CE 201 Statics

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CE 201 - Statics

• Lecture 2

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Contents

• Vector Operations
• Multiplication and Division of Vectors
• Addition of Vectors
• Subtraction of vectors
• Resolution of a Vector
• Vector Addition of Forces
• Analysis of Problems

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Vector Operations

• Multiplication and Division of a Vector by a
  Scalar
• Vector A
• Scalar a
• A ? a aA
• Magnitude of aA
• Direction of A if a is positive ()
• Direction of A (opposite) if a is negative (-)

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Vector Addition

• Vectors are added according to the parallelogram
  law
• The resultant R is the diagonal of the
  parallelogram
• If two vectors are co-linear (both have the same
  line of action), they are added algebraically

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Vector Subtraction

• The resultant is the difference between vectors A
  and B

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Resolution of a Vector

• If lines of action are known, the resultant R can
  be resolved into two components acting along
  those lines (i.e. a and b).

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Vector addition of Forces

• Force!
• Is it vector OR scalar? Why?
• The two common problems encountered in STATICS
  are
• 1. Finding the RESULTANT (by knowing the
  COMPONENTS).
• OR
• 2. Resolving a FORCE into its COMPONENTS (by
  applying the parallelogram law).
• If more than two forces are to be added!!
• Apply the same law more than once depending on
  the number of forces.

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3 Forces
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Four Forces
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Analysis of Problems

• Two procedures to be followed
• Parallelogram law
• Trigonometry
• sine and/or cosine laws may be used

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Sine Law

• A/sin (a) B/sin (b) C/sin (c)

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Cosine Law

• C ?A2B2-2ABcos (c)

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Examples

• 2.1
• 2.2
• 2.3
• 2.4
• Problem 2-8
• Problem 2-25

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