Calculations show that, under concentrated load, ratio of pressures and deflections along beam are constant if beam has infinite length; when analysis of beams of infinite length, resting on elastic-isotropic half-space, is based on coefficient k of subgrade, reaction bending moments are overestimated, contact pressures and deflections underestimated; recommended analytical procedures for beams of various length.
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Aleksandar B. Vesić (1961) studied this question.