Related Variational and Energy Principles - Mechanics of Structures: Variational and Computational Methods - page 158

FIGURE 3.12
Truss.

δ δ

similarly: M is the internal moment due to a virtual (unit) applied moment, and M t is the

net internal torque due to a virtual (unit) applied torque.
This equivalence of the unit loa d term and the rate of change of force, with respect to
the applied load, e.g., P, permits problems in which no applied loads occur

at the position where the response is sought to be treated by the addition of a dummy or
”fictitious” load at this point. Then, after the application of this load, the fictitious load is
set to zero. This is then an alternative, equivalent procedure for the use of a unit load at the
location where the response is desired. The fictitious load approach to the unit load method
is discussed in Chapter 3 of the first edition of this topic.

δ N = ∂ N /∂

3.2.3 Theorem of Least Work

The theorem of least work can be considered as a special case of Castligliano's theorem,
part II. It is sometimes also referred to as Engesser's second theorem or Engesser's theorem of
compatibility and it is usually employed to study statically indeterminate structures. The
quantities (state variables) in a structure that cannot be determined by using the conditions
of equilibrium alone are referred to as redundants . The number of redundant stress resultants
in a solid is equal to the number of independent forces and/or moments less the number