CE 201 Statics

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CE 201 - Statics

• Lecture 11

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MOMENT OF A FORCE-VECTOR FORMULATION

• In scalar formulation, we have seen that the
  moment of a force F about point O or a bout a
  moment axis passing through point O is equal to
• MO F ? d
• where d is the perpendicular distance between the
  force and point O.
• In vector form, the moment can be expressed as
• MO r ? F
• where r is the position vector drawn from O to
  any point on the line of action of F. The moment
  has both magnitude and direction.

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• Magnitude
• MO r ? F r ? F ? sin ? F ? (r ? sin ?)
  F ? d

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Transmissibility of a Force

• F has a moment about point O equals to
• MO r ? F
• We have seen that r can be extended from point O
  to any point on the line of action of force F.
  Then
• MO rA ? F rB ? F rC ? F
• Then F has the property of a sliding vector and,
  therefore can act at any point along its line of
  action. F is therefore a transmissible force.

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Cartesian Vector Formulation

• If F and r are expressed as Cartesian vectors,
  then
• i j
  k
• MO r ? F rx ry rz
  
• Fx Fy
  Fz
• If the determinant was determined, then,
• MO (ryFz - rzFy) i (rxFz rzFx) j
  (rxFy ryFx) k

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• The vector formulation method has the benefit of
  solving three-dimensional problem easier.
  Position vectors can be easily formed rather than
  perpendicular distance ( d ).

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Resultant Moment of a System of Forces

• MRO ? ( r ? F )

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Principle of Moments

• If F F1 F2 MO ( r ? F1 ) ( r ? F2 )
  r ? (F1 F2 ) r ? F
• The principle of moments states that the moment
  of a force about a point is equal to the sum of
  the moments of the forces components about the
  point.

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