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Virtual Work and Displacements
Using the concept of virtual displacements, and virtual work, we can derive the equations of motion of lumped parameter systems.
Example 1 Mass/Spring System
Here number of degrees of freedom =1 Co-ordinate to describe the motion is x Now consider free-body diagram, at some time t
General one degree of freedom system If q1 is the co-ordinate used to describe the movement then the general form of δW is as follows:
we call δq1 – generalised displacement Q1 – generalised force. From principle of virtual work
Example Referring to the mass/spring system again
x= q1
Example 2
Simple pendulum
This is another one degree of freedom system. During a virtual displacement, δθ, the virtual work done is
Example 3 – two degrees of freedom system
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FAQs on Virtual Work & Displacements - Engineering Mechanics - Civil Engineering (CE)
| 1. What is virtual work? |  |
Ans. Virtual work is a concept used in engineering and physics to calculate the work done by external forces on a system. It involves calculating the displacement of a system under external forces and determining the work done by these forces based on the virtual displacements.
| 2. How is virtual work related to displacements? | |
Ans. Virtual work is directly related to displacements as it involves calculating the work done by external forces on a system based on the virtual displacements. By considering the virtual displacements of a system, we can determine the forces acting on it and calculate the work done.
| 3. How is virtual work different from actual work? | |
Ans. Virtual work and actual work differ in their approach and calculation. Actual work is calculated based on the actual displacements of a system, whereas virtual work is calculated based on the virtual displacements. Virtual work is a mathematical tool used to determine the forces and displacements of a system without the need for considering actual physical movements.
| 4. What are the applications of virtual work in engineering? | |
Ans. Virtual work has various applications in engineering, including structural analysis, mechanical systems design, and optimization. It is commonly used in finite element analysis (FEA) to determine the forces and displacements in complex structures. Virtual work also plays a crucial role in analyzing the stability and equilibrium of structures.
| 5. How is virtual work used in the field of physics? | |
Ans. In physics, virtual work is used to analyze the equilibrium and motion of systems. It is commonly employed in the study of rigid body dynamics, where it helps determine the forces and displacements on a body in equilibrium. Virtual work principles are also applied in areas such as fluid mechanics and thermodynamics to analyze the behavior of systems under external forces.
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Nov 22, 2024 Last updated |
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