Virtual work in statics refers to the work done by a force or moment during a virtual displacement of a body. It's not the body itself that does the work, but rather the external forces or moments acting upon it. According to the reference provided, virtual work is the work done by force or moment during a virtual displacement of the body.
Understanding Virtual Work
To grasp the concept, let's break it down:
- Virtual Displacement: This is an infinitesimal (extremely small) and imaginary displacement of a body from its equilibrium position. Crucially, this displacement is compatible with the constraints on the system. It's a theoretical displacement used for analysis.
- Force or Moment: These are external influences that can cause the body to move or rotate.
- Work Done: In mechanics, work is done when a force causes a displacement. Mathematically, work is the dot product of the force vector and the displacement vector. Similarly, a moment (torque) does work when it causes an angular displacement.
Therefore, virtual work is calculated by multiplying the force (or moment) by the virtual displacement (or virtual rotation) in the direction of the force (or moment).
Example
Imagine a simple lever.
- Real Situation: If you apply a force to one end of the lever and it moves, real work is being done.
- Virtual Work Application: In the method of virtual work, we imagine a small, virtual displacement of the lever. We then calculate the virtual work done by all the forces and moments acting on the lever during this imaginary displacement. The principle of virtual work states that if the lever is in equilibrium, the total virtual work done by all forces and moments must be zero.
Application of Virtual Work Principle
The principle of virtual work is a powerful tool for:
- Determining Equilibrium: If the total virtual work done by all forces and moments is zero for any arbitrary virtual displacement, the system is in equilibrium.
- Analyzing Complex Structures: It simplifies the analysis of complex systems with multiple constraints.
- Finding Reaction Forces: It can be used to determine unknown reaction forces in structures without directly solving force equilibrium equations.
Key Takeaways
- Virtual work involves imaginary displacements.
- The focus is on the work done by forces or moments, not the body itself.
- The principle states that for a system in equilibrium, the total virtual work is zero.
