Lec1_Introduction-to-Engineering-Mechanics.pdf

Lec1_Introduction-to-Engineering-Mechanics.pdf

• 1.
  Introduction to Engineering Mechanics:Statics
• 2.
  Overview • Engineering Mechanics •Force • Force Systems • Component of a Force • Moment of a Force
• 3.
  What is EngineeringMechanics? • Mechanics - branch of physics that considers the action of forces on bodies or fluids that are at rest or in motion • Engineering Mechanics – science which considers the effects of forces on rigid bodies. • Rigid bodies - an idealization of a body that does not deform or change shape. Steel Frames and Trusses Source: https://eastlandtruss.com.au/products/steel- frames-trusses/
• 4.
  What is EngineeringMechanics? Mechanics is consist of: 1. Mechanics of rigid bodies – “engineering mechanics: statics and dynamics” 2. Mechanics of deformable bodies – “study of strength of materials” 3. Mechanics of Fluids - study of fluid behavior at rest and in motion and the forces on them.
• 5.
  What is EngineeringMechanics? Subdivided into: • Statics – considers the effects and distribution of forces on rigid bodies which remain at rest. • Dynamics – consider the motion of rigid bodies caused by the forces acting upon them .
• 6.
  Fundamental Concepts andPrinciples Newton’s Law of Motion First Law: If the resultant force acting on a particle is zero, the particle remains at rest (if originally at rest) or moves with constant speed in a straight line Second Law: If the resultant force acting on a particle is not zero, the particle has an acceleration proportional to the magnitude of the resultant and in the direction of this resultant force. 𝑭 = 𝑚𝒂 F = net force; m = mass of the object; a = acceleration (rate of change in velocity)
• 7.
  Fundamental Concepts andPrinciples Newton’s Law of Motion Third Law: The forces of action and reaction between bodies in contact have the same magnitude, same line of action, and opposite sense. Newton’s Law of Gravitation: Two particles of mass M and m are mutually attracted with equal and opposite forces F and -F of magnitude F, given by 𝐹 = 𝐺 𝑀𝑚 𝑟2 F = attracting force; M = mass of the larger object; m = mass of the smaller object; G = constant of gravitation; r = distance between the objects
• 8.
  Fundamental Concepts andPrinciples Basic Quantities: • Length – use to locate the position in space. • Time – a succession of events • Mass – measure of a quantity of matter that is used to compare the action of one body with that of another. • Force – considered as a “push” or “pull” exerted by one body to another; action of one body on another.
• 9.
  Units of Measurement U.S.Customary or British System of Units (FPS) Mass in Slug Length in feet (ft) Time in Seconds (s) Force in Pounds (lb) International System of Units or Metric Units (SI) Mass in kilogram (kg) Length in metre (m) Time in Seconds (s) Force in Newton (N)
• 10.
  Units of Measurement U.S.Customary or British System of Units (FPS) 𝐹 = 𝑚𝑎 𝐹 – force, lb 𝑚 – mass, slug (𝑙𝑏 ∙ Τ 𝑠2 𝑓𝑡) 𝑎 – acceleration, ft/s2 1 slug is the mass which is given an acceleration of 1 ft/sec2 when acted upon by a force of 1 lb. International System of Units or Metric Units (SI) 𝐹 = 𝑚𝑎 𝐹 – force, N 𝑚 – mass, kg 𝑎 – acceleration, m/s2 1 Newton is the force required to give a mass of 1 kg an acceleration of 1 m/s2
• 11.
  Units of Measurement U.S.Customary or British System of Units (FPS) Weight W = mg 𝑊 – weight, lb 𝑚 – mass, slug (𝑙𝑏 ∙ Τ 𝑠2 𝑓𝑡) 𝑔 – gravitational acceleration, 32.17ft/s2 International System of Units or Metric Units (SI) Weight W = mg 𝑊 – weight, N 𝑚 – mass, kg 𝑔 – gravitational acceleration, 9.81 m/s2
• 13.
  What is aForce? • Force – an action that changes or tends to change the state of motion of a body (i.e., external effect of a force). • Internal effects perspective, a force that produces stress and deformation in the body at which the force is exerted (mechanics of deformable bodies). • Force is characterized by a) point of application, b) magnitude, c) its direction.
• 14.
  What is aForce? • Magnitude - is the amount, quantity or intensity of a force which is represented in terms of vectors. • Direction - is the direction of the line along which it acts and may be expressed as vertical, horizontal, or at some angle with the vertical or horizontal. • Point of application - is the point of contact between two bodies or the point where the force acts in the body. • Sense - is the way its acts along its line of action upward, downward to the right or left and its generally denoted by an arrowhead.
• 15.
  What is aForce? Principle of Transmissibility of a force states that the external effect of a force on a body is the same for all points of application along its line of action. e.g., when you want to move a block forward, you can either push it or pull it forward. Source: http://mechanicsmap.psu.edu/websites/2_equilibrium_concurrent/2- 3_principle_of_transmissibility/principleoftransmissibility.html
• 16.
  Force Systems • Forcesystems – any arrangement where two or more forces act on a body or on a group of related bodies. • Types of force systems: 1. Coplanar – line of action of all the forces in a force system lie in one plane. 2. Non-coplanar – line of action of the forces in a force system lie in more than one plane.
• 17.
  Force Systems Coplanar ForceSystem None-Coplanar Force System Angle bars bolted in plate System of forces acting on the corner of the prism Source: https://www.hkdivedi.com/2019/11/classification-of-force-system-in.html
• 18.
  Collinear Force System CollinearForce System • when the lines of action of all the forces of a system act along the same line. • when a set of forces will have a common line of action. Source: https://www.hkdivedi.com/2019/11/classificatio n-of-force-system-in.html
• 19.
  Concurrent Force System ConcurrentForce System • Forces when extended will pass through a single point called point of concurrency. • Lines of actions of all forces meet at the point of concurrency. • Concurrent forces can be coplanar or non-coplanar. Angle bars bolted on a plate 𝐹1 𝐹2 𝐹3 𝐹4 𝐹5 𝐶 “If all the forces lie in a single plane and meet at one point, coplanar and concurrent force system”
• 20.
  Concurrent Force System ConcurrentForce System • Forces when extended will pass through a single point called point of concurrency. • Lines of actions of all forces meet at the point of concurrency. • Concurrent forces can be coplanar or non-coplanar. A tower supported by three cables. “If all the forces lie in a different planes but pass through a single point, non- coplanar and concurrent force system”
• 21.
  Parallel Force System ParallelForce System • the line of action of a set of forces are parallel. • These forces can also be a coplanar of non-coplanar. Your arm at 90° when holding a load source: https://www.hkdivedi.com/2019/11/classifi cation-of-force-system-in.html “If all the forces lie in a single plane and their line of action are parallel, coplanar and parallel force system”
• 22.
  Parallel Force System ParallelForce System • the line of action of a set of forces are parallel. • These forces can also be a coplanar of non-coplanar. Table with its support “If all the forces do not lie in a single plane but their line of action are parallel, non- coplanar and parallel force system”
• 23.
  Non-Concurrent Force System Non-ConcurrentForce System • The line of action of the forces neither parallel nor intersect a common point. • When the forces of a system do not meet at a common point of concurrency “If the line of action of the forces lie on a single plane and neither parallel nor intersect a common point , coplanar and non-concurrent force system otherwise non-coplanar and non-concurrent force system”
• 24.
  Non-Concurrent Force System Non-ConcurrentForce System • The line of action of the forces neither parallel nor intersect a common point. • When the forces of a system do not meet at a common point of concurrency. “If the line of action of the forces lie on a single plane and neither parallel nor intersect a common point , coplanar and non- concurrent force system otherwise non-coplanar and non-concurrent force system” A tower with various cables connected Non coplanar and non-concurrent force system
• 25.
  Components of aForce • Force is a vector, it has magnitude and direction. • Force vector can be resolve into two perpendicular forces called components (i.e., 𝐹𝑥, x-component and 𝐹𝑦, y-component). • Vector notation of force F is, 𝑭 = 𝐹𝑥𝒊 + 𝐹𝑦𝒋 Note: Positive (force to the right; upward force) Negative (force to the left; downward force)
• 26.
  Components of aForce Take the force F in the figure, 𝐹𝑥 = 𝐹 cos 𝜃𝑥 = 𝐹 sin 𝜃𝑦 𝐹𝑦 = 𝐹 sin 𝜃𝑥 = 𝐹 cos 𝜃𝑦 If components are known (𝐹𝑥, 𝐹𝑦), we can solve the magnitude as 𝐹 = 𝐹𝑥 2 + 𝐹𝑦 2
• 27.
  Components of aForce The angle 𝜃𝑥 or the direction of the force F can be determine from its components using, 𝜃𝑥 = tan−1 𝐹𝑦 𝐹𝑥
• 28.
  Components of aForce What if, given is the slope of the force’s line of action instead of angle? 𝑟 = ℎ2 + 𝑣2 𝐹𝑥 = 𝐹 ℎ 𝑟 𝐹𝑦 = 𝐹 𝑣 𝑟
• 29.
  Components of aForce In quadrant II, 𝐹𝑥 = −𝐹 cos 𝜃𝑥 = −𝐹 sin 𝜃𝑦 𝐹𝑦 = 𝐹 sin 𝜃𝑥 = 𝐹 cos 𝜃𝑦 𝐹 = 𝐹𝑥 2 + 𝐹𝑦 2 𝜃𝑥 = tan−1 𝐹𝑦 𝐹𝑥
• 30.
  Components of aForce In quadrant III, 𝐹𝑥 = −𝐹 cos 𝜃𝑥 = −𝐹 sin 𝜃𝑦 𝐹𝑦 = −𝐹 sin 𝜃𝑥 = −𝐹 cos 𝜃𝑦 𝐹 = 𝐹𝑥 2 + 𝐹𝑦 2 𝜃𝑥 = tan−1 𝐹𝑦 𝐹𝑥
• 31.
  Components of aForce In quadrant IV, 𝐹𝑥 = 𝐹 cos 𝜃𝑥 = 𝐹 sin 𝜃𝑦 𝐹𝑦 = −𝐹 sin 𝜃𝑥 = −𝐹 cos 𝜃𝑦 𝐹 = 𝐹𝑥 2 + 𝐹𝑦 2 𝜃𝑥 = tan−1 𝐹𝑦 𝐹𝑥
• 32.
  Components of aForce 𝐹𝑥 = 𝐹 cos 𝜃𝑥 𝐹𝑦 = 𝐹 cos 𝜃𝑦 𝐹𝑧 = 𝐹 cos 𝜃𝑧 𝐹 = 𝐹𝑥 2 + 𝐹𝑦 2 + 𝐹𝑧 2 𝜃𝑥 = cos−1 𝐹𝑥 𝐹 𝜃𝑦 = cos−1 𝐹𝑦 𝐹 𝜃𝑧 = cos−1 𝐹𝑧 𝐹 Components Angles/Direction Resultant A 3D force (i.e., force in space)
• 33.
  Components of aForce Determine the x and y components of the forces with respect to the x and y axes.
• 34.
  Forces 𝐹𝑥 𝐹𝑦 𝐹158 cos 30 = 𝟓𝟎. 𝟐𝟑 58 sin 30 = 𝟐𝟗 𝐹2 −50 cos 45 = −𝟑𝟓. 𝟑𝟔 50 sin 45 = 𝟑𝟓. 𝟑𝟔 𝐹3 −45 5 13 = −𝟏𝟕. 𝟑𝟏 −45 12 13 = −𝟒𝟏. 𝟓𝟒 𝐹4 𝟒𝟎 𝟎
• 35.
  Components of aForce in a rotated axis Find the components in the x, y, u and v directions of the force P.
• 36.
  Find the xand y components (i.e., with respect to x, y axes). 𝐹𝑥 = 10 cos 60 = 𝟓 𝒌𝑵 𝐹𝑦 = 10 sin 60 = 𝟖. 𝟔𝟔 𝒌𝑵
• 37.
  Find the uand u components (i.e., with respect to u, v axes). 𝐹𝑢 = 10 cos 40 = 𝟕. 𝟔𝟔 𝒌𝑵 𝐹𝑣 = 10 sin 40 = 𝟔. 𝟒𝟑 𝒌𝑵
• 38.
  Moment of aForce • Moment - measures of the capacity or ability of the force to produce twisting or turning effect about an axis. • Magnitude of the moment is the product of the force and the perpendicular distance from the axis to the line of action of the force. 𝑀 = 𝐹 ∙ 𝑑 𝐹 – force perpendicular to the axis d – moment arm (perpendicular distance)
• 39.
  Moment of aForce Calculate the moment at point A, 𝑀𝐴 = 5 30 = 150 𝑁 ∙ 𝑐𝑚 Note the moment with respect to an axis or point is calculated using the perpendicular force and perpendicular distance. A 5 N 30cm Note: Positive moment: clockwise direction Negative moment: counterclockwise direction
• 40.
  Moment of aForce We calculate the moment at A, 𝑀𝐴 = 𝑃𝑥 0 − 𝑃𝑦 5 𝑀𝐴 = −50 sin 30 5 𝑀𝐴 = −𝟏𝟐𝟓 𝒌𝑵 ∙ 𝒎 Moment is zero about a point if the force’s line of action passes through that point.
• 41.
  Moment of aForce Why is it that moment is zero about a point if the force’s line of action passes through that point? In the figure, take the moment of the force F about A. 𝑀𝐴 = 𝐹𝑥 3 − 𝐹𝑦 4 𝑀𝐴 = 8 3 − 6 4 = 𝟎𝒌𝑵 ∙ 𝒎
• 42.
  End of Topic