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The displacement amplitudes and the phase angles of vertically vibrating rigid circular plates on an elastic isotropic homogeneous half‐space have been expressed in terms of the mass of the plate, the static spring constant multiplied by a frequency‐dependent function, and a damping term. The results have been modified to apply to vibrating soil‐foundation systems. The effects of hysteresis damping, nonlinear load‐deflection characteristics of soils, the static prepressure, the change of soil properties with depth, and the difference between static and dynamic stress‐strain relations of soils have been considered. The mathematical model has been compared with data on vibrations of circular foundations. The agreement between the model and the experimental data for cohesive soils is very good.

Underground conduits are subjected to external loads caused by the weight of the backfill material and by loads applied at the surface of the fill. These external loads will produce circumferential bending moments in the conduit wall. The magnitude and distribution of the bending moments have been determined by measurements of the circumferential fiber strains in thin‐walled metal tubes subjected to the external loads. The effects of different backfill materials, different trench width, and trench depth have been investigated. Bending moments caused by static and dynamic loads have been compared. The bending moments are finally expressed in terms of the required crushing strength.

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