Concurrent force system

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Lecture 4

• Concurrent force system
• Scalars and Vectors

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Concurrent Force System

• A Force system is a group of forces
• If a force system acting on a body produces no
  external effect and the body experiences no
  change in motion, then the forces are in
  equilibrium. ?F 0
• The resultant of a force system is the simplest
  equivalent system to which the original system
  will reduce.

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Concurrent Force System

• Characteristics
• Magnitude (kN).
• Direction (slope/sense)
• specified by ?
• or dimensions
• Point of Application.
• A straight line extending through the point of
  application in the direction of the force is
  called the line of action.

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Example
0.6 kN
Show all of the forces acting on the painting.
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W0.6 kN
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4

• Solution
• From equilibrium the sum of the vertical forces
  must be zero, therefore the vertical component of
  the force in the two wires must be equal to 0.6
  kN.
• From symmetry this value is 0.3 kN

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Example

• From geometry the horizontal force must be 0.4
  kN.
• The force in each wire must be
• sqrt(0.320.42) 0.5 kN

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Scalars and Vectors

• Scalars Completely described by a number
  (magnitude).
• length, volume, mass, etc.
• Vectors Magnitude and direction.
• Force,moment, velocity, acceleration, etc.
• Use the parallelogram law for addition.
• Types free, sliding, fixed.

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Vectors

• Position Vector Determines a fixed point in
  space.
• Free Vector Line of action does not pass
  through a unique point.
• Sliding Vector Line of action passes through a
  unique point and the vector can be anywhere along
  its line of action.
• Fixed Vector Line of action passes through a
  unique point and the point of application is
  confined to a fixed point on its line of action.

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Forces

• Principle of Transmissibility. (rigid bodies)
• the external effect of a force on a rigid body is
  the same for all points of application of the
  force along its line of action.
• Classification of forces
• surface forces (friction)
• body forces (self weight)
• uniformly distributed load (superimposed dead
  load)
• linearly varying distributed load (water
  pressure)
• concentrated load (wheel of a truck)

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Force Systems

• Any number of forces constitute a force system.
• A force system is
• concurrent if the lines of action of all the
  forces intersect at a common point.
• coplanar when all forces lie in the same plane.
• collinear if it has a common line of action.
  (truss element)

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Example
Resultant of two concurrent forces.
Method 1 Graphically (parallelogram law/triangle
law)
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Example
Method 2 Trigonometry
?
Sine Law a/sin? b/sin? c/sin? Cosine Law c2
a2b2-2abcos?
c
b
?
?
a
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Additional Material

• Read Sections 2.1-2.3
• Problems Section 2
• 2,6,10,20,27,29