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In calculating pipe lying on the ground, rails and sleepers,
tanks, belting fundamental building structures, ship hulls by a
core theory, motor roads and other such objects we have to deal
with the beams, which all their lengths are held on the base,
which can be deformed and has elastic properties (Fig. 8.1 a).
Clearly, the beam on the elastic foundation is a statistically
indefinite system, in which internal efforts cannot be found
without considering strains.

а) b)

Figure 8.1

To calculate the beam elastic properties of the base are
very important. The simplest model of a foundation is Winkler’s
model. It can be represented as a set of springs that completely
distributed and not related to each other (Fig. 8.1, b). We assume
that the springs are soldered to the beam and when a negative
deflection the reaction of the base will be downward. Such links
of beams and foundations are called bilateral. For such a base the
reaction at each point of the beam sole will be proportional to the
deflection at this point, and the reaction per unit length can be
represented as

r   x  kby   x , (8.1)

where b - the width of the beam, k - stiffness of the elastic
foundation (modulus of subgrade reaction).

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