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Principle of Superposition

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Kazuhiro Suga

Text book for the mechanics of materials [Part VIII] Principle of Superposition (in English) note: Your feedback is welcome!

Engineering
1 of 4
Principle of Superposition Goal 1. Understanding of Superposition 2. Employing Principle of Superposition
Principle of Superposition P2P1 l 2 l 2 A, E Δl ＝ Δl1 Δl2＋ P1 l 2 Δl1 P2 l Δl2 For linear elastic structures, the load effects caused by multiple loads are the sum of the load effects caused by each load.
Solving Statically Independent Beam by Principle of Superposition l1 l2 P A, E a b c l = l1 + l2 x RcRa P l1 Rc AE Pl1 ΔlP＝ AE Rcl Δl ＝Rc ΔlP ΔlRc ＝＋ 0 Rc l1 l2＋ l1 ＝ P− Geometric condition Ra RcP ＝＋ ＋ 0 Ra＝− l1 l2＋ l2 P Equilibrium of force
Summary 1. Understanding of Superposition 2. Employing Principle of Superposition ＝ ＋ For linear elastic structures, the load effects caused by multiple loads are the sum of the load effects caused by each load.

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Principle of Superposition

  • 1. Principle of Superposition Goal 1. Understanding of Superposition 2. Employing Principle of Superposition
  • 2. Principle of Superposition P2P1 l 2 l 2 A, E Δl ＝ Δl1 Δl2＋ P1 l 2 Δl1 P2 l Δl2 For linear elastic structures, the load effects caused by multiple loads are the sum of the load effects caused by each load.
  • 3. Solving Statically Independent Beam by Principle of Superposition l1 l2 P A, E a b c l = l1 + l2 x RcRa P l1 Rc AE Pl1 ΔlP＝ AE Rcl Δl ＝Rc ΔlP ΔlRc ＝＋ 0 Rc l1 l2＋ l1 ＝ P− Geometric condition Ra RcP ＝＋ ＋ 0 Ra＝− l1 l2＋ l2 P Equilibrium of force
  • 4. Summary 1. Understanding of Superposition 2. Employing Principle of Superposition ＝ ＋ For linear elastic structures, the load effects caused by multiple loads are the sum of the load effects caused by each load.