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To use the boundary condition (8.12) we find
2
d y 2   x
  2C  e cos x  sin   x , (8.17)
1
dx 2
3
d y 3   x
 4C  e cos x . (8.18)
1
dx 3
Equating the right sides of formulas (8.18) and (8.12) we
obtain
P
C  .
1 3
8EJ 
z
Substituting C in the equations (8.15) - (8.18) we obtain
1
the final equations for the deflection, angles of rotation of the
cross sections, bending moments and transverse forces
P
y   x   ; (8.19)
1
8EJ  3
z
P
   x    ; (8.20)
4
4EJ  2
z
P
M   x   ; (8.21)
z 2
4
P
Q   x    , (8.22)
y 3
2
Where  x   i 4 , 1 - the functions of dimensionless argument
i
 x that are defined as follows:
  e   x cos x  sin x ;
1 
  e   x cos x  sin x ;
2  (8.23)
  e   x cos x ;
3 
  e   x sin x . 
4 

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