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where we denote
kb
  4 .
4EJ
z
The general integral of the equation (8.3) has the form

y  y  y  e   x C cos x C  sin   x 
1 2 1 2
(8.4)
 e  x C cos x C  sin   x  y ,
3 4 2
where y – the general integral of the homogeneous equation
1
(with q  ); y – partial solution, depending on the type of the
0
2
right side of the equation, i.e. on the load q  q   x .
The steel integrationC , C , C and C are determined
1 2 3 4
considering the loading and leaning of the beam.
In the particular case the load is distributed linearly
q  q  q x  , (8.5)
0 0
the solution y can also be represented as the linear function
2
y  A Bx . (8.6)
2
By substituting formulas (8.5) and (8.6) in equation (8.3),
we obtain

kb
A q  4 4 EJ   q / kb q  4 4 EJ   q   .
  і B 
0 z 0 0 z 0
So, in this case, a partial solution for the load

q q  q x 
y   0 0 .
2
kb kb
(8.7)

Figure 8.2 The function y 2   x
determines the absorbing of a
foundation from the load q , which is
applied directly to the surface of the foundation (Fig. 8.2).
Obviously, the choice of a partial solution in the form (8.7) is

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