Principle of virtual work: When a body in equilibrium is subjected to an infinitesimally small imagined displacement, the corresponding imagined work is called what?

Introduction / Context:

The principle of virtual work is a powerful energy method in statics. It asserts that for a system in equilibrium, the total virtual work done by external forces during any kinematically admissible virtual displacement is zero. This approach often simplifies calculations of reactions and internal forces when direct force balance is cumbersome.

Given Data / Assumptions:

• Body/system is in static equilibrium.
• A virtual displacement is infinitesimally small and consistent with constraints.
• No change in actual loads; only an imagined compatibility-preserving motion is considered.

Concept / Approach:

Virtual work is not physical work performed; instead, it is a mathematical device. If δr denotes a virtual displacement, the virtual work δW = Σ(F · δr). For equilibrium, ΣδW = 0 for all permissible δr. This allows solving for unknown reactions without explicitly writing all component equilibrium equations.

Step-by-Step Solution:

Verification / Alternative check:

Results obtained via virtual work can be checked against conventional ΣF = 0 and ΣM = 0 equations in simple cases, ensuring consistency.

Why Other Options Are Wrong:

• “Imaginary work” is a colloquial phrase but not a defined mechanics term.
• “Negative work” refers to work opposite to displacement direction, not to the method.
• “Complementary work” is used in elastic energy methods, not this principle.

Common Pitfalls:

• Using virtual displacements that violate constraints (e.g., fixed supports allowed to move).
• Confusing virtual work (mathematical) with actual energy transfer.

Final Answer:

virtual work