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The equation (6.38) is nonlinear, so its integration even in
simple cases of beam load is quite a challenge.
6.9 Method of initial parameters
The problem of integration of the approximate differential
equation of beam curved axis can be easily solved if its right side
is a continuous function. If this condition is not met, then a single
equation should be set up for each site of the beam and determine
the constants of integration, which number is twice the number of
sections of the beam. The problem may be quite cumbersome. It
would be very convenient to have one analytical entry for bending
moment along the length of the beam. To do this, use a supporting
function, called the Heaviside’s unit function:
0, if x ; a
x
a
1, if x . a
Figure 6.18
Consider a console beam (fig. 6.18). The origin of coordinates
will always be placed at the left end of the beam. When writing the
equation of bending moments to preserve the same structure of
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