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To determine the shear force and bending moment the method
of sections is used(fig. 6.2). The shear force of given console of
the beam crosses the imaginary plane perpendicular to the axis of
the beam at an arbitrary distance x from the free end (fig. 6.2 a).

a) b)
Figure 6.2

Shear force Q in any cross-section of the beam is numerically
y
equal to the algebraic sum of the projections on the axis of the
cross-section of all external forces placed on the one side of it.
Bending moment M in an arbitrary cross-section of the beam is
z
numerically equal to the algebraic sum of the moments about the
axis z of the section of all external forces placed on the one side
of it.
To the right of the beam (fig. 6.2, b) we obtain
 Y  0  Q  P  P ;
1
2
i
y

 M iz  0  M z   M  P 1  x  l 1   P 2  x  l 2 .

For Q and M we can adop the following sign rules:
y z
- shear force Q is considered to be positive if its vector tries to
y
rotate the cut off part of the beam clockwise relative to the position
of the cut (fig. 6.3 a);

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