Ishik University / Sulaimani Architecture Department. Structure. ARCH 214 Chapter 5 Equilibrium of a Rigid Body


 Elwin Robinson
 1 years ago
 Views:
Transcription
1 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 the concept of the freebody diagram for a rigid body. To show how to solve rigidbody equilibrium problems using the Equations of equilibrium. 1
2 CHAPTER OUTLINE FreeBody Diagrams Equations of Equilibrium Two and ThreeForce Members Constraints for a Rigid Body FBD is the best method to represent all the known and unknown forces in a system. FreeBody Diagrams FBD is a sketch of the outlined shape of the body, which represents it being isolated from its surroundings. Necessary to show all the forces and couple moments that the surroundings exert on the body so that these effects can be accounted for when equations of equilibrium are applied. 4 2
3 FreeBody Diagrams 5 FreeBody Diagrams 6 3
4 FreeBody Diagrams 7 8 4
5 Support Reactions If the support prevents the translation of a body in a given direction, then a force is developed on the body in that direction. If rotation is prevented, a couple moment is exerted on the body. Consider the three ways a horizontal member, beam is supported at the end.  roller, cylinder  pin 9  fixed support Support Reactions Roller or cylinder Prevent the beam from translating in the vertical direction. Roller can only exerts a force on the beam in the vertical direction. 10 5
6 Support Reactions Pin The pin passes through a hold in the beam and two leaves that are fixed to the ground. Prevents translation of the beam in any direction Φ. The pin exerts a force F on the beam in this direction. 11 Support Reactions Fixed Support This support prevents both translation and rotation of the beam. A couple and moment must be developed on the beam at its point of connection. Force is usually represented in x and y components. 12 6
7 Cable exerts a force on the bracket Type 1 connections Rocker support for this bridge girder allows horizontal movements so that the bridge is free to expand and contract due to temperature Type 5 connections 13 Concrete Girder rest on the ledge that is assumed to act as a smooth contacting surface Type 6 connections Utility building is pin supported at the top of the column Type 8 connections 14 7
8 Floor beams of this building are welded together and thus form fixed connections Type 10 connections 15 External and Internal Forces A rigid body is a composition of particles, both external and internal forces may act on it. For FBD, internal forces act between particles which are contained within the boundary of the FBD, are not represented. Particles outside this boundary exert external forces on the system and must be shown on FBD. FBD for a system of connected bodies may be used for analysis. 16 8
9 Weight and Center of Gravity When a body is subjected to gravity, each particle has a specified weight. For entire body, consider gravitational forces as a system of parallel forces acting on all particles within the boundary. The system can be represented by a single resultant force, known as weight W of the body. Location of the force application is known as the center of gravity. 17 Idealized Models Consider a steel beam used to support the roof joists of a building. For force analysis, reasonable to assume rigid body since small deflections occur when beam is loaded. Bolted connection at A will allow for slight rotation when load is applied => use Pin. Support at B offers no resistance to horizontal movement => use Roller. Building code requirements used to specify the roof loading (calculations of the joist forces). Large roof loading forces account for extreme loading cases and for dynamic or vibration effects. Weight is neglected when it is small compared to the load the beam supports. 18 9
10 Example 5.1 Draw the freebody diagram of the uniform beam. The beam has a mass of 100kg. 19 Solution FreeBody Diagram 20 10
11 Solution Support at A is a fixed wall. Three forces acting on the beam at A denoted as A x, A y, A z, drawn in an arbitrary direction. Unknown magnitudes of these vectors. Assume sense of these vectors. For uniform beam, Weight, W = 100(9.81) = 981N acting through beam s center of gravity, 3m from A. 21 Example 5.2 Draw the freebody diagram of member AB, which is supported by a roller at A and a pin at B. Explain the significance of each force on the diagram
12 Solution 23 Example 5.3 Draw the freebody diagram of the beam which supports the 80 kg load and is supported by the pin at A and a cable which wraps around the pulley at D. Explain the significance of each force on the diagram
13 Solution 25 Equations of Equilibrium For equilibrium of a rigid body in 2D, F x = 0; F y = 0; M O = 0 F x and F y represent the algebraic sums of the x and y components of all the forces acting on the body. M O represents the algebraic sum of the couple moments and moments of the force components about an axis perpendicular to xy plane and passing through arbitrary point O, which may lie on or off the body
14 Alternative Sets of Equilibrium Equations For coplanar equilibrium problems, F x = 0; F y = 0; M O = 0 can be used Two alternative sets of three independent equilibrium equations may also be used. F a = 0; M A = 0; M B = 0 When applying these equations, it is required that a line passing through points A and B is not perpendicular to the a axis. 27 Alternative Sets of Equilibrium Equations Consider FBD of an arbitrarily shaped body. All the forces on FBD may be replaced by an equivalent resultant force F R = F acting at point A and a resultant moment M RA = M A If M A = 0 is satisfied, M RA =
15 Alternative Sets of Equilibrium Equations A second set of alternative equations is M A = 0; M B = 0; M C = 0 Points A, B and C do not lie on the same line. Consider FBD, if M A = 0, M RA = 0 M A = 0 is satisfied if line of action of F R passes through point B. M C = 0 where C does not lie on line AB. F R = 0 and the body is in equilibrium. 29 Example
16 Solution
17 Example 5.5 The cord supports a force of 500N and wraps over the frictionless pulley. Determine the tension in the cord at C and the horizontal and vertical components at pin A. 33 Solution Equations of Equilibrium M A 0; 500N(0.2m) T(0.2m) 0 T 500N Tension remains constant as cord passes over the pulley (true for any angle at which the cord is directed and for any radius of the pulley
18 Solution F A Ax 250N F A A y y x y x 500sin 30 N 0 500N 500cos N 0; 0; N 0 35 Example 5.6 The link is pinconnected at a and rest a smooth support at B. Compute the horizontal and vertical components of reactions at pin A
19 Solution FBD Reaction N B is perpendicular to the link at B. Horizontal and vertical components of reaction are represented at A. 37 Solution Equations of Equilibrium; M 90N. m 60N(1m ) N N F A x B A 0; 200N x 200sin 30 N 0 Ax 100N F A A y y y 233N 0; 0; 60N 200cos 30 B N 0 (0.75m)
20 Example Solution 40 20
21 41 Example
22 Solution
23 Example Solution 46 23
24 47 Two and ThreeForce Members Simplify some equilibrium problems by recognizing members that are subjected top only 2 or 3 forces. TwoForce Members When a member is subject to no couple moments and forces are applied at only two points on a member, the member is called a twoforce member
25 TwoForce Members Hence, only the force magnitude must be determined or stated. Other examples of the twoforce members held in equilibrium are shown in the figures to the right. 49 ThreeForce Members If a member is subjected to only three forces, it is necessary that the forces be either concurrent or parallel for the member to be in equilibrium. To show the concurrency requirement, consider a body with any two of the three forces acting on it, to have line of actions that intersect at point O. To satisfy moment equilibrium about O, the third force must also pass through O, which then makes the force concurrent. If two of the three forces parallel, the point of currency O, is considered at infinity. Third force must parallel to the other two forces to insect at this point
26 Example 5.10 Determine the normal reactions at A and B. 51 Solution 52 26
27 Example 5.11 Determine the tension in the cord and the horizontal and vertical components of reaction at support A of the beam. 53 Solution 54 27
28 Example 5.12 Determine the horizontal and vertical components of reaction at C and the tension in the cable AB for the truss. 55 Solution 56 28
29 Homework 5.1 Determine the horizontal and vertical components of reaction at the pin A and the force in the cable BC. Neglect the thickness of the members. 57 Homework 5.2 Determine the horizontal and vertical components or reaction at the pin A and the reaction on the beam fit C
30 Homework 5.3 Determine the normal reaction at the roller A and horizontal and vertical components at pin B for equilibrium of the member
3.1 CONDITIONS FOR RIGIDBODY EQUILIBRIUM
3.1 CONDITIONS FOR RIGIDBODY 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 informationEQUILIBRIUM OF RIGID BODIES
EQUILIBRIUM OF RIGID BODIES Equilibrium A body in equilibrium is at rest or can translate with constant velocity F = 0 M = 0 EQUILIBRIUM IN TWO DIMENSIONS Case where the force system acting on a rigid
More informationEQUATIONS OF EQUILIBRIUM & TWOAND THREEFORCE MEMEBERS
EQUATIONS OF EQUILIBRIUM & TWOAND THREEFORCE MEMEBERS Today s Objectives: Students will be able to: a) Apply equations of equilibrium to solve for unknowns, and, b) Recognize twoforce members. READING
More informationEQUATIONS OF EQUILIBRIUM & TWO AND THREEFORCE MEMEBERS
EQUATIONS OF EQUILIBRIUM & TWO AND THREEFORCE MEMEBERS Today s Objectives: Students will be able to: a) Apply equations of equilibrium to solve for unknowns, and, b) Recognize twoforce members. InClass
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 freebody diagram for a rigid body
More informationENGR1100 Introduction to Engineering Analysis. Lecture 13
ENGR1100 Introduction to Engineering Analysis Lecture 13 EQUILIBRIUM OF A RIGID BODY & FREEBODY DIAGRAMS Today s Objectives: Students will be able to: a) Identify support reactions, and, b) Draw a freebody
More informationEQUILIBRIUM OF A RIGID BODY
EQUILIBRIUM OF A RIGID BODY Today s Objectives: Students will be able to a) Identify support reactions, and, b) Draw a free diagram. APPLICATIONS A 200 kg platform is suspended off an oil rig. How do we
More informationChapter Objectives. Copyright 2011 Pearson Education South Asia Pte Ltd
Chapter Objectives To develop the equations of equilibrium for a rigid body. To introduce the concept of the freebody diagram for a rigid body. To show how to solve rigidbody equilibrium problems using
More informationEQUILIBRIUM OF A RIGID BODY & FREEBODY DIAGRAMS
Today s Objectives: Students will be able to: EQUILIBRIUM OF A RIGID BODY & FREEBODY DIAGRAMS a) Identify support reactions, and, b) Draw a freebody diagram. InClass Activities: Check Homework Reading
More informationEquilibrium of a Rigid Body. Engineering Mechanics: Statics
Equilibrium of a Rigid Body Engineering Mechanics: Statics Chapter Objectives Revising equations of equilibrium of a rigid body in 2D and 3D for the general case. To introduce the concept of the freebody
More informationAnnouncements. Equilibrium of a Rigid Body
Announcements Equilibrium of a Rigid Body Today s Objectives Identify support reactions Draw a free body diagram Class Activities Applications Support reactions Free body diagrams Examples Engr221 Chapter
More informationEQUATIONS OF EQUILIBRIUM & TWO AND THREEFORCE MEMBERS
EQUATIONS OF EQUILIBRIUM & TWO AND THREEFORCE MEMBERS Today s Objectives: Students will be able to: a) Apply equations of equilibrium to solve for unknowns, and, b) Recognize twoforce members. APPLICATIONS
More informationThe case where there is no net effect of the forces acting on a rigid body
The case where there is no net effect of the forces acting on a rigid body Outline: Introduction and Definition of Equilibrium Equilibrium in TwoDimensions Special cases Equilibrium in ThreeDimensions
More informationThe centroid of an area is defined as the point at which (122) The distance from the centroid of a given area to a specified axis may be found by
Unit 12 Centroids Page 121 The centroid of an area is defined as the point at which (122) The distance from the centroid of a given area to a specified axis may be found by (125) For the area shown
More informationChapter  1. Equilibrium of a Rigid Body
Chapter  1 Equilibrium of a Rigid Body Dr. Rajesh Sathiyamoorthy Department of Civil Engineering, IIT Kanpur hsrajesh@iitk.ac.in; http://home.iitk.ac.in/~hsrajesh/ Condition for RigidBody Equilibrium
More informationChapter 5: Equilibrium of a Rigid Body
Chapter 5: Equilibrium of a Rigid Body Chapter Objectives To develop the equations of equilibrium for a rigid body. To introduce the concept of a freebody diagram for a rigid body. To show how to solve
More informationChapter 5: Equilibrium of a Rigid Body
Chapter 5: Equilibrium of a Rigid Body Develop the equations of equilibrium for a rigid body Concept of the freebody diagram for a rigid body Solve rigidbody equilibrium problems using the equations
More informationEngineering Mechanics Statics
Mechanical Systems Engineering _ 2016 Engineering Mechanics Statics 7. Equilibrium of a Rigid Body Dr. Rami Zakaria Conditions for RigidBody Equilibrium Forces on a particle Forces on a rigid body The
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 informationEquilibrium of a Particle
ME 108  Statics Equilibrium of a Particle Chapter 3 Applications For a spool of given weight, what are the forces in cables AB and AC? Applications For a given weight of the lights, what are the forces
More informationTUTORIAL SHEET 1. magnitude of P and the values of ø and θ. Ans: ø =74 0 and θ= 53 0
TUTORIAL SHEET 1 1. The rectangular platform is hinged at A and B and supported by a cable which passes over a frictionless hook at E. Knowing that the tension in the cable is 1349N, determine the moment
More informationChapter 7: Bending and Shear in Simple Beams
Chapter 7: Bending and Shear in Simple Beams Introduction A beam is a long, slender structural member that resists loads that are generally applied transverse (perpendicular) to its longitudinal axis.
More informationEQUILIBRIUM OF RIGID BODIES IN TWO DIMENSIONS
EQUILIBRIUM OF RIGID BODIES IN TWO DIMENSIONS If the resultant of all external forces acting on a rigid body is zero, then the body is said to be in equilibrium. Therefore, in order for the rigid body
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 informationPAT 101 FUNDAMENTAL OF ENGINEERING MECHANICS EQUILIBREQUILIBRIUM OF A RIGID BODY IUM OF A RIGID BODY
PAT 101 FUNDAMENTAL OF ENGINEERING MECHANICS EQUILIBREQUILIBRIUM OF A RIGID BODY IUM OF A RIGID BODY MARDHIAH FARHANA BINT OMAR Week 56 EQUILIBRIUM OF A RIGID BODY Conditions for Rigid Equilibrium FreeBody
More informationEQUATIONS OF EQUILIBRIUM & TWO AND THREEFORCE MEMEBERS
EQUATIONS OF EQUILIBRIUM & TWO AND THREEFORCE MEMEBERS Today s Objectives: Students will be able to: a) Apply equations of equilibrium to solve for unknowns, and b) Recognize twoforce members. InClass
More informationMECHANICS OF STRUCTURES SCI 1105 COURSE MATERIAL UNIT  I
MECHANICS OF STRUCTURES SCI 1105 COURSE MATERIAL UNIT  I Engineering Mechanics Branch of science which deals with the behavior of a body with the state of rest or motion, subjected to the action of forces.
More informationKINGS COLLEGE OF ENGINEERING ENGINEERING MECHANICS QUESTION BANK UNIT I  PARTA
KINGS COLLEGE OF ENGINEERING ENGINEERING MECHANICS QUESTION BANK Sub. Code: CE1151 Sub. Name: Engg. Mechanics UNIT I  PARTA Sem / Year II / I 1.Distinguish the following system of forces with a suitable
More informationStatics Chapter II Fall 2018 Exercises Corresponding to Sections 2.1, 2.2, and 2.3
Statics Chapter II Fall 2018 Exercises Corresponding to Sections 2.1, 2.2, and 2.3 2 3 Determine the magnitude of the resultant force FR = F1 + F2 and its direction, measured counterclockwise from the
More informationSTATICS. Bodies. Vector Mechanics for Engineers: Statics VECTOR MECHANICS FOR ENGINEERS: Design of a support
4 Equilibrium CHAPTER VECTOR MECHANICS FOR ENGINEERS: STATICS Ferdinand P. Beer E. Russell Johnston, Jr. Lecture Notes: J. Walt Oler Texas Tech University of Rigid Bodies 2010 The McGrawHill Companies,
More informationCHAPTER 2: EQUILIBRIUM OF RIGID BODIES
For a rigid body to be in equilibrium, the net force as well as the net moment about any arbitrary point O must be zero Summation of all external forces. Equilibrium: Sum of moments of all external forces.
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 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 information5.2 Rigid Bodies and TwoDimensional Force Systems
5.2 Rigid odies and TwoDimensional Force Systems 5.2 Rigid odies and TwoDimensional Force Systems Procedures and Strategies, page 1 of 1 Procedures and Strategies for Solving Problems Involving Equilibrium
More informationAnnouncements. Trusses Method of Joints
Announcements Mountain Dew is an herbal supplement Today s Objectives Define a simple truss Trusses Method of Joints Determine the forces in members of a simple truss Identify zeroforce members Class
More informationChapter 8. Rotational Equilibrium and Rotational Dynamics. 1. Torque. 2. Torque and Equilibrium. 3. Center of Mass and Center of Gravity
Chapter 8 Rotational Equilibrium and Rotational Dynamics 1. Torque 2. Torque and Equilibrium 3. Center of Mass and Center of Gravity 4. Torque and angular acceleration 5. Rotational Kinetic energy 6. Angular
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 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. 42 Introduction For a rigid body, the
More informationVALLIAMMAI ENGINEERING COLLEGE SRM NAGAR, KATTANKULATHUR DEPARTMENT OF MECHANICAL ENGINEERING
VALLIAMMAI ENGINEERING COLLEGE SRM NAGAR, KATTANKULATHUR 603203 DEPARTMENT OF MECHANICAL ENGINEERING BRANCH: MECHANICAL YEAR / SEMESTER: I / II UNIT 1 PART A 1. State Newton's three laws of motion? 2.
More informationStatics deal with the condition of equilibrium of bodies acted upon by forces.
Mechanics It is defined as that branch of science, which describes and predicts the conditions of rest or motion of bodies under the action of forces. Engineering mechanics applies the principle of mechanics
More informationLecture 14 February 16, 2018
Statics  TAM 210 & TAM 211 Lecture 14 February 16, 2018 SoonTrending.com Announcements Structured office hours of working through practice problems will be held during Sunday office hours, starting Sunday
More information7 STATICALLY DETERMINATE PLANE TRUSSES
7 STATICALLY DETERMINATE PLANE TRUSSES OBJECTIVES: This chapter starts with the definition of a truss and briefly explains various types of plane truss. The determinancy and stability of a truss also will
More informationEquilibrium. Rigid Bodies VECTOR MECHANICS FOR ENGINEERS: STATICS. Eighth Edition CHAPTER. Ferdinand P. Beer E. Russell Johnston, Jr.
Eighth E 4 Equilibrium CHAPTER VECTOR MECHANICS FOR ENGINEERS: STATICS Ferdinand P. Beer E. Russell Johnston, Jr. Lecture Notes: J. Walt Oler Texas Tech University of Rigid Bodies Contents Introduction
More informationAnna University May/June 2013 Exams ME2151 Engineering Mechanics Important Questions.
Anna University May/June 2013 Exams ME2151 Engineering Mechanics Important Questions 1. Find the resultant force and its direction for the given figure 2. Two forces are acting at a point O as shown in
More informationEng Sample Test 4
1. An adjustable tow bar connecting the tractor unit H with the landing gear J of a large aircraft is shown in the figure. Adjusting the height of the hook F at the end of the tow bar is accomplished by
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 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 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 information11.1 Virtual Work Procedures and Strategies, page 1 of 2
11.1 Virtual Work 11.1 Virtual Work rocedures and Strategies, page 1 of 2 rocedures and Strategies for Solving roblems Involving Virtual Work 1. Identify a single coordinate, q, that will completely define
More informationSection 6: 6: Kinematics Kinematics 61
61 Section 6: Kinematics Biomechanics  angular kinematics Same as linear kinematics, but There is one vector along the moment arm. There is one vector perpendicular to the moment arm. MA F RMA F RD F
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 informationC7047. PART A Answer all questions, each carries 5 marks.
7047 Reg No.: Total Pages: 3 Name: Max. Marks: 100 PJ DUL KLM TEHNOLOGIL UNIVERSITY FIRST SEMESTER.TEH DEGREE EXMINTION, DEEMER 2017 ourse ode: E100 ourse Name: ENGINEERING MEHNIS PRT nswer all questions,
More informationEQUILIBRIUM OF A PARTICLE, THE FREEBODY DIAGRAM & COPLANAR FORCE SYSTEMS
EQUILIBRIUM OF PRTICLE, THE FREEBODY DIGRM & COPLNR FORCE SYSTEMS Today s Objectives: Students will be able to : a) Draw a free body diagram (FBD), and, b) pply equations of equilibrium to solve a 2D
More informationSupport Idealizations
IVL 3121 nalysis of Statically Determinant Structures 1/12 nalysis of Statically Determinate Structures nalysis of Statically Determinate Structures The most common type of structure an engineer will analyze
More informationTHE WORK OF A FORCE, THE PRINCIPLE OF WORK AND ENERGY & SYSTEMS OF PARTICLES
THE WORK OF A FORCE, THE PRINCIPLE OF WORK AND ENERGY & SYSTEMS OF PARTICLES Today s Objectives: Students will be able to: 1. Calculate the work of a force. 2. Apply the principle of work and energy to
More informationEngineering Mechanics: Statics in SI Units, 12e
Engineering Mechanics: Statics in SI Units, 12e 3 Equilibrium of a Particle 1 Chapter Objectives Concept of the freebody diagram for a particle Solve particle equilibrium problems using the equations
More informationChapter 6: Structural Analysis
Chapter 6: Structural Analysis APPLICATIONS Trusses are commonly used to support a roof. For a given truss geometry and load, how can we determine the forces in the truss members and select their sizes?
More informationEquilibrium & Elasticity
PHYS 101 Previous Exam Problems CHAPTER 12 Equilibrium & Elasticity Static equilibrium Elasticity 1. A uniform steel bar of length 3.0 m and weight 20 N rests on two supports (A and B) at its ends. A block
More informationOutline: Frames Machines Trusses
Outline: Frames Machines Trusses Properties and Types Zero Force Members Method of Joints Method of Sections Space Trusses 1 structures are made up of several connected parts we consider forces holding
More informationEQUATIONS OF EQUILIBRIUM & TWO AND THREEFORCE MEMBERS
EQUATIONS OF EQUILIBRIUM & TWO AND THREEFORCE MEMBERS Today s Objectives: Students will be able to: a) Apply equations of equilibrium to solve for unknowns b) Identify support reactions c) Recognize
More informationENGINEERING MECHANICS SOLUTIONS UNITI
LONG QUESTIONS ENGINEERING MECHANICS SOLUTIONS UNITI 1. A roller shown in Figure 1 is mass 150 Kg. What force P is necessary to start the roller over the block A? =90+25 =115 = 90+25.377 = 115.377 = 360(115+115.377)
More informationDept of ECE, SCMS Cochin
B B2B109 Pages: 3 Reg. No. Name: APJ ABDUL KALAM TECHNOLOGICAL UNIVERSITY SECOND SEMESTER B.TECH DEGREE EXAMINATION, MAY 2017 Course Code: BE 100 Course Name: ENGINEERING MECHANICS Max. Marks: 100 Duration:
More information1 MR SAMPLE EXAM 3 FALL 2013
SAMPLE EXAM 3 FALL 013 1. A merrygoround rotates from rest with an angular acceleration of 1.56 rad/s. How long does it take to rotate through the first rev? A) s B) 4 s C) 6 s D) 8 s E) 10 s. A wheel,
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 informationCourse Overview. Statics (Freshman Fall) Dynamics: x(t)= f(f(t)) displacement as a function of time and applied force
Course Overview Statics (Freshman Fall) Engineering Mechanics Dynamics (Freshman Spring) Strength of Materials (Sophomore Fall) Mechanism Kinematics and Dynamics (Sophomore Spring ) Aircraft structures
More informationSTATICS. Bodies VECTOR MECHANICS FOR ENGINEERS: Ninth Edition CHAPTER. Ferdinand P. Beer E. Russell Johnston, Jr.
N E 4 Equilibrium CHAPTER VECTOR MECHANICS FOR ENGINEERS: STATICS Ferdinand P. Beer E. Russell Johnston, Jr. Lecture Notes: J. Walt Oler Texas Tech University of Rigid Bodies 2010 The McGrawHill Companies,
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 informationUnit 21 Couples and Resultants with Couples
Unit 21 Couples and Resultants with Couples Page 211 Couples A couple is defined as (215) Moment of Couple The coplanar forces F 1 and F 2 make up a couple and the coordinate axes are chosen so that
More informationwhere x and y are any two nonparallel directions in the xyplane. iii) One force equation and one moment equation.
Concurrent Force System ( of Particles) Recall that the resultant of a concurrent force system is a force F R that passes through the point of concurrency, which we label as point O. The moment equation,
More informationE 490 FE Exam Prep. Engineering Mechanics
E 490 FE Exam Prep Engineering Mechanics 2008 E 490 Course Topics Statics Newton s Laws of Motion Resultant Force Systems Moment of Forces and Couples Equilibrium Pulley Systems Trusses Centroid of an
More informationPHY 1150 Doug Davis Chapter 8; Static Equilibrium 8.3, 10, 22, 29, 52, 55, 56, 74
PHY 1150 Doug Davis Chapter 8; Static Equilibrium 8.3, 10, 22, 29, 52, 55, 56, 74 8.3 A 2kg ball is held in position by a horizontal string and a string that makes an angle of 30 with the vertical, as
More informationSTATICS. Friction VECTOR MECHANICS FOR ENGINEERS: Eighth Edition CHAPTER. Ferdinand P. Beer E. Russell Johnston, Jr.
Eighth E 8 Friction CHAPTER VECTOR MECHANICS FOR ENGINEERS: STATICS Ferdinand P. Beer E. Russell Johnston, Jr. Lecture Notes: J. Walt Oler Texas Tech University Contents Introduction Laws of Dry Friction.
More informationEquilibrium of a Rigid Body. Chapter 5
Equilibrium of a Rigid Body Chapter 5 Overview Rigid Body Equilibrium Free Body Diagrams Equations of Equilibrium 2 and 3Force Members Statical Determinacy CONDITIONS FOR RIGIDBODY EQUILIBRIUM Recall
More informationPhysics 211 Week 10. Statics: Walking the Plank (Solution)
Statics: Walking the Plank (Solution) A uniform horizontal beam 8 m long is attached by a frictionless pivot to a wall. A cable making an angle of 37 o, attached to the beam 5 m from the pivot point, supports
More information2016 ENGINEERING MECHANICS
Set No 1 I B. Tech I Semester Regular Examinations, Dec 2016 ENGINEERING MECHANICS (Com. to AE, AME, BOT, CHEM, CE, EEE, ME, MTE, MM, PCE, PE) Time: 3 hours Max. Marks: 70 Question Paper Consists of PartA
More informationChapter 12 Static Equilibrium
Chapter Static Equilibrium. Analysis Model: Rigid Body in Equilibrium. More on the Center of Gravity. Examples of Rigid Objects in Static Equilibrium CHAPTER : STATIC EQUILIBRIUM AND ELASTICITY.) The Conditions
More informationwhere G is called the universal gravitational constant.
UNITI BASICS & STATICS OF PARTICLES 1. What are the different laws of mechanics? First law: A body does not change its state of motion unless acted upon by a force or Every object in a state of uniform
More informationJNTU World. Subject Code: R13110/R13
Set No  1 I B. Tech I Semester Regular Examinations Feb./Mar.  2014 ENGINEERING MECHANICS (Common to CE, ME, CSE, PCE, IT, Chem E, Aero E, AME, Min E, PE, Metal E) Time: 3 hours Max. Marks: 70 Question
More informationSIMPLE TRUSSES, THE METHOD OF JOINTS, & ZEROFORCE MEMBERS
SIMPLE TRUSSES, THE METHOD OF JOINTS, & ZEROFORCE MEMBERS Today s Objectives: Students will be able to: a) Define a simple truss. b) Determine the forces in members of a simple truss. c) Identify zeroforce
More informationThe University of Melbourne Engineering Mechanics
The University of Melbourne 436291 Engineering Mechanics Tutorial Four Poisson s Ratio and Axial Loading Part A (Introductory) 1. (Problem 922 from Hibbeler  Statics and Mechanics of Materials) A short
More informationPhysics 8, Fall 2017, Practice Exam.
Physics 8, Fall 2017, Practice Exam. Name: This openbook takehome exam is 10% of your course grade. (The inclass final exam will be 20% of your course grade. For the inclass exam, you can bring one
More informationEquilibrium Equilibrium and Trusses Trusses
Equilibrium and Trusses ENGR 221 February 17, 2003 Lecture Goals 64 Equilibrium in Three Dimensions 71 Introduction to Trusses 72Plane Trusses 73 Space Trusses 74 Frames and Machines Equilibrium Problem
More informationJNTU World. Subject Code: R13110/R13 '' '' '' ''' '
Set No  1 I B. Tech I Semester Supplementary Examinations Sept.  2014 ENGINEERING MECHANICS (Common to CE, ME, CSE, PCE, IT, Chem E, Aero E, AME, Min E, PE, Metal E) Time: 3 hours Max. Marks: 70 Question
More information.VALLIAMMAI ENGINEERING COLLEGE
.VALLIAMMAI ENGINEERING COLLEGE SRM Nagar, Kattankulathur 603 203 DEPARTMENT OF GENERAL ENGINEERING QUESTION BANK II SEMESTER GE 8292 Engineering Mechanics Regulation 2017 Academic Year 2017 18 VALLIAMMAI
More informationEQUILIBRIUM and ELASTICITY
PH 2211D Spring 2013 EQUILIBRIUM and ELASTICITY Lectures 3032 Chapter 12 (Halliday/Resnick/Walker, Fundamentals of Physics 9 th edition) 1 Chapter 12 Equilibrium and Elasticity In this chapter we will
More informationEngineering Mechanics Department of Mechanical Engineering Dr. G. Saravana Kumar Indian Institute of Technology, Guwahati
Engineering Mechanics Department of Mechanical Engineering Dr. G. Saravana Kumar Indian Institute of Technology, Guwahati Module 3 Lecture 6 Internal Forces Today, we will see analysis of structures part
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 informationENGR1100 Introduction to Engineering Analysis. Lecture 23
ENGR1100 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 informationThe University of Melbourne Engineering Mechanics
The University of Melbourne 436291 Engineering Mechanics Tutorial Eleven Instantaneous Centre and General Motion Part A (Introductory) 1. (Problem 5/93 from Meriam and Kraige  Dynamics) For the instant
More informationMechanics of Materials
Mechanics of Materials 2. Introduction Dr. Rami Zakaria References: 1. Engineering Mechanics: Statics, R.C. Hibbeler, 12 th ed, Pearson 2. Mechanics of Materials: R.C. Hibbeler, 9 th ed, Pearson 3. Mechanics
More informationPhysics 8 Wednesday, October 25, 2017
Physics 8 Wednesday, October 25, 2017 HW07 due Friday. It is mainly rotation, plus a couple of basic torque questions. And there are only 8 problems this week. For today, you read (in Perusall) Onouye/Kane
More informationEngineering Mechanics: Statics in SI Units, 12e
Engineering Mechanics: Statics in SI Units, 12e 3 Equilibrium of a Particle Chapter Objectives To introduce the concept of the freebody diagram for a particle To show how to solve particle equilibrium
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 information4.0 m s 2. 2 A submarine descends vertically at constant velocity. The three forces acting on the submarine are viscous drag, upthrust and weight.
1 1 wooden block of mass 0.60 kg is on a rough horizontal surface. force of 12 N is applied to the block and it accelerates at 4.0 m s 2. wooden block 4.0 m s 2 12 N hat is the magnitude of the frictional
More informationEquilibrium of Rigid Bodies
Equilibrium of Rigid Bodies 1 2 Contents Introduction FreeBod Diagram Reactions at Supports and Connections for a wodimensional Structure Equilibrium of a Rigid Bod in wo Dimensions Staticall Indeterminate
More informationSOLUTION 8 1. a+ M B = 0; N A = 0. N A = kn = 16.5 kn. Ans. + c F y = 0; N B = 0
8 1. The mine car and its contents have a total mass of 6 Mg and a center of gravity at G. If the coefficient of static friction between the wheels and the tracks is m s = 0.4 when the wheels are locked,
More informationMethod of Sections for Truss Analysis
Method of Sections for Truss Analysis Notation: (C) = shorthand for compression P = name for load or axial force vector (T) = shorthand for tension Joint Configurations (special cases to recognize for
More informationCIV100: Mechanics. Lecture Notes. Module 1: Force & Moment in 2D. You Know What to Do!
CIV100: Mechanics Lecture Notes Module 1: Force & Moment in 2D By: Tamer ElDiraby, PhD, PEng. Associate Prof. & Director, I2C University of Toronto Acknowledgment: Hesham Osman, PhD and Jinyue Zhang,
More informationLecture 23. ENGR1100 Introduction to Engineering Analysis FRAMES S 1
ENGR1100 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 informationEQUATIONS OF MOTION: GENERAL PLANE MOTION (Section 17.5) Today s Objectives: Students will be able to analyze the planar kinetics of a rigid body
EQUATIONS OF MOTION: GENERAL PLANE MOTION (Section 17.5) Today s Objectives: Students will be able to analyze the planar kinetics of a rigid body undergoing general plane motion. APPLICATIONS As the soil
More information