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The virtual work method, also referred to as the method of virtual force or unit-load method, uses the law of conservation of energy to obtain the deflection and slope at a point in a structure. This method was developed in 1717 by John Bernoulli.
The principle of virtual work states that the virtual work of the applied forces is zero for all virtual movements of the system from static equilibrium.
Virtual Work Principle of Virtual Work: •If a particle is in equilibrium, the total virtual work of forces acting on the particle is zero for any virtual displacement. • If a rigid body is in equilibrium • total virtual work of external forces acting on the body is zero for any virtual displacement of the body
Explore the principle of Virtual Work in Statics, its applications in engineering, and how it revolutionizes structural analysis and design.
The Principle of Virtual Work Definitions: Virtual work is the work done by a real force acting through a virtual displace-ment or a virtual force acting through a real displacement. A virtual displacement is any displacement consistent with the constraints of the structure, i.e., that satisfy the boundary conditions at the supports.
In virtual work method, compatible virtual displacements (besides rigid-body virtual displace- ments) are to be used, where second-order ( not first-order) straining of members in a system is permitted in drawing virtual displacement diagrams.
The virtual work approach provides a unified framework for deriving various structural analysis techniques, such as the moment-area method, the conjugate beam method, and the force method; Virtual work principles can be extended to dynamic analysis and nonlinear problems, making it a versatile tool in structural mechanics
The key concepts in virtual work method include: work of a force, work of a moment, displacement center, compatible virtual displacement , and radian measure formula.
Apply Virtual Work: • Consider δs, which is an arbitrary displacement for the system, then the virtual work associated with this displacement is: δWF= xyδδx+Fy +Fzzδ • Note that δs may violate the applied constraints, because F contains constraint forces • Combine Newton and Virtual Work x y z Fxmxx Fymy Fzmzz y δ δ δ δ δ δ
Bernoulli is the originator of the principle of virtual work in statics. Let us consider (with Bernoulli) a problem of statics in which a concurrent force system is in equilibrium, or L~=l £1 = O.