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- bending moment M is considered to be positive if it tries to
z
compress the upper beam fiber (fig. 6.3, b).
In the absence of shear forces, i.e. when, Q  , and M 
0
0
y z
the bend is called clean.

a) b)
Figure 6.3

6.2 Differential equations of equilibrium

Consider a beam loaded by distributed load of intensity   x
q
(fig. 6.4). Select from the beam an element with the length dx . It
is influenced by a distributed load that can be considered
uniformly distributed on the length dx , and bending moments and
shear forces (take them positive direction), replace the action of
parts of the beam on a selected item (fig. 6.5).
From the equilibrium conditions we obtain:
 Y  Q   x  q   x dx    Q   x  dQ   x   0;


dx
 M  M   x  Q   x dx q x dx     M   x  dM   0 .

c
2
The first equation gives the condition

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