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Representing Distributed Force with Single Force & Couple of Moment: ES2501 Statics Unit 12-1

Learn how to represent distributed forces over lines, areas, or volumes using load density. Understand the difference between load and load density, special cases in 1D, and how to calculate resultant forces using integration methods. Examples provided for better comprehension.

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Representing Distributed Force with Single Force & Couple of Moment: ES2501 Statics Unit 12-1

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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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