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possible not only for the linear law (8.5), but also for other loads
q (x ) , if there is the condition of equality to zero of the fourth
kb
  q x
derivative of the function y x     , which follows
2
directly from equation (8.3).

8.3 Calculation of infinitely long beam

Consider the infinitely long beam, loaded with only one
concentrated force P (Figure 8.3). Since   0q x  , then the
equation (8.3) takes the form

4
d y 4
 4 y  0 , (8.8)
dx 4
and its general solution

y   x  e   x C cos x C  sin   x 
1 2
(8.9)
 e  x C 3 cos x C  4 sin   x .
Since the total reaction of the substrate must equal P , i.e.
it is a finite value, then
y   0  . (8.10)

Due to restricting of a movement we also obtain
 dy 
     0. (8.11)
  
 dx  x

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