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Introduction to Engineering Mechanics
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# Engineering Mechanics Fundamentals

Fundamental concepts of Engineering Mechanics

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### Engineering Mechanics Fundamentals

1. 1. Fundamentals Of EngineeringFundamentals Of Engineering MechanicsMechanics Fundamentals Of EngineeringFundamentals Of Engineering MechanicsMechanics
2. 2. EngineeringEngineering The profession in which knowledge of the mathematical and natural sciences gained by study, experience, and practice is applied with judgment to develop ways to use economically the materials and forces of nature for the benefit of mankind OR The discipline dealing with the art or science of applying scientific knowledge to practical problems.
3. 3. What is MechanicsWhat is Mechanics Mechanics is a branch of the physical sciences that is concerned with the state of rest or motion of bodies that are subjected to the action of forces. • Knowledge of Engineering Mechanics is very essential for an engineer in planning, designing and construction of various types of structures & machines.
4. 4. MechanicsMechanics Mechanics is divided into two areas; • Satatics & • Dynamics Satatics deals with the equilibrium of bodies , those that are either at rest or move with a constant velocity OR Statics is branch of mechanics, which deals with the forces and their effects, while acting upon the bodies at rest.
5. 5. MechanicsMechanics Dynamics • Dynamics is concerned with the accelerated motion of bodies OR • Dynamics is branch of mechanics, which deals with the forces and their effects, while acting upon the bodies in motion.
6. 6. Rigid BodyRigid Body • A body is said to be rigid if the position of its various particles remain fixed relative to one another. • A rigid body can be considered as a combination of a large number of particles in which all the particles remain at a fixed distance from one another, both before and after applying a load.
7. 7. MassMass It is matter contained in a body. Mass is scalar property of matter that does not change from one location to another.
8. 8. WeightWeight • It is force by which the body is attracted towards the center of earth. • The weight of an object is defined as the force of gravity on the object and may be calculated as the mass times the acceleration of gravity, w = mg. • Since the weight is a force, its SI unit is the Newton.
9. 9. Newton’s laws of motionsNewton’s laws of motions • Newton's First Law of Motion: It states that Every object in a state of rest or of uniform motion tends to remain in that state unless an external force is applied to it.
10. 10. Newton’s laws of motionsNewton’s laws of motions • Newton's Second Law of Motion: It states that “the rate of change of momentum is directly proportional to the force and takes place in the same direction in which the force acts”. The relationship between an object's mass m, its acceleration a, and the applied force F is F = ma. • Newton's Third Law of Motion For every action there is an equal and opposite reaction.
11. 11. Newton’s Law of Gravitational AttractionNewton’s Law of Gravitational Attraction • After formulating his three laws of motion, Newton postulated a law governing the gravitational attraction between any two particles, Stated mathematically,
12. 12. ForceForce • Force is considered as “push” or “pull” exerted by one body on another. • Its unit is N. • When force is applied to an object , the velocity of that object changes. This change in velocity constitutes an acceleration. • Force is a vector quantity, therefore a force is completely described by; magnitude, direction and point of application
13. 13. Types of ForcesTypes of Forces • Concurrent Force System The force system in which line of action of forces intersects through a common point. • Parallel Force System The force system in which line of action of forces are parallel to each other.
14. 14. Types of ForcesTypes of Forces • Collinear Force System The force system in which line of action of forces lie on the same path. -------------------------------------------- -------------------------------------------- • Coplanar Force System The force system in which line of action of forces lie on the same plane.
15. 15. Force systemForce system • Concentrated Force. A concentrated force represents the effect of a loading which is assumed to act at a point on a body. We can represent a load by a concentrated force, provided the area over which the load is applied is very small compared to the overall size of the body. An example would be the contact force between a wheel and ground.
16. 16. Units of MeasurementUnits of Measurement Fundamental Units • Every quantity is measured in terms of some arbitrary, but internationally accept units, called fundamental units. • Length • Mass and • Time Derived Units • Some units are expressed in terms of other units, which are derived from some fundamentals units are known as derived units. • E.g. units of force, area, velocity, acceleration, pressure etc.
17. 17. Units of MeasurementUnits of Measurement • The basic quantities - length, time, mass, and force are not all independent from one another; in fact, they are related by Newton’s second law of motion. • The equality F = ma is maintained only if three of the four units, called base units (length, time, mass) , are defined and the fourth unit (force) is then derived from the equation.
18. 18. System of unitsSystem of units International System of units (SI Units) •The International System of units, abbr. SI is a modern version of the metric system which has received worldwide recognition. As shown in Table 1–1, the 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 thus, 1 N is equal to a force required to give 1 kilogram of mass an acceleration of 1 m/s2 (N = kg x m/s2 ). F = maF = ma
19. 19. System of unitsSystem of units • If the weight of a body located at the “standard location” is to be determined in newtons, then Eq. W = mg must be applied. Here measurements give g = 9.806 65 m/s2, however for calculations, the value g = 9.81 m/s2 is be used. • Thus, W = mg (g = 9.81 m/s2 ), Therefore, a body of mass 1 kg has a weight of 9.81 N, and 2-kg body weighs 19.62 N, and so on, Fig. (a).
20. 20. Units of MeasurementUnits of Measurement
21. 21. System of unitsSystem of units U.S. Customary system of units (FPS Units) •In the U.S. Customary system of units (FPS) length is measured in feet (ft), time in seconds (s), and force in pounds (lb), •Table 1–1.The unit of mass, called a slug, is derived from •Hence,1 slug is equal to the amount of matter accelerated at 1 ft/s2 when acted upon by a force of 1 lb (slug = lb.s2 /ft) F = maF = ma
22. 22. System of unitsSystem of units • Therefore, if the measurements are made at the “standard location,” where g = 32.2 ft/s2 then from Eq. W = mg OR m = W/g, (g = 32.2 ft/s2 ) • So a body weighing 32.2 lb has a mass of 1 slug, a 64.4-lb body has a mass of 2 slugs, and so on.. .Fig-b
23. 23. Conversion of UnitsConversion of Units Table 1–2 provides a set of direct conversion factors between FPS and SI units for the basic quantities. We also know, in the FPS system, 1 ft = 12 in. (inches), 5280 ft = 1 mi (mile), 1000 lb=1 kip (kilo-pound),and 2000 lb=1ton
24. 24. PrefixesPrefixes • When a numerical quantity is either very large or very small, the units used to define its size may be modified by using a prefix.
25. 25. General Procedure for AnalysisGeneral Procedure for Analysis • The most effective way of learning the principles of engineering mechanics is to solve problems. • It is important to always present the work in a logical and orderly manner as suggested by the following sequence of steps: • Read the problem carefully and try to correlate the actual physical situation with the theory studied.
26. 26. General Procedure for AnalysisGeneral Procedure for Analysis 1. Tabulate the problem data and draw any necessary diagrams. 2. Apply the relevant principles, generally in mathematical form. Be sure equations are dimensionally homogeneous. 3. Solve the necessary equations, and report the answer with three significant figures. 4. Study the answer with technical judgment and common sense to determine whether or not it seems reasonable.
27. 27. Important Points (Review)Important Points (Review)
28. 28. Important Points (Review)Important Points (Review)
29. 29. ExampleExample
30. 30. Exercise:1 (solution)Exercise:1 (solution)
31. 31. Exercise: 2 (solution)Exercise: 2 (solution)
32. 32. Exercise:2 (solution)Exercise:2 (solution)
33. 33. Exercise:2 (solution)Exercise:2 (solution)
34. 34. Finding Unknown AnglesFinding Unknown Angles • For solving problems it is necessary to find the required unknown angle by applying basic geometric facts. • As you have studied in lower classes, the basic facts about angles, triangles and quadrilaterals, some important are given here.
35. 35. Angle FactsAngle Facts • Vertical angles have equal measure. • The sum of adjacent angles on a straight line is 1800 .
36. 36. • The sum of adjacent angles around a point is 3600 • Triangle Facts The angle sum of any triangle is 1800 (The three angles always add to 180°)
37. 37. Triangle FactsTriangle Facts • When one angle of a triangle is a right angle, the other two angles add up to 900 • The exterior angle of a triangle is equal to the sum of the interior opposite angles.
38. 38. Triangle FactsTriangle Facts • Base angles of an isosceles triangle are equal. (A triangle containing two equal sides and angels) • Each interior angle of equilateral triangle is 600 (3 equal sides, 3 equal angles, always 60°) Scalene Triangle: No equal sides, No equal angles
39. 39. Quadrilateral FactsQuadrilateral Facts • Opposite angles in a parallelogram are equal. • We already know that the sum of interior angles of a triangle is 1800, and sum of Quadrilateral is 360
40. 40. • For a right triangle: • a2 + b2 = c2 • sin(θ) = b/c =opposite side/hypotenuse • cos(θ) = a/c = near side/hypotenuse • tan(θ) = b/a =opposite side/near side
41. 41. For a general triangle: α + β + γ = 180ο •Sine law: •Cosine law:
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