TAM 2xx References

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Virtual Work

A force does work when it produces a displacement along its line of action. Virtual work (\( dU \)) is the work produced by a force over an infinitesimally small displacement \( dr \).
$$ dU = F\cdot dr\ $$
Virtual work of a couple moment:
$$ dU = \vec{M}\cdot d\theta \vec{k}\ $$
Fig: VWorkCoupleMoment
Virtual work \( dU \) completed by a couple moment, \( M \) .

Need to add a coordinate system to this picture. Taken from lecture 34.

We can use virtual work to solve for the forces in a system without needing to solve for all of the support reactions. For example, if a truss is completely pinned on one end, it doesn't move, which means there is no virtual work completed on that pin because there are no virtual displacements!

Virtual displacements

A virtual displacement is an infinitesimally small displacement (or rotation) that is possible in the system, denoted usually as \( dx \) or \( d\theta \). It's important to note that virtual displacements are assumed to be possible but don't actually exist.

Principle of Virtual Work

If a body is in equilibrium, the sum of the virtual work done by all the forces and couple moments acting on the body is zero.
Fig: PVW
Principle of virtual work.

Taken from lecture 34.

Virtual work analysis

Fig: VWAnalysis
Analysis procedure for virtual work problems.

Taken from lecture 34.