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2 GENERAL METHODS OF DEFLECTION
DETERMINATION

2.1 The work of elastic forces. The potential energy of
deflection of the rod with an arbitrary load

Work force that statistically acts on an arbitrary elastic
system can be represented by the half of the product of the final
value of this force on the final value corresponding to its moving
P 
A  . (2.1)
2
Here, under the power of P we mean generalized force,
i.e. any force action: concentrated force, a group of forces,
distributed loads, concentrated time, etc. Under the movement 
we mean a generalized displacement, that is the kind of
movement where the generalized force does the work.
Recall that during the deformation of the body work is
done not only by external but also internal forces that resist
deformation. This work is numerically equal to the work of
external forces, but it is opposite in sign.
Experiencing elastic deformation, the body accumulates
potential energy. The reason for this is to change its
configuration, i.e. the change in relative position of the particles
of the body compared to the so-called zero-configuration - the
unstrained state. Numerically, the potential energy of deformation
of the present work is the internal force factors. It is essential that
each of the six internal force factors Q , Q , N , M , M and
y z x z y
M correspond to such movements, in which the other five do
x
not perform work. Therefore, in general, the forces of potential
energy of deformation of the rod U is the sum of all internal
work force factors which is responsible for tensile deformation,
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