Journal of Engineering Mechanics

Most finite element solutions of soil‐structure interaction problems assume a horizontally layered soil that unavoidably extends to infinity and is bounded at the bottom by a bedrock. In this paper, a model consisting of a soil deposit included in a viscoelastic half‐space is used to analyze numerically the effects of the shape of the soil deposit and the existence of a compliant bedrock on the dynamic compliances of strip footings. The soil deposit is assumed to be semielliptical and in order to achieve a parametric study several aspect ratios going from infinity (boundless horizontal layer) to one (semi‐circle) are considered. The rigidity of the half‐space is given several values including infinity (rigid bedrock). The foundation compliances are computed using a frequency domain formulation of the Boundary Element Method for zoned viscoelastic media.

The theory of a rough crack model for nonlinear finite element analysis of reinforced concrete is presented. The model accounts for shear dilation, degradation under cyclic loading, and other effects. The smeared crack approach is used in the derivation, but the model could also be used for discrete cracks. The concept, theory, and computational procedure are described, and examples are presented.

An approximate solution is developed for the extreme‐value distribution of a stationary Gaussian process with a spectral density function that exhibits two well‐separated modes. Processes of this type arise in the analysis of the combined dynamic response to two loads or to one load that excites two of a structure's modes of vibration. Spectral moments of each of the modes taken separately are used to characterize the process; two envelope processes are then used to approximate the extreme value distribution. The proposed distribution is compared with other approximations and with results from Monte Carlo simulations.

The paper describes a theoretical and experimental study of steady exchange flow in a horizontal pipe that connects to regions containing fluids of differing densities. The exchange flow rate for an inviscid fluid is controlled by the diameter of the connecting pipe and the densities of the fluids. Viscosity causes a reduction in the rate of exchange and the extent of this change is investigated using an approximately equivalent flow, field to describe the boundary layer development in the exchange pipe. In laminar flow the normalized exchange flow rate can be expressed in terms of a single parameter involving the length to diameter ratio of the connecting pipe and the Reynolds number of the pipe flow.

A finite strip method is developed for the analysis of linear elastic curved plate systems that are continuous over non‐rigid supports. This approach incorporates the effect of the support elements in a direct stiffness methodology. The stiffness contribution of the support elements are derived and given as strip stiffness matrices which are combined with the plate strip matrices at the element level prior to assembly. This summation of plate and support stiffness contributions forms a substructure which is termed a compound strip. The compound strip methodology may be used readily to enhance computer programs based on traditional finite strip procedures. The validity of the compound strip method is demonstrated in several illustrative analyses. The compound strip methodology compares favorably to the finite element method for displacement and moment.

Previous work on stochastic models of stress distributions in granular half-spaces is extended to include the presence of horizontal as well as vertical surface forces. The resulting model is that of a standard stochastic process with a preferential drift in the direction of the horizontal surface force. The linear elastic stress distributions can be fitted into the general framework of this model. The theory is incomplete in the sense that certain quantities are indeterminate, particularly in the three-dimensional case. However, with the help of certain assumptions, stress distributions can be derived that possess the following realistic physical features: they fall off more sharply than the elastic distributions in a horizontal direction; and the diagonal components do not become tensile, in contrast to the elastic case. Finally, it is indicated how the theory may be generalized to the multilayer case.