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In the first condition statically applied force P perform
1
on move  actual work
11
1
A  P .
1
11
2
In the second condition the load to the beam, which has
force P , more force P is applied. Consequently, in the direction
1 2
of force P move  occurs, on which the force P performs
1 12 1
potential (virtual) work
A  P . (2.3)
мож 1 12

2.2 Theorems of reciprocal works and reciprocal
deflection

The theorem of reciprocity of works (Betty’s theorem) is
formulated as follows. The product of possible work of forces of
the first condition and move in their directions that is caused by
forces of the second condition equals to the product of possible
work of forces of second condition and move in their direction
but caused by forces of the first condition (fig. 2.2)
P   P  . (2.4)
m mn n nm

The theorem of
reciprocity movement
(Maxwell's theorem) is a
special case of Betty’s
theorem. Under two equal
forces displacement caused
by the first condition forces
in the direction of the forces
of the second condition
equals to displacement,
which is caused by the
second condition forces in

the direction of the forces of
Figure 2.2 the first condition. So
if P  P , then
m n
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