Journal of Engineering Mechanics

Dynamics of an elastic structure subjected to simultaneous horizontal and vertical earthquake ground accelerations are considered. The Liapunov method is used and several general bounds on the maximum responses are developed. Using a stored energy and an optimal Liapunov function, specific bounds on the motion of multidegree‐of‐freedom structures are obtained. Particular attention is given to the case of a single‐degree‐of‐freedom column structure subjected to horizontal‐vertical earthquake excitations. It is observed that the vertical acceleration enhances the peak horizontal response. The predicted bounds are compared with the response spectra of several earthquakes. It is shown that when an appropriate choice for the effective time duration is used the estimated maximum responses become quite reasonable.

By the combined use of reduced integration and addition of non‐conforming displacement modes, a highly effective new plate element has been established. The displacement field of this element is formed by adding nonconforming modes only to transverse displacement component of Ahmad‐Irons element and the element matrices are computed by the numerical integrations with modified orders. Compared to other elements, the superiority of both the NC8‐4.1 and NC8‐5.1 elements over the elements previously studied has been observed. The solutions with these elements converge to the true solutions very rapidly as the mesh is refined. These elements are also shown to be applicable to the wide range of thick and very thin plate problems.

A common design criterion for plastic frame or truss structures is that the probability of formation of a mechanism should be below some specified value. However, a mechanism formation need not be catastrophic because the masses of the structure must be accelerated in order to move the mechanism. If the load on the structure varies randomly in time, the load may change such that the plastic movement stops shortly after it has started. The relevant design parameter may therefore be related to the accumulated plastic deformation of the structure rather than to the mere formation of a mechanism. The problem of calculating this plastic movement process is studied for a single degree of freedom linear elastic‐ideal plastic oscillator subject to stationary Gaussian process excitation. It is assumed that the events of plastic movements are rare and of short duration such that the movement process may be modeled as a compound Poisson process. The study concentrates on the calculation of the distribution of the single jumps of the process. The tool for this is the concept of Slepian model process displayed in several interesting applications, in particular by G. Lindgren and co‐workers. Under certain general assumptions it may be concluded that the plastic displacement resulting from a single isolated exceedance of an elasticity limit as a first approximation has an exponential distribution. Special problems appear for narrow band responses with clumping of level crossing. The problem is analysed in some detail at the end of the paper.

An effective method of weight reduction for a beam in pure bending is to remove material near the neutral axis, often in the form of holes. Minimizing the stress concentration around these holes is an important consideration in engineering design. One of the methods to minimize the stress concentration is to change the hole shape itself until the optimized shape with minimum stress concentration factor (s.c.f.) is reached within specified geometric constraints and loading condition. In the present note, using conformal transformation technique, centrally located quasi‐square holes in isotropic beams under pure bending are analyzed. It is well‐known that for circular hole with $d/W⩽0.45$ there will be no stress concentration and hence the hole does not weaken the beams. The present study shows that with the optimized quasi‐square hole shapes, holes as large as $d/W=0.6$ can be introduced without producing any stress concentration.

This paper describes an effective method of obtaining covariances in recursive form for a multiple‐degree of freedom linear structural system subjected to multiple support nonstationary seismic excitations. The study is an extension of a case of a shaking table type excitation to multiple shaking table type excitations. The accuracy and efficiency were numerically justified.

Charts are provided for the rapid estimation of the response of an elastoplastic single-degree-of-freedom system to a decaying exponential load. The integral of the load was equated to the overpressure impulse from either the HULL code or the Speicher-Brode representation of blast wave overpressures. Plots were thus derived of the scaled duration and of the exponential characteristic parameter as a function of overpressure. Variations in both positive overpressure impulse and positive phase duration are well within the overpressure uncertainty for the scaled heights-of-burst of interest over the pressure range considered. A parametric response chart of the system is provided, which covers a very wide range of displacements, fundamental periods, and loading pressures. The chart is a graph of the results of the solution of 750 individual cases using the Newmark beta method of numerical integration.