Virtual work principle

Definition

The virtual work principle states that the work done by external forces on a system in a virtual displacement is equal to the internal work done by the system's internal forces. This concept is fundamental in structural analysis, allowing engineers to analyze structures under various loading conditions, calculate deflections, and understand the relationships between different elements within a structure.

5 Must Know Facts For Your Next Test

1. The virtual work principle can be applied to both static and dynamic systems, making it versatile in structural analysis.
2. By using the virtual work principle, engineers can determine deflections of structures without having to derive complex differential equations.
3. This principle provides a powerful method for analyzing redundant structures by considering compatibility conditions along with equilibrium.
4. The application of influence lines is enhanced by the virtual work principle, as it allows for the evaluation of how different loading scenarios affect structural responses.
5. In continuous beams, virtual work aids in calculating moments and shear forces effectively by simplifying the analysis of internal forces.

Review Questions

• How does the virtual work principle relate to the analysis of influence lines in structural engineering?
  • The virtual work principle is essential when analyzing influence lines because it allows engineers to assess how external loads affect displacements at specific points within a structure. By applying virtual displacements at desired locations along an influence line, one can calculate the resultant deflections due to varying load positions. This relationship helps visualize how moving loads impact different parts of a structure and enables more efficient design and safety assessments.
• Discuss how the virtual work principle is utilized in energy methods for deflection analysis.
  • In energy methods for deflection analysis, the virtual work principle facilitates calculations by relating external work done by loads to internal strain energy within a structure. By assuming a virtual displacement and calculating the work done during this displacement, engineers can find deflections at critical points. This method simplifies complex problems and provides clear insight into how energy is distributed throughout structural members, allowing for precise design evaluations.
• Evaluate how the application of the virtual work principle affects the analysis of continuous beams with redundant supports.
  • The application of the virtual work principle in analyzing continuous beams with redundant supports significantly enhances problem-solving capabilities. It allows for establishing relationships between displacements and internal forces while considering compatibility conditions required for redundancy. This means that engineers can effectively address complex loading scenarios by leveraging this principle to manage unknown support reactions and ensure proper load distribution throughout multiple spans, ultimately leading to safer and more efficient designs.

Related terms

Virtual Displacement: A hypothetical small change in the position of a system that occurs without any time element, used in conjunction with the virtual work principle.

Equilibrium: A state in which the sum of forces and moments acting on a body is zero, leading to no acceleration or movement.

Work-Energy Principle: A principle stating that the work done on a system is equal to the change in kinetic energy of that system, closely related to the virtual work principle.