1. Chapter Summary
Principle of Virtual Work
The forces on a body will do virtual work when
the body undergoes an imaginary differential
displacement or rotation
For equilibrium, the sum of virtual work done by
all the forces acting on the body must be equal
to zero for any virtual displacement
This is referred to as the principle of virtual work,
and it is used to find the equilibrium
configuration for a mechanism or a reactive force
acting on a series of connected members
2. Chapter Summary
Principle of Virtual Work
If this system has one degree of freedom, its
position can be specified by one independent
coordinate q
To apply principle of virtual work, use position
coordinates to locate all the forces and
mechanism that will do work when the
mechanism undergoes a virtual movement δq
The coordinates are related to the independent
coordinate q and these expressions differentiated
to relate the virtual coordinate displacements to
δq
3. Chapter Summary
Principle of Virtual Work
Equation of virtual work is written for the
mechanism in terms of the common
displacement δq, then it is set to zero
By factoring δq out of the equation, it is
possible to determine either the unknown
force or couple moment, or the equilibrium
position q
4. Chapter Summary
Potential Energy Criterion for Equilibrium
When a system is subjected only to
conservative forces, such as the weight or
spring forces, then the equilibrium
configuration can be determined using the
potential energy function V for the system
This function is established by expressing the
weight and spring potential energy for the
system in terms of the independent
coordinate q
Once it is formulated, first derivative, dV/dq
=0
5. Chapter Summary
Potential Energy Criterion for Equilibrium
The solution yields equilibrium position qeq for
the system
Stability of the system can be investigated by
taking the second derivative of V
If this is evaluated at qeq and d2V/dq2 > 0, stable
equilibrium occurs
If this is evaluated at qeq and d2V/dq2 < 0,
unstable equilibrium occurs
If all higher derivatives equals zero, the system
is in neutral equilibrium
