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Figure 2.5

Let’s define the virtual work of external and internal
forces on the movement of a single state, caused by the action of
freight condition.
The work of external forces

A  P . (2.10)
зов
The work of internal forces (fig. 2.5)
M dx
вн 
A  M zd , де d  z ,
l EJ z
that is
M zM dx
вн 
A  z . (2.11)
l EJ z
Equating the right sides of (2.10) and (2.11) we obtain
Mora’s formula (Mora’s integral)
M zM dx
   z . (2.12)
l EJ z
Here M - expression of the bending moment that occurs
z
in a single state M - an expression of the bending moment in the
z
load condition.
If you need to determine the angular displacement at the
point A, then in the formation of a single state instead of a single
force P a single time M  1must be applied.
In the case of a spatial problem, following the formula
(2.2), we obtain
N xN dx M xM dx M zM dx M yM dx
   x   x   z   y . (2.13)
l EF l GJ k l EJ z l EJ y

2.5 Calculation of Mora’s integral
by Vereshchagin’s method

Each of the integrals which is included in the formula
(2.13) can be presented as

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