect, so plate will be in a biaxial stress state.

10 Boundary conditions for thin-plates FIGURE Illustration of different boundary conditions. The left is (a) clamped, (b) simply supported, and (c) free.

11 1.2 GOVERNING EQUATIONS FOR SYMMETRIC BENDING OF CIRCULAR PLATES, SOME TYPICAL SOLUTIONS The only unknown is the plate deflection w which depends on coordinates r only (w = w(r)) and determines all the forces, moments, stresses, strains and displacement in the plate. (1) Axial Symmetry σ r, σ θ, τ rθ, (τ rθ =0); M r, M θ, Q r, (Q θ =0)

12 (2) Hooke s law is expressed in terms of w, as follows (3) Bending moment and shear force This equation is very useful (b is the radius of a central hole, for solid plate, b = 0) (4) Governing equation

13 Boundary conditions - to determine the constants of integral of the governing equation (1) Along a clamped edge, (2) Along a simply supported edge, (3) Along a free edge, (4) At r = a,

14 Example solutions (1) Plate with Edge Moment From the relation: since Qr = 0 in this case (q = 0), the above equation yields the second and third integration yield, respectively, If the center does not displace, then w = 0 at r = 0 C3 = 0 At r = a, Mr = Mo, substituting into we find (This is bending to a spherical surface, we can check that M r = M θ = M o throughout the plate. Note that constant C3 represents only the rigid body translation along z axis)

15 (2) Plate with Concentrated Center Force and Clamped Edge In this case, substituting into equation and after three integration, we have Finally we have Discussion: This is due to the concentrated force which does not really exist, in reality, P is distributed as qda, then there is no such phenomena.

16 (3) Other loadings and boundary conditions FIGURE Simply supported plate with a central hole of radius b, uniformly load by pressure q o over region c < r < a. By using equation, we get inner and outer solutions, there are a total of 6 constants of integration, solved by 6 boundary conditions:

17 (4) Finite element solution Usually, no analytical solution is available if the loading lacks axial symmetry - then the problem can be solved numerically by finite element method. FIGURE Circular plate, clamped over half its boundary and loaded by a 100-N transverse force at one edge. Diameter = 100mm, thickness = 2.0mm, E = 200GPa, υ = Contours of stresses σ x, σ y, σ max on the upper surface,and of lateral deflection w, are numerically equidistant.

18 Solution by superposition Example: Determine the deflection w of a simply supported circular plate loaded by a concentrated center force P. (a) Solution (a) = Solution (b) + Solution (c) (b) Clamped edge, at r = a, (c) Plate with edge moment M o = +P/ 4 π, using the previous solution (note here the plate is simply supported, the original solution for w should be translated downward an amount equal to w at r = a), we have amount of translation, so that w = 0 at r = a Superposition results of (b) and (c), we obtain result for (a):

19 A short catalog of solutions:

20

21

22

23

24 Find the maximum deflection of the plate (r = a) = + Find the maximum flexural stress in the plate (r = a) case 6 case 7 = + case 6 case 5 (M=0) Find the center deflection in the plate (r = 0) = + case 5 & 6

### 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

### 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

### Module 4 : Deflection of Structures Lecture 4 : Strain Energy Method

Module 4 : Deflection of Structures Lecture 4 : Strain Energy Method Objectives In this course you will learn the following Deflection by strain energy method. Evaluation of strain energy in member under

### Lecture 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

### 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

### Mechanical Engineering Ph.D. Preliminary Qualifying Examination Solid Mechanics February 25, 2002

student personal identification (ID) number on each sheet. Do not write your name on any sheet. #1. A homogeneous, isotropic, linear elastic bar has rectangular cross sectional area A, modulus of elasticity

### 2. (a) Explain different types of wing structures. (b) Explain the advantages and disadvantages of different materials used for aircraft

Code No: 07A62102 R07 Set No. 2 III B.Tech II Semester Regular/Supplementary Examinations,May 2010 Aerospace Vehicle Structures -II Aeronautical Engineering Time: 3 hours Max Marks: 80 Answer any FIVE

### Advanced Structural Analysis EGF Section Properties and Bending

Advanced Structural Analysis EGF316 3. Section Properties and Bending 3.1 Loads in beams When we analyse beams, we need to consider various types of loads acting on them, for example, axial forces, shear

### 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

### Module 3 : Equilibrium of rods and plates Lecture 15 : Torsion of rods. The Lecture Contains: Torsion of Rods. Torsional Energy

The Lecture Contains: Torsion of Rods Torsional Energy This lecture is adopted from the following book 1. Theory of Elasticity, 3 rd edition by Landau and Lifshitz. Course of Theoretical Physics, vol-7

[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

### Chapter 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.

### Stresses 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:

### 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

### 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

### 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:

### 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

Torsion Torsion: Torsion refers to the twisting of a structural member that is loaded by couples (torque) that produce rotation about the member s longitudinal axis. In other words, the member is loaded

### BEAM 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 cross-sectional area of a beam. Supports that apply a moment

### 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.

### 7.6 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

### ME325 EXAM I (Sample)

ME35 EXAM I (Sample) NAME: NOTE: COSED BOOK, COSED NOTES. ONY A SINGE 8.5x" ORMUA SHEET IS AOWED. ADDITIONA INORMATION IS AVAIABE ON THE AST PAGE O THIS EXAM. DO YOUR WORK ON THE EXAM ONY (NO SCRATCH PAPER

### 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

### Nomenclature. Length of the panel between the supports. Width of the panel between the supports/ width of the beam

omenclature a b c f h Length of the panel between the supports Width of the panel between the supports/ width of the beam Sandwich beam/ panel core thickness Thickness of the panel face sheet Sandwich

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

STRENGTH OF MATERIALS-I Unit-1 Simple stresses and strains 1. What is the Principle of surveying 2. Define Magnetic, True & Arbitrary Meridians. 3. Mention different types of chains 4. Differentiate between

### 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

### PURE BENDING. If a simply supported beam carries two point loads of 10 kn as shown in the following figure, pure bending occurs at segment BC.

BENDING STRESS The effect of a bending moment applied to a cross-section of a beam is to induce a state of stress across that section. These stresses are known as bending stresses and they act normally

### Mechanics of Materials II. Chapter III. A review of the fundamental formulation of stress, strain, and deflection

Mechanics of Materials II Chapter III A review of the fundamental formulation of stress, strain, and deflection Outline Introduction Assumtions and limitations Axial loading Torsion of circular shafts

### 6. 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

### Cork Institute of Technology. Autumn 2007 Mechanics of Materials (Time: 3 Hours)

Cork Institute of Technology Bachelor of Engineering (Honours) in Mechanical Engineering- Stage 2 (NFQ Level 8) Autumn 2007 Mechanics of Materials (Time: 3 Hours) Instructions Answer Five Questions Question

### Sample Question Paper

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

### CHAPTER -6- BENDING Part -1-

Ishik University / Sulaimani Civil Engineering Department Mechanics of Materials CE 211 CHAPTER -6- BENDING Part -1-1 CHAPTER -6- Bending Outlines of this chapter: 6.1. Chapter Objectives 6.2. Shear and

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

Stress Analysis Lecture 3 ME 276 Spring 2017-2018 Dr./ Ahmed Mohamed Nagib Elmekawy Axial Stress 2 Beam under the action of two tensile forces 3 Beam under the action of two tensile forces 4 Shear Stress

### Chapter 12 Plate Bending Elements. Chapter 12 Plate Bending Elements

CIVL 7/8117 Chapter 12 - Plate Bending Elements 1/34 Chapter 12 Plate Bending Elements Learning Objectives To introduce basic concepts of plate bending. To derive a common plate bending element stiffness

### Simulation of Geometrical Cross-Section for Practical Purposes

Simulation of Geometrical Cross-Section 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,

### Structural Dynamics Lecture Eleven: Dynamic Response of MDOF Systems: (Chapter 11) By: H. Ahmadian

Structural Dynamics Lecture Eleven: Dynamic Response of MDOF Systems: (Chapter 11) By: H. Ahmadian ahmadian@iust.ac.ir Dynamic Response of MDOF Systems: Mode-Superposition Method Mode-Superposition Method:

### CHAPTER 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

### 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,

### MECHANICS OF MATERIALS

STATICS AND MECHANICS OF MATERIALS Ferdinand P. Beer E. Russell Johnston, Jr, John T. DeWolf David E Mazurek \Cawect Mc / iur/» Craw SugomcT Hilt Introduction 1 1.1 What is Mechanics? 2 1.2 Fundamental

### Purpose of this Guide: To thoroughly prepare students for the exact types of problems that will be on Exam 3.

ES230 STRENGTH OF MTERILS Exam 3 Study Guide Exam 3: Wednesday, March 8 th in-class Updated 3/3/17 Purpose of this Guide: To thoroughly prepare students for the exact types of problems that will be on

### 3 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

### MAAE 2202 A. Come to the PASS workshop with your mock exam complete. During the workshop you can work with other students to review your work.

It is most beneficial to you to write this mock final exam UNDER EXAM CONDITIONS. This means: Complete the exam in 3 hours. Work on your own. Keep your textbook closed. Attempt every question. After the

### PLAT DAN CANGKANG (TKS 4219)

PLAT DAN CANGKANG (TKS 4219) SESI I: PLATES Dr.Eng. Achfas Zacoeb Dept. of Civil Engineering Brawijaya University INTRODUCTION Plates are straight, plane, two-dimensional structural components of which

### 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

### UNIVERSITY OF SASKATCHEWAN ME MECHANICS OF MATERIALS I FINAL EXAM DECEMBER 13, 2008 Professor A. Dolovich

UNIVERSITY OF SASKATCHEWAN ME 313.3 MECHANICS OF MATERIALS I FINAL EXAM DECEMBER 13, 2008 Professor A. Dolovich A CLOSED BOOK EXAMINATION TIME: 3 HOURS For Marker s Use Only LAST NAME (printed): FIRST

### Mechanics 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 cross-section of a beam may consists of a resultant normal force,

### PES Institute of Technology

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

### ELASTICITY AND FRACTURE MECHANICS. Vijay G. Ukadgaonker

THEORY OF ELASTICITY AND FRACTURE MECHANICS y x Vijay G. Ukadgaonker Theory of Elasticity and Fracture Mechanics VIJAY G. UKADGAONKER Former Professor Indian Institute of Technology Bombay Delhi-110092

### Members Subjected to Torsional Loads

Members Subjected to Torsional Loads Torsion of circular shafts Definition of Torsion: Consider a shaft rigidly clamped at one end and twisted at the other end by a torque T = F.d applied in a plane perpendicular

### SEMM Mechanics PhD Preliminary Exam Spring Consider a two-dimensional rigid motion, whose displacement field is given by

SEMM Mechanics PhD Preliminary Exam Spring 2014 1. Consider a two-dimensional 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

### 3. 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

### QUESTION BANK DEPARTMENT: CIVIL SEMESTER: III SUBJECT CODE: CE2201 SUBJECT NAME: MECHANICS OF SOLIDS UNIT 1- STRESS AND STRAIN PART A

DEPARTMENT: CIVIL SUBJECT CODE: CE2201 QUESTION BANK SEMESTER: III SUBJECT NAME: MECHANICS OF SOLIDS UNIT 1- STRESS AND STRAIN PART A (2 Marks) 1. Define longitudinal strain and lateral strain. 2. State

### 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,

### WORKBOOK MECHANICS OF MATERIALS AND ELEMENTS OF ENGINEERING STRUCTURES

WORKBOOK MECHANICS OF MATERIALS AND ELEMENTS OF ENGINEERING STRUCTURES LUBLIN 014 Authors: Sylwester Samborski, Andrzej Teter and Marcin Bocheński Desktop publishing: Sylwester Samborski, Andrzej Teter

### The University of Melbourne Engineering Mechanics

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

### D : SOLID MECHANICS. Q. 1 Q. 9 carry one mark each.

GTE 2016 Q. 1 Q. 9 carry one mark each. D : SOLID MECHNICS Q.1 single degree of freedom vibrating system has mass of 5 kg, stiffness of 500 N/m and damping coefficient of 100 N-s/m. To make the system

### 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

### CHAPTER 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 Euler-Bernoulli assumptions One of its dimensions

### BENCHMARK LINEAR FINITE ELEMENT ANALYSIS OF LATERALLY LOADED SINGLE PILE USING OPENSEES & COMPARISON WITH ANALYTICAL SOLUTION

BENCHMARK LINEAR FINITE ELEMENT ANALYSIS OF LATERALLY LOADED SINGLE PILE USING OPENSEES & COMPARISON WITH ANALYTICAL SOLUTION Ahmed Elgamal and Jinchi Lu October 07 Introduction In this study: I) The response

### Lecture 8. Stress Strain in Multi-dimension

Lecture 8. Stress Strain in Multi-dimension Module. General Field Equations General Field Equations [] Equilibrium Equations in Elastic bodies xx x y z yx zx f x 0, etc [2] Kinematics xx u x x,etc. [3]

### STRESS 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

### Lecture 8 Viscoelasticity and Deformation

Read: pg 130 168 (rest of Chpt. 4) 1 Poisson s Ratio, µ (pg. 115) Ratio of the strain in the direction perpendicular to the applied force to the strain in the direction of the applied force. For uniaxial

### Mechanics 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) Ki-Bok Min, PhD Assistant Professor Energy Resources Engineering i Seoul National University Shear

. Stresses in Pavements.1. Stresses in Fleible Pavements.1.1. Stresses in Homogeneous Mass Boussinesq formulated models for the stresses inside an elastic half-space due to a concentrated load applied

### For more Stuffs Visit Owner: N.Rajeev. R07

Code.No: 43034 R07 SET-1 JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD II.B.TECH - I SEMESTER REGULAR EXAMINATIONS NOVEMBER, 2009 FOUNDATION OF SOLID MECHANICS (AERONAUTICAL ENGINEERING) Time: 3hours

### Fig. 1. Circular fiber and interphase between the fiber and the matrix.

Finite element unit cell model based on ABAQUS for fiber reinforced composites Tian Tang Composites Manufacturing & Simulation Center, Purdue University West Lafayette, IN 47906 1. Problem Statement In

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

SET - 1 II B. Tech I Semester Regular Examinations, Jan - 2015 MECHANICS OF SOLIDS (Com. to ME, AME, AE, MTE) Time: 3 hours Max. Marks: 70 Note: 1. Question Paper consists of two parts (Part-A and Part-B)

### Chapter 4 Deflection and Stiffness

Chapter 4 Deflection and Stiffness Asst. Prof. Dr. Supakit Rooppakhun Chapter Outline Deflection and Stiffness 4-1 Spring Rates 4-2 Tension, Compression, and Torsion 4-3 Deflection Due to Bending 4-4 Beam

### Bending of Simply Supported Isotropic and Composite Laminate Plates

Bending of Simply Supported Isotropic and Composite Laminate Plates Ernesto Gutierrez-Miravete 1 Isotropic Plates Consider simply a supported rectangular plate of isotropic material (length a, width b,

### PROBLEM #1.1 (4 + 4 points, no partial credit)

PROBLEM #1.1 ( + points, no partial credit A thermal switch consists of a copper bar which under elevation of temperature closes a gap and closes an electrical circuit. The copper bar possesses a length

### FINAL EXAMINATION. (CE130-2 Mechanics of Materials)

UNIVERSITY OF CLIFORNI, ERKELEY FLL SEMESTER 001 FINL EXMINTION (CE130- Mechanics of Materials) Problem 1: (15 points) pinned -bar structure is shown in Figure 1. There is an external force, W = 5000N,

### 4. SHAFTS. A shaft is an element used to transmit power and torque, and it can support

4. SHAFTS A shaft is an element used to transmit power and torque, and it can support reverse bending (fatigue). Most shafts have circular cross sections, either solid or tubular. The difference between

### 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

### DEPARTMENT OF MECHANICAL ENIGINEERING, UNIVERSITY OF ENGINEERING & TECHNOLOGY LAHORE (KSK CAMPUS).

DEPARTMENT OF MECHANICAL ENIGINEERING, UNIVERSITY OF ENGINEERING & TECHNOLOGY LAHORE (KSK CAMPUS). Lab Director: Coordinating Staff: Mr. Muhammad Farooq (Lecturer) Mr. Liaquat Qureshi (Lab Supervisor)

### MODIFIED HYPERBOLIC SHEAR DEFORMATION THEORY FOR STATIC FLEXURE ANALYSIS OF THICK ISOTROPIC BEAM

MODIFIED HYPERBOLIC SHEAR DEFORMATION THEORY FOR STATIC FLEXURE ANALYSIS OF THICK ISOTROPIC BEAM S. Jasotharan * and I.R.A. Weerasekera University of Moratuwa, Moratuwa, Sri Lanka * E-Mail: jasos91@hotmail.com,

### 4. 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

### KINGS COLLEGE OF ENGINEERING DEPARTMENT OF MECHANICAL ENGINEERING QUESTION BANK. Subject code/name: ME2254/STRENGTH OF MATERIALS Year/Sem:II / IV

KINGS COLLEGE OF ENGINEERING DEPARTMENT OF MECHANICAL ENGINEERING QUESTION BANK Subject code/name: ME2254/STRENGTH OF MATERIALS Year/Sem:II / IV UNIT I STRESS, STRAIN DEFORMATION OF SOLIDS PART A (2 MARKS)

### Assumptions: beam is initially straight, is elastically deformed by the loads, such that the slope and deflection of the elastic curve are

*12.4 SLOPE & DISPLACEMENT BY THE MOMENT-AREA METHOD Assumptions: beam is initially straight, is elastically deformed by the loads, such that the slope and deflection of the elastic curve are very small,

### 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.

### Using the finite element method of structural analysis, determine displacements at nodes 1 and 2.

Question 1 A pin-jointed plane frame, shown in Figure Q1, is fixed to rigid supports at nodes and 4 to prevent their nodal displacements. The frame is loaded at nodes 1 and by a horizontal and a vertical

### 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.

### Lab Exercise #5: Tension and Bending with Strain Gages

Lab Exercise #5: Tension and Bending with Strain Gages Pre-lab 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

### Lecture 8 Viscoelasticity and Deformation

HW#5 Due 2/13 (Friday) Lab #1 Due 2/18 (Next Wednesday) For Friday Read: pg 130 168 (rest of Chpt. 4) 1 Poisson s Ratio, μ (pg. 115) Ratio of the strain in the direction perpendicular to the applied force

### MECE 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

### BEAM 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

### Torsion Stresses in Tubes and Rods

Torsion Stresses in Tubes and Rods This initial analysis is valid only for a restricted range of problem for which the assumptions are: Rod is initially straight. Rod twists without bending. Material is

### [7] Torsion. [7.1] Torsion. [7.2] Statically Indeterminate Torsion. [7] Torsion Page 1 of 21

[7] Torsion Page 1 of 21 [7] Torsion [7.1] Torsion [7.2] Statically Indeterminate Torsion [7] Torsion Page 2 of 21 [7.1] Torsion SHEAR STRAIN DUE TO TORSION 1) A shaft with a circular cross section is

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:

### UNIT-I Introduction & Plane Stress and Plane Strain Analysis

SIDDHARTH INSTITUTE OF ENGINEERING & TECHNOLOGY:: PUTTUR (AUTONOMOUS) Siddharth Nagar, Narayanavanam Road 517583 QUESTION BANK (DESCRIPTIVE) Subject with Code : Advanced Solid Mechanics (18CE1002) Year

### 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

### CE6306 STRENGTH OF MATERIALS TWO MARK QUESTIONS WITH ANSWERS ACADEMIC YEAR

CE6306 STRENGTH OF MATERIALS TWO MARK QUESTIONS WITH ANSWERS ACADEMIC YEAR 2014-2015 UNIT - 1 STRESS, STRAIN AND DEFORMATION OF SOLIDS PART- A 1. Define tensile stress and tensile strain. The stress induced

### Montgomery County Community College EGR 213 Mechanics of Materials 3-2-2

Montgomery County Community College EGR 213 Mechanics of Materials 3-2-2 COURSE DESCRIPTION: This course covers the deformation of beams and shafts using energy methods and structural analysis, the analysis

### Application of Finite Element Method to Create Animated Simulation of Beam Analysis for the Course of Mechanics of Materials

International Conference on Engineering Education and Research "Progress Through Partnership" 4 VSB-TUO, Ostrava, ISSN 156-35 Application of Finite Element Method to Create Animated Simulation of Beam

### 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

Frequently Asked Questions Why do we have to make the assumption that plane sections plane? How about bars with non-axis symmetric cross section? The formulae derived look very similar to beam and axial

### SRI CHANDRASEKHARENDRA SARASWATHI VISWA MAHAVIDHYALAYA

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

CHAPTER OBJECTIVES qanalyze the stress developed in thin-walled pressure vessels qreview the stress analysis developed in previous chapters regarding axial load, torsion, bending and shear qdiscuss the

### 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.

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

### 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

### FIXED BEAMS IN BENDING

FIXED BEAMS IN BENDING INTRODUCTION Fixed or built-in beams are commonly used in building construction because they possess high rigidity in comparison to simply supported beams. When a simply supported