1. a) Discuss how finite element is evolved in engineering field. (8) b) Explain the finite element idealization of structures with examples.

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "1. a) Discuss how finite element is evolved in engineering field. (8) b) Explain the finite element idealization of structures with examples."

Transcription

1 M.TECH. DEGREE EXAMINATION Branch: Civil Engineering Specialization Geomechanics and structures Model Question Paper - I MCEGS FINITE ELEMENT ANALYSIS Time: 3 hours Maximum: 100 Marks Answer ALL questions 1. a) Discuss how finite element is evolved in engineering field. (8) b) Explain the finite element idealization of structures with examples. (8) c) Find the displacement in the free ends and forces in the members of the truss shown in figure. (9) 45 L Q P 2. a) A circular plate of radius R supported on a semi- infinite space is loaded by a uniform pressure q. For a stress analysis of the problem, what are the component displacements,strains and stresses which are significant? Write down the relevant strain displacement and stress- strain relations. (8) b) Explain plane stress and plane strain problems. (8) c) Using Rayleigh Ritz method obtain an approximate solution for the following problem -d 2 u - u + x 2 = 0 0<x<1 dx 2 With the boundary conditions u (0) =0, du (1) = u (1) = 1 (9) dx

2 (Page 1/3) 3. a) Describe interpolation functions. (7) b) Derive shape function for the five shape functions for the transition element in (x,y) system. If the coordinates are transformed to a nondimensional system (ξ,ή) with node 1 as (-1,-1) and node 3 as (1,1) rewrite the shape functions. y (9) 4 3 x c) Briefly describe generalized coordinates and natural coordinates. (9) 4. a) Derive the relationship between natural (area) coordinates and Cartesian coordinates of a triangular element. (8) b) The two nodes 1 and 2 of the isosceles plane stress CST element in fig. are fixed If poisons ratio = 0.Determine the stiffness matrix associated with the dof at the unrestrained node 3. (8) 3 a 1 2 a a c) Explain weighted residual method in detail. (9)

3 (Page 2/3) 5. For a three bar truss shown in figure determine the nodal displacements and the stress in each member. Find support reactions also. Take modulus of elasticity as 200GPa. Assume area of cross section for element 1 =1500 mm 2,elements 2, 3 =2000 mm 2. (25) C 150 kn 400 mm A B 6. Assemble element stiffness matrices for the rigid frame shown in figure. Explain how you proceed further to solve the problem. E=200GPa, I 0 =40x10-6 m 4,A=4x10-3 m 2 (25) 20kN/m 30kN 400 mm 400 mm 2I o 3m I o I o 4 m 7. a) Write short notes on Numerical Integration. Evaluate the integral I= cos п/ 2 x dx using two-point and three-point Gauss rule. (13) b) Discuss different types of plate bending elements used in FEM. (12) 8. a) Discuss Kirchhoff s and Mindlin s plate bending theories. (13) b) Write short note on finite elements for shell analysis. (12)

4 M.TECH. DEGREE EXAMINATION Branch: Civil Engineering Specialization Geomechanics and structures Model Question Paper - II (For admission 2011 onwards) (Page 3/3) MCEGS FINITE ELEMENT ANALYSIS Time: 3 hours Maximum: 100 Marks Answer ALL questions 9. a) Discuss the various steps in finite element analysis of a elastic static problem. (8) b) In a plane strain problem, we have σ x = 12000MPa, σ y = 1000 MPa, E= 210 GPa and γ = Determine the value of the stress σ z. (5) c) An axial bar shown in figure 1 is subjected to a load P at a distance of L/2 from one of the fixed ends. Use the principle of stationary potential energy to calculate the reactions R 1 and R 2. (12) P/2 R 1 R 2 Fig1 P/2 10. a) What is meant by variational method? Discuss its applications in finite element analysis. (9) b) Figure 2 shows a truss subjected to a vertical load 50kN at joint 1. Using the principle of virtual displacement, compute the deflections u and v. Also find the forces in the members of the truss. Fig 2 50 kn (10)

5 (Page1/3) c) Explain mathematical modeling in finite element analysis. (6) 11. a) Derive stiffness matrix for CST element. (7) b) Assemble equations of equilibrium for the spring system by direct approach. Show that minimization of potential energy also yields the same result. (9) F 1 F 2 F 3 k 1 k 2 k 3 u 1 u 2 u 3 Fig 3 c) Using Galerkins method obtain an approximate solution for the following problem -d 2 u / dx 2 - u + x 2 = 0 0<x<1 With the boundary conditions u(0)=0, du(1)/dx =u (1)=1 (9) 12. a) Calculate the Jacobian ( J ) for the element shown in Figure 4 at the sampling point 3. (10) 4(20,100) Y 1(10,20) 3(80,60) 2(100,20) 3 2 η 1 4 ξ X Fig 4 b) Using Rayleigh Ritz method determine the expressions for deflection in a simply supported beam subjected to uniformly distributed load w over the entire span. (9) c) Discuss compatibility and convergence criteria in FEA. (6) (Page2/3)

6 13. Find deflections, moments and shears in a continuous beam shown in figure 5. Take modulus of elasticity as 200GPa. Assume I =10 5 mm 4. (25) 20 N/mm 400 mm 400 mm 400 mm Fig Assemble element stiffness matrices for the rigid frame shown in figure 6. Explain how you proceed further to solve the problem. E=200GPa,I 0 =1000cm 4,A=100cm 2 (25) 20 kn/cm 30 cm 30 cm 40 cm Fig a) Write short notes on Numerical Integration. Evaluate the integral I= e x x dx x using ( + 2) 1 one-point and two-point Gauss rule. Compare with exact solution. (13) b) Discuss applications of soil and rock mechanics in FEM. (12) 16. a) Derive the stiffness matrix for Mindlin s plate element. (13) b) Write short notes on finite elements for plate analysis. (12) (Page 3/3)

The Basics of FEA Procedure

The Basics of FEA Procedure CHAPTER 2 The Basics of FEA Procedure 2.1 Introduction This chapter discusses the spring element, especially for the purpose of introducing various concepts involved in use of the FEA technique. A spring

More information

The elements used in commercial codes can be classified in two basic categories:

The elements used in commercial codes can be classified in two basic categories: CHAPTER 3 Truss Element 3.1 Introduction The single most important concept in understanding FEA, is the basic understanding of various finite elements that we employ in an analysis. Elements are used for

More information

FUNDAMENTAL FINITE ELEMENT ANALYSIS AND APPLICATIONS

FUNDAMENTAL FINITE ELEMENT ANALYSIS AND APPLICATIONS FUNDAMENTAL FINITE ELEMENT ANALYSIS AND APPLICATIONS With Mathematica and MATLAB Computations M. ASGHAR BHATTI WILEY JOHN WILEY & SONS, INC. CONTENTS OF THE BOOK WEB SITE PREFACE xi xiii 1 FINITE ELEMENT

More information

New approaches in Eurocode 3 efficient global structural design

New approaches in Eurocode 3 efficient global structural design New approaches in Eurocode 3 efficient global structural design Part 1: 3D model based analysis using general beam-column FEM Ferenc Papp* and József Szalai ** * Associate Professor, Department of Structural

More information

Finite Element Formulation for Beams - Handout 2 -

Finite Element Formulation for Beams - Handout 2 - Finite Element Formulation for Beams - Handout 2 - Dr Fehmi Cirak (fc286@) Completed Version Review of Euler-Bernoulli Beam Physical beam model midline Beam domain in three-dimensions Midline, also called

More information

Finite Element Method (ENGC 6321) Syllabus. Second Semester 2013-2014

Finite Element Method (ENGC 6321) Syllabus. Second Semester 2013-2014 Finite Element Method Finite Element Method (ENGC 6321) Syllabus Second Semester 2013-2014 Objectives Understand the basic theory of the FEM Know the behaviour and usage of each type of elements covered

More information

METHODS FOR ACHIEVEMENT UNIFORM STRESSES DISTRIBUTION UNDER THE FOUNDATION

METHODS FOR ACHIEVEMENT UNIFORM STRESSES DISTRIBUTION UNDER THE FOUNDATION International Journal of Civil Engineering and Technology (IJCIET) Volume 7, Issue 2, March-April 2016, pp. 45-66, Article ID: IJCIET_07_02_004 Available online at http://www.iaeme.com/ijciet/issues.asp?jtype=ijciet&vtype=7&itype=2

More information

Module 2. Analysis of Statically Indeterminate Structures by the Matrix Force Method. Version 2 CE IIT, Kharagpur

Module 2. Analysis of Statically Indeterminate Structures by the Matrix Force Method. Version 2 CE IIT, Kharagpur Module Analysis of Statically Indeterminate Structures by the Matrix Force Method esson 11 The Force Method of Analysis: Frames Instructional Objectives After reading this chapter the student will be able

More information

CAE -Finite Element Method

CAE -Finite Element Method 16.810 Engineering Design and Rapid Prototyping Lecture 3b CAE -Finite Element Method Instructor(s) Prof. Olivier de Weck January 16, 2007 Numerical Methods Finite Element Method Boundary Element Method

More information

COMPUTATIONAL ENGINEERING OF FINITE ELEMENT MODELLING FOR AUTOMOTIVE APPLICATION USING ABAQUS

COMPUTATIONAL ENGINEERING OF FINITE ELEMENT MODELLING FOR AUTOMOTIVE APPLICATION USING ABAQUS International Journal of Advanced Research in Engineering and Technology (IJARET) Volume 7, Issue 2, March-April 2016, pp. 30 52, Article ID: IJARET_07_02_004 Available online at http://www.iaeme.com/ijaret/issues.asp?jtype=ijaret&vtype=7&itype=2

More information

Finite Element Formulation for Plates - Handout 3 -

Finite Element Formulation for Plates - Handout 3 - Finite Element Formulation for Plates - Handout 3 - Dr Fehmi Cirak (fc286@) Completed Version Definitions A plate is a three dimensional solid body with one of the plate dimensions much smaller than the

More information

CAE -Finite Element Method

CAE -Finite Element Method 16.810 Engineering Design and Rapid Prototyping CAE -Finite Element Method Instructor(s) Prof. Olivier de Weck January 11, 2005 Plan for Today Hand Calculations Aero Æ Structures FEM Lecture (ca. 45 min)

More information

ENGI 8673 Subsea Pipeline Engineering Faculty of Engineering and Applied Science

ENGI 8673 Subsea Pipeline Engineering Faculty of Engineering and Applied Science GUIDANCE NOTE LECTURE 12 THERMAL EXPANSION ANALYSIS OVERVIEW The calculation procedure for determining the longitudinal pipeline response can be formulated on the basis of strain. The longitudinal strain

More information

STRESS AND DEFORMATION ANALYSIS OF LINEAR ELASTIC BARS IN TENSION

STRESS AND DEFORMATION ANALYSIS OF LINEAR ELASTIC BARS IN TENSION Chapter 11 STRESS AND DEFORMATION ANALYSIS OF LINEAR ELASTIC BARS IN TENSION Figure 11.1: In Chapter10, the equilibrium, kinematic and constitutive equations for a general three-dimensional solid deformable

More information

Finite Elements for 2 D Problems

Finite Elements for 2 D Problems Finite Elements for 2 D Problems General Formula for the Stiffness Matrix Displacements (u, v) in a plane element are interpolated from nodal displacements (ui, vi) using shape functions Ni as follows,

More information

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

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

More information

Shear Forces and Bending Moments

Shear Forces and Bending Moments Chapter 4 Shear Forces and Bending Moments 4.1 Introduction Consider a beam subjected to transverse loads as shown in figure, the deflections occur in the plane same as the loading plane, is called the

More information

The Matrix Stiffness Method for 2D Trusses

The Matrix Stiffness Method for 2D Trusses The Matrix Stiffness Method for D Trusses Method CEE 4L. Matrix Structural Analysis Department of Civil and Environmental Engineering Duke University Henri P. Gavin Fall, 04. Number all of the nodes and

More information

Design Analysis and Review of Stresses at a Point

Design Analysis and Review of Stresses at a Point Design Analysis and Review of Stresses at a Point Need for Design Analysis: To verify the design for safety of the structure and the users. To understand the results obtained in FEA, it is necessary to

More information

820446 - ACMSM - Computer Applications in Solids Mechanics

820446 - ACMSM - Computer Applications in Solids Mechanics Coordinating unit: 820 - EUETIB - Barcelona College of Industrial Engineering Teaching unit: 737 - RMEE - Department of Strength of Materials and Structural Engineering Academic year: Degree: 2015 BACHELOR'S

More information

An Overview of the Finite Element Analysis

An Overview of the Finite Element Analysis CHAPTER 1 An Overview of the Finite Element Analysis 1.1 Introduction Finite element analysis (FEA) involves solution of engineering problems using computers. Engineering structures that have complex geometry

More information

EDEXCEL NATIONAL CERTIFICATE/DIPLOMA FURTHER MECHANICAL PRINCIPLES AND APPLICATIONS UNIT 11 - NQF LEVEL 3 OUTCOME 2 - STRESS AND STRAIN

EDEXCEL NATIONAL CERTIFICATE/DIPLOMA FURTHER MECHANICAL PRINCIPLES AND APPLICATIONS UNIT 11 - NQF LEVEL 3 OUTCOME 2 - STRESS AND STRAIN EDEXCEL NATIONAL CERTIICATE/DIPLOMA URTHER MECHANICAL PRINCIPLES AND APPLICATIONS UNIT 11 - NQ LEVEL 3 OUTCOME - STRESS AND STRAIN TUTORIAL 1 - SHEAR CONTENT Be able to determine the stress in structural

More information

MECHANICS OF SOLIDS - BEAMS TUTORIAL 3 THE DEFLECTION OF BEAMS

MECHANICS OF SOLIDS - BEAMS TUTORIAL 3 THE DEFLECTION OF BEAMS MECHANICS OF SOLIDS - BEAMS TUTORIAL THE DEECTION OF BEAMS This is the third tutorial on the bending of beams. You should judge your progress by completing the self assessment exercises. On completion

More information

Module 4. Analysis of Statically Indeterminate Structures by the Direct Stiffness Method. Version 2 CE IIT, Kharagpur

Module 4. Analysis of Statically Indeterminate Structures by the Direct Stiffness Method. Version 2 CE IIT, Kharagpur Module Analysis of Statically Indeterminate Structures by the Direct Stiffness Method Version CE IIT, haragpur esson 7 The Direct Stiffness Method: Beams Version CE IIT, haragpur Instructional Objectives

More information

Modeling Beams on Elastic Foundations Using Plate Elements in Finite Element Method

Modeling Beams on Elastic Foundations Using Plate Elements in Finite Element Method Modeling Beams on Elastic Foundations Using Plate Elements in Finite Element Method Yun-gang Zhan School of Naval Architecture and Ocean Engineering, Jiangsu University of Science and Technology, Zhenjiang,

More information

CHAPTER 3. INTRODUCTION TO MATRIX METHODS FOR STRUCTURAL ANALYSIS

CHAPTER 3. INTRODUCTION TO MATRIX METHODS FOR STRUCTURAL ANALYSIS 1 CHAPTER 3. INTRODUCTION TO MATRIX METHODS FOR STRUCTURAL ANALYSIS Written by: Sophia Hassiotis, January, 2003 Last revision: February, 2015 Modern methods of structural analysis overcome some of the

More information

Nonlinear analysis and form-finding in GSA Training Course

Nonlinear analysis and form-finding in GSA Training Course Nonlinear analysis and form-finding in GSA Training Course Non-linear analysis and form-finding in GSA 1 of 47 Oasys Ltd Non-linear analysis and form-finding in GSA 2 of 47 Using the GSA GsRelax Solver

More information

Finite Element Simulation of Simple Bending Problem and Code Development in C++

Finite Element Simulation of Simple Bending Problem and Code Development in C++ EUROPEAN ACADEMIC RESEARCH, VOL. I, ISSUE 6/ SEPEMBER 013 ISSN 86-48, www.euacademic.org IMPACT FACTOR: 0.485 (GIF) Finite Element Simulation of Simple Bending Problem and Code Development in C++ ABDUL

More information

CIVL 7/8117 Chapter 3a - Development of Truss Equations 1/80

CIVL 7/8117 Chapter 3a - Development of Truss Equations 1/80 CIV 7/87 Chapter 3a - Development of Truss Equations /8 Development of Truss Equations Having set forth the foundation on which the direct stiffness method is based, we will now derive the stiffness matri

More information

Worked Examples of mathematics used in Civil Engineering

Worked Examples of mathematics used in Civil Engineering Worked Examples of mathematics used in Civil Engineering Worked Example 1: Stage 1 Engineering Surveying (CIV_1010) Tutorial - Transition curves and vertical curves. Worked Example 1 draws from CCEA Advanced

More information

Finite Element Method

Finite Element Method 16.810 (16.682) Engineering Design and Rapid Prototyping Finite Element Method Instructor(s) Prof. Olivier de Weck deweck@mit.edu Dr. Il Yong Kim kiy@mit.edu January 12, 2004 Plan for Today FEM Lecture

More information

Stresses in Beam (Basic Topics)

Stresses in Beam (Basic Topics) Chapter 5 Stresses in Beam (Basic Topics) 5.1 Introduction Beam : loads acting transversely to the longitudinal axis the loads create shear forces and bending moments, stresses and strains due to V and

More information

DYNAMIC ANALYSIS OF THICK PLATES SUBJECTED TO EARTQUAKE

DYNAMIC ANALYSIS OF THICK PLATES SUBJECTED TO EARTQUAKE DYNAMIC ANALYSIS OF THICK PLATES SUBJECTED TO EARTQUAKE ÖZDEMİR Y. I, AYVAZ Y. Posta Adresi: Department of Civil Engineering, Karadeniz Technical University, 68 Trabzon, TURKEY E-posta: yaprakozdemir@hotmail.com

More information

Lap Fillet Weld Calculations and FEA Techniques

Lap Fillet Weld Calculations and FEA Techniques Lap Fillet Weld Calculations and FEA Techniques By: MS.ME Ahmad A. Abbas Sr. Analysis Engineer Ahmad.Abbas@AdvancedCAE.com www.advancedcae.com Sunday, July 11, 2010 Advanced CAE All contents Copyright

More information

Optimum proportions for the design of suspension bridge

Optimum proportions for the design of suspension bridge Journal of Civil Engineering (IEB), 34 (1) (26) 1-14 Optimum proportions for the design of suspension bridge Tanvir Manzur and Alamgir Habib Department of Civil Engineering Bangladesh University of Engineering

More information

SLAB DESIGN. Introduction ACI318 Code provides two design procedures for slab systems:

SLAB DESIGN. Introduction ACI318 Code provides two design procedures for slab systems: Reading Assignment SLAB DESIGN Chapter 9 of Text and, Chapter 13 of ACI318-02 Introduction ACI318 Code provides two design procedures for slab systems: 13.6.1 Direct Design Method (DDM) For slab systems

More information

Approximate Analysis of Statically Indeterminate Structures

Approximate Analysis of Statically Indeterminate Structures Approximate Analysis of Statically Indeterminate Structures Every successful structure must be capable of reaching stable equilibrium under its applied loads, regardless of structural behavior. Exact analysis

More information

Stress Recovery 28 1

Stress Recovery 28 1 . 8 Stress Recovery 8 Chapter 8: STRESS RECOVERY 8 TABLE OF CONTENTS Page 8.. Introduction 8 8.. Calculation of Element Strains and Stresses 8 8.. Direct Stress Evaluation at Nodes 8 8.. Extrapolation

More information

MECHANICS OF SOLIDS - BEAMS TUTORIAL TUTORIAL 4 - COMPLEMENTARY SHEAR STRESS

MECHANICS OF SOLIDS - BEAMS TUTORIAL TUTORIAL 4 - COMPLEMENTARY SHEAR STRESS MECHANICS OF SOLIDS - BEAMS TUTORIAL TUTORIAL 4 - COMPLEMENTARY SHEAR STRESS This the fourth and final tutorial on bending of beams. You should judge our progress b completing the self assessment exercises.

More information

Finite Element Methods (in Solid and Structural Mechanics)

Finite Element Methods (in Solid and Structural Mechanics) CEE570 / CSE 551 Class #1 Finite Element Methods (in Solid and Structural Mechanics) Spring 2014 Prof. Glaucio H. Paulino Donald Biggar Willett Professor of Engineering Department of Civil and Environmental

More information

8.2 Elastic Strain Energy

8.2 Elastic Strain Energy Section 8. 8. Elastic Strain Energy The strain energy stored in an elastic material upon deformation is calculated below for a number of different geometries and loading conditions. These expressions for

More information

DESIGN OF SLABS. 3) Based on support or boundary condition: Simply supported, Cantilever slab,

DESIGN OF SLABS. 3) Based on support or boundary condition: Simply supported, Cantilever slab, DESIGN OF SLABS Dr. G. P. Chandradhara Professor of Civil Engineering S. J. College of Engineering Mysore 1. GENERAL A slab is a flat two dimensional planar structural element having thickness small compared

More information

AN INTRODUCTION TO THE FINITE ELEMENT METHOD FOR YOUNG ENGINEERS

AN INTRODUCTION TO THE FINITE ELEMENT METHOD FOR YOUNG ENGINEERS AN INTRODUCTION TO THE FINITE ELEMENT METHOD FOR YOUNG ENGINEERS By: Eduardo DeSantiago, PhD, PE, SE Table of Contents SECTION I INTRODUCTION... 2 SECTION II 1-D EXAMPLE... 2 SECTION III DISCUSSION...

More information

Problem 1: Computation of Reactions. Problem 2: Computation of Reactions. Problem 3: Computation of Reactions

Problem 1: Computation of Reactions. Problem 2: Computation of Reactions. Problem 3: Computation of Reactions Problem 1: Computation of Reactions Problem 2: Computation of Reactions Problem 3: Computation of Reactions Problem 4: Computation of forces and moments Problem 5: Bending Moment and Shear force Problem

More information

Nonlinear Models of Reinforced and Post-tensioned Concrete Beams

Nonlinear Models of Reinforced and Post-tensioned Concrete Beams 111 Nonlinear Models of Reinforced and Post-tensioned Concrete Beams ABSTRACT P. Fanning Lecturer, Department of Civil Engineering, University College Dublin Earlsfort Terrace, Dublin 2, Ireland. Email:

More information

ENGINEERING COUNCIL CERTIFICATE LEVEL

ENGINEERING COUNCIL CERTIFICATE LEVEL ENGINEERING COUNCIL CERTIICATE LEVEL ENGINEERING SCIENCE C103 TUTORIAL - BASIC STUDIES O STRESS AND STRAIN You should judge your progress by completing the self assessment exercises. These may be sent

More information

Lecture 4: Basic Review of Stress and Strain, Mechanics of Beams

Lecture 4: Basic Review of Stress and Strain, Mechanics of Beams MECH 466 Microelectromechanical Sstems Universit of Victoria Dept. of Mechanical Engineering Lecture 4: Basic Review of Stress and Strain, Mechanics of Beams 1 Overview Compliant Mechanisms Basics of Mechanics

More information

MCE380: Measurements and Instrumentation Lab. Chapter 9: Force, Torque and Strain Measurements

MCE380: Measurements and Instrumentation Lab. Chapter 9: Force, Torque and Strain Measurements MCE380: Measurements and Instrumentation Lab Chapter 9: Force, Torque and Strain Measurements Topics: Elastic Elements for Force Measurement Dynamometers and Brakes Resistance Strain Gages Holman, Ch.

More information

3 Concepts of Stress Analysis

3 Concepts of Stress Analysis 3 Concepts of Stress Analysis 3.1 Introduction Here the concepts of stress analysis will be stated in a finite element context. That means that the primary unknown will be the (generalized) displacements.

More information

MECHANICS OF SOLIDS - BEAMS TUTORIAL 1 STRESSES IN BEAMS DUE TO BENDING. On completion of this tutorial you should be able to do the following.

MECHANICS OF SOLIDS - BEAMS TUTORIAL 1 STRESSES IN BEAMS DUE TO BENDING. On completion of this tutorial you should be able to do the following. MECHANICS OF SOLIDS - BEAMS TUTOIAL 1 STESSES IN BEAMS DUE TO BENDING This is the first tutorial on bending of beams designed for anyone wishing to study it at a fairly advanced level. You should judge

More information

4 Shear Forces and Bending Moments

4 Shear Forces and Bending Moments 4 Shear Forces and ending oments Shear Forces and ending oments 8 lb 16 lb roblem 4.3-1 alculate the shear force and bending moment at a cross section just to the left of the 16-lb load acting on the simple

More information

MECHANICAL PRINCIPLES HNC/D PRELIMINARY LEVEL TUTORIAL 1 BASIC STUDIES OF STRESS AND STRAIN

MECHANICAL PRINCIPLES HNC/D PRELIMINARY LEVEL TUTORIAL 1 BASIC STUDIES OF STRESS AND STRAIN MECHANICAL PRINCIPLES HNC/D PRELIMINARY LEVEL TUTORIAL 1 BASIC STUDIES O STRESS AND STRAIN This tutorial is essential for anyone studying the group of tutorials on beams. Essential pre-requisite knowledge

More information

Mechanics of Materials. Chapter 4 Shear and Moment In Beams

Mechanics of Materials. Chapter 4 Shear and Moment In Beams Mechanics of Materials Chapter 4 Shear and Moment In Beams 4.1 Introduction The term beam refers to a slender bar that carries transverse loading; that is, the applied force are perpendicular to the bar.

More information

Instructors Manual Finite Element Method Laboratory Sessions

Instructors Manual Finite Element Method Laboratory Sessions Instructors Manual Finite Element Method Laboratory Sessions Dr. Waluyo Adi Siswanto 6 July 2010 Universiti Tun Hussein Onn Malaysia (UTHM) This document is written in LYX 1.6.7 a frontend of LATEX Contents

More information

Solved with COMSOL Multiphysics 4.3

Solved with COMSOL Multiphysics 4.3 Vibrating String Introduction In the following example you compute the natural frequencies of a pre-tensioned string using the 2D Truss interface. This is an example of stress stiffening ; in fact the

More information

Tower Cross Arm Numerical Analysis

Tower Cross Arm Numerical Analysis Chapter 7 Tower Cross Arm Numerical Analysis In this section the structural analysis of the test tower cross arm is done in Prokon and compared to a full finite element analysis using Ansys. This is done

More information

Analysis of Stresses and Strains

Analysis of Stresses and Strains Chapter 7 Analysis of Stresses and Strains 7.1 Introduction axial load = P / A torsional load in circular shaft = T / I p bending moment and shear force in beam = M y / I = V Q / I b in this chapter, we

More information

ENGINEERING SCIENCE H1 OUTCOME 1 - TUTORIAL 3 BENDING MOMENTS EDEXCEL HNC/D ENGINEERING SCIENCE LEVEL 4 H1 FORMERLY UNIT 21718P

ENGINEERING SCIENCE H1 OUTCOME 1 - TUTORIAL 3 BENDING MOMENTS EDEXCEL HNC/D ENGINEERING SCIENCE LEVEL 4 H1 FORMERLY UNIT 21718P ENGINEERING SCIENCE H1 OUTCOME 1 - TUTORIAL 3 BENDING MOMENTS EDEXCEL HNC/D ENGINEERING SCIENCE LEVEL 4 H1 FORMERLY UNIT 21718P This material is duplicated in the Mechanical Principles module H2 and those

More information

Structural Analysis - II Prof. P. Banerjee Department of Civil Engineering Indian Institute of Technology, Bombay. Lecture - 02

Structural Analysis - II Prof. P. Banerjee Department of Civil Engineering Indian Institute of Technology, Bombay. Lecture - 02 Structural Analysis - II Prof. P. Banerjee Department of Civil Engineering Indian Institute of Technology, Bombay Lecture - 02 Good morning. Today is the second lecture in the series of lectures on structural

More information

Reliable FE-Modeling with ANSYS

Reliable FE-Modeling with ANSYS Reliable FE-Modeling with ANSYS Thomas Nelson, Erke Wang CADFEM GmbH, Munich, Germany Abstract ANSYS is one of the leading commercial finite element programs in the world and can be applied to a large

More information

Statics and Mechanics of Materials

Statics and Mechanics of Materials Statics and Mechanics of Materials Chapter 4-1 Internal force, normal and shearing Stress Outlines Internal Forces - cutting plane Result of mutual attraction (or repulsion) between molecules on both

More information

Numerical analysis of boundary conditions to tunnels

Numerical analysis of boundary conditions to tunnels Global journal of multidisciplinary and applied sciences Available online at www.gjmas.com 2015 GJMAS Journal-2015-3-2/37-41 ISSN 2313-6685 2015 GJMAS Numerical analysis of boundary conditions to tunnels

More information

Structural Axial, Shear and Bending Moments

Structural Axial, Shear and Bending Moments Structural Axial, Shear and Bending Moments Positive Internal Forces Acting Recall from mechanics of materials that the internal forces P (generic axial), V (shear) and M (moment) represent resultants

More information

CHAP 4 FINITE ELEMENT ANALYSIS OF BEAMS AND FRAMES INTRODUCTION

CHAP 4 FINITE ELEMENT ANALYSIS OF BEAMS AND FRAMES INTRODUCTION CHAP FINITE EEMENT ANAYSIS OF BEAMS AND FRAMES INTRODUCTION We learned Direct Stiffness Method in Chapter imited to simple elements such as D bars we will learn Energ Method to build beam finite element

More information

P4 Stress and Strain Dr. A.B. Zavatsky MT07 Lecture 3 Statically Indeterminate Structures

P4 Stress and Strain Dr. A.B. Zavatsky MT07 Lecture 3 Statically Indeterminate Structures 4 Stress and Strain Dr... Zavatsky MT07 ecture 3 Statically Indeterminate Structures Statically determinate structures. Statically indeterminate structures (equations of equilibrium, compatibility, and

More information

Development of Membrane, Plate and Flat Shell Elements in Java

Development of Membrane, Plate and Flat Shell Elements in Java Development of Membrane, Plate and Flat Shell Elements in Java by Kaushalkumar Kansara Thesis submitted to the Faculty of the Virginia Polytechnic Institute & State University In partial fulfillment of

More information

Introduction to Solid Modeling Using SolidWorks 2012 SolidWorks Simulation Tutorial Page 1

Introduction to Solid Modeling Using SolidWorks 2012 SolidWorks Simulation Tutorial Page 1 Introduction to Solid Modeling Using SolidWorks 2012 SolidWorks Simulation Tutorial Page 1 In this tutorial, we will use the SolidWorks Simulation finite element analysis (FEA) program to analyze the response

More information

Introduction to Beam. Area Moments of Inertia, Deflection, and Volumes of Beams

Introduction to Beam. Area Moments of Inertia, Deflection, and Volumes of Beams Introduction to Beam Theory Area Moments of Inertia, Deflection, and Volumes of Beams Horizontal structural member used to support horizontal loads such as floors, roofs, and decks. Types of beam loads

More information

MECHANICS OF SOLIDS - BEAMS TUTORIAL 2 SHEAR FORCE AND BENDING MOMENTS IN BEAMS

MECHANICS OF SOLIDS - BEAMS TUTORIAL 2 SHEAR FORCE AND BENDING MOMENTS IN BEAMS MECHANICS OF SOLIDS - BEAMS TUTORIAL 2 SHEAR FORCE AND BENDING MOMENTS IN BEAMS This is the second tutorial on bending of beams. You should judge your progress by completing the self assessment exercises.

More information

Deflections. Question: What are Structural Deflections?

Deflections. Question: What are Structural Deflections? Question: What are Structural Deflections? Answer: The deformations or movements of a structure and its components, such as beams and trusses, from their original positions. It is as important for the

More information

A Case Study Comparing Two Approaches for Applying Area Loads: Tributary Area Loads vs Shell Pressure Loads

A Case Study Comparing Two Approaches for Applying Area Loads: Tributary Area Loads vs Shell Pressure Loads 1 A Case Study Comparing Two Approaches for Applying Area Loads: Tributary Area Loads vs Shell Pressure Loads By Dr. Siriwut Sasibut (Application Engineer) S-FRAME Software Inc. #1158 13351 Commerce Parkway

More information

Design of Steel Structures Prof. S.R.Satish Kumar and Prof. A.R.Santha Kumar

Design of Steel Structures Prof. S.R.Satish Kumar and Prof. A.R.Santha Kumar Problem 1 Design a hand operated overhead crane, which is provided in a shed, whose details are: Capacity of crane = 50 kn Longitudinal spacing of column = 6m Center to center distance of gantry girder

More information

Distribution of Forces in Lateral Load Resisting Systems

Distribution of Forces in Lateral Load Resisting Systems Distribution of Forces in Lateral Load Resisting Systems Part 2. Horizontal Distribution and Torsion IITGN Short Course Gregory MacRae Many slides from 2009 Myanmar Slides of Profs Jain and Rai 1 Reinforced

More information

Interaction between plate and column buckling

Interaction between plate and column buckling Delft, University of Technology Engineering office of Public works Rotterdam Interaction between plate and column buckling Master Thesis Name: Alex van Ham Student number: 1306138 Email: vanham.alex@gmail.com

More information

Analysis of deep beam using Finite Element Method

Analysis of deep beam using Finite Element Method www.ijaser.com 2012 by the authors Licensee IJASER- Under Creative Commons License 3.0 editorial@ijaser.com Research article ISSN 2277 9442 Analysis of deep beam using Finite Element Method 1 Enem, J.I.,

More information

Study of Analysis System for Bridge Test

Study of Analysis System for Bridge Test Study of Analysis System for Bridge Test Chen Ke, Lu Jian-Ming, Research Institute of Highway, 100088, Beijing, China (chenkezi@163.com, lujianming@263.net) Summary Analysis System for Bridge Test (Chinese

More information

Stress and Deformation Analysis. Representing Stresses on a Stress Element. Representing Stresses on a Stress Element con t

Stress and Deformation Analysis. Representing Stresses on a Stress Element. Representing Stresses on a Stress Element con t Stress and Deformation Analysis Material in this lecture was taken from chapter 3 of Representing Stresses on a Stress Element One main goals of stress analysis is to determine the point within a load-carrying

More information

Introduction to the Finite Element Method (FEM)

Introduction to the Finite Element Method (FEM) Introduction to the Finite Element Method (FEM) ecture First and Second Order One Dimensional Shape Functions Dr. J. Dean Discretisation Consider the temperature distribution along the one-dimensional

More information

INTRODUCTION TO BEAMS

INTRODUCTION TO BEAMS CHAPTER Structural Steel Design LRFD Method INTRODUCTION TO BEAMS Third Edition A. J. Clark School of Engineering Department of Civil and Environmental Engineering Part II Structural Steel Design and Analysis

More information

Indeterminate Analysis Force Method 1

Indeterminate Analysis Force Method 1 Indeterminate Analysis Force Method 1 The force (flexibility) method expresses the relationships between displacements and forces that exist in a structure. Primary objective of the force method is to

More information

MECHANICS OF MATERIALS

MECHANICS OF MATERIALS T dition CHTR MCHNICS OF MTRIS Ferdinand. Beer. Russell Johnston, Jr. John T. DeWolf ecture Notes: J. Walt Oler Texas Tech University Stress and Strain xial oading - Contents Stress & Strain: xial oading

More information

EDEXCEL NATIONAL CERTIFICATE/DIPLOMA MECHANICAL PRINCIPLES OUTCOME 2 ENGINEERING COMPONENTS TUTORIAL 1 STRUCTURAL MEMBERS

EDEXCEL NATIONAL CERTIFICATE/DIPLOMA MECHANICAL PRINCIPLES OUTCOME 2 ENGINEERING COMPONENTS TUTORIAL 1 STRUCTURAL MEMBERS ENGINEERING COMPONENTS EDEXCEL NATIONAL CERTIFICATE/DIPLOMA MECHANICAL PRINCIPLES OUTCOME ENGINEERING COMPONENTS TUTORIAL 1 STRUCTURAL MEMBERS Structural members: struts and ties; direct stress and strain,

More information

STATIC AND DYNAMIC ANALYSIS ON TATRA CHASSIS

STATIC AND DYNAMIC ANALYSIS ON TATRA CHASSIS Vol.2, Issue.1, pp-086-094 ISSN: 2249-6645 STATIC AND DYNAMIC ANALYSIS ON TATRA CHASSIS Sairam Kotari 1, V.Gopinath 2 PG student, Associate Professor, Department of Mechanical Engineering QIS College Of

More information

DESIGN OF BEAM-COLUMNS - I

DESIGN OF BEAM-COLUMNS - I 13 DESIGN OF BEA-COLUNS - I INTRODUCTION Columns in practice rarely experience concentric axial compression alone. Since columns are usually parts of a frame, they experience both bending moment and axial

More information

Introduction, Method of Sections

Introduction, Method of Sections Lecture #1 Introduction, Method of Sections Reading: 1:1-2 Mechanics of Materials is the study of the relationship between external, applied forces and internal effects (stress & deformation). An understanding

More information

FINITE ELEMENT : MATRIX FORMULATION. Georges Cailletaud Ecole des Mines de Paris, Centre des Matériaux UMR CNRS 7633

FINITE ELEMENT : MATRIX FORMULATION. Georges Cailletaud Ecole des Mines de Paris, Centre des Matériaux UMR CNRS 7633 FINITE ELEMENT : MATRIX FORMULATION Georges Cailletaud Ecole des Mines de Paris, Centre des Matériaux UMR CNRS 76 FINITE ELEMENT : MATRIX FORMULATION Discrete vs continuous Element type Polynomial approximation

More information

ANALYTICAL AND EXPERIMENTAL EVALUATION OF SPRING BACK EFFECTS IN A TYPICAL COLD ROLLED SHEET

ANALYTICAL AND EXPERIMENTAL EVALUATION OF SPRING BACK EFFECTS IN A TYPICAL COLD ROLLED SHEET International Journal of Mechanical Engineering and Technology (IJMET) Volume 7, Issue 1, Jan-Feb 2016, pp. 119-130, Article ID: IJMET_07_01_013 Available online at http://www.iaeme.com/ijmet/issues.asp?jtype=ijmet&vtype=7&itype=1

More information

Solid Mechanics. Stress. What you ll learn: Motivation

Solid Mechanics. Stress. What you ll learn: Motivation Solid Mechanics Stress What you ll learn: What is stress? Why stress is important? What are normal and shear stresses? What is strain? Hooke s law (relationship between stress and strain) Stress strain

More information

Vibrations of a Free-Free Beam

Vibrations of a Free-Free Beam Vibrations of a Free-Free Beam he bending vibrations of a beam are described by the following equation: y EI x y t 4 2 + ρ A 4 2 (1) y x L E, I, ρ, A are respectively the Young Modulus, second moment of

More information

Study of Energy Absorption of Rectangular Tube of Bumper of Light Commercial Vehicle during Oblique Loading

Study of Energy Absorption of Rectangular Tube of Bumper of Light Commercial Vehicle during Oblique Loading Study of Energy Absorption of Rectangular Tube of Bumper of Light Commercial Vehicle during Oblique Loading S. B. Tuljapure 1, Dr. S. S. Sarawade 2 Ph. D. Student, Department of Mechanical Engineering,

More information

A quadrilateral 2-D finite element based on mixed interpolation of tensorial

A quadrilateral 2-D finite element based on mixed interpolation of tensorial A quadrilateral 2-D finite element based on mixed interpolation of tensorial components Eduardo N. Dvorkin and Sara I. Vassolo* Instituto de Materiales y Estructuras, Facultad de Ingenieria, Universidad

More information

IMPROVING THE STRUT AND TIE METHOD BY INCLUDING THE CONCRETE SOFTENING EFFECT

IMPROVING THE STRUT AND TIE METHOD BY INCLUDING THE CONCRETE SOFTENING EFFECT International Journal of Civil Engineering and Technology (IJCIET) Volume 7, Issue 2, March-April 2016, pp. 117 127, Article ID: IJCIET_07_02_009 Available online at http://www.iaeme.com/ijciet/issues.asp?jtype=ijciet&vtype=7&itype=2

More information

Retrofitting of RCC Structure WIH Strengthening of Shear Wall with External Post Tensioning Cables

Retrofitting of RCC Structure WIH Strengthening of Shear Wall with External Post Tensioning Cables Retrofitting of RCC Structure WIH Strengthening of Shear Wall with External Post Tensioning Cables Yogesh Ghodke, G. R. Gandhe Department of Civil Engineering, Deogiri Institute of Engineering and Management

More information

2. Axial Force, Shear Force, Torque and Bending Moment Diagrams

2. Axial Force, Shear Force, Torque and Bending Moment Diagrams 2. Axial Force, Shear Force, Torque and Bending Moment Diagrams In this section, we learn how to summarize the internal actions (shear force and bending moment) that occur throughout an axial member, shaft,

More information

Stress Analysis Verification Manual

Stress Analysis Verification Manual Settle3D 3D settlement for foundations Stress Analysis Verification Manual 007-01 Rocscience Inc. Table of Contents Settle3D Stress Verification Problems 1 Vertical Stresses underneath Rectangular Footings

More information

Examples of New version for Designing members of Reinforced Concrete, Steel or Timber according to Eurocode 2, Eurocode 3 and Eurocode 5

Examples of New version for Designing members of Reinforced Concrete, Steel or Timber according to Eurocode 2, Eurocode 3 and Eurocode 5 Examples of New version for Designing members of Reinforced Concrete, Steel or Timber according to Eurocode 2, Eurocode 3 and Eurocode 5 Copyright RUNET Software www.runet-software.com 1 1. Examples 1.1

More information

EFFECTS ON NUMBER OF CABLES FOR MODAL ANALYSIS OF CABLE-STAYED BRIDGES

EFFECTS ON NUMBER OF CABLES FOR MODAL ANALYSIS OF CABLE-STAYED BRIDGES EFFECTS ON NUMBER OF CABLES FOR MODAL ANALYSIS OF CABLE-STAYED BRIDGES Yang-Cheng Wang Associate Professor & Chairman Department of Civil Engineering Chinese Military Academy Feng-Shan 83000,Taiwan Republic

More information

Dead Load Analysis of Cable-Stayed Bridge

Dead Load Analysis of Cable-Stayed Bridge 2011 International Conference on Intelligent Building and Management Proc.of CSIT vol.5 (2011) (2011) IACSIT Press, Singapore Dead Load Analysis of Cable-Stayed Bridge Tao Zhang 1,2 +, ZhiMin Wu 1 1 Department

More information

Structural Design Criteria & Design Loads on Delhi Metro Rail and Checking of Safety of Radial Joints in Tunnel Lining Segments

Structural Design Criteria & Design Loads on Delhi Metro Rail and Checking of Safety of Radial Joints in Tunnel Lining Segments International Journal of Scientific and Research Publications, Volume 5, Issue 7, July 2015 1 Structural Design Criteria & Design Loads on Delhi Metro Rail and Checking of Safety of Radial Joints in Tunnel

More information

Chapter 5: Indeterminate Structures Force Method

Chapter 5: Indeterminate Structures Force Method Chapter 5: Indeterminate Structures Force Method 1. Introduction Statically indeterminate structures are the ones where the independent reaction components, and/or internal forces cannot be obtained by

More information