Timothy A. Philpot - Mechanics of materials _ an integrated learning system-John Wiley (2017)

CHAPTER17
Energy Methods
17.1 Introduction
When a solid body deforms as a consequence of applied loads, work is done on the body
by these loads. Since the applied loads are external to the body, this work is called external
work. As deformation occurs in the body, internal work, commonly referred to as strain
energy, is stored within the body as potential energy. If the proportional limit of the material
is not exceeded (i.e., if the material remains elastic), then no energy dissipation occurs
and all strain energy is completely recoverable. For this situation, the principle of conservation
of energy can be stated as follows: The work performed on an elastic body in static
equilibrium by external forces is equal to the strain energy stored in the body.
From this principle, internal deformations in a body can be related to the external
loads acting on the body. Energies related to axial, bending, torsional, and shear loadings
will be considered next.
The load–deformation relationships that will be presented here are based on energy
principles and will be limited to linearly elastic systems (although these energy principles
are applicable to any conservative system). 1 These relationships make possible the application
of powerful methods to the analysis of elastic bodies, particularly with regard to statically
indeterminate structures, trusses, frames, and beams. Energy methods are also quite
useful in investigating the effects of dynamic loads on solid bodies.
1
A conservative system is a system in which the work done in moving a particle between two points is
independent of the path taken and the final energy of the system is equal to the initial energy of the system.
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