Journal of Engineering Mechanics

A foundation medium is divided into a number of horizontal layers, Each layer is idealized by a system of multiple one‐dimensional vertical columns interconnected by shear springs. The model is defined by two parameters, which are found to be uniquely defined by the material properties of the layer only. Formulations are proposed to obtain the model parameters from the elastic constants of the layer medium. Using the model, the responses of the elastic slab resting on an elastic foundation are formulated. Good agreement is found between the responses computed by the present formulation and a finite element method.

The strain rate and strain rate history effects on the inelastic stressstrain behavior of annealed A‐36 structural steel at room temperature are examined experimentally under monotonic and cyclic loading conditions. The strain rate used is between ${10}^{-6}-{10}^{-1}/\sec \text{,}$ which covers the range that might be experienced by steel building frames during earthquake ground motions. An axial‐torsional, electrohydraulic, servocontrolled testing system with strain control is used for all the tests. Test results show relatively more significant strain rate sensitivity of the material for monotonic loading and less significant strain rate sensitivity for cyclic loading. Strain rate hfstory effect is not significant in most of the tests.

Materials exhibiting nonassodated flow should, according to Drucker's stability postulate, become unstable when exposed to certain stress paths inside the failure surface. Results of a series of triaxial tests designed to expose the type of behavior displayed by granular materials are presented and discussed. The sand dilates during shear, it exhibits nonassociated flow, and when exposed to stress paths in the region of potential instability, none is observed. The reliability of the test results, the possible influence of viscous effects on the stability, and the effect of release of elastic energy are studied and discussed in detail. Thus, Drucker's stability postulate is not applicable to granular materials. The type of volume‐change behavior displayed by the material is of great importance in the question of stability of granular materials.

An efficient and accurate method for computing probabilities of failure, $p_f\text{,}$ of structural and mechanical components is presented. Limit state equations can be of any continuous functional form, and the basic variables can have any distribution. The algorithm that is an extension of the Rackwitz‐Fiessler and Chen‐Lind methods has the following qualities: (1) It employs an optimization routine to approxirhate nonnormal variants as equivalent normals; (2) approximates the limit state by a quadratic at the design point; and (3) transforms the quadratic form to a linear one, thereby approximating the limit state as linear in normal design factors. Exhaustive testing of the algorithm has indicated not only that computational time is “negligible,” but also that errors in $p_f$ are consistently less than 10% in all realistic physical problems and are usually much less. Examples are presented to illustrate the performance of this fast probability integration method.

The purposes of the paper are: (1) To derive differential equations of equilibrium for a tapered I‐beam; and (2) to formulate a finite element for the beam that takes into account the effect of nonuniform torsion. In the virtual work formulation, the updated Lagrangian approach is adopted, in which the effect of geometric nonlinearity is considered. The present formulation requires obtaining a rigorous expression for the strains based on the membrane theory of shells, through which the effect of tapering is considered. The displacements of each cross section are determined with Vlasov's thin‐walled beam assumptions. The derived finite element model, in terms of the linear and geometric stiffness matrices, is useful in a buckling or an incremental large displacement analysis. Using the present theory, one is able to investigate various torsional‐flexural instability problems. Examples are prepared and comparisons are made with existing solutions.

The stress concentration of the clamped edge is investigated in the longitudinal shear problem for isotropy and orthogonal anisotropy. The value of the stress concentration at the end of a rounded corner can be expressed by an infinite series of terms of the radius of curvature and the order of stress singularity at the corner. The accuracy of the expression that takes the first few terms in the series is investigated, and it is proved that the expression is effective. The relation of the stress concentration between isotropy and orthogonal anisotropy can be obtained.

A critical review of classical optimal control algorithms is made with respect to the specific application of structural control under seismic excitations. With the earthquake ground acceleration being the major source of continuous external disturbances, the Riccati closed‐loop control does not satisfy the optimal condition. New optimal control algorithms are proposed herein, including the instantaneous optimal open‐loop control, instantaneous optimal closed‐loop control, and instantaneous optimal closed‐open‐loop control. These new control laws are developed for providing feasible control algorithms that can easily be implemented for applications to seismic‐excited structures. Numerical examples are worked out to demonstrate the control efficiency of the proposed control algorithms. Experimental verifications have been carried out.

The present study is initiated to investigate the possible causes for excessive lamp failure rates on high‐mast illumination towers in the state of Minnesota. The study consists of an experimental effort during which one of the illumination towers is instrumented and motion data is collected for various wind conditions. The final step of the study includes evaluation of the numerical as well as the experimental data that has been obtained from the preceding steps. This evaluation includes the identification of modes of vibration in the frequency domain, filtering of data for assessment of modal effects, and comparisons between experimental and numerical results.

A rigid body motion test is proposed for verifying the legitimacy of a finite element to be used in a geometrically nonlinear analysis. The test requires that the initial forces acting on an element rotate or translate with the rigid body motion while the magnitudes of the initial forces remain unchanged, so as to preserve the equilibrium of the element during the rigid body motion. Such a test is consistent with basic physical laws, and is, therefore, more rational than previous considerations on rigid body motions. This paper also demonstrates the significance of using a consistent procedure for calculating the member forces in an incremental nonlinear, solution process. When a consistent element is used along with a consistent force calculation procedure, convergent and accurate solutions can be obtained for various nonlinear problems.

An analytical solution to the response of a long trapezoidal‐section dam on a foundation consisting of an elastic half‐space and subjected to simulated earthquake morion is developed. An optimum seismic design is achieved when the cross section of the dam is triangular. The effect of soil structure interaction is to lower the strain occurring in the dam.