GENERAL FORCE SYSTEMS

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• Lecture 14
• GENERAL FORCE SYSTEMS

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GENERAL FORCE SYSTEMS

• General force system can be represented by
• (a) a system of noncoplanar,concurrent forces
  through the origin O that have the same
  magnitudes and directions as the forces of the
  original system,and
• (b) a system of noncoplanar couples.

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CONCURRENT FORCE SYSTEM

• the resultant of the concurrent force system
  through the origin can be expressed as

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NONCOPLANAR COUPLES

• The resultant of the system of noncoplanar
  couples can be expressed as

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EXAMPLE 1

• Problem
• Replace the force system with a force R
  through point C and a couple.

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EXAMPLE 1

• Solution
• (1) determine the Cartesian vector for each force

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EXAMPLE 1

• (2) the resultant,

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EXAMPLE 1

• (3) the couple of the forces about point c
• determine the positive vectors

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EXAMPLE 1
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EXAMPLE 2

• Problem
• replace the system of forces with a force
• through pt O and a couple

250
250
8
5
6
600
150
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EXAMPLE 2

• Solution
• (1) resolve the 225 N force into components
• (2) the resultant,

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EXAMPLE 2

• (3) the couple

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EXAMPLE 3

• Problem
• Determine (a)the magnitude and direction of the
  resultant force, R.
• (b)the perpendicular distance
  from pt.O to the line of action
• of the resultant.

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EXAMPLE 3

• Solution

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EXAMPLE 3
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EXAMPLE 4

• Problem
• Reduce the forces to a wrench and locate the
• intersection of the wrench with the x-y plane.

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EXAMPLE 4

• Solution
• (1) determine the Cartesian vector of each force
• (2) position vector

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EXAMPLE 4

• (3) the resultant
• (4) direction cosine of

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EXAMPLE 4

• (5) unit vector

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EXAMPLE 4

• (6) the resultant couple

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EXAMPLE 4

• (7) the component of

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EXAMPLE 4

• (8) locate the intersection of C with the x,y
  plane

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• ADDITIONAL MATERIAL
• Read Section 5.1-5.2
• Problems Section 5
• 2, 4, 9, 10