TABLE OF CONTENTS We consider a beam resting on an elastic solid (a "foundation") and carrying a load, as shown in Fig. 8-40a. To explain by simple examples the differences between two basic models describing a beam's behavior we assume that it is so rigid that it can be treated as undeformable. On account of symmetry the beam will move downward by a constant amount, as seen in Fig. 8-40b. Such a problem, known as a stamp problem, has been solved using equations of the theory of elasticity (see, for example [10, pp. 45-60])]. It was found that the diagram of the normal stress under the rigid stamp has the form shown in Fig. 8-40b. It is seen that the stress is not only nonuniform, but that it even grows infinitely near the ends of the stamp. Now we consider another case, shown in Fig. 8-41a. This time the "foundation" is composed of many identical independent elastic columns (with no friction between adjacent columns). It is evident that although the rigid beam will be displaced in exactly the same way as before, the response of the foundation will be quite difference. Since the ends of all the columns are displaced by the same amount, their responses the end stresses will also be identical, as shown in Fig. 8-41b. In the second model the stress distribution along the beam is proportional to the deformation, in the first it is not.
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