Engineering Mechanics: STATICS

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Engineering MechanicsSTATICS

• Anthony Bedford and Wallace Fowler
• SI Edition

Teaching Slides Chapter 3 Forces
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Chapter Outline

• Types of Forces
• Analysis of Forces
• 2-Dimensional Force Systems
• 3-Dimensional Force Systems
• Computational Mechanics

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3.1 Types of Forces

• Terminology
• Line of Action
• The straight line collinear with the force vector

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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

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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

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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

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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

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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)

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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

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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)

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3.1 Types of Forces

• Surfaces
• Consider 2 plane surfaces in contact
• Force exerted on right surface by left surface F

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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

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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

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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

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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

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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

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3.1 Types of Forces

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

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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

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3.1 Types of Forces

• Springs
• To exert contact forces in mechanical devices
• E.g. suspension of cars

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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

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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

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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

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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

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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

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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