# Indeterminacy STATIC INDETERMINACY. Where, Static Indeterminacy I=Internal Static Indeterminacy E= External Static Indeterminacy

Save this PDF as:

Size: px
Start display at page:

Download "Indeterminacy STATIC INDETERMINACY. Where, Static Indeterminacy I=Internal Static Indeterminacy E= External Static Indeterminacy"

## Transcription

1 Indeterminacy After calculating the load on the structure it becomes necessary to find the ways by which the structure can be solved. A structure can be solved by two means 1) Statically 2) Kinematically In Statical method we solve the structure by treating the reaction and internal force as unknown. In Kinematics, we solve the structure by finding the displacement and rotation as unknown. Determinate A structure is said to be determinate if total number of unknown is equal to total number of equilibrium equations. Indeterminate A structure is said to be indeterminate if total number of unknown is more than total number of equilibrium equations. Unstable A structure is said to be unstable if total number of unknown is less than total number of equilibrium equations STATIC INDETERMINACY Where, Static Indeterminacy I=Internal Static Indeterminacy E= External Static Indeterminacy F=Number of unknown reactions U=Equation of static equilibrium available m = 3 for 2-Dimension and m=6 for 3-Dimension R=Any additional equation available. 2-Dimension Beams:- For beam generally the internal Indeterminacy is zero, as no closed loop can be formed in beam For calculating the number of unknown Reaction(1) Roller gives one reaction (2) Hinge gives two reaction (3) Fixed support gives three reaction U=Equation of static equilibrium available =3 1 Example:- Find the Indeterminacy of the beams. F=2+1=3 U=3 E=3-3=0 hence beam is statically determinate. F=2+1+1=4 U=3 E=4-3=1 Beam is indeterminate of 1 degree. F=3+1=4 U=3 E=4-3=1 Beam is indeterminate of 1 degree F=2+2=4 U=3 E=4-3=1 Beam is indeterminate of 1 degree F=3+3=6 U=3 E=6-3=3 Beam is indeterminate of 3 degree

2 F=1+2+3=6 U=3 E=6-3=3 Beam is indeterminate of 3 degree F= =6 U=3 E=6-3=3 Beam is indeterminate of 3 degree F=2+2+2=6 U=3 E=6-3=3 Beam is indeterminate of 3 degree Internal Hinge:-it is denoted by it is just like a pin in the structure, which can transmit the vertical load but unable to transmit the bending moment from one joint to other. Hence, it provide additional equation =n-1 where n is the number of members joined at the hinge. If the number of members jointed are 2 than additional equation provided will be 1. If 3 members are jointed at the hinge than additional equation provided will be 2 and if the number of members joined are 4 than the additional equation provided will be 3. Example:- F=3+1=4 U=3 R=2-1=1 E=4-3-1=0 hence beam is statically determinate 2 F=2+1=3 U=3 R=2-1=1 E=3-3-1=-1 hence beam is unstable F= =6 U=3 R=2-1=1 E=6-3-1=2 F=3+3=6 U=3 R= =2 E=6-3-2=1 2-Dimension Frame:- A frame is a structure comprising of beam and column jointed by rigid joint. Rigid Joint :- A joint is said to be rigid, if it can transfer the axial load, shear force and bending moment from the one member to the other member without any change in the angle between the members. All the member in the flexural frame in this course will be treated like rigid joint. For calculating the number of unknown Reaction(1) Roller gives one reaction (2) Hinge gives two reaction (3) Fixed support gives three reaction U=Equation of static equilibrium available =3 )

3 Example:- Find the Indeterminacy of the Frames:- E=2+2-3=1 I=0 E=2+1-3=0 I=0 E=3+3-3=3 I=0 E=3-3=0 I=0 E=3+3-3=3 I=0 E=3+2-3=2 I = 3 E= =5 I=3*2=6 E= =5 I=3*0=0 E=3+3-3=3 E=3+3-3=3 I=3*0=6 R =2-1=1 I=3*0=6 R =2-1=1 E= =7 I=3*3=9 R =(3-1)+(3-1)=4

4 TREE METHOD Every tress with fixed base is a determinate structure. As shown in Fig. the tree with many branches is same as a structure with a column with fixed support jointed to beam with rigid joint. In this method we divide the structure into tree shape by providing the cuts. The Indeterminacy of the structure = Where, C= Number of cuts and R is no of constraint applied to make the support fixed or joint to be rigid (if joint is not rigid) Example:- Find the Indeterminacy of the Frames E=3+2-3=2 I= 3*2=6 4 E= =8 I=0 E= =7 I=0 E=2+2-3=1 I=3*4=12

5 E= =5 I=3*2=6 R =4-1=3 E= =5 I=3*2=6 R =2-1=1 E= =2 I=3*0=0 R =0 5 Special When the structure is not having external support than,as shown below than the indeterminacy = I=3*4=12 E=-3 At point B horizontal displacement and rotation is permitted. E=3+3-3=3 Two additional equation is available R=2 Link link is structure used to join two different structure. The point where link is joined, will have only rotation but no vertical or horizontal deflection. Hence link gives two additional information. As shown in next diagram.

6 CD is a Link one additional equation at D and one additional equation at C hence E= =3 R=2 Stability of Structure There should be no reactions that are neither concurrent (concurrent mean meeting at a point) nor parallel The structure shown on left is unable as both the roller reaction meets at a point (concurrent) The beam shown on left is unstable as all the reactions are parallel 6 Space Frame In space Frame the fixed support gives 6 reaction ( the hinge gives 3 reaction ( the two side roller gives one reaction the one side roller gives two reactions ( The available equations will be 6 ( For internal indeterminacy the m=6 For using tree method one cut will provide 6 indeterminacy. The internal hinge will be 3*(n-1) additional equations where n is number of member joined at internal hinge. E= =18 I=6*1=6 Using Tree method 4 cuts are required hence

7 E= =18 I=6*1=6 R=3*(3-1)+3*(2-1)=9 When not given treat the roller as two way roller E= =10 I=6*1=6 E= =14 I=2*6=12 R=3*(4-1)+3*(4-1)+3*(2-1)=21 7 E= =14 I=(7-1)*6=36 R=3*(5-1)+3*(5-1)+3*(2-1) =27 E= =24 I=(11-2)*6=54 R=0

8 Kinematic Indeterminacy In Kinematic Indeterminacy we measure the total number of degree of freedom possible at joints. Degree of freedom is displacement and rotation at a joint and it is opposite of reaction. For 2 dimension, Fixed support gives 3 reaction viz is one rotation and 2 translation hence degree of freedom at fixed support is 0, Hinge gives 2 reaction both translation and no rotation reaction hence degree of freedom at hinge is 1 viz is rotation, and roller gives 1 reaction in translation direction hence degree of freedom at roller is 2 viz is one rotation and one translation. Similarly, for a 2 dimension rigid joint or free end the number of degree of freedom at a joint is 3 (one rotation and 2 translation). For internal hinge, the degree of freedom is 4, two rotational and 2 translational. Generally K.I=3*j r + i where j is no. of joint and r is number of reactions and Ii is no. of internal hinge. For 3 dimension, Fixed support gives 6 reaction viz is 3 rotation and 3 translation hence degree of freedom at fixed support is 0, Hinge gives 3 reaction all in translation and no rotation reaction hence degree of freedom at hinge is 3 viz is rotation in all three direction, and roller gives 1 reaction in translation direction hence degree of freedom at roller is 5 viz is 3 rotation and 2 translation, For a 3 dimension rigid join or free end the number of degree of freedom at a joint is 6 (3 rotations and 3 translations) For internal hinge, the degree of freedom is 9, 6 rotational and 3 translational. Ignoring axial deformation if we ignore axial deformation than the kinematic indeterminacy will decrease Kinematic indeterminacy after ignoring the axial deformation is kinematic indeterminacy-number of members in the structure. 8 K.I = 0+3=3 Ignoring axial deformation K.I = 3-1=2 j=2 r=3 K.I=3*2-3=3 Ignoring axial deformation K.I = 3-1=2 K.I = 1+2=3 Ignoring axial deformation K.I = 3-1=2 j=2 r=3 K.I=3*2-3=3 Ignoring axial deformation K.I = 3-1=2 K.I = 0+2=2 Ignoring axial deformation K.I = 2-1=1 j=2 r=4 K.I=3*2-4=2 Ignoring axial deformation K.I = 2-1=1 K.I = 1+2+2=5 Ignoring axial deformation K.I = 5-2=3 j=3 r=4 K.I=3*3-4=5 Ignoring axial deformation K.I = 5-2=3 K.I = 2+1=3 Ignoring axial deformation K.I = 3-2=1 j=3 r=6 K.I=3*3-6=3 Ignoring axial deformation K.I = 3-2=1

9 K.I = 3+2+1=6 Ignoring axial deformation K.I = 6-3=3 j=4 r=6 K.I=3*4-6=6 Ignoring axial deformation K.I = 6-3=3 K.I = 1+4+2=7 Ignoring axial deformation K.I = 7-2=5 j=3 r=3 i=1 K.I=3*3-3+1=7 Ignoring axial deformation K.I = 7-2=5 K.I = =9 Ignoring axial deformation K.I = 9-3=6 j=4 r=4 i=1 K.I=3*4-4+1=9 Ignoring axial deformation K.I = 9-3=6 K.I = =14 Ignoring axial deformation K.I = 14-5=9 j=6 r=6 i=2 K.I=3*6-6+2=14 Ignoring axial deformation K.I = 14-5=9 j=4 r=6 K.I=3*4-6=06 j=4 r=3 K.I=3*4-3=09 Igoring axial deformation K.I = 6-3=3 Ignoring axial deformation K.I=09-3=06 9. j=4 r=4 K.I=3*4-4=08 Ignoring axial deformation K.I = 8-3=5 j=5 r=3 K.I=3*5-3=12 Ignoring axial deformation K.I = 12-4=8 j=6 r=3 i=1 K.I=3*6-3+1=16 Ignoring axial deformation K.I = 16-5=8 j=7 r=11 K.I=3*7-11=10 Ignoring axial deformation K.I = 10-6=4

10 Find the reaction and draw the bending moment diagram for the beam having internal hinges. Taking moment about at left side of the internal hinge. Σ Mc=0 Taking moment about right side of the internal hinge Σ Mc=0 Taking moment about A Σ M A =0 Solving 1 and 2 The BMD is shown in the above Fig. The free body diagram method to solve the above problem is as follows. Find the reaction for the beams shown in below 10 Since C is a hinge, hence bending moment at C is zero on either side of the C. Taking right side of the C Since C is a hinge, hence bending moment at C is zero on either side of the C. Taking right side of the C

### 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

### 4.2 Free Body Diagrams

CE297-FA09-Ch4 Page 1 Friday, September 18, 2009 12:11 AM Chapter 4: Equilibrium of Rigid Bodies A (rigid) body is said to in equilibrium if the vector sum of ALL forces and all their moments taken about

### Advanced Structural Analysis. Prof. Devdas Menon. Department of Civil Engineering. Indian Institute of Technology, Madras. Module - 5.3.

Advanced Structural Analysis Prof. Devdas Menon Department of Civil Engineering Indian Institute of Technology, Madras Module - 5.3 Lecture - 29 Matrix Analysis of Beams and Grids Good morning. This is

### Statically determinate structures

Statically determinate structures A statically determinate structure is the one in which reactions and internal forces can be determined solely from free-body diagrams and equations of equilibrium. These

### Statically Indeterminate Structure. : More unknowns than equations: Statically Indeterminate

Statically Indeterminate Structure : More unknowns than equations: Statically Indeterminate 1 Plane Truss :: Determinacy No. of unknown reactions = 3 No. of equilibrium equations = 3 : Statically Determinate

### 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

### SECTION 5 ANALYSIS OF CONTINUOUS SPANS DEVELOPED BY THE PTI EDC-130 EDUCATION COMMITTEE LEAD AUTHOR: BRYAN ALLRED

SECTION 5 ANALYSIS OF CONTINUOUS SPANS DEVELOPED BY THE PTI EDC-130 EDUCATION COMMITTEE LEAD AUTHOR: BRYAN ALLRED NOTE: MOMENT DIAGRAM CONVENTION In PT design, it is preferable to draw moment diagrams

### Use of Computers in Mechanics Education at Ohio State University*

Int. J. Engng Ed. Vol. 16, No. 5, pp. 394±400, 2000 0949-149X/91 \$3.00+0.00 Printed in Great Britain. # 2000 TEMPUS Publications. Use of Computers in Mechanics Education at Ohio State University* GEORGE

### Mechanics lecture 7 Moment of a force, torque, equilibrium of a body

G.1 EE1.el3 (EEE1023): Electronics III Mechanics lecture 7 Moment of a force, torque, equilibrium of a body Dr Philip Jackson http://www.ee.surrey.ac.uk/teaching/courses/ee1.el3/ G.2 Moments, torque and

### 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

### Chapter 11 Equilibrium

11.1 The First Condition of Equilibrium The first condition of equilibrium deals with the forces that cause possible translations of a body. The simplest way to define the translational equilibrium of

### BASIC CONCEPTS AND CONVENTIONAL METHODS OF STUCTURAL ANALYSIS (LECTURE NOTES)

BASIC CONCEPTS AND CONVENTIONA METHODS OF STUCTURA ANAYSIS (ECTURE NOTES) DR. MOHAN KAANI (Retired Professor of Structural Engineering) DEPARTMENT OF CIVI ENGINEERING INDIAN INSTITUTE OF TECHNOOGY (BOMBAY)

### Chapter 1: Statics. A) Newtonian Mechanics B) Relativistic Mechanics

Chapter 1: Statics 1. The subject of mechanics deals with what happens to a body when is / are applied to it. A) magnetic field B) heat C ) forces D) neutrons E) lasers 2. still remains the basis of most

NEESR SG: Behavior, Analysis and Design of Complex Wall Systems The laboratory testing presented here was conducted as part of a larger effort that employed laboratory testing and numerical simulation

### 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

### Design of Steel Structures Prof. S.R.Satish Kumar and Prof. A.R.Santha Kumar. Fig. 7.21 some of the trusses that are used in steel bridges

7.7 Truss bridges Fig. 7.21 some of the trusses that are used in steel bridges Truss Girders, lattice girders or open web girders are efficient and economical structural systems, since the members experience

### 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

### Solving Simultaneous Equations and Matrices

Solving Simultaneous Equations and Matrices The following represents a systematic investigation for the steps used to solve two simultaneous linear equations in two unknowns. The motivation for considering

### Tutorial for Assignment #2 Gantry Crane Analysis By ANSYS (Mechanical APDL) V.13.0

Tutorial for Assignment #2 Gantry Crane Analysis By ANSYS (Mechanical APDL) V.13.0 1 Problem Description Design a gantry crane meeting the geometry presented in Figure 1 on page #325 of the course textbook

### ARCH 331 Structural Glossary S2014abn. Structural Glossary

Structural Glossary Allowable strength: Nominal strength divided by the safety factor. Allowable stress: Allowable strength divided by the appropriate section property, such as section modulus or cross

### Miss S. S. Nibhorkar 1 1 M. E (Structure) Scholar,

Volume, Special Issue, ICSTSD Behaviour of Steel Bracing as a Global Retrofitting Technique Miss S. S. Nibhorkar M. E (Structure) Scholar, Civil Engineering Department, G. H. Raisoni College of Engineering

### Qualitative Influence Lines. Qualitative Influence Lines. Qualitative Influence Lines. Qualitative Influence Lines. Qualitative Influence Lines

IL 32 Influence Lines - Muller-reslau Principle /5 In 886, Heinrich Müller-reslau develop a method for rapidly constructing the shape of an influence line. Heinrich Franz ernhard Müller was born in Wroclaw

COURSE: CE 201 (STATICS) LECTURE NO.: 28 to 30 FACULTY: DR. SHAMSHAD AHMAD DEPARTMENT: CIVIL ENGINEERING UNIVERSITY: KING FAHD UNIVERSITY OF PETROLEUM & MINERALS, DHAHRAN, SAUDI ARABIA TEXT BOOK: ENGINEERING

### BACHELOR OF SCIENCE DEGREE

BACHELOR OF SCIENCE DEGREE GENERAL EDUCATION CURRICULUM and Additional Degree Requirements Engineering Science Brett Coulter, Ph.D. - Director The Engineering Science degree is a wonderful way for liberal

### Mechanics of Materials Summary

Mechanics of Materials Summary 1. Stresses and Strains 1.1 Normal Stress Let s consider a fixed rod. This rod has length L. Its cross-sectional shape is constant and has area. Figure 1.1: rod with a normal

### DISTANCE DEGREE PROGRAM CURRICULUM NOTE:

Bachelor of Science in Electrical Engineering DISTANCE DEGREE PROGRAM CURRICULUM NOTE: Some Courses May Not Be Offered At A Distance Every Semester. Chem 121C General Chemistry I 3 Credits Online Fall

### THEORETICAL MECHANICS

PROF. DR. ING. VASILE SZOLGA THEORETICAL MECHANICS LECTURE NOTES AND SAMPLE PROBLEMS PART ONE STATICS OF THE PARTICLE, OF THE RIGID BODY AND OF THE SYSTEMS OF BODIES KINEMATICS OF THE PARTICLE 2010 0 Contents

### Pancake-type collapse energy absorption mechanisms and their influence on the final outcome (complete version)

Report, Structural Analysis and Steel Structures Institute, Hamburg University of Technology, Hamburg, June, 2013 Pancake-type collapse energy absorption mechanisms and their influence on the final outcome

### 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

### Statics problem solving strategies, hints and tricks

Statics problem solving strategies, hints and tricks Contents 1 Solving a problem in 7 steps 3 1.1 To read.............................................. 3 1.2 To draw..............................................

### SOLID MECHANICS TUTORIAL MECHANISMS KINEMATICS - VELOCITY AND ACCELERATION DIAGRAMS

SOLID MECHANICS TUTORIAL MECHANISMS KINEMATICS - VELOCITY AND ACCELERATION DIAGRAMS This work covers elements of the syllabus for the Engineering Council exams C105 Mechanical and Structural Engineering

### Indetermination in Granular Mechanics

Indetermination in Granular Mechanics J. J. Moreau Laboratoire de Mécanique et Génie Civil CNRS-Université Montpellier II, France e-mail: moreau@lmgc.univ-montp2.fr Workshop: Discrete numerical simulations

### Bridging Your Innovations to Realities

Graphic User Interface Graphic User Interface Modeling Features Bridge Applications Segmental Bridges Cable Bridges Analysis Features Result Evaluation Design Features 02 07 13 17 28 34 43 48 2 User Interface

### 1. When we deform a material and it recovers its original shape, we say that it is a) Rigid

UNIT 05 TEST TECHNOLOGY 1º ESO GROUP: A DATE: / / 1. When we deform a material and it recovers its original shape, we say that it is 2. When we try to deform a material and it doesn t change its shape,

### ETABS. Integrated Building Design Software. Concrete Shear Wall Design Manual. Computers and Structures, Inc. Berkeley, California, USA

ETABS Integrated Building Design Software Concrete Shear Wall Design Manual Computers and Structures, Inc. Berkeley, California, USA Version 8 January 2002 Copyright The computer program ETABS and all

### B.TECH. (AEROSPACE ENGINEERING) PROGRAMME (BTAE) Term-End Examination December, 2011 BAS-010 : MACHINE DESIGN

No. of Printed Pages : 7 BAS-01.0 B.TECH. (AEROSPACE ENGINEERING) PROGRAMME (BTAE) CV CA CV C:) O Term-End Examination December, 2011 BAS-010 : MACHINE DESIGN Time : 3 hours Maximum Marks : 70 Note : (1)

### SEISMIC RETROFITTING OF STRUCTURES

SEISMIC RETROFITTING OF STRUCTURES RANJITH DISSANAYAKE DEPT. OF CIVIL ENGINEERING, FACULTY OF ENGINEERING, UNIVERSITY OF PERADENIYA, SRI LANKA ABSTRACT Many existing reinforced concrete structures in present

### DEVELOPMENT AND APPLICATIONS OF TUNED/HYBRID MASS DAMPERS USING MULTI-STAGE RUBBER BEARINGS FOR VIBRATION CONTROL OF STRUCTURES

13 th World Conference on Earthquake Engineering Vancouver, B.C., Canada August 1-6, 2004 Paper No. 2243 DEVELOPMENT AND APPLICATIONS OF TUNED/HYBRID MASS DAMPERS USING MULTI-STAGE RUBBER BEARINGS FOR

### 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

### Face detection is a process of localizing and extracting the face region from the

Chapter 4 FACE NORMALIZATION 4.1 INTRODUCTION Face detection is a process of localizing and extracting the face region from the background. The detected face varies in rotation, brightness, size, etc.

### Bedford, Fowler: Statics. Chapter 4: System of Forces and Moments, Examples via TK Solver

System of Forces and Moments Introduction The moment vector of a force vector,, with respect to a point has a magnitude equal to the product of the force magnitude, F, and the perpendicular distance from

### Course in. Nonlinear FEM

Course in Introduction Outline Lecture 1 Introduction Lecture 2 Geometric nonlinearity Lecture 3 Material nonlinearity Lecture 4 Material nonlinearity continued Lecture 5 Geometric nonlinearity revisited

### HØGSKOLEN I GJØVIK Avdeling for teknologi, økonomi og ledelse. Løsningsforslag for kontinuasjonseksamen i Mekanikk 4/1-10

Løsningsforslag for kontinuasjonseksamen i 4/1-10 Oppgave 1 (T betyr tension, dvs. strekk, og C betyr compression, dvs. trykk.) Side 1 av 9 Leif Erik Storm Oppgave 2 Løsning (fra http://www.public.iastate.edu/~statics/examples/vmdiags/vmdiaga.html

### 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

### DESIGN OF BLAST RESISTANT BUILDINGS IN AN LNG PROCESSING PLANT

DESIGN OF BLAST RESISTANT BUILDINGS IN AN LNG PROCESSING PLANT Troy Oliver 1, Mark Rea 2 ABSTRACT: This paper provides an overview of the work undertaken in the design of multiple buildings for one of

### A vector is a directed line segment used to represent a vector quantity.

Chapters and 6 Introduction to Vectors A vector quantity has direction and magnitude. There are many examples of vector quantities in the natural world, such as force, velocity, and acceleration. A vector

### Draft report. Innovative Design for a Rapidly Deployable Shelter. Written 17/12/2007. Jonathan TAYLOR MEng,

Draft report Innovative Design for a Rapidly Deployable Shelter Written 17/12/2007 Jonathan TAYLOR MEng, Research Assistant, Department of Engineering Science, University of Oxford, Oxford, OX1 3PJ E-mail:

### Analyze and Evaluate a Truss

#3 Learning Activity #3: Analyze and Evaluate a Truss Overview of the Activity In this learning activity, we will analyze and evaluate one of the main trusses from the Grant Road Bridge. We will create

### Modeling Mechanical Systems

chp3 1 Modeling Mechanical Systems Dr. Nhut Ho ME584 chp3 2 Agenda Idealized Modeling Elements Modeling Method and Examples Lagrange s Equation Case study: Feasibility Study of a Mobile Robot Design Matlab

### International Journal of Engineering Research-Online A Peer Reviewed International Journal Articles available online http://www.ijoer.

RESEARCH ARTICLE ISSN: 2321-7758 DESIGN AND DEVELOPMENT OF A DYNAMOMETER FOR MEASURING THRUST AND TORQUE IN DRILLING APPLICATION SREEJITH C 1,MANU RAJ K R 2 1 PG Scholar, M.Tech Machine Design, Nehru College

### PREDICTION OF MACHINE TOOL SPINDLE S DYNAMICS BASED ON A THERMO-MECHANICAL MODEL

PREDICTION OF MACHINE TOOL SPINDLE S DYNAMICS BASED ON A THERMO-MECHANICAL MODEL P. Kolar, T. Holkup Research Center for Manufacturing Technology, Faculty of Mechanical Engineering, CTU in Prague, Czech

### Highly flexible couplings

Construction and operation 8.03.00 Instructions for installation 8.03.00 Types of stress 8.04.00 Diagrams for static deformation of the coupling ring 8.05.00 Coupling size 8.07.00 Examples of combinations

### UNIT 13 DESIGN OF GUIDEWAYS AND SPINDLE

UNIT 13 DESIGN OF GUIDEWAYS AND SPINDLE Design of Guideways and Spindle Structure 13.1 Introduction Ojectives 13. Functions of Guideways 13.3 Types of Guideways 13.3.1 Guideways with Sliding Friction 13.3.

### 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

### Lecture 8 : Dynamic Stability

Lecture 8 : Dynamic Stability Or what happens to small disturbances about a trim condition 1.0 : Dynamic Stability Static stability refers to the tendency of the aircraft to counter a disturbance. Dynamic

### 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

### Reinforced Concrete Design

FALL 2013 C C Reinforced Concrete Design CIVL 4135 ii 1 Chapter 1. Introduction 1.1. Reading Assignment Chapter 1 Sections 1.1 through 1.8 of text. 1.2. Introduction In the design and analysis of reinforced

### 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.

### Topology optimization based on graph theory of crash loaded flight passenger seats

7. LS-DYNA Anwenderforum, Bamberg 2008 Optimierung III Topology optimization based on graph theory of crash loaded flight passenger seats Axel Schumacher, Christian Olschinka, Bastian Hoffmann Hamburg

### Physics 2A, Sec B00: Mechanics -- Winter 2011 Instructor: B. Grinstein Final Exam

Physics 2A, Sec B00: Mechanics -- Winter 2011 Instructor: B. Grinstein Final Exam INSTRUCTIONS: Use a pencil #2 to fill your scantron. Write your code number and bubble it in under "EXAM NUMBER;" an entry

### 3D analysis of RC frames using effective-stiffness models

3D analysis of RC frames using effective-stiffness models C. Dundar &.F. Kara Department of Civil Engineering, Cukurova University, dana, Turkey BSTRCT: n the present study, a computer program has been

### Technical Notes 3B - Brick Masonry Section Properties May 1993

Technical Notes 3B - Brick Masonry Section Properties May 1993 Abstract: This Technical Notes is a design aid for the Building Code Requirements for Masonry Structures (ACI 530/ASCE 5/TMS 402-92) and Specifications

### 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

### Angular acceleration α

Angular Acceleration Angular acceleration α measures how rapidly the angular velocity is changing: Slide 7-0 Linear and Circular Motion Compared Slide 7- Linear and Circular Kinematics Compared Slide 7-

### جامعة البلقاء التطبيقية

AlBalqa Applied University تا سست عام 997 The curriculum of associate degree in Air Conditioning, Refrigeration and Heating Systems consists of (7 credit hours) as follows: Serial No. Requirements First

### DINAMIC AND STATIC CENTRE OF PRESSURE MEASUREMENT ON THE FORCEPLATE. F. R. Soha, I. A. Szabó, M. Budai. Abstract

ACTA PHYSICA DEBRECINA XLVI, 143 (2012) DINAMIC AND STATIC CENTRE OF PRESSURE MEASUREMENT ON THE FORCEPLATE F. R. Soha, I. A. Szabó, M. Budai University of Debrecen, Department of Solid State Physics Abstract

### State of Stress at Point

State of Stress at Point Einstein Notation The basic idea of Einstein notation is that a covector and a vector can form a scalar: This is typically written as an explicit sum: According to this convention,

### Kyu-Jung Kim Mechanical Engineering Department, California State Polytechnic University, Pomona, U.S.A.

MECHANICS: STATICS AND DYNAMICS Kyu-Jung Kim Mechanical Engineering Department, California State Polytechnic University, Pomona, U.S.A. Keywords: mechanics, statics, dynamics, equilibrium, kinematics,

### Module 2 - GEARS Lecture 7 - SPUR GEAR DESIGN

Module 2 - GEARS Lecture 7 - SPUR GEAR DESIGN Contents 7.1 Spur gear tooth force analysis 7.2 Spur gear - tooth stresses 7.3 Tooth bending stress Lewis equation 7.4 Tooth bending stress AGMA procedure

### Biomechanics of the Lumbar Spine

Biomechanics of the Lumbar Spine Biomechanics of the Spine 6 degrees of freedom Extension & Flexion Translation Rotation Compression & Distraction The disc/annulus/all/pll complex is the major restraint

### STEEL BUILDINGS IN EUROPE. Single-Storey Steel Buildings Part 5: Detailed Design of Trusses

STEEL BUILDIGS I EUROPE Single-Storey Steel Buildings Part 5: Detailed Design of Trusses Single-Storey Steel Buildings Part 5: Detailed Design of Trusses 5 - ii Part 5: Detailed Design of Trusses FOREWORD

### National Council of Examiners for Engineering and Surveying. Principles and Practice of Engineering Structural Examination

Structural Effective Beginning with the April 2011 The structural engineering exam is a breadth and exam examination offered in two components on successive days. The 8-hour Vertical Forces (Gravity/Other)

### OPTIMAL DIAGRID ANGLE TO MINIMIZE DRIFT IN HIGH-RISE STEEL BUILDINGS SUBJECTED TO WIND LOADS

International Journal of Civil Engineering and Technology (IJCIET) Volume 6, Issue 11, Nov 215, pp. 1-1, Article ID: IJCIET_6_11_1 Available online at http://www.iaeme.com/ijciet/issues.asp?jtype=ijciet&vtype=6&itype=11

### ME 115(b): Solution to Homework #1

ME 115(b): Solution to Homework #1 Solution to Problem #1: To construct the hybrid Jacobian for a manipulator, you could either construct the body Jacobian, JST b, and then use the body-to-hybrid velocity

### 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

### PAPERS AND DISCUSSIONS

May, 1930.] 919 AMERICAN SOCIETY OF CIVIL ENGINEERS INSTITUTED 1852 PAPERS AND DISCUSSIONS Tbis Society is not responsible for any statement made or opίnion expresβed in its publications. ANALYSIS OF CONTINUOUS

### ANTALYA INTERNATIONAL UNIVERSITY DEPARTMENT OF CIVIL ENGINEERING UNDERGRADUATE PROGRAM COURSE DESCRIPTIONS

CORE COURSES MATH 101 - Calculus I Trigonometric functions and their basic properties. Inverse trigonometric functions. Logarithmic and exponential functions. Limits and continuity of functions of a single

### Practice Problems on Boundary Layers. Answer(s): D = 107 N D = 152 N. C. Wassgren, Purdue University Page 1 of 17 Last Updated: 2010 Nov 22

BL_01 A thin flat plate 55 by 110 cm is immersed in a 6 m/s stream of SAE 10 oil at 20 C. Compute the total skin friction drag if the stream is parallel to (a) the long side and (b) the short side. D =

### The University of Birmingham (Live System)

The University of Birmingham (Live System) Behaviour of Structural Insulated Panels (SIPs) under both short-term and long-term loadings Yang, Jian; Rungthonkit, Prathan Document Version Author final version

### Rear Impact Guard TEST METHOD 223. Standards and Regulations Division. Issued: December 2003

Transport Canada Safety and Security Road Safety Transports Canada Sécurité et sûreté Sécurité routière Standards and Regulations Division TEST METHOD 223 Rear Impact Guard Issued: December 2003 Standards

### ETABS. Integrated Building Design Software. Composite Floor Frame Design Manual. Computers and Structures, Inc. Berkeley, California, USA

ETABS Integrated Building Design Software Composite Floor Frame Design Manual Computers and Structures, Inc. Berkeley, California, USA Version 8 January 2002 Copyright The computer program ETABS and all

### Solution Derivations for Capa #11

Solution Derivations for Capa #11 1) A horizontal circular platform (M = 128.1 kg, r = 3.11 m) rotates about a frictionless vertical axle. A student (m = 68.3 kg) walks slowly from the rim of the platform

### 1.3. DOT PRODUCT 19. 6. If θ is the angle (between 0 and π) between two non-zero vectors u and v,

1.3. DOT PRODUCT 19 1.3 Dot Product 1.3.1 Definitions and Properties The dot product is the first way to multiply two vectors. The definition we will give below may appear arbitrary. But it is not. It

### This week. CENG 732 Computer Animation. Challenges in Human Modeling. Basic Arm Model

CENG 732 Computer Animation Spring 2006-2007 Week 8 Modeling and Animating Articulated Figures: Modeling the Arm, Walking, Facial Animation This week Modeling the arm Different joint structures Walking

### 3600 s 1 h. 24 h 1 day. 1 day

Week 7 homework IMPORTANT NOTE ABOUT WEBASSIGN: In the WebAssign versions of these problems, various details have been changed, so that the answers will come out differently. The method to find the solution

### Synthesis of Constrained nr Planar Robots to Reach Five Task Positions

Synthesis of Constrained nr Planar Robots to Reach Five Task Positions Gim Song Soh Robotics and Automation Laboratory University of California Irvine, California 9697-3975 Email: gsoh@uci.edu J. Michael

### State Newton's second law of motion for a particle, defining carefully each term used.

5 Question 1. [Marks 20] An unmarked police car P is, travelling at the legal speed limit, v P, on a straight section of highway. At time t = 0, the police car is overtaken by a car C, which is speeding

### In-situ Load Testing to Evaluate New Repair Techniques

In-situ Load Testing to Evaluate New Repair Techniques W.J. Gold 1 and A. Nanni 2 1 Assistant Research Engineer, Univ. of Missouri Rolla, Dept. of Civil Engineering 2 V&M Jones Professor, Univ. of Missouri

### State Newton's second law of motion for a particle, defining carefully each term used.

5 Question 1. [Marks 28] An unmarked police car P is, travelling at the legal speed limit, v P, on a straight section of highway. At time t = 0, the police car is overtaken by a car C, which is speeding

### Abaqus Technology Brief. Automobile Roof Crush Analysis with Abaqus

Abaqus Technology Brief Automobile Roof Crush Analysis with Abaqus TB-06-RCA-1 Revised: April 2007. Summary The National Highway Traffic Safety Administration (NHTSA) mandates the use of certain test procedures

### Mesh Moving Techniques for Fluid-Structure Interactions With Large Displacements

K. Stein Department of Physics, Bethel College, St. Paul, MN 55112 T. Tezduyar Mechanical Engineering, Rice University, MS 321, Houston, TX 77005 R. Benney Natick Soldier Center, Natick, MA 01760 Mesh

### CE591 Fall 2013 Lecture 26: Moment Connections

CE591 Fall 2013 Lecture 26: Moment Connections Explain basic design procedure for moment (FR) connections Explain considerations for connections in momentresisting frames for seismic demands Describe problems

### Redesigning Cycle Rickshaw Wheel using QFD Technique to Minimize Accident Probability and Severity

SUST Journal of Science and Technology, Vol. 19, No. 5, 2012; P:60-70 Redesigning Cycle Rickshaw Wheel using QFD Technique to Minimize Accident Probability and Severity (Submitted: June 10, 2012; Accepted

### Common Core Unit Summary Grades 6 to 8

Common Core Unit Summary Grades 6 to 8 Grade 8: Unit 1: Congruence and Similarity- 8G1-8G5 rotations reflections and translations,( RRT=congruence) understand congruence of 2 d figures after RRT Dilations

### Numerical and Experimental Analysis of a Cantilever Beam: a Laboratory Project to Introduce Geometric Nonlinearity in Mechanics of Materials*

Int. J. Engng Ed. Vol. 19, No. 6, pp. 885±892, 2003 0949-149X/91 \$3.00+0.00 Printed in Great Britain. # 2003 TEMPUS Publications. Numerical and Experimental Analysis of a Cantilever Beam: a Laboratory

### INTRODUCTION TO LIMIT STATES

4 INTRODUCTION TO LIMIT STATES 1.0 INTRODUCTION A Civil Engineering Designer has to ensure that the structures and facilities he designs are (i) fit for their purpose (ii) safe and (iii) economical and

### Analysis and Repair of an Earthquake-Damaged High-rise Building in Santiago, Chile

Analysis and Repair of an Earthquake-Damaged High-rise Building in Santiago, Chile J. Sherstobitoff Ausenco Sandwell, Vancouver, Canada P. Cajiao AMEC, Vancouver, Canada P. Adebar University of British

### Physics 9e/Cutnell. correlated to the. College Board AP Physics 1 Course Objectives

Physics 9e/Cutnell correlated to the College Board AP Physics 1 Course Objectives Big Idea 1: Objects and systems have properties such as mass and charge. Systems may have internal structure. Enduring