Principle Of Virtual Work

The Principle of Virtual Work states that for a system in equilibrium, the total virtual work done by internal and external forces is zero for any infinitesimal displacement consistent with constraints.

Minimum Potential Energy Theorem

This section discusses the Minimum Potential Energy Theorem, stating that the equilibrium configuration of an elastic system corresponds to a state of minimum total potential energy.

Castigliano’s Theorems

Castigliano's theorems provide methods to calculate displacements and rotations in elastic structures using energy principles.

First Theorem (For Linearly Elastic Structures)

The First Theorem provides a key relationship between deflection and strain energy in linearly elastic structures, simplifying the analysis of such systems.

Second Theorem (For Redundant Structures)

The Second Theorem by Castigliano is a vital tool for analyzing redundant structures by employing fictitious forces and energy derivatives.

Maxwell’s Reciprocal Theorem

Maxwell's Reciprocal Theorem states that the deflection at one point due to a unit load at another point is equal to the deflection at the latter point due to a unit load at the former.