抄録
Lack of information about the spatial distribution of the modulus of subgrade reaction results in significant uncertainty with respect to the true value of the calculated displacements, shear forces and moments in the analysis of "beams on elastic support". In order to incorporate this uncertainty into the analysis, the spatial distribution of the modulus of subgrade reaction is modeled here as a homogeneous low pass Normal random function of the space coordinate along the beam, and an approximate solution of the resulting random differential equation is derived. The paper considers the case of an infinite bean acted upon by a single concentrated load. For this case explicit solutions are presented for the spatial distributions of standard deviations of displacements, moments, and shear forces at every point along the beam. In addition the correlation coefficient between displacement at different points is evaluated. This information is sufficient for the determination of probability distributions of settlements, differential settlements, shear forces, and moments, at every point along the beam, thus making it possible to carry out a complete probabilistic design of such beams.
