The document discusses the principle of superposition in linear elastic structures, emphasizing its role in understanding and employing this principle. It states that the load effects from multiple loads are the sum of individual load effects. A mathematical framework is provided for solving statically independent beams using this principle.

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.