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Engineering Mechanics: STATICS

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Internal force one part of a given object is subjected to a force by another ... Coil springs commonly used in mechanical devices exert a force approximately ... – PowerPoint PPT presentation

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Title: Engineering Mechanics: STATICS


1
Engineering MechanicsSTATICS
  • Anthony Bedford and Wallace Fowler
  • SI Edition

Teaching Slides Chapter 3 Forces
2
Chapter Outline
  • Types of Forces
  • Analysis of Forces
  • 2-Dimensional Force Systems
  • 3-Dimensional Force Systems
  • Computational Mechanics

3
3.1 Types of Forces
  • Terminology
  • Line of Action
  • The straight line collinear with the force vector

4
3.1 Types of Forces
  • System of Forces
  • Coplanar or 2 dimensional line of action of the
    forces lie in a plane
  • 3 dimensional
  • Concurrent lines of action of the forces
    intersect at a point
  • Parallel lines of action are parallel

5
3.1 Types of Forces
  • External Internal Forces
  • External force given object is subjected to a
    force exerted by a different object
  • Internal force one part of a given object is
    subjected to a force by another part of the same
    object
  • Requires clear definition of object in
    consideration

6
3.1 Types of Forces
  • Body Surface Forces
  • Body Force force acting on the volume of an
    object
  • E.g. gravitational force on an object
  • Surface Force force acting on the surface of an
    object
  • Can be exerted on an object by contact with
    another object
  • Both body contact forces can result from
    electromagnetic effects

7
3.1 Types of Forces
  • Gravitational Forces
  • The force exerted on an object by the earths
    gravity
  • Gravitational force, or weight, of an object can
    be represented by a vector

8
3.1 Types of Forces
  • Gravitational Forces
  • Magnitude of an objects weight is related to its
    mass by
  • W mg
  • where g 9.81 m/s2 in SI units
  • (acceleration due to gravity at sea level)

9
3.1 Types of Forces
  • Gravitational forces electromagnetic forces act
    at a distance
  • The objects they act on are not necessarily in
    contact with the objects exerting the forces

10
3.1 Types of Forces
  • Contact Forces
  • Forces that result from contacts between objects
  • E.g. push on a wall ? exert a contact force
  • Surface of hand exerts a force F on surface of
    wall
  • Wall exerts an equal opposite force ?F on your
    hand (Newtons 3rd Law)

11
3.1 Types of Forces
  • Surfaces
  • Consider 2 plane surfaces in contact
  • Force exerted on right surface by left surface F

12
3.1 Types of Forces
  • Surfaces
  • Force exerted on right surface by left surface F
  • Resolve F into
  • Normal force N (normal to surface)
  • Friction force f (parallel to surface)
  • Smooth surfaces friction force assumed to be
    negligible
  • Rough surfaces friction force cannot be
    neglected

13
3.1 Types of Forces
  • If the contacting surfaces are curved
  • Normal force friction force are perpendicular
    parallel to the plane tangent to the surface at
    their point of contact

14
3.1 Types of Forces
  • Ropes Cables
  • Contact force can be exerted on an object by
    attaching a rope or cable to the object pulling
    on it

15
3.1 Types of Forces
  • Ropes Cables
  • Example
  • Cable exerts a force T on container
  • Magnitude of T tension in cable
  • Line of action of T collinear with cable
  • Cable exerts an equal opposite force ?T on
    crane

16
3.1 Types of Forces
  • Assumption
  • Cable is straight
  • Tension where cable is connected to container
    tension near crane
  • Approximately true if weight of cable ltlt tension

17
3.1 Types of Forces
  • Pulley wheel with grooved rim that can be used
    to change the direction of a rope or cable

18
3.1 Types of Forces
  • Assumption
  • Tension is the same on both sides of a pulley
  • True when pulley can turn freely the rope or
    cable is either stationary or turns at a constant
    rate

19
3.1 Types of Forces
  • Springs
  • To exert contact forces in mechanical devices
  • E.g. suspension of cars

20
3.1 Types of Forces
  • Consider a coil spring of unstretched length Lo
  • When stretched L ? Lo
  • Pulls on the object to which it is attached with
    force F
  • Object exerts an equal opposite force ?F on
    spring
  • When compressed L ? Lo
  • Compressed too much ? buckle

21
3.1 Types of Forces
  • Spring designed to exert a force by being
    compressed is often provided with lateral support
    to prevent buckling
  • E.g. enclosing it in a cylindrical sleeve
  • Shock absorbers within coils in car suspensions

22
3.1 Types of Forces
  • Coil springs commonly used in mechanical devices
    exert a force approximately proportional to the
    change in length
  • F kL ? Lo
    (3.1)
  • Force is a linear function of change in length
    linear spring

23
3.1 Types of Forces
  • Spring constant k depends on material design
    of spring (units force/length)
  • From Eq. (3.1) k magnitude of the force
    required to stretch or compress the spring a unit
    of length

24
3.1 Types of Forces
  • Example Lo 1 m k 3000 N/m, L 1.2 m
  • Magnitude of the pull spring exerts
  • kL ? Lo 3000(1.2 ? 1) 600 N

25
3.1 Types of Forces
  • Springs can be used to model situations in which
    forces depend on displacements
  • E.g. force necessary to bend steel beam is a
    linear function of displacement ? if ? is not
    too large
  • F k?
  • ? model force-deflection behaviour of beam with a
    linear spring
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