MECHANICS OF STRUCTURES SCI 1105 COURSE MATERIAL UNIT - I

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "MECHANICS OF STRUCTURES SCI 1105 COURSE MATERIAL UNIT - I"

Transcription

1 MECHANICS OF STRUCTURES SCI 1105 COURSE MATERIAL UNIT - I

2 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. Much of modern engineering mechanics is based on Issac Newton s Laws of motion while the modern practice of their application can be traced back to Stephen Timoshenko, who is said to be the father of modern engineering mechanics.

3 Applied mechanics Branch of engineering mechanics which deals with the study of different laws of mechanics as applied to the solution of engineering problems. The advances and research in Applied Mechanics has wide application in many departments. Some of the departments that put the subject into practice are Civil Engineering, Mechanical Engineering, Construction Engineering, Materials Science and Engineering, Aerospace Engineering, Chemical Engineering, Electrical Engineering, Nuclear Engineering, Structural Engineering and Bioengineering.

4 Applied mechanics examines the response of bodies (solids and fluids) or systems of bodies to external forces. Some examples of mechanical systems include the flow of a liquid under pressure, the fracture of a solid from an applied force, or the vibration of an ear in response to sound.

5 Mechanics of Rigid Bodies Engineerin g Mechanics Mechanics of Deformable Bodies Mechanics of Fluids Statics (Study of Body at Rest) Dynamics (Study of Body in Motion) Kinematic s Kinetics

6 Rigid Body It is composed of large number of particles, which occupy fixed positions with respect to each other before and after applying load. Relative distances of its particles remains invariable.

7 Force It is agent which changes or tends to change the state of rest or of uniform motion of a body upon which it acts. It represents the action of one body on another. It is the pull or Push exerted by one body on another. Force is characterized by Magnitude : Newton Line of action : Infinite straight line along which the force acts. Direction : angle with the fixed axis and the sense of force. Y 50 N 45 0 X

8 Force system When several forces act simultaneously on a body, they constitute a system of forces Types of Force System: 1. Coplanar Force Force in Plane 2. Non Coplanar Force Force in Space

9

10 Collinear forces Line of action of all the forces act along the same line. Eg. : Forces on a rope in a tug of war.

11 Coplanar parallel forces All forces are parallel to each other and lie in a single plane. Eg. : System of forces acting on a beam subjected to vertical loads (including reactions).

12 Coplanar like parallel Forces All forces are parallel to each other, lie in a single plane and are acting in the same direction. Eg. : Weight of a stationary train on a rail when the track is straight.

13 Coplanar concurrent forces Line of action of all forces pass through a single point and forces lie in the same plane. Eg. : Forces on a rod resting against a wall.

14 Coplanar non-concurrent Forces All forces do not meet at a point, but lie in a single plane. Eg. : Forces on a ladder resting against a wall when a person stands on a rung which is not at its centre of gravity

15 Non-coplanar parallel Forces All the forces are parallel to each other, but not in same plane. Eg. : The weight of benches in a classroom.

16 Non-coplanar concurrent Forces All forces do not lie in the same plane, but their lines of action pass through a single point. Eg. : A tripod carrying a camera

17 Non-coplanar non-concurrent forces All forces do not lie in the same plane and their lines of action do not pass through a single point. Eg. : Forces acting on a moving bus.

18 Resultant Force If a number of forces acting on a particle simultaneously are replaced by a single force, which could produce the same effect as produced by the given forces. These are the equivalent forces of all the given Resultant Force forces. a 1 N 2 N 3 N F 1 F 2 F 3 b a 6 N b

19 Resolution of Force The resolved part of a force F along X- axis = F. cos θ The resolved part of a force F along y- axis = F. sin θ Where, θ = angle between F and x-axis

20 Laws of Mechanics The following are the fundamental laws of mechanics: Newton s first law Newton s second law Newton s third law Newton s law of gravitation Law of transmissibility of forces, and Parallelogram law of forces.

21 Newton s First Law It states that every body continues in its state of rest or of uniform motion in a straight line unless it is compelled by external agency acting on it. This leads to the definition of force as the external agency which changes or tends to change the state of rest or uniform linear motion of the body.

22 Newton s Second Law It states that the rate of change of momentum of a body is directly proportional to the impressed force and it takes place in the direction of the force acting on it.

23 Newton s Third Law It states that for every action there is an equal and opposite reaction. Consider the two bodies in contact with each other. Let one body applies a force F on another. According to this law the second body develops a reactive force R which is equal in magnitude to force F and acts in the line same as F but in the opposite direction. Figure shows the action R Reaction of the F - Force ball and the reaction from the floor. Ball R F Floor

24 Newton s Law of Gravitation Everybody attracts the other body. The force of attraction between any two bodies is directly proportional to their masses and inversely proportional to the square of the distance between them

25 Law of Transmissibility of Force According to this law the state of rest or motion of the rigid body is unaltered if a force acting on the body is replaced by another force of the same magnitude and direction but acting anywhere on the body along the line of action of the replaced force.

26 Parallelogram Law of Forces: It states that If two forces acting simultaneously on a particle by represented in magnitude and direction, by 2 adjacent sides of a parallelogram, then the resultant may be in magnitude and direction, by the diagonal of the parallelogram which passes through their point of interaction.

27

28 Triangle Law of Forces: It states that if 2 forces acting simultaneously on a R particle be represented F in magnitude 2 and direction by 2 sides of a θ triangle taken in order, their resultant may be represented F 1 in magnitude and direction, by the third side of the triangle taken in opposite order.

29 Lami s Theorem In statics, Lami's theorem is an equation that relates the magnitudes of three coplanar, concurrent and noncollinear forces, that keeps a body in static equilibrium. Let A, B and C are the magnitudes of three coplanar, concurrent and non-collinear forces, which keep the object in static equilibrium and α, β and γ are the angles directly opposite to the forces A, B and C respectively

30 It states that If three coplanar forces acting on a point be in equilibrium, then each force is proportional to the sine of the angle between the other two.

31 Condition of Equilibrium The basic tool in structural analysis is the usage of the equilibrium equations. 3 conditions are; The algebraic sum of the horizontal components of all the forces should be zero. H = 0 The algebraic sum of the vertical components of all the forces should be zero. V = 0 The algebraic sum of the moments of all the forces should be zero. M = 0

32 Equilibrium and Equilibrant: θ R E A particle subjected to a 3 coplanar concurrent forces. θ Let the resultant force of the force system is R with direction with horizontal. Due to this resultant force, the particle may starts moving in the direction of resultant force. But, if an additional force is applied of same magnitude but in opposite direction in the line of action.

33 Then, the movement of the particle will be arrested or the particle is said to be in equilibrium. The force E which bring the particle to equilibrium is known as Equilibrant. Principle of Equilibrium developed from the force law of Equilibrium, F = 0

34 Types of Structural Members Structure: Structure refers to a system of connected parts used to support load, such as buildings, bridges, towers, etc. Types of structural members: Tension members Compression members or columns Flexural members Members subjected to combined loading

35 Tension members: Tension members are structural elements that are subjected to axial tensile forces. Eg: Bracing for buildings and bridges, truss members, and cables.

36 Tension members

37 Compression members Compression members are structural elements that are pushed together or carry a load subjected only to axial compressive forces. Eg: Column, top chords of trusses, diagonal, bracing members,etc.

38 Flexural members( Beams) Horizontal or inclined structural member spanning a distance between one or more supports, and carrying vertical loads across its longitudinal axis. When the cross section of the beam varies along the length it is called as tapered or haunched beam. It is designed to resist bending moment and shear force.

39 Types of beam Simply supported beam Fixed beam Cantilever beam Continuous beam Overhanging beam

40 Simply supported: Beam which is supported at both the ends alone is referred to as simply supported beam. Fixed beam: Beam which is held rigid at both the ends is called fixed beam.

41 Cantilever beam : Beam which is fixed at one end and free at the other end is called as a cantilever beam. Continuous beam: Beam which consists of more than two number of supports is called continuous beam.

42 Overhanging beam: If the span of the beam is extending beyond the supports, it is referred to as overhanging beam. The extended part beyond the support is called overhang. There are two types of overhanging beam. Single side overhanging beam Double side overhanging beam

43 If the span of beam is extended only on one side, it is called as single side overhanging beam. If the span is extended on both the sides of support, it is called double side overhanging beam. Members subjected to combined loading: Columns subjected to flexural forces in addition to axial forces are called as beam columns.

44 Types of Load Dead load: Dead loads are permanent or stationary loads which are transferred to structure throughout the life span. Dead load is primarily due to self weight of structural members. Live load or Imposed load : Live loads moving loads It is due to the occupancy of the building like weights of movable partitions or furniture etc. The floor slabs have to be designed to carry either uniformly distributed loads or concentrated loads whichever produce greater stresses in the part under consideration.

45 Impact loads: Types of Load Sudden application of load is called impact. Impact load is caused by vibration or impact or acceleration. Wind loads: Wind load is horizontal load caused by the movement of air relative to earth. Wind load is required to be considered in design especially when the open area of the building exceeds two times the dimensions transverse to the exposed wind surface.

46 Earthquake load : Earthquake loads are horizontal loads caused by the earthquake and shall be computed in accordance with IS For monolithic reinforced concrete structures located in the seismic zone 2, and 3 without more than 5 storey high and importance factor less than 1, the seismic forces are not critical.

47 Types of Support The types of support used in structural members Roller Pinned Simply supported Fixed These supports can be located anywhere along a structural element. They are found at the ends, at midpoints, or at any other intermediate points. The type of support connection determines the type of load that the support can resist. The support type also has a great effect on the load bearing capacity of each element.

48 Types of Support

49 Roller support Roller supports are free to rotate and translate along the surface upon which the roller rests. The surface can be horizontal, vertical, or sloped at any angle. The resulting reaction force is always a single force that is perpendicular to, and away from, the surface. Roller supports are commonly located at one end of long bridges. This allows the bridge structure to expand and contract with temperature changes. Roller supports can also take the form of rubber bearings, rockers, or a set of gears which are designed to allow a limited amount of lateral movement. A roller support cannot provide resistance to a lateral forces.

50 Pinned support A pinned support can resist both vertical and horizontal forces but not a moment. They will allow the structural member to rotate, but not to translate in any direction. Many connections are assumed to be pinned connections even though they might resist a small amount of moment in reality. Pinned connection could allow rotation in only one direction; providing resistance to rotation in any other direction. The knee can be idealized as a connection which allows rotation in only one direction and provides resistance to lateral movement.

51 Fixed support Fixed supports can resist vertical and horizontal forces as well as a moment. Since they restrain both rotation and translation, they are also known as rigid supports. This means that a structure only needs one fixed support in order to be stable. A structure with a fixed support becomes a statically determinate structure. All three equations of equilibrium can be satisfied.

52 Simple support It is almost similar to pinned support. Simple supports are idealized by some to be frictionless surface supports. A simple support can be found as a type of support for long bridges or roof span. Simple supports are often found in zones of frequent seismic activity.

53 Concept of Transfer of Forces BEAMS It is a horizontal structural member which is transverse to its axis. Simplest structural element used to support loads It may be curved or straight. Internal stresses that develop in a beam are axial forces, bending moment and shear force.

54 Transfer of loads in beams: In a beam, loads are assumed to act on a beam in a plane containing the axis of symmetry. It carry the loads by deflecting in the same plane without twisting. It transfers the load by bending action.

55 PLANE TRUSSES Rigid skeletal structures usually with triangle shaped frames are stable. Consists of short thin members connected by hinges in triangulated platform. Trusses carry axial forces only. Members are subjected to compressive and tensile stresses.

56 COLUMN It is a vertical member in which compression the predominant internal force. In order to withstand the external force, the column should have sufficient compressive strength.

Chapter 7: Bending and Shear in Simple Beams

Chapter 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 information

Introduction to Engineering Mechanics

Introduction to Engineering Mechanics CHPTER 1 Introduction to Engineering Mechanics The state of rest and state of motion of the bodies under the action of different forces has engaged the attention of philosophers, mathematicians and scientists

More information

MECHANICS OF MATERIALS. Prepared by Engr. John Paul Timola

MECHANICS OF MATERIALS. Prepared by Engr. John Paul Timola MECHANICS OF MATERIALS Prepared by Engr. John Paul Timola Mechanics of materials branch of mechanics that studies the internal effects of stress and strain in a solid body. stress is associated with the

More information

Emanthra.com ...(2.1) For more visit our Website. Lecture 2: Equation of Equilibrium

Emanthra.com ...(2.1) For more visit our Website. Lecture 2: Equation of Equilibrium Lecture 2: Equation of Equilibrium A particle is in equilibrium if it is stationary or it moves uniformly relative to an inertial frame of reference. A body is in equilibrium if all the particles that

More information

UNIT 1 STRESS STRAIN AND DEFORMATION OF SOLIDS, STATES OF STRESS 1. Define stress. When an external force acts on a body, it undergoes deformation.

UNIT 1 STRESS STRAIN AND DEFORMATION OF SOLIDS, STATES OF STRESS 1. Define stress. When an external force acts on a body, it undergoes deformation. UNIT 1 STRESS STRAIN AND DEFORMATION OF SOLIDS, STATES OF STRESS 1. Define stress. When an external force acts on a body, it undergoes deformation. At the same time the body resists deformation. The magnitude

More information

EQUILIBRIUM and ELASTICITY

EQUILIBRIUM and ELASTICITY PH 221-1D Spring 2013 EQUILIBRIUM and ELASTICITY Lectures 30-32 Chapter 12 (Halliday/Resnick/Walker, Fundamentals of Physics 9 th edition) 1 Chapter 12 Equilibrium and Elasticity In this chapter we will

More information

Seismic design of bridges

Seismic design of bridges NATIONAL TECHNICAL UNIVERSITY OF ATHENS LABORATORY FOR EARTHQUAKE ENGINEERING Seismic design of bridges Lecture 3 Ioannis N. Psycharis Capacity design Purpose To design structures of ductile behaviour

More information

ARCH 614 Note Set 2 S2011abn. Forces and Vectors

ARCH 614 Note Set 2 S2011abn. Forces and Vectors orces and Vectors Notation: = name for force vectors, as is A, B, C, T and P = force component in the direction = force component in the direction h = cable sag height L = span length = name for resultant

More information

Hong Kong Institute of Vocational Education (Tsing Yi) Higher Diploma in Civil Engineering Structural Mechanics. Chapter 1 PRINCIPLES OF STATICS

Hong Kong Institute of Vocational Education (Tsing Yi) Higher Diploma in Civil Engineering Structural Mechanics. Chapter 1 PRINCIPLES OF STATICS PRINCIPLES OF STTICS Statics is the study of how forces act and react on rigid bodies which are at rest or not in motion. This study is the basis for the engineering principles, which guide the design

More information

APPLIED MATHEMATICS AM 02

APPLIED MATHEMATICS AM 02 AM SYLLABUS (2013) APPLIED MATHEMATICS AM 02 SYLLABUS Applied Mathematics AM 02 Syllabus (Available in September) Paper I (3 hrs)+paper II (3 hrs) Applied Mathematics (Mechanics) Aims A course based on

More information

MECHANICS OF SOLIDS Credit Hours: 6

MECHANICS OF SOLIDS Credit Hours: 6 MECHANICS OF SOLIDS Credit Hours: 6 Teaching Scheme Theory Tutorials Practical Total Credit Hours/week 4 0 6 6 Marks 00 0 50 50 6 A. Objective of the Course: Objectives of introducing this subject at second

More information

Structural Steelwork Eurocodes Development of A Trans-national Approach

Structural Steelwork Eurocodes Development of A Trans-national Approach Structural Steelwork Eurocodes Development of A Trans-national Approach Course: Eurocode Module 7 : Worked Examples Lecture 0 : Simple braced frame Contents: 1. Simple Braced Frame 1.1 Characteristic Loads

More information

Module 6. Approximate Methods for Indeterminate Structural Analysis. Version 2 CE IIT, Kharagpur

Module 6. Approximate Methods for Indeterminate Structural Analysis. Version 2 CE IIT, Kharagpur Module 6 Approximate Methods for Indeterminate Structural Analysis Lesson 35 Indeterminate Trusses and Industrial rames Instructional Objectives: After reading this chapter the student will be able to

More information

SERVICEABILITY LIMIT STATE DESIGN

SERVICEABILITY LIMIT STATE DESIGN CHAPTER 11 SERVICEABILITY LIMIT STATE DESIGN Article 49. Cracking Limit State 49.1 General considerations In the case of verifications relating to Cracking Limit State, the effects of actions comprise

More information

3. BEAMS: STRAIN, STRESS, DEFLECTIONS

3. BEAMS: STRAIN, STRESS, DEFLECTIONS 3. BEAMS: STRAIN, STRESS, DEFLECTIONS The beam, or flexural member, is frequently encountered in structures and machines, and its elementary stress analysis constitutes one of the more interesting facets

More information

Simplified Structural Analysis and Design for Architects

Simplified 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 information

Mechanical Design in Optical Engineering

Mechanical Design in Optical Engineering OPTI Buckling Buckling and Stability: As we learned in the previous lectures, structures may fail in a variety of ways, depending on the materials, load and support conditions. We had two primary concerns:

More information

Equilibrium of a Rigid Body. Engineering Mechanics: Statics

Equilibrium 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 free-body

More information

7.4 The Elementary Beam Theory

7.4 The Elementary Beam Theory 7.4 The Elementary Beam Theory In this section, problems involving long and slender beams are addressed. s with pressure vessels, the geometry of the beam, and the specific type of loading which will be

More information

Sports biomechanics explores the relationship between the body motion, internal forces and external forces to optimize the sport performance.

Sports biomechanics explores the relationship between the body motion, internal forces and external forces to optimize the sport performance. What is biomechanics? Biomechanics is the field of study that makes use of the laws of physics and engineering concepts to describe motion of body segments, and the internal and external forces, which

More information

Static equilibrium. Biomechanics 2 Static Equilibrium. Free-Body diagram Internal forces of structures. Last week: Forces and Moments

Static equilibrium. Biomechanics 2 Static Equilibrium. Free-Body diagram Internal forces of structures. Last week: Forces and Moments Static equilibrium Biomechanics 2 Static Equilibrium Free-Body diagram Internal forces of structures Last week: Forces and Moments Force F: tends to change state of rest or motion Moment M: force acting

More information

Forces. Isaac Newton stated 3 laws that deal with forces and describe motion. Backbone of Physics

Forces. Isaac Newton stated 3 laws that deal with forces and describe motion. Backbone of Physics FORCES Forces Isaac Newton stated 3 laws that deal with forces and describe motion. Backbone of Physics Inertia Tendency of an object to remain in the same state of motion. Resists a change in motion.

More information

Chapter 5 CENTRIC TENSION OR COMPRESSION ( AXIAL LOADING )

Chapter 5 CENTRIC TENSION OR COMPRESSION ( AXIAL LOADING ) Chapter 5 CENTRIC TENSION OR COMPRESSION ( AXIAL LOADING ) 5.1 DEFINITION A construction member is subjected to centric (axial) tension or compression if in any cross section the single distinct stress

More information

Upthrust and Archimedes Principle

Upthrust and Archimedes Principle 1 Upthrust and Archimedes Principle Objects immersed in fluids, experience a force which tends to push them towards the surface of the liquid. This force is called upthrust and it depends on the density

More information

2008 FXA THREE FORCES IN EQUILIBRIUM 1. Candidates should be able to : TRIANGLE OF FORCES RULE

2008 FXA THREE FORCES IN EQUILIBRIUM 1. Candidates should be able to : TRIANGLE OF FORCES RULE THREE ORCES IN EQUILIBRIUM 1 Candidates should be able to : TRIANGLE O ORCES RULE Draw and use a triangle of forces to represent the equilibrium of three forces acting at a point in an object. State that

More information

PHYS 101 Previous Exam Problems. Force & Motion I

PHYS 101 Previous Exam Problems. Force & Motion I PHYS 101 Previous Exam Problems CHAPTER 5 Force & Motion I Newton s Laws Vertical motion Horizontal motion Mixed forces Contact forces Inclines General problems 1. A 5.0-kg block is lowered with a downward

More information

Equilibrium & Elasticity

Equilibrium & 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 information

MECHANICAL PROPERTIES OF SOLIDS

MECHANICAL PROPERTIES OF SOLIDS Chapter Nine MECHANICAL PROPERTIES OF SOLIDS MCQ I 9.1 Modulus of rigidity of ideal liquids is (a) infinity. (b) zero. (c) unity. (d) some finite small non-zero constant value. 9. The maximum load a wire

More information

two structural analysis (statics & mechanics) APPLIED ACHITECTURAL STRUCTURES: DR. ANNE NICHOLS SPRING 2017 lecture STRUCTURAL ANALYSIS AND SYSTEMS

two structural analysis (statics & mechanics) APPLIED ACHITECTURAL STRUCTURES: DR. ANNE NICHOLS SPRING 2017 lecture STRUCTURAL ANALYSIS AND SYSTEMS APPLIED ACHITECTURAL STRUCTURES: STRUCTURAL ANALYSIS AND SYSTEMS DR. ANNE NICHOLS SPRING 2017 lecture two structural analysis (statics & mechanics) Analysis 1 Structural Requirements strength serviceability

More information

Physics. Assignment-1(UNITS AND MEASUREMENT)

Physics. Assignment-1(UNITS AND MEASUREMENT) Assignment-1(UNITS AND MEASUREMENT) 1. Define physical quantity and write steps for measurement. 2. What are fundamental units and derived units? 3. List the seven basic and two supplementary physical

More information

Concept of Force and Newton s Laws of Motion

Concept of Force and Newton s Laws of Motion Concept of Force and Newton s Laws of Motion 8.01 W02D2 Chapter 7 Newton s Laws of Motion, Sections 7.1-7.4 Chapter 8 Applications of Newton s Second Law, Sections 8.1-8.4.1 Announcements W02D3 Reading

More information

CAPACITY DESIGN FOR TALL BUILDINGS WITH MIXED SYSTEM

CAPACITY DESIGN FOR TALL BUILDINGS WITH MIXED SYSTEM 13 th World Conference on Earthquake Engineering Vancouver, B.C., Canada August 1-6, 24 Paper No. 2367 CAPACITY DESIGN FOR TALL BUILDINGS WITH MIXED SYSTEM M.UMA MAHESHWARI 1 and A.R.SANTHAKUMAR 2 SUMMARY

More information

Chapter 7 FORCES IN BEAMS AND CABLES

Chapter 7 FORCES IN BEAMS AND CABLES hapter 7 FORES IN BEAMS AN ABLES onsider a straight two-force member AB subjected at A and B to equal and opposite forces F and -F directed along AB. utting the member AB at and drawing the free-body B

More information

Static Equilibrium. University of Arizona J. H. Burge

Static Equilibrium. University of Arizona J. H. Burge Static Equilibrium Static Equilibrium Definition: When forces acting on an object which is at rest are balanced, then the object is in a state of static equilibrium. - No translations - No rotations In

More information

4.0 m s 2. 2 A submarine descends vertically at constant velocity. The three forces acting on the submarine are viscous drag, upthrust and weight.

4.0 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 information

UNIVERSITY PHYSICS I. Professor Meade Brooks, Collin College. Chapter 12: STATIC EQUILIBRIUM AND ELASTICITY

UNIVERSITY PHYSICS I. Professor Meade Brooks, Collin College. Chapter 12: STATIC EQUILIBRIUM AND ELASTICITY UNIVERSITY PHYSICS I Professor Meade Brooks, Collin College Chapter 12: STATIC EQUILIBRIUM AND ELASTICITY Two stilt walkers in standing position. All forces acting on each stilt walker balance out; neither

More information

Mechanics of Solids. Mechanics Of Solids. Suraj kr. Ray Department of Civil Engineering

Mechanics of Solids. Mechanics Of Solids. Suraj kr. Ray Department of Civil Engineering Mechanics Of Solids Suraj kr. Ray (surajjj2445@gmail.com) Department of Civil Engineering 1 Mechanics of Solids is a branch of applied mechanics that deals with the behaviour of solid bodies subjected

More information

Chapter Test A. Teacher Notes and Answers Forces and the Laws of Motion. Assessment

Chapter Test A. Teacher Notes and Answers Forces and the Laws of Motion. Assessment Assessment Chapter Test A Teacher Notes and Answers Forces and the Laws of Motion CHAPTER TEST A (GENERAL) 1. c 2. d 3. d 4. c 5. c 6. c 7. c 8. b 9. d 10. d 11. c 12. a 13. d 14. d 15. b 16. d 17. c 18.

More information

AP Physics 1 Review. On the axes below draw the horizontal force acting on this object as a function of time.

AP Physics 1 Review. On the axes below draw the horizontal force acting on this object as a function of time. P Physics Review. Shown is the velocity versus time graph for an object that is moving in one dimension under the (perhaps intermittent) action of a single horizontal force. Velocity, m/s Time, s On the

More information

APPLIED MATHEMATICS IM 02

APPLIED MATHEMATICS IM 02 IM SYLLABUS (2013) APPLIED MATHEMATICS IM 02 SYLLABUS Applied Mathematics IM 02 Syllabus (Available in September) 1 Paper (3 hours) Applied Mathematics (Mechanics) Aims A course based on this syllabus

More information

Chapter 4: Newton s Second Law F = m a. F = m a (4.2)

Chapter 4: Newton s Second Law F = m a. F = m a (4.2) Lecture 7: Newton s Laws and Their Applications 1 Chapter 4: Newton s Second Law F = m a First Law: The Law of Inertia An object at rest will remain at rest unless, until acted upon by an external force.

More information

Design of a Balanced-Cantilever Bridge

Design of a Balanced-Cantilever Bridge Design of a Balanced-Cantilever Bridge CL (Bridge is symmetric about CL) 0.8 L 0.2 L 0.6 L 0.2 L 0.8 L L = 80 ft Bridge Span = 2.6 L = 2.6 80 = 208 Bridge Width = 30 No. of girders = 6, Width of each girder

More information

Equilibrium of Rigid Bodies

Equilibrium of Rigid Bodies Equilibrium of Rigid Bodies 1 2 Contents Introduction Free-Bod Diagram Reactions at Supports and Connections for a wo-dimensional Structure Equilibrium of a Rigid Bod in wo Dimensions Staticall Indeterminate

More information

act concurrently on point P, as shown in the diagram. The equilibrant of F 1

act concurrently on point P, as shown in the diagram. The equilibrant of F 1 Page 1 of 10 force-friction-vectors review Name 12-NOV-04 1. A 150.-newton force, F1, and a 200.-newton force, F 2, are applied simultaneously to the same point on a large crate resting on a frictionless,

More information

PLATE GIRDERS II. Load. Web plate Welds A Longitudinal elevation. Fig. 1 A typical Plate Girder

PLATE GIRDERS II. Load. Web plate Welds A Longitudinal elevation. Fig. 1 A typical Plate Girder 16 PLATE GIRDERS II 1.0 INTRODUCTION This chapter describes the current practice for the design of plate girders adopting meaningful simplifications of the equations derived in the chapter on Plate Girders

More information

What Every Engineer Should Know About Structures Part B Statics Applications

What Every Engineer Should Know About Structures Part B Statics Applications What Every Engineer Should Know About Structures by Professor Patrick L. Glon, P.E. This is the second course of a series in the area of study of engineering mechanics called Statics and Strength of Materials.

More information

Chapter Four Holt Physics. Forces and the Laws of Motion

Chapter Four Holt Physics. Forces and the Laws of Motion Chapter Four Holt Physics Forces and the Laws of Motion Physics Force and the study of dynamics 1.Forces - a. Force - a push or a pull. It can change the motion of an object; start or stop movement; and,

More information

UNIT-II MOVING LOADS AND INFLUENCE LINES

UNIT-II MOVING LOADS AND INFLUENCE LINES UNIT-II MOVING LOADS AND INFLUENCE LINES Influence lines for reactions in statically determinate structures influence lines for member forces in pin-jointed frames Influence lines for shear force and bending

More information

Modeling Mechanical Systems

Modeling Mechanical Systems Modeling Mechanical Systems Mechanical systems can be either translational or rotational. Although the fundamental relationships for both types are derived from Newton s law, they are different enough

More information

276 Calculus and Structures

276 Calculus and Structures 76 Calculus and Structures CHAPTER THE CONJUGATE BEA ETHOD Calculus and Structures 77 Copyright Chapter THE CONJUGATE BEA ETHOD.1 INTRODUCTION To find the deflection of a beam you must solve the equation,

More information

Physics A - PHY 2048C

Physics A - PHY 2048C Physics A - PHY 2048C Mass & Weight, Force, and Friction 10/04/2017 My Office Hours: Thursday 2:00-3:00 PM 212 Keen Building Warm-up Questions 1 Did you read Chapters 6.1-6.6? 2 In your own words: What

More information

PHYS 1303 Final Exam Example Questions

PHYS 1303 Final Exam Example Questions PHYS 1303 Final Exam Example Questions (In summer 2014 we have not covered questions 30-35,40,41) 1.Which quantity can be converted from the English system to the metric system by the conversion factor

More information

PLAT DAN CANGKANG (TKS 4219)

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

More information

CHAPTER -6- BENDING Part -1-

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

More information

Physics, Chapter 3: The Equilibrium of a Particle

Physics, Chapter 3: The Equilibrium of a Particle University of Nebraska - Lincoln DigitalCommons@University of Nebraska - Lincoln Robert Katz Publications Research Papers in Physics and Astronomy 1-1958 Physics, Chapter 3: The Equilibrium of a Particle

More information

Newton s Laws. A force is simply a push or a pull. Forces are vectors; they have both size and direction.

Newton s Laws. A force is simply a push or a pull. Forces are vectors; they have both size and direction. Newton s Laws Newton s first law: An object will stay at rest or in a state of uniform motion with constant velocity, in a straight line, unless acted upon by an external force. In other words, the bodies

More information

SERVICEABILITY OF BEAMS AND ONE-WAY SLABS

SERVICEABILITY OF BEAMS AND ONE-WAY SLABS CHAPTER REINFORCED CONCRETE Reinforced Concrete Design A Fundamental Approach - Fifth Edition Fifth Edition SERVICEABILITY OF BEAMS AND ONE-WAY SLABS A. J. Clark School of Engineering Department of Civil

More information

Newton s Laws and Free-Body Diagrams General Physics I

Newton s Laws and Free-Body Diagrams General Physics I Newton s Laws and Free-Body Diagrams In the next few sections, we will be exploring some of the most fundamental laws of our universe, laws that govern the relationship actions and motion. These laws are

More information

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

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

More information

UNIT II SLOPE DEFLECION AND MOMENT DISTRIBUTION METHOD

UNIT II SLOPE DEFLECION AND MOMENT DISTRIBUTION METHOD SIDDHARTH GROUP OF INSTITUTIONS :: PUTTUR Siddharth Nagar, Narayanavanam Road 517583 QUESTION BANK (DESCRIPTIVE) Subject with Code : SA-II (13A01505) Year & Sem: III-B.Tech & I-Sem Course & Branch: B.Tech

More information

ME 101: Engineering Mechanics

ME 101: Engineering Mechanics ME 101: Engineering Mechanics Rajib Kumar Bhattacharjya Department of Civil Engineering Indian Institute of Technology Guwahati M Block : Room No 005 : Tel: 2428 www.iitg.ernet.in/rkbc ME101: Division

More information

Two Hanging Masses. ) by considering just the forces that act on it. Use Newton's 2nd law while

Two Hanging Masses. ) by considering just the forces that act on it. Use Newton's 2nd law while Student View Summary View Diagnostics View Print View with Answers Edit Assignment Settings per Student Exam 2 - Forces [ Print ] Due: 11:59pm on Tuesday, November 1, 2011 Note: To underst how points are

More information

Finite Element Modelling with Plastic Hinges

Finite Element Modelling with Plastic Hinges 01/02/2016 Marco Donà Finite Element Modelling with Plastic Hinges 1 Plastic hinge approach A plastic hinge represents a concentrated post-yield behaviour in one or more degrees of freedom. Hinges only

More information

Mechanics: Scalars and Vectors

Mechanics: Scalars and Vectors Mechanics: Scalars and Vectors Scalar Onl magnitude is associated with it Vector e.g., time, volume, densit, speed, energ, mass etc. Possess direction as well as magnitude Parallelogram law of addition

More information

Statics and Vectors. ME 202 Topics. Statics. Engineering Mechanics

Statics and Vectors. ME 202 Topics. Statics. Engineering Mechanics Engineering Mechanics Statics and Vectors ME 202 Mechanical System: One whose behavior can be completely described in terms of force, mass, distance, time and temperature. Engineering mechanics: Branch

More information

Flexure: Behavior and Nominal Strength of Beam Sections

Flexure: Behavior and Nominal Strength of Beam Sections 4 5000 4000 (increased d ) (increased f (increased A s or f y ) c or b) Flexure: Behavior and Nominal Strength of Beam Sections Moment (kip-in.) 3000 2000 1000 0 0 (basic) (A s 0.5A s ) 0.0005 0.001 0.0015

More information

Dynamics; Newton s Laws of Motion

Dynamics; Newton s Laws of Motion Dynamics; Newton s Laws of Motion Force A force is any kind of push or pull on an object. An object at rest needs a force to get it moving; a moving object needs a force to change its velocity. The magnitude

More information

SIR MICHELANGELO REFALO CENTRE FOR FURTHER STUDIES VICTORIA GOZO

SIR MICHELANGELO REFALO CENTRE FOR FURTHER STUDIES VICTORIA GOZO SIR MICHELANGELO REFALO CENTRE FOR FURTHER STUDIES VICTORIA GOZO Half-Yearly Exam 2013 Subject: Physics Level: Advanced Time: 3hrs Name: Course: Year: 1st This paper carries 200 marks which are 80% of

More information

Name. ME 270 Fall 2005 Final Exam PROBLEM NO. 1. Given: A distributed load is applied to the top link which is, in turn, supported by link AC.

Name. ME 270 Fall 2005 Final Exam PROBLEM NO. 1. Given: A distributed load is applied to the top link which is, in turn, supported by link AC. Name ME 270 Fall 2005 Final Exam PROBLEM NO. 1 Given: A distributed load is applied to the top link which is, in turn, supported by link AC. Find: a) Draw a free body diagram of link BCDE and one of link

More information

Concept Question: Normal Force

Concept Question: Normal Force Concept Question: Normal Force Consider a person standing in an elevator that is accelerating upward. The upward normal force N exerted by the elevator floor on the person is 1. larger than 2. identical

More information

THE TWENTY-SECOND ANNUAL SLAPT PHYSICS CONTEST SOUTHERN ILLINOIS UNIVERSITY EDWARDSVILLE APRIL 21, 2007 MECHANICS TEST. g = 9.

THE TWENTY-SECOND ANNUAL SLAPT PHYSICS CONTEST SOUTHERN ILLINOIS UNIVERSITY EDWARDSVILLE APRIL 21, 2007 MECHANICS TEST. g = 9. THE TWENTY-SECOND ANNUAL SLAPT PHYSICS CONTEST SOUTHERN ILLINOIS UNIVERSITY EDWARDSVILLE APRIL 21, 27 MECHANICS TEST g = 9.8 m/s/s Please answer the following questions on the supplied answer sheet. You

More information

Newton's second law of motion

Newton's second law of motion OpenStax-CNX module: m14042 1 Newton's second law of motion Sunil Kumar Singh This work is produced by OpenStax-CNX and licensed under the Creative Commons Attribution License 2.0 Abstract Second law of

More information

Theory and Analysis of Structures

Theory and Analysis of Structures 7 Theory and nalysis of Structures J.Y. Richard iew National University of Singapore N.E. Shanmugam National University of Singapore 7. Fundamental Principles oundary Conditions oads and Reactions Principle

More information

Nonlinear static analysis PUSHOVER

Nonlinear static analysis PUSHOVER Nonlinear static analysis PUSHOVER Adrian DOGARIU European Erasmus Mundus Master Course Sustainable Constructions under Natural Hazards and Catastrophic Events 520121-1-2011-1-CZ-ERA MUNDUS-EMMC Structural

More information

(a) On the dots below that represent the students, draw and label free-body diagrams showing the forces on Student A and on Student B.

(a) On the dots below that represent the students, draw and label free-body diagrams showing the forces on Student A and on Student B. 2003 B1. (15 points) A rope of negligible mass passes over a pulley of negligible mass attached to the ceiling, as shown above. One end of the rope is held by Student A of mass 70 kg, who is at rest on

More information

Chapter 5. Force and Motion-I

Chapter 5. Force and Motion-I Chapter 5 Force and Motion-I 5.3 Newton s First Law Newton s First Law: If no force acts on a body, the body s velocity cannot change The purpose of Newton s First Law is to introduce the special frames

More information

Physics 2210 Homework 18 Spring 2015

Physics 2210 Homework 18 Spring 2015 Physics 2210 Homework 18 Spring 2015 Charles Jui April 12, 2015 IE Sphere Incline Wording A solid sphere of uniform density starts from rest and rolls without slipping down an inclined plane with angle

More information

Theme 2 - PHYSICS UNIT 2 Forces and Moments. A force is a push or a pull. This means that whenever we push or pull something, we are doing a force.

Theme 2 - PHYSICS UNIT 2 Forces and Moments. A force is a push or a pull. This means that whenever we push or pull something, we are doing a force. Forces A force is a push or a pull. This means that whenever we push or pull something, we are doing a force. Forces are measured in Newtons (N) after the great physicist Sir Isaac Newton. The instrument

More information

Ground Rules. PC1221 Fundamentals of Physics I. Force. Zero Net Force. Lectures 9 and 10 The Laws of Motion. A/Prof Tay Seng Chuan

Ground Rules. PC1221 Fundamentals of Physics I. Force. Zero Net Force. Lectures 9 and 10 The Laws of Motion. A/Prof Tay Seng Chuan PC1221 Fundamentals of Physics I Lectures 9 and 10 The Laws of Motion A/Prof Tay Seng Chuan 1 Ground Rules Switch off your handphone and pager Switch off your laptop computer and keep it No talking while

More information

Static Equilibrium and Torque

Static Equilibrium and Torque 10.3 Static Equilibrium and Torque SECTION OUTCOMES Use vector analysis in two dimensions for systems involving static equilibrium and torques. Apply static torques to structures such as seesaws and bridges.

More information

Rigid and Braced Frames

Rigid and Braced Frames RH 331 Note Set 12.1 F2014abn Rigid and raced Frames Notation: E = modulus of elasticit or Young s modulus F = force component in the direction F = force component in the direction FD = free bod diagram

More information

Written Homework problems. Spring (taken from Giancoli, 4 th edition)

Written Homework problems. Spring (taken from Giancoli, 4 th edition) Written Homework problems. Spring 014. (taken from Giancoli, 4 th edition) HW1. Ch1. 19, 47 19. Determine the conversion factor between (a) km / h and mi / h, (b) m / s and ft / s, and (c) km / h and m

More information

Kinematics and Dynamics

Kinematics and Dynamics AP PHYS 1 Test Review Kinematics and Dynamics Name: Other Useful Site: http://www.aplusphysics.com/ap1/ap1- supp.html 2015-16 AP Physics: Kinematics Study Guide The study guide will help you review all

More information

Civil Engineering Design (1) Analysis and Design of Slabs 2006/7

Civil Engineering Design (1) Analysis and Design of Slabs 2006/7 Civil Engineering Design (1) Analysis and Design of Slabs 006/7 Dr. Colin Caprani, Chartered Engineer 1 Contents 1. Elastic Methods... 3 1.1 Introduction... 3 1. Grillage Analysis... 4 1.3 Finite Element

More information

Figure 1: Representative strip. = = 3.70 m. min. per unit length of the selected strip: Own weight of slab = = 0.

Figure 1: Representative strip. = = 3.70 m. min. per unit length of the selected strip: Own weight of slab = = 0. Example (8.1): Using the ACI Code approximate structural analysis, design for a warehouse, a continuous one-way solid slab supported on beams 4.0 m apart as shown in Figure 1. Assume that the beam webs

More information

2.1 Forces and Free-Body Diagrams

2.1 Forces and Free-Body Diagrams 2.1 Forces and Free-Body Diagrams A is a push or a pull. Forces act on objects, and can result in the acceleration, compression, stretching, or twisting of objects. Forces can also act to stabilize an

More information

AP Physics C: Mechanics Practice (Newton s Laws including friction, resistive forces, and centripetal force).

AP Physics C: Mechanics Practice (Newton s Laws including friction, resistive forces, and centripetal force). AP Physics C: Mechanics Practice (Newton s Laws including friction, resistive forces, and centripetal force). 1981M1. A block of mass m, acted on by a force of magnitude F directed horizontally to the

More information

UNIT 4 NEWTON S THIRD LAW, FORCE DIAGRAMS AND FORCES. Objectives. To understand and be able to apply Newton s Third Law

UNIT 4 NEWTON S THIRD LAW, FORCE DIAGRAMS AND FORCES. Objectives. To understand and be able to apply Newton s Third Law UNIT 4 NEWTON S THIRD LAW, FORCE DIAGRAMS AND FORCES Objectives To understand and be able to apply Newton s Third Law To be able to determine the object that is exerting a particular force To understand

More information

EGR 1301 Introduction to Static Analysis

EGR 1301 Introduction to Static Analysis Slide 1 EGR 1301 Introduction to Static Analysis Presentation adapted from Distance Learning / Online Instructional Presentation Originally created by Mr. Dick Campbell Presented by: Departments of Engineering

More information

Lecture 2. Lecture 1. Forces on a rotating planet. We will describe the atmosphere and ocean in terms of their:

Lecture 2. Lecture 1. Forces on a rotating planet. We will describe the atmosphere and ocean in terms of their: Lecture 2 Lecture 1 Forces on a rotating planet We will describe the atmosphere and ocean in terms of their: velocity u = (u,v,w) pressure P density ρ temperature T salinity S up For convenience, we will

More information

Simulation of Nonlinear Behavior of Wall-Frame Structure during Earthquakes

Simulation of Nonlinear Behavior of Wall-Frame Structure during Earthquakes Simulation of Nonlinear Behavior of Wall-Frame Structure during Earthquakes b Masaomi Teshigawara 1, Hiroshi Fukuama 2, Hiroto Kato 2, Taiki Saito 2, Koichi Kusunoki 2, Tomohisa Mukai 2 ABSTRACT The reinforced

More information

Practice Test 3. Name: Date: ID: A. Multiple Choice Identify the choice that best completes the statement or answers the question.

Practice Test 3. Name: Date: ID: A. Multiple Choice Identify the choice that best completes the statement or answers the question. Name: Date: _ Practice Test 3 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. A wheel rotates about a fixed axis with an initial angular velocity of 20

More information

ENGR-1100 Introduction to Engineering Analysis. Lecture 13

ENGR-1100 Introduction to Engineering Analysis. Lecture 13 ENGR-1100 Introduction to Engineering Analysis Lecture 13 EQUILIBRIUM OF A RIGID BODY & FREE-BODY DIAGRAMS Today s Objectives: Students will be able to: a) Identify support reactions, and, b) Draw a free-body

More information

Module 3. Analysis of Statically Indeterminate Structures by the Displacement Method

Module 3. Analysis of Statically Indeterminate Structures by the Displacement Method odule 3 Analysis of Statically Indeterminate Structures by the Displacement ethod Lesson 14 The Slope-Deflection ethod: An Introduction Introduction As pointed out earlier, there are two distinct methods

More information

PHY218 SPRING 2016 Review for Final Exam: Week 14 Final Review: Chapters 1-11, 13-14

PHY218 SPRING 2016 Review for Final Exam: Week 14 Final Review: Chapters 1-11, 13-14 Final Review: Chapters 1-11, 13-14 These are selected problems that you are to solve independently or in a team of 2-3 in order to better prepare for your Final Exam 1 Problem 1: Chasing a motorist This

More information

Seismic Assessment of a RC Building according to FEMA 356 and Eurocode 8

Seismic Assessment of a RC Building according to FEMA 356 and Eurocode 8 1 Seismic Assessment of a RC Building according to FEMA 356 and Eurocode 8 Ioannis P. GIANNOPOULOS 1 Key words: Pushover analysis, FEMA 356, Eurocode 8, seismic assessment, plastic rotation, limit states

More information

Design of reinforced concrete sections according to EN and EN

Design of reinforced concrete sections according to EN and EN Design of reinforced concrete sections according to EN 1992-1-1 and EN 1992-2 Validation Examples Brno, 21.10.2010 IDEA RS s.r.o. South Moravian Innovation Centre, U Vodarny 2a, 616 00 BRNO tel.: +420-511

More information

Chapter (7) Lateral Earth Pressure

Chapter (7) Lateral Earth Pressure Chapter (7) Lateral Earth Pressure Introduction Vertical or near vertical slopes of soil are supported by retaining walls, cantilever sheet-pile walls, sheet-pile bulkheads, braced cuts, and other similar

More information

Physics Mechanics. Lecture 11 Newton s Laws - part 2

Physics Mechanics. Lecture 11 Newton s Laws - part 2 Physics 170 - Mechanics Lecture 11 Newton s Laws - part 2 Newton s Second Law of Motion An object may have several forces acting on it; the acceleration is due to the net force: Newton s Second Law of

More information