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Figure 5.2
For finding the direction and building diagrams M use the
x
following rule of signs: twisting moment is considered to be
positive if on looking at the face end of a rod cutoff, it tries to
rotate it the clockwise (fig. 5.2).

5.2 Differential equations of equilibrium

Consider the rod that loaded by distributed twisting moment
m
with the intensity   x . Cut the element of a rod with the length
dx (fig. 5.3).

Figure 5.3

It is loaded by balance twisting moments (in the right section –
M and the left – M  dM ) and external distributed load   x ,
m
x x x
which can be regarded as uniformly distributed due to the
smallness dx .
Setting up the equilibrium equation:

 M  M  m   x dx  M  dM x  0 , from here
x
x
x

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