Principle of Superposition

Text book for the mechanics of materials
[Part VIII] Principle of Superposition (in English)

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1. Principle of Superposition Goal 1. Understanding of Superposition 2 . Employing Principle of Superposition

2. Principle of Superposition P 2 P 1 l 2 l 2 A, E Δ l ＝ Δ l 1 Δ l 2 ＋ P 1 l 2 Δ l 1 P 2 l Δ l 2 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 B eam by Principle of Superposition l 1 l 2 P A, E a b c l = l 1 + l 2 x R c R a P l 1 R c A E P l 1 Δ l P ＝ A E R c l Δ l ＝ R c Δ l P Δ l R c ＝ ＋ R c l 1 l 2 ＋ l 1 ＝ P − Geometric condition R a R c P ＝ ＋ ＋ R a ＝ − l 1 l 2 ＋ l 2 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.