Forces in Three Dimensions
|
|
- Curtis Barrett
- 6 years ago
- Views:
Transcription
1 Forces in Three Dimensions
2 Introduction In previous chapters, we learned how to handle a variety of problems, parallel forces, non-concurrent forces, concurrent forces, trusses, and finally frames. But all of these were coplanar systems. That is, they existed in and were appropriately analyzed in two-dimensions. However, not all structures can be analyzed as such 2
3 Introduction There are a number of force systems that are non-coplanar. From the standpoint of architecture, space frames are such a structure and cannot be analyzed in two-dimensions 3
4 Introduction From the standpoint of mechanical design, an example might be a right angle gearbox or perhaps a shaft transmitting power to a series of belt drives. To handle these systems we must look at them in all three dimensions 4
5 Introduction Dealing with force systems in three dimensions is virtually identical to dealing with coplanar force systems. The only difference is you will take a three dimensional view and project it into two or three 2-dimensional views, then solve them simultaneously. Before we do so, let's do a quick review of a three dimensional coordinate axis 5
6 The 3-D Axis The positive x-axis to the right, the positive y-axis in the positive upward direction and the positive z-axis projecting out of the surface of the paper (or should I say computer screen?). Of course, on a two-dimensional sheet of paper, the positive z-axis is drawn downward and to the left at a 45 o angle 6
7 The 3-D Axis When dealing with moments in three dimensions, we will always maintain a counterclockwise moment as a positive moment regardless of which plane into which we project the structure. For example, looking at the coordinate system above, we can draw the following 2-dimensional projections: 7
8
9 Now let's take a look at how we might resolve a parallel force system into a single equivalent force. To do so, the resultant force must have a magnitude equivalent to the system we are resolving and it must produce the same moment. Consider the following example 9
10 What we need to do is determine the magnitude of 'R' and the location of 'R'. The location of 'R' is determined by determining distances 'x' and 'z'. The shown location and sense of 'R' is assumed. The algebraic signs of the calculated distances and magnitude will validate our assumption. The resultant is determined by summing all forces in the system: F = = 90 R = 90 Caution: In this problem, we are finding a force resultant, not reactions. In the case of finding a resultant, the negative sign is absolute. That is, it indicates actual direction in accordance with our sign convention. 10
11 The location of 'R' must be such that it causes a moment equal to the moment of the system. To do so, it is easier to visualize the problem if we redraw the system in a two dimensional view. First, let's look down the x-axis into the y-z plane and draw an appropriate free body diagram 11
12 Take a moment about the x-axis: R z = Since we know the magnitude of 'R' is 90: 90 z = z = Note: The negative sign on the 90 z term indicates the resultant causes a negative moment. It does not reflect the sense of the resultant. However, the negative sign on 'z' indicates that our assumption of R being located behind the x-axis is incorrect. It is actually located in the first quadrant with a z-dimension of 4.55 units. 12
13 Now let's look at a FBD as viewed along the z axis. 13
14 Take a moment about the z-axis R x = Since we know the value of the resultant 'R' is 90: 90 x = x = As before, the negative sign on the 90 z term indicates the resultant causes a negative moment. It does not reflect the sense of the resultant. However, the negative sign on 'z' indicates that our assumption of R being located right of the x-axis is incorrect. It is located 4.55 units left of the z-axis. (The fact x=z is purely coincidental) 14
15 The resultant force would be located as shown. This single force is equivalent to the parallel force system with which we started. 15
VELAMMAL COLLEGE OF ENGINEERING AND TECHNOLOGY MADURAI DEPARTMRNT OF MECHANICAL ENGINEERING. Subject Code. Mechanics
VELAMMAL COLLEGE OF ENGINEERING AND TECHNOLOGY MADURAI 625 009 DEPARTMRNT OF MECHANICAL ENGINEERING Year / Sem / Branch I Year / II Sem / CSE Subject Code GE 204 Subject Name Engineering Mechanics Faculty
More informationTo show how to determine the forces in the members of a truss using the method of joints and the method of sections.
5 Chapter Objectives To show how to determine the forces in the members of a truss using the method of joints and the method of sections. To analyze the forces acting on the members of frames and machines
More informationIshik University / Sulaimani Architecture Department. Structure. ARCH 214 Chapter -5- Equilibrium of a Rigid Body
Ishik University / Sulaimani Architecture Department 1 Structure ARCH 214 Chapter -5- Equilibrium of a Rigid Body CHAPTER OBJECTIVES To develop the equations of equilibrium for a rigid body. To introduce
More informationFORCE ANALYSIS OF MACHINERY. School of Mechanical & Industrial Engineering, AAiT
1 FORCE ANALYSIS OF MACHINERY School of Mechanical & Industrial Engineering, AAiT INTRODUCTION 2 A machine is a device that performs work and, as such, transmits energy by means mechanical force from a
More informationENGR-1100 Introduction to Engineering Analysis. Lecture 23
ENGR-1100 Introduction to Engineering Analysis Lecture 23 Today s Objectives: Students will be able to: a) Draw the free body diagram of a frame and its members. FRAMES b) Determine the forces acting at
More informationthree Point Equilibrium 1 and planar trusses ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN DR. ANNE NICHOLS SUMMER 2014 lecture
ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN DR. ANNE NICHOLS SUMMER 2014 lecture three point equilibrium http:// nisee.berkeley.edu/godden and planar trusses Point Equilibrium 1 Equilibrium balanced
More informationSimilar to trusses, frames are generally fixed, load carrying structures.
Similar to trusses, frames are generally fixed, load carrying structures. The main difference between a frame and a truss is that in a frame at least one member is a multi force member (çoklu kuvvet elemanı).
More informationLecture 23. ENGR-1100 Introduction to Engineering Analysis FRAMES S 1
ENGR-1100 Introduction to Engineering Analysis Lecture 23 Today s Objectives: Students will be able to: a) Draw the free body diagram of a frame and its members. FRAMES b) Determine the forces acting at
More informationARC 341 Structural Analysis II. Lecture 10: MM1.3 MM1.13
ARC241 Structural Analysis I Lecture 10: MM1.3 MM1.13 MM1.4) Analysis and Design MM1.5) Axial Loading; Normal Stress MM1.6) Shearing Stress MM1.7) Bearing Stress in Connections MM1.9) Method of Problem
More information141EE0402-Engineering Mechanics. UNIT- I : Basics and Statics of Particles
141EE0402-Engineering Mechanics UNIT- I : Basics and Statics of Particles Force Force is an agent which produces or tends to produce, destroys or tends to destroy the motion of body or particles. Vector
More informationTrusses - Method of Sections
Trusses - Method of Sections ME 202 Methods of Truss Analsis Method of joints (previous notes) Method of sections (these notes) 2 MOS - Concepts Separate the structure into two parts (sections) b cutting
More informationWhen a rigid body is in equilibrium, both the resultant force and the resultant couple must be zero.
When a rigid body is in equilibrium, both the resultant force and the resultant couple must be zero. 0 0 0 0 k M j M i M M k R j R i R F R z y x z y x Forces and moments acting on a rigid body could be
More information6.6 FRAMES AND MACHINES APPLICATIONS. Frames are commonly used to support various external loads.
6.6 FRAMES AND MACHINES APPLICATIONS Frames are commonly used to support various external loads. How is a frame different than a truss? How can you determine the forces at the joints and supports of a
More informationChapter 5 Newton s Laws of Motion. Copyright 2010 Pearson Education, Inc.
Chapter 5 Newton s Laws of Motion Force and Mass Units of Chapter 5 Newton s First Law of Motion Newton s Second Law of Motion Newton s Third Law of Motion The Vector Nature of Forces: Forces in Two Dimensions
More informationForce System Resultants. Engineering Mechanics: Statics
Force System Resultants Engineering Mechanics: Statics Chapter Objectives To discuss the concept of the moment of a force and show how to calculate it in 2-D and 3-D systems. Definition of the moment of
More informationREADING QUIZ. 2. When using the method of joints, typically equations of equilibrium are applied at every joint. A) Two B) Three C) Four D) Six
READING QUIZ 1. One of the assumptions used when analyzing a simple truss is that the members are joined together by. A) Welding B) Bolting C) Riveting D) Smooth pins E) Super glue 2. When using the method
More informationVector Addition INTRODUCTION THEORY
Vector Addition INTRODUCTION All measurable quantities may be classified either as vector quantities or as scalar quantities. Scalar quantities are described completely by a single number (with appropriate
More informationNewton s Third Law Newton s Third Law: For each action there is an action and opposite reaction F
FRAMES AND MACHINES Learning Objectives 1). To evaluate the unknown reactions at the supports and the interaction forces at the connection points of a rigid frame in equilibrium by solving the equations
More informationEngineering Mechanics: Statics in SI Units, 12e
Engineering Mechanics: Statics in SI Units, 12e 5 Equilibrium of a Rigid Body Chapter Objectives Develop the equations of equilibrium for a rigid body Concept of the free-body diagram for a rigid body
More informationThe centroid of an area is defined as the point at which (12-2) The distance from the centroid of a given area to a specified axis may be found by
Unit 12 Centroids Page 12-1 The centroid of an area is defined as the point at which (12-2) The distance from the centroid of a given area to a specified axis may be found by (12-5) For the area shown
More informationfive moments ELEMENTS OF ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN DR. ANNE NICHOLS SPRING 2014 lecture ARCH 614
ELEMENTS OF ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN DR. ANNE NICHOLS SPRING 2014 lecture five moments Moments 1 Moments forces have the tendency to make a body rotate about an axis http://www.physics.umd.edu
More informationModule 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
More informationQuestion Bank Chapter -4- Part -2-
Ishik University / Sulaimani Civil Engineering Department Question Bank Chapter -4- Part -2-1 Problem -1- Determine the magnitude of F so that the resultant couple moment acting on the beam is 1.5 kn m
More informationCH. 5 TRUSSES BASIC PRINCIPLES TRUSS ANALYSIS. Typical depth-to-span ratios range from 1:10 to 1:20. First: determine loads in various members
CH. 5 TRUSSES BASIC PRINCIPLES Typical depth-to-span ratios range from 1:10 to 1:20 - Flat trusses require less overall depth than pitched trusses Spans: 40-200 Spacing: 10 to 40 on center - Residential
More informationFRAMES AND MACHINES Learning Objectives 1). To evaluate the unknown reactions at the supports and the interaction forces at the connection points of a
FRAMES AND MACHINES Learning Objectives 1). To evaluate the unknown reactions at the supports and the interaction forces at the connection points of a rigid frame in equilibrium by solving the equations
More informationENG202 Statics Lecture 16, Section 7.1
ENG202 Statics Lecture 16, Section 7.1 Internal Forces Developed in Structural Members - Design of any structural member requires an investigation of the loading acting within the member in order to be
More informationElements of Physics II. Agenda for Today
Physics 132: Lecture e 18 Elements of Physics II Agenda for Today Magnets and the Magnetic Field Magnetic fields caused by charged particles B-field from a current-carrying wire Magnetic fields and forces
More information3.1 CONDITIONS FOR RIGID-BODY EQUILIBRIUM
3.1 CONDITIONS FOR RIGID-BODY EQUILIBRIUM Consider rigid body fixed in the x, y and z reference and is either at rest or moves with reference at constant velocity Two types of forces that act on it, the
More informationCE 201 Statics. 2 Physical Sciences. Rigid-Body Deformable-Body Fluid Mechanics Mechanics Mechanics
CE 201 Statics 2 Physical Sciences Branch of physical sciences 16 concerned with the state of Mechanics rest motion of bodies that are subjected to the action of forces Rigid-Body Deformable-Body Fluid
More informationF R. + F 3x. + F 2y. = (F 1x. j + F 3x. i + F 2y. i F 3y. i + F 1y. j F 2x. ) i + (F 1y. ) j. F 2x. F 3y. = (F ) i + (F ) j. ) j
General comments: closed book and notes but optional one page crib sheet allowed. STUDY: old exams, homework and power point lectures! Key: make sure you can solve your homework problems and exam problems.
More information7.6 Journal Bearings
7.6 Journal Bearings 7.6 Journal Bearings Procedures and Strategies, page 1 of 2 Procedures and Strategies for Solving Problems Involving Frictional Forces on Journal Bearings For problems involving a
More informationForce Couple Systems = Reduction of a Force to an Equivalent Force and Moment (Moving a Force to Another Point) acting on a body has two effects:
ESULTANTS orce Couple Systems = eduction of a orce to an Equivalent orce and Moment (Moving a orce to Another Point) The force acting on a body has two effects: the first one is the tendency to push or
More informationUnit 21 Couples and Resultants with Couples
Unit 21 Couples and Resultants with Couples Page 21-1 Couples A couple is defined as (21-5) Moment of Couple The coplanar forces F 1 and F 2 make up a couple and the coordinate axes are chosen so that
More informationthree Equilibrium 1 and planar trusses ELEMENTS OF ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN DR. ANNE NICHOLS SPRING 2015 lecture ARCH 614
ELEMENTS OF ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN DR. ANNE NICHOLS SPRING 2015 lecture three equilibrium and planar trusses Equilibrium 1 Equilibrium balanced steady resultant of forces
More informationLOVELY PROFESSIONAL UNIVERSITY BASIC ENGINEERING MECHANICS MCQ TUTORIAL SHEET OF MEC Concurrent forces are those forces whose lines of action
LOVELY PROFESSIONAL UNIVERSITY BASIC ENGINEERING MECHANICS MCQ TUTORIAL SHEET OF MEC 107 1. Concurrent forces are those forces whose lines of action 1. Meet on the same plane 2. Meet at one point 3. Lie
More informationIshik University / Sulaimani Architecture Department Structure ARCH 214 Chapter -4- Force System Resultant
Ishik University / Sulaimani Architecture Department 1 Structure ARCH 214 Chapter -4- Force System Resultant 2 1 CHAPTER OBJECTIVES To discuss the concept of the moment of a force and show how to calculate
More informationMoment of a force (scalar, vector ) Cross product Principle of Moments Couples Force and Couple Systems Simple Distributed Loading
Chapter 4 Moment of a force (scalar, vector ) Cross product Principle of Moments Couples Force and Couple Systems Simple Distributed Loading The moment of a force about a point provides a measure of the
More informationTABLE OF CONTENTS. Preface...
TABLE OF CONTENTS Preface...................................... xiv 1 Introduction........................................ 1 1.1 Engineering and Statics.............................. 1 1.2 A Brief History
More informationChapter 7 INTERNAL FORCES
Chapter 7 INTERNAL FORCES READING QUIZ 1. In a multiforce member, the member is generally subjected to an internal. A) normal force B) shear force C) bending moment D) All of the above. 2. In mechanics,
More informationModule 2. Analysis of Statically Indeterminate Structures by the Matrix Force Method
Module 2 Analysis of Statically Indeterminate Structures by the Matrix Force Method Lesson 8 The Force Method of Analysis: Beams Instructional Objectives After reading this chapter the student will be
More informationENGINEERING MECHANICS
ENGINEERING MECHANICS BASUDEB BHATTACHARYYA Assistant Professor Department of Applied Mechanics Bengal Engineering and Science University Shibpur, Howrah OXJFORD UNIVERSITY PRESS Contents Foreword Preface
More information6. Vectors. Given two points, P 0 = (x 0, y 0 ) and P 1 = (x 1, y 1 ), a vector can be drawn with its foot at P 0 and
6. Vectors For purposes of applications in calculus and physics, a vector has both a direction and a magnitude (length), and is usually represented as an arrow. The start of the arrow is the vector s foot,
More informationChapter 2: Deflections of Structures
Chapter 2: Deflections of Structures Fig. 4.1. (Fig. 2.1.) ASTU, Dept. of C Eng., Prepared by: Melkamu E. Page 1 (2.1) (4.1) (2.2) Fig.4.2 Fig.2.2 ASTU, Dept. of C Eng., Prepared by: Melkamu E. Page 2
More informationMEE224: Engineering Mechanics Lecture 4
Lecture 4: Structural Analysis Part 1: Trusses So far we have only analysed forces and moments on a single rigid body, i.e. bars. Remember that a structure is a formed by and this lecture will investigate
More informationIntroduction to Statics
Introduction to Statics.PDF Edition Version 0.95 Unit 22 Equivalent Force Systems Helen Margaret Lester Plants Late Professor Emerita Wallace Starr Venable Emeritus Associate Professor West Virginia University,
More informationShafts: Torsion of Circular Shafts Reading: Crandall, Dahl and Lardner 6.2, 6.3
M9 Shafts: Torsion of Circular Shafts Reading: Crandall, Dahl and Lardner 6., 6.3 A shaft is a structural member which is long and slender and subject to a torque (moment) acting about its long axis. We
More informationChapter 5 Lecture. Pearson Physics. Newton's Laws of Motion. Prepared by Chris Chiaverina Pearson Education, Inc.
Chapter 5 Lecture Pearson Physics Newton's Laws of Motion Prepared by Chris Chiaverina Chapter Contents Newton's Laws of Motion Applying Newton's Laws Friction Newton's Laws of Motion Two of the most important
More informationSTATICS SECOND EDITION
Engineering Mechanics STATICS SECOND EDITION Michael E. Plesha Department of Engineering Physics University of Wisconsin-Madison Gary L. Gray Department of Engineering Science and Mechanics Penn State
More informationEQUATIONS OF EQUILIBRIUM & TWO-AND THREE-FORCE MEMEBERS
EQUATIONS OF EQUILIBRIUM & TWO-AND THREE-FORCE MEMEBERS Today s Objectives: Students will be able to: a) Apply equations of equilibrium to solve for unknowns, and, b) Recognize two-force members. READING
More informationSTATICS. FE Review. Statics, Fourteenth Edition R.C. Hibbeler. Copyright 2016 by Pearson Education, Inc. All rights reserved.
STATICS FE Review 1. Resultants of force systems VECTOR OPERATIONS (Section 2.2) Scalar Multiplication and Division VECTOR ADDITION USING EITHER THE PARALLELOGRAM LAW OR TRIANGLE Parallelogram Law: Triangle
More informationExaminers' comments Question 1: planar kinematics (four-bar mechanism and slider) Part (a) was answered well by most candidates. Recurring problems were: incorrect or missing direction information; diagrams
More informationChapter 2. Preview. Objectives One Dimensional Motion Displacement Average Velocity Velocity and Speed Interpreting Velocity Graphically
Section 1 Displacement and Velocity Preview Objectives One Dimensional Motion Displacement Average Velocity Velocity and Speed Interpreting Velocity Graphically Section 1 Displacement and Velocity Objectives
More informationME Statics. Structures. Chapter 4
ME 108 - Statics Structures Chapter 4 Outline Applications Simple truss Method of joints Method of section Germany Tacoma Narrows Bridge http://video.google.com/videoplay?docid=-323172185412005564&q=bruce+lee&pl=true
More informationStructural Analysis. Method of Joints. Method of Pins
Structural nalysis / Method of Pins I m reading a book about an1gravity. It s impossible to put down. Pop Quiz What is today s date? 2 1 Trusses Trusses are common means of transferring loads from their
More informationKINESIOLOGY PT617 HOMEWORK Mechanical Principles : Free Body Diagrams and Equilibrium
KINESIOLOGY PT617 HOMEWORK Mechanical Principles : Free Body Diagrams and Equilibrium 1) A man is standing still on his right leg, as shown in the figure. The person experiences only a normal reaction
More informationLecture 20. ENGR-1100 Introduction to Engineering Analysis THE METHOD OF SECTIONS
ENGR-1100 Introduction to Engineering Analysis Lecture 20 THE METHOD OF SECTIONS Today s Objectives: Students will be able to determine: 1. Forces in truss members using the method of sections. In-Class
More informationENGR-1100 Introduction to Engineering Analysis. Lecture 20
ENGR-1100 Introduction to Engineering Analysis Lecture 20 Today s Objectives: THE METHOD OF SECTIONS Students will be able to determine: 1. Forces in truss members using the method of sections. In-Class
More informationFor a general development of the theoretical aspects of mechanics, however, a more rigorous treatment is possible by using vector analysis. A vector may be denoted by drawing a short arrow above the letter
More informationPhysics 2B Notes - Capacitors Spring 2018
Definition of a Capacitor Special Case: Parallel Plate Capacitor Capacitors in Series or Parallel Capacitor Network Definition of a Capacitor Webassign Chapter 0: 8, 9, 3, 4, 5 A capacitor is a device
More informationSTATICS Chapter 1 Introductory Concepts
Contents Preface to Adapted Edition... (v) Preface to Third Edition... (vii) List of Symbols and Abbreviations... (xi) PART - I STATICS Chapter 1 Introductory Concepts 1-1 Scope of Mechanics... 1 1-2 Preview
More informationIntroduction. 1.1 Introduction. 1.2 Trigonometrical definitions
Introduction 1.1 Introduction Stress analysis is an important part of engineering science, as failure of most engineering components is usually due to stress. The component under a stress investigation
More informationChapter 04 Equilibrium of Rigid Bodies
Chapter 04 Equilibrium of Rigid Bodies Application Engineers designing this crane will need to determine the forces that act on this body under various conditions. 4-2 Introduction For a rigid body, the
More informationINTERNAL FORCES Today s Objective: Students will be able to: 1. Use the method of sections for determining internal forces in 2-D load cases.
INTERNAL FORCES Today s Objective: Students will be able to: 1. Use the method of sections for determining internal forces in 2-D load cases. In-Class Activities: Check Homework, if any Reading Quiz Applications
More informationDeflections. Deflections. Deflections. Deflections. Deflections. Deflections. dx dm V. dx EI. dx EI dx M. dv w
CIVL 311 - Conjugate eam 1/5 Conjugate beam method The development of the conjugate beam method has been atributed to several strucutral engineers. any credit Heinrich üller-reslau (1851-195) with the
More informationExperiment 3: Vector Addition
Experiment 3: Vector Addition EQUIPMENT Force Table (4) Pulleys (4) Mass Hangers Masses Level (TA s Table) (2) Protractors (2) Rulers (4) Colored Pencils (bold colors) Figure 3.1: Force Table 15 16 Experiment
More informationCENTRAL TEXAS COLLEGE SYLLABUS FOR ENGR 2301 Engineering Mechanics - Statics. Semester Hours Credit: 3
CENTRAL TEXAS COLLEGE SYLLABUS FOR ENGR 2301 Engineering Mechanics - Statics Semester Hours Credit: 3 I. INTRODUCTION A. ENGR 2301, Engineering Mechanics Statics, is a three-semester hour course that is
More informationStructural Continuity
Architecture 324 Structures II Structural Continuity Continuity in Beams Deflection Method Slope Method Three-Moment Theorem Millennium Bridge, London Foster and Partners + Arup Photo by Ryan Donaghy University
More informationENGR-1100 Introduction to Engineering Analysis. Lecture 9
ENGR-1100 Introduction to Engineering Analysis Lecture 9 MOMENT OF A FORCE (SCALAR FORMULATION), CROSS PRODUCT, MOMENT OF A FORCE (VECTOR FORMULATION), & PRINCIPLE OF MOMENTS Today s Objectives : Students
More informationISBN :
ISBN : 978-81-909042-4-7 - www.airwalkpublications.com ANNA UNIVERSITY - R2013 GE6253 ENGINEERING MECHANICS UNIT I: BASICS AND STATICS OF PARTICLES 12 Introduction Units and Dimensions Laws of Mechanics
More informationLECTURE 27: Gravitational potential energy
Lectures Page 1 LECTURE 27: Gravitational potential energy Select LEARNING OBJECTIVES: i. ii. Construct an expression for the work due to gravity, defining this expression as gravitational potential energy
More informationChapter 1: Logic systems
Chapter 1: Logic systems 1: Logic gates Learning Objectives: At the end of this topic you should be able to: identify the symbols and truth tables for the following logic gates: NOT AND NAND OR NOR XOR
More informationENGR 1100 Introduction to Mechanical Engineering
ENGR 1100 Introduction to Mechanical Engineering Mech. Engineering Objectives Newton s Laws of Motion Free Body Diagram Transmissibility Forces and Moments as vectors Parallel Vectors (addition/subtraction)
More informationUNIT-05 VECTORS. 3. Utilize the characteristics of two or more vectors that are concurrent, or collinear, or coplanar.
UNIT-05 VECTORS Introduction: physical quantity that can be specified by just a number the magnitude is known as a scalar. In everyday life you deal mostly with scalars such as time, temperature, length
More informationAPPLICATIONS OF DIFFERENTIATION
4 APPLICATIONS OF DIFFERENTIATION APPLICATIONS OF DIFFERENTIATION Many applications of calculus depend on our ability to deduce facts about a function f from information concerning its derivatives. APPLICATIONS
More informationPh.D. Preliminary Examination Analysis
UNIVERSITY OF CALIFORNIA, BERKELEY Spring Semester 2017 Dept. of Civil and Environmental Engineering Structural Engineering, Mechanics and Materials Name:......................................... Ph.D.
More informationThe hitch in all of this is figuring out the two principal angles and which principal stress goes with which principal angle.
Mohr s Circle The stress basic transformation equations that we developed allowed us to determine the stresses acting on an element regardless of its orientation as long as we know the basic stresses σx,
More informationUNIT-07. Newton s Three Laws of Motion
1. Learning Objectives: UNIT-07 Newton s Three Laws of Motion 1. Understand the three laws of motion, their proper areas of applicability and especially the difference between the statements of the first
More informationWhat Every Engineer Should Know About Structures. Part A Statics Fundamentals
What Every Engineer Should Know About Structures Part A Statics Fundamentals by Professor Patrick L. Glon, P.E. This is the first course of a series in the area of study of engineering mechanics called
More informationGraphical Vector Addition
Vectors Chapter 4 Vectors and Scalars Measured quantities can be of two types Scalar quantities: only require magnitude (and proper unit) for description. Examples: distance, speed, mass, temperature,
More informationChapter 3. Vectors and. Two-Dimensional Motion Vector vs. Scalar Review
Chapter 3 Vectors and Two-Dimensional Motion Vector vs. Scalar Review All physical quantities encountered in this text will be either a scalar or a vector A vector quantity has both magnitude (size) and
More informationVECTORS. 3-1 What is Physics? 3-2 Vectors and Scalars CHAPTER
CHAPTER 3 VECTORS 3-1 What is Physics? Physics deals with a great many quantities that have both size and direction, and it needs a special mathematical language the language of vectors to describe those
More informationIshik University / Sulaimani Civil Engineering Department. Chapter -2-
Ishik University / Sulaimani Civil Engineering Department Chapter -- 1 orce Vectors Contents : 1. Scalars and Vectors. Vector Operations 3. Vector Addition of orces 4. Addition of a System of Coplanar
More informationME 274 Spring 2017 Examination No. 2 PROBLEM No. 2 (20 pts.) Given:
PROBLEM No. 2 (20 pts.) Given: Blocks A and B (having masses of 2m and m, respectively) are connected by an inextensible cable, with the cable being pulled over a small pulley of negligible mass. Block
More informationMOMENT OF A FORCE ABOUT A POINT
MOMENT OF A FORCE ABOUT A POINT The tendency of a body to rotate about an axis passing through a specific point O when acted upon by a force (sometimes called a torque). 1 APPLICATIONS A torque or moment
More informationStatics - TAM 211. Lecture 14 October 19, 2018
Statics - TAM 211 Lecture 14 October 19, 2018 Announcements Students are encouraged to practice drawing FBDs, writing out equilibrium equations, and solving these by hand using your calculator. Expending
More informationChapter 6: Structural Analysis
Chapter 6: Structural Analysis Chapter Objectives To show how to determine the forces in the members of a truss using the method of joints and the method of sections. To analyze the forces acting on the
More informationErrata Sheet for S. D. Rajan, Introduction to Structural Analysis & Design (1 st Edition) John Wiley & Sons Publication
S D Rajan, Introduction to Structural Analsis & Design ( st Edition) Errata Sheet for S D Rajan, Introduction to Structural Analsis & Design ( st Edition) John Wile & Sons Publication Chapter Page Correction
More information2.1 Scalars and Vectors
2.1 Scalars and Vectors Scalar A quantity characterized by a positive or negative number Indicated by letters in italic such as A e.g. Mass, volume and length 2.1 Scalars and Vectors Vector A quantity
More informationChapter -4- Force System Resultant
Ishik University / Sulaimani Civil Engineering Department Chapter -4- Force System Resultant 1 2 1 CHAPTER OBJECTIVES To discuss the concept of the moment of a force and show how to calculate it in two
More informationIf the pull is downward (Fig. 1), we want C to point into the page. If the pull is upward (Fig. 2), we want C to point out of the page.
11.5 Cross Product Contemporary Calculus 1 11.5 CROSS PRODUCT This section is the final one about the arithmetic of vectors, and it introduces a second type of vector vector multiplication called the cross
More informationIf the solution does not follow a logical thought process, it will be assumed in error.
Please indicate your group number (If applicable) Circle Your Instructor s Name and Section: MWF 8:30-9:20 AM Prof. Kai Ming Li MWF 2:30-3:20 PM Prof. Fabio Semperlotti MWF 9:30-10:20 AM Prof. Jim Jones
More informationSimplified Structural Analysis and Design for Architects
Simplified Structural Analysis and Design for Architects Second Edition Rima Taher, PhD, PE New Jersey Institute of Technology Bassim Hamadeh, CEO and Publisher Kassie Graves, Director of Acquisitions
More informationCombined Stress. Axial Stress. Axial vs. Eccentric Load Combined Stress Interaction Formulas
Architecture 324 Structures II Combined Stress Axial vs. Eccentric Load Combined Stress Interaction Formulas from Man und Frau den Mond betrachtend 1830-35 by Caspar David Friedrich Alte Nationalgalerie,
More informationREVIEW. Final Exam. Final Exam Information. Final Exam Information. Strategy for Studying. Test taking strategy. Sign Convention Rules
Final Exam Information REVIEW Final Exam (Print notes) DATE: WEDNESDAY, MAY 12 TIME: 1:30 PM - 3:30 PM ROOM ASSIGNMENT: Toomey Hall Room 199 1 2 Final Exam Information Comprehensive exam covers all topics
More informationContinuing Education Course #207 What Every Engineer Should Know About Structures Part B Statics Applications
1 of 6 Continuing Education Course #207 What Every Engineer Should Know About Structures Part B Statics Applications 1. As a practical matter, determining design loads on structural members involves several
More informationPlease review the following statement: I certify that I have not given unauthorized aid nor have I received aid in the completion of this exam.
Please review the following statement: I certify that I have not given unauthorized aid nor have I received aid in the completion of this exam. Signature: INSTRUCTIONS Begin each problem in the space provided
More informationLOVELY PROFESSIONAL UNIVERSITY BASIC ENGINEERING MECHANICS MCQ TUTORIAL SHEET OF MEC Concurrent forces are those forces whose lines of action
LOVELY PROFESSIONAL UNIVERSITY BASIC ENGINEERING MECHANICS MCQ TUTORIAL SHEET OF MEC 107 1. Concurrent forces are those forces whose lines of action 1. Meet on the same plane 2. Meet at one point 3. Lie
More informationFigure Figure
Figure 4-12. Equal probability of selection with simple random sampling of equal-sized clusters at first stage and simple random sampling of equal number at second stage. The next sampling approach, shown
More informationTheory of structure I 2006/2013. Chapter one DETERMINACY & INDETERMINACY OF STRUCTURES
Chapter one DETERMINACY & INDETERMINACY OF STRUCTURES Introduction A structure refers to a system of connected parts used to support a load. Important examples related to civil engineering include buildings,
More informationSAULT COLLEGE OF APPLIED ARTS AND TECHNOLOGY SAULT STE. MARIE, ONTARIO COURSE OUTLINE CODE NO. : MCH110 SEMESTER: TWO
SAULT COLLEGE OF APPLIED ARTS AND TECHNOLOGY SAULT STE. MARIE, ONTARIO COURSE OUTLINE COURSE TITLE: APPLIED MECHANICS CODE NO. : SEMESTER: TWO PROGRAM: AUTHOR: DATE: APPROVED: TOTAL CREDITS: PREREQUISITE(S):
More information