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Modulus of subgrade reaction is experimentally
determined by pressing a hard punch into the base (soil).
Numerically, it is equal to the force that is required to press into
2
the ground the punch with the area 1м on the depth у 1 м ; the
3
dimension of the modulus  Нk  м .
Thus, the intensity of the reaction at each point is
determined by the beam deflection. To solve the problem first we
find the equation of the elastic line y  f   x , and then the
formulas for determining the bending moment and transverse
force.

8.2 The differential equation of beam on elastic
foundation

Find the equation of the curved axis for the beam of
constant cross-section (Fig. 8.1, a), which is laid on an elastic
foundation and loaded by distributed load intensity   x .
q
The total intensity of the distributed load q at some
сум
point of the beam
q  q r  q kby . (8.2)
сум
Let’s write the differential equation of the curved axis of
the beam of constant cross-section in bending
d 4 у
EI  q (x ) ,
z 4 сум
dx
Taking into account the formula (8.2) the last correlation
takes the form
4
d y
EJ  q kby ,
z 4
dx
or
4
d y 4 q
 4 y  , (8.3)
dx 4 EJ z

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