Key Concepts:The principle of virtual work provides
another method to calculate the
equilibrium
of structures subjected to external loads.For equilibrium the total virtual work
of
the external forces applied to the structure must be zero for any virtual
displacement.
i.e.Virtual Work(δW=0for equilibrium)
In a Nutshell:Virtual
Work is the work of all external forces and couples acting on the
structure
during a virtual displacement.
Definitions:Virtual Displacement – An imagined small
displacement of a structure
consistent
with any existing constraints such as pins, rollers, etc.
Forces
that do no work include reactions at supports,
internal forces at connections,
and
forces exerted by inextensible cords and cables.
Strategy:
1.
Determine
the (DOF) degrees of freedom of the structure and identify the variable (or
variables) that determine the position of the structure.
2.
Pick
coordinate axes with a fixed origin to locate the external forces and
moments that do virtual work during a virtual displacement of the
structure.
3.
Calculate
the coordinates and take the derivative to obtain the virtual
displacements.The virtual
displacements must be consistent with the
kinematic
constraints.
4.
Calculate
the dot product of the external forces with the virtual displacements to
establish the virtual work performed during a virtual displacement.
5.
Set
the virtual work equal to zero and solve for the desired unknown (or
unknowns).