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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