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ES2501: Statics/Unit 12-1: Statically Equivalent Systems

Representing a distributed force by a single force and a single couple of moment:. ES2501: Statics/Unit 12-1: Statically Equivalent Systems. Distributed force ------ a force distributed over a line (1D), an area (2D), or a volume (3D).

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ES2501: Statics/Unit 12-1: Statically Equivalent Systems

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  1. Representing a distributed force by a single force and a single couple of moment: ES2501: Statics/Unit 12-1: Statically Equivalent Systems Distributed force ------ a force distributed over a line (1D), an area (2D), or a volume (3D) Water pressure on a reservoir door Air pressure on An airplane wing Weight of a 3D Object Specification: a distributed force is specified by its load density Note Difference between load and load density ------ force per unit length [F/L] ------ force per unit area [F/L2] ------ force per unit volume [F/L3]

  2. Representing a distributed force by a single force and a single couple of moment: 1D Special Cases ES2501: Statics/Unit 12-2: Statically Equivalent Systems Distributed Forces Statically equivalent x x O O A Resultant force over interval (x, x+dx] Discrete form Integration

  3. Representing a distributed force by a single force and a single couple of moment: Extensions ES2501: Statics/Unit 12-3: Statically Equivalent Systems Distributed Forces • Distributed load density vector --- 1D cases: • 2D cases: • 3D cases:

  4. F --- total area xA--- position of the canter Examples: ES2501: Statics/Unit 12-4: Statically Equivalent Systems Distributed Forces A By direct integration Also calculated by the method of Composites

  5. Examples: Statically equivalent force of the uniformly distributed load ES2501: Statics/Unit 12-5: Statically Equivalent Systems Distributed Forces Statically equivalent force of the triangularly distributed load Resultant force Line of action of

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