Journal of Engineering Mechanics

Conventional analysis of mean squared values is extended to calculation of the fourth moment of the response of a linear system. This provides a way to investigate the non‐normality of structural response, due to a non‐normal excitation. Studies are made for a linear SDF structure subjected to fairly simple non‐normal forces, which include a “white noise” process and filtered processes. Each filtered non‐normal process is generated by passing a “white noise” non‐normal process through a linear second‐order filter. The non‐normality of the structural response is investigated by integration in both the time domain and the frequency domain and by a more efficient technique that is an extension of the Lyapunov equation. This latter method reduces the calculation of the fourth moment of the response to solving a set of simultaneous linear algebraic equations.

A formula for the stress concentration of a rounded notch cut in a clamped edge is derived. In this investigation a notched semi‐infinite plate is subjected to two situations: Uniform tension and uniform shear. The notch has a rounded corner at the end. It is shown that the maximum stress at the tip of a rounded corner can be represented by an infinite series expressed in forms of radius of curvature and the order of Williams stress singularity. The approximate expressions which include only the first few terms of an infinite series are compared with the analytical results. A rational mapping function and complex stress functions are used for the analysis of this displacement boundary value problem.

Consideration of the spatial as well as temporal variation of earthquake ground motions may be important in the design of structures with spatially extended foundations and lifeline systems. In this paper, the ground motion during a specific earthquake event is conceived as the realization of a space‐time random field. Following a brief review of pertinent results from the second‐order theory of random fields and a description of spectral estimators, accelerograms recorded by the SMART 1 seismograph array in Lotung, Taiwan, are examined to determine the frequency‐dependent spatial correlation of earthquake ground motions. A scheme for processing seismograph array data is proposed, and similarities and differences in the motions recorded during different events are noted. Finally, key parameters characterizing the correlation structures are identified and a preliminary mathematical model is suggested for the space‐time correlations.

Static and dynamic analysis of fully clamped shallow spherical shells, subjected to uniform normal pressure on concave side and continuously supported on Pasternak foundation on the convex side, is made using Berger's and modified Berger's techniques. Expressions for large static deflections are obtained and results compared with those of Nash and Modeer. The preceding techniques are employed to get the approximate expressions for natural frequency. Values of nondimensional natural frequency obtained by various methods are compared with results of Reissner, Nowacki, Bucco, and others. While a modified Berger's approach gives very good results for static analysis of fully clamped shells, the original Berger's approach is found to be more suitable for free vibration analysis, as results tally with those obtained by Réissner, using Rayleigh's method, even for higher ratios of $(H/h)\text{.}$ The modified Berger's technique gives sufficiently accurate values of natural frequencies only for smaller values of $(H/h)\text{.}$

An experimental procedure is developed for the testing of full‐ or large‐scale structures under simulated seismic deformations in a quasi‐static fashion. The procedure, pseudo‐dynamic testing, is based on active modal control theory. The pseudo‐dynamic testing procedure is a simultaneous simulation and control process in which inertia and damping properties are simulated and stiffness properties are acquired from the structure. The procedure calculates a set of dynamic displacements based on active control theory, utilizing the simulated inertia and damping properties and acquired stiffness properties under a hypothetical ground motion, and simulates the response of the structure under seismic motion in a quasi‐static fashion. A detailed implementation procedure is presented for structures that can be modeled as discrete mass systems. The application of the procedure is simulated on the 1/5‐Scale model of the US‐Japan seven‐story reinforced concrete frame wall structure.

Exact solutions are presented for the load‐deflection behavior of a free‐free beam on an elastic (Winkler type) foundation, which is subjected to a concentrated load at midlength. Two constitutive models are considered: Rigid‐perfectly‐plastic and elastic‐perfectly‐plastic (ideal section), and in each case the problem is reduced to the solution of a nonlinear ordinary differential equation with associated initial conditions. The initial value problems are solved numerically using the fourth order Runge‐Kutta method. For loads greater than the threshold value at which the three‐hinge mechanism forms, both exact solutions produce practically identical results for long beams. This leads to the conclusion that elastic effects are insignificant in a long elastic plastic floating beam, after the three‐hinge mechanism is formed. The second iteration solution of an approximate method of analysis for the rigid‐plastic beam is also presented. Good agreement is found between the approximate and the exact rigid‐plastic results.

For the Lehigh-Purdue concrete plasticity model, there seems to be certain limitations on the choice of material properties to ensure the convexity of the limiting surfaces describing the model. A set of inequalities is derived, the satisfaction of which ensures that the initial discontinuous, subsequent loading and failure surfaces have the desired shape. An example is given to show that the model fails for a feasible choice of material parameters not satisfying the aforementioned inequalities.