Engineering Mechanics-Module 1 (Introduction)

Engineering Mechanics-Intro

1. University of Engineering & Technology Peshawar CE-117: Engineering Mechanics MODULE 1: Introduction to Engineering Mechanics (some of Fundamental concepts) Prof. Dr. Mohammad Javed and Dr. Muhammad Fahim [email protected] 1

2. Contents Introduction to Mechanics Definitions Newton’s Three Laws of Motion Classification of Force Types of Structural Loads Units of Measurement Famous Structural Failures

3. Lecture’s Objectives To define and discuss various branches of Mechanics To discuss some of fundamental concepts used in Engineering Mechanics To discuss system of units used in Engineering

4. 1. Introduction to Mechanics Mechanics is the branch of Science which deals with the effect of forces on bodies . Figure 1 : What is the effect of 2kg mass ( Force ?) on attached cables (Body) ? Figure 2 : What is the effect of 800 N reaction ( Force ? ) on Tendon ( Body ?) Figure 1 Figure 2 4

5. 1. Introduction to Mechanics Figure 3 : What is the effect of Force ‘F’ on rod (Body) of length ‘L’? Figure 3 5

6. Mechanics Rigid bodies Fluids Deformable bodies Engineering Mechanics Statics Dynamics Kinematics Kinetics (Engineering Mechanics) (Solid Mechanics) (Fluid Mechanics) 1. Introduction to Mechanics: Branches

7. RIGID BODY MECHANICS Rigid body: Anybody which doesn’t undergo deformation (change in length or change in area or change in shape) under the action of forces is said to be rigid body Deformable body Rigid body Rigid body (Engineering Mechanics ) Deformable body (Mechanics of Solid) 1. Introduction to Mechanics

8. Consider the given figure. The calculation of the tension in the cable which supports the boom of a mobile crane under load is essentially unaffected by the small internal deformations in the structural members of the boom. 8 For the purpose of determining the external forces which act on the boom, we may treat it as a rigid body . Actually solid bodies are never rigid; they deform under the action of applied forces. In many cases this deformation is negligible compared to the size of the body and the body is assumed to be rigid RIGID BODY MECHANICS 1. Introduction to Mechanics

9. Statics : It is that branch of Engineering Mechanics, which deals with the forces and their effects, while acting upon the bodies at rest or or moving with constant velocity (acceleration = 0 ?). Dynamics : It is that branch of Engineering Mechanics, which deals with the forces and their effects, while acting upon the bodies in motion. The subject of Dynamics may be further sub-divided into the following two branches : 1. Kinetics, and 2. Kinematics. Kinematics: Kinematics is the branch of mechanics which deals with motion parameters without considering the forces responsible for motion. Kinetics: Kinetics is the branch of mechanics which deals with motion parameters as well as forces responsible for motion. CLASSIFICATION OF RIGID BODY MECHANICS S= v i t +1/2 at 2 F i = ma 1. Introduction to Mechanics

10. Applications of Statics 10 1. Introduction to Mechanics

11. Deformable Body : Bodies in which appreciable deformation is produced under application of load. Deformable Body Mechanics Deformable body mechanics ( Mechanics of solids course) deals with how forces are distributed inside bodies, and with the deformations caused by these internal force distributions. These internal force produce " stresses " in the body, which could ultimately result in the failure of the material itself. 11 DEFORMABLE BODY MECHANICS 1. Introduction to Mechanics

12. The Mechanics of fluids is the branch of mechanics that deals with liquids or gases. Fluids are commonly used in engineering applications. They can be classified as incompressible , or c ompressible . While all real fluids are compressible to some degree, most liquids can be analyzed as incompressible in many engineering applications. Applications of fluid mechanics abound, from hydraulics and general flow in pipes to air flow in ducts to advanced applications in turbines and aerospace. The study of the mechanics of fluids will be studied in courses called Fluid Mechanics, Hydraulics and other relevant subjects. 12 FLUID MECHANICS 1. Introduction to Mechanics

13. Mechanics of solids I &II (2 nd & 3 rd semester) Fluid Mechanics I &II (3 rd & 4 th semester) Hydraulics Engineering (5 th semester) Irrigation Engg and Water Management (8 th semester) Structural Analysis I &II (4 th & 5 th semester) Reinforced concrete design I & II (6 th & 7 th semester) Steel Structures (8 th semester) Geotechnical Engineering I &II (4 th & 5 th semester) Foundation Engineering (6 th semester) Introduction to Structural Dynamics and Earthquake Engineering (8 th semester) CE courses requiring knowledge of Engineering Mechanics as pre-requisite 1. Introduction to Mechanics

14. 2. Definitions Space : It is the geometric region occupied by bodies whose positions are described by linear and angular measurements relative to a coordinate system . For three-dimensional problems, three independent coordinates are needed. For two-dimensional problems, only two coordinates are required. Time : It is conceived as a succession of events . Although the principles of statics are time independent, this quantity plays an important role in the study of dynamics . Two dimensional rectangular Coordinate system Three dimensional Coordinate system 14

15. 2. Definitions Mass : The quantity of the matter possessed by a body is called mass . The mass of a body will not change unless the body is damaged and part of it is physically separated. When a body is taken out in a space craft, the mass will not change but its weight may change due to change in gravitational force. Even the body may become weightless when gravitational force vanishes but the mass remain the same. 15

16. 2. Definitions Particle : A particle is an object whose mass is concentrated at a point . For this reason, a particle is also called a point mass , and it is said to have zero volume 16 Size of earth is insignificant compared to the size of its orbit. Earth can be modelled as a particle when studying its orbital motion Body : A body has mass and occupies a volume of space

17. Force may be defined as any action that tends to change the state of rest or motion of a body to which it is applied . The action of a force is completely characterized by 1. its magnitude, 2. direction of its action, and 3. Its point of application . 17 2. Definitions

18. 3. Newton’s Three Laws of Motion Engineering mechanics is formulated on the basis of Newton’s three laws of motion, the validity of which is based on experimental observation. These laws apply to the motion of a particle as measured from a nonaccelerating reference frame. First Law: Every body continues in its state of rest or of uniform motion unless or until some external force acts on it. A football will remain at rest unless acted upon by unbalanced force 18

19. 3. Newton’s Three Laws of Motion Second Law : A particle acted upon by an unbalanced force F experiences an acceleration a that has the same direction as the force and a magnitude that is directly proportional to the force. If F is applied to a particle of mass m , this law may be expressed mathematically as F = m a 19

20. 3. Newton’s Three Laws of Motion Third Law : The forces of action and reaction between bodies in contact are equal in magnitude, opposite in direction and collinear (same line of action). 20 Examples of Newton third law of motion

21. 4. Classification of Force 21

22. 22 4. Classification of Force

23. 23 4. Classification of Force

24. 24 Concentrated force concentrated forces exerted at point or location 2. Distributed force A force applied along a length or over an area. The distribution can be uniform or non-uniform. Concentrated forces, P 1 , P 2 What are other concentrated forces ? Distributed forces 4. Classification of Force

25. External and Internal Effects of a force External force For the bracket of Fig. 2/1 the effects of P external to the bracket are the reactive forces (not shown) exerted on the bracket by the foundation and bolts because of the action of P . Forces external to a body can be either applied forces or reactive forces. 25 Applied force What are the other external effects ? 4. Classification of Force

26. Internal force The effects of P internal to the bracket are the resulting internal forces and deformations distributed throughout the material of the bracket. The relation between internal forces and internal deformations depends on the material properties of the body and is studied in strength of material (also known as Mechanics of Solids or Mechanics of materials ) 26 4. Classification of Force External and Internal Effects of a force

27. Principle of Transmissibility “A force may be applied at any point on its given line of action without altering the resultant effects of the force external to the rigid body on which it acts“ 27 What are the external effects on the given body ? 4. Classification of Force

28. 28 Type of Internal forces Tension 4. Classification of Force

29. Stress is a term used to express the internal force or resistance, offered by a particle to the adjacent particle in a body under the action of external loads . Stress is the internal resistance per unit area. 29 4. Classification of Force

30. 30 Torsional Normal 4. Classification of Force

31. 31 Classification of Force system 4. Classification of Force

32. TYPES OF FORCES & FORCE SYSTEM collinear forces concurrent forces Parallel forces Non-concurrent & non-parallel forces Classification of Coplanar Force system 4. Classification of Force

33. Load   is a term frequently used in engineering to mean the force exerted on a surface or body. 33 5. Types of Structural loads

34. Dead Loads :  Vertical loads that are fixed in position and are produced by the weight of the elements of the structure or the whole structure with all its permanent components.  Examples are : own weight of structural member and super imposed loads (e.g. walls and flooring cover) 34 5. Types of Structural loads

35. Live Loads :  consist mainly of occupancy loads ( e.g. people and furniture ) in buildings and traffic loads on bridges. They may be either fully or partially in place or not present at all, and may also change in location. 35 5. Types of Structural loads

36.  Wind Loads : are the positive or negative pressures exerted on a building when it obstructs the flow of moving air. Wind loads generally act perpendicular the surface of the structure. Value of load varies depending on the geographic location of the building and its height . 36 5. Types of Structural loads

37. Seismic Loads:  are the inertial forces that act on the structure due to earthquake-induced ground motions. 37 5. Types of Structural loads Ground acceleration, a Inertial force = ma

38. Snow Loads:  the amount of snow load on a roof structure is dependent on a variety of factors: • Roof geometry, • Size of the structure, • Insulation of the structure, • Wind frequency, • Snow duration, • Geographical location of the structure. 38 5. Types of Structural loads

39. Lateral Soil and Hydro-static Loads: 39 5. Type of Structural loads

40. Thermal and Settlement Loads: 40 5. Type of Structural loads Thermal Loads Settlement Loads

41. 6. Units of Measurement In mechanics we use four fundamental quantities called fundamental mechanical dimensions . These are length, mass, force, and time. Although there are a number of different systems of units major systems of units are The International System of Units (SI units) U.S. Customary Units 41

42. 6. Units of Measurement SI Units . The International System of units, abbreviated SI is a modern version of the metric system which has received worldwide recognition. SI system defines length in meters (m), time in seconds (s),and mass in kilograms (kg). The unit of force, called a newton (N), is derived from F = m a . Thus, 1 newton is equal to a force required to give 1 kilogram of mass an acceleration of 1 m/s 2 (N = kg .m/s 2 ) . 42

43. 6. Units of Measurement U.S. Customary . In the U.S. Customary system of units (FPS) length is measured in feet ( ft ), time in seconds (s), and force in pounds ( lb ). The unit of mass, called a slug , is derived from F = m a . Hence, 1 slug is equal to the amount of matter accelerated at 1 ft /s 2 when acted upon by a force of 1 lb (slug = lb.s 2 / ft ) . 43

44. In U.S. units the pound is also used on occasion as a unit of mass. When distinction between the two units is necessary, the force unit is frequently written as lbf and the mass unit as lbm Also, in the U.S. units (some time also called FPS system of units), following relations are used 1 ft = 12 in. (inches), 1 yard (yd)= 3 ft, 1 mile (mi)= 1760 yd= 5280 ft , 1 kilo-pound (kip)= 1000 lb ; 1 ton = 2000 lb ; 1 tonne = 1000 kg * = 2205 lb 44 6. Units of Measurement * In the MKS (meter, kilogram, second) gravitational system, which has been used for many years in non-English-speaking countries, the kilogram, like the pound, has been used both as a unit of force and as a unit of mass.

45. Abbreviation for inch. Note that in previous slide the abbreviation for inch is “in.”, which contains a period. This is unusual, but is done because without the period, the abbreviation would also be the same as a word in the English language, and this might lead to confusion. 45 6. Units of Measurement

46. Common pitfall Weight and mass are different. It is unfortunately common for people, especially lay people, to refer to weight using mass units. For example, when a person says, “I weigh 70 kg.”, the person really means “My mass is 70 kg” 46 6. Units of Measurement

47. Dimensions versus units. Dimensions and units are different. Dimensions are a measurable extent of some kind, while Units are used to measure a dimension. For example, length and time are both dimensions, and meter and second, respectively, are units used to measure these dimensions 47 6. Units of Measurement

48. Common prefixes used in the SI unit systems. 48 6. Units of Measurement

49. Conversion of Units Following table provides a set of direct conversion factors between FPS and SI units for the basic quantities. 49 6. Units of Measurement

50. Example 1 50 6. Units of Measurement Conversion of Units

51. Problem 2 51 6. Units of Measurement Conversion of Units

52. Omitting units in equations. The most serious mistake made when performing unit conversions (as well as when writing equations in general) is to omit units in equations. Although writing units in equations takes a few moments longer, doing so will help avoid the errors that are sure to result if you do not make this a practice 52 Common pitfall 6. Units of Measurement

53. 53 1.1 1. 2 1.3 Ans:24.6 m/s Ans: 101 kPa Ans: 6. Units of Measurement Conversion of Units: Practice Problems

54. 54 1. 5 1.4 Ans: Ans: 98.1 N, 4.9mN, 44.1 kN 6. Units of Measurement Conversion of Units: Practice Problems

55. 7. Famous Structural Failures Among all of the goals confronting engineers when they design structures and machines, the most crucial goal is to develop designs that are as safe as possible. Unfortunately, despite all human efforts to meet this goal, sometimes we do not, and for reasons that are almost always unexpected, failure occurs. When failure occurs, we must learn from it so that our mistakes and/or lack of foresight is not repeated in the future 55

56. Tacoma Narrows bridge Escambia Bay bridge. 56 7. Famous Structural Failures

57. 3. Kansas City Hyatt Regency Hotel. On July 17, 1981, two suspended walkways at the Kansas City Hyatt Regency hotel collapsed during a dance party, killing 114 people and seriously injuring many more. 57 7. Famous Structural Failures

58. 4. Tropicana Casino parking garage . On October 30, 2003, a 10-story parking garage under construction at the Tropicana Casino and Resort in Atlantic City, New Jersey, collapsed, killing 4 workers and injuring 21 others The design of the building itself was adequate, but the design of structures needed for fabrication was not. Note that concrete requires time after pouring (28 days is common) to reach its full design strength. 58 7. Famous Structural Failures

59. 59 Any Question??