Subject : Structural Analysis 1

Topic : General Principles

Difficulty : High

The raciprocal theorem states that the work done by forces acting through displacement of the second system is the same as the work done by the second system of forces acting the displacement of the first system.

1. Consider a simply supported beam of span l as shown in figure.
2. Let the beam be loaded by two systems of forces $P_{1}$ and $P_{2}$ separately as shown in figure.
3. Let $u_{21}$ be the deflection below the load point $P_{2}$ when only load $P_{1}$ is acting.
4. Similarly, Let $u_{12}$ be the deflection below the load point $P_{1}$ when only load $P_{2}$ is acting on the beam.

Hence, According to Reciprocal Theorem,

$P_{1}\times u_{12}=P_{2}\times u_{21}$