Journal of Engineering Mechanics

Theoretical investigation is presented for the along‐wind motion of a multistory building under random wind load excitation, taking into account the effect of soil compliancy under the footing. Assuming that the super‐structure is composed of identically constructed story‐units and the soil behavior is characterized by a known frequency dependent impedance matrix, closed form solutions are obtained for the frequency response functions and the spectral densities of structural response. Numerical examples show that soil compliancy decreases the structural response of a moderately tall 10‐story building by about 17%, but increases the response of a more flexible 40‐story building by 21–22%. Some of the frequency response functions are found to be dominated not by the first mode; thus, spectral peaks can theoretically occur near some higher mode frequencies if sufficient wind energy is available around these frequencies. The Davenport spectrum used in the numerical examples, however, has a dominant peak at a very low frequency and diminishes very quickly as frequency increases, resulting in only two peaks in the response spectra in both examples.

The first‐passage time problem for the response amplitude of a linear lightly damped single‐degree‐of‐freedom oscillator under evolutionary random excitation is considered. A Markovian approximation of the amplitude allows the use of a Fokker‐Planck equation for the formulation of the problem. This equation is solved exactly for the special case of a step function‐modulated stationary excitation. These results are used in determining a solution for the general excitation case via a Galerkin technique. Pertinent digital simulation data demonstrate the reliability and extreme efficiency of the developed solution method.

A semi‐infinite plate, of which a part on the boundary is rigidly stiffened and in which a crack initiates from an end of the stiffened edge as a problem of a mixed boundary value of thin plate bending, is analyzed. The problem is solved by a complex variable method which uses a rational mapping function. Two analytical methods are described: one method can apply to general loads and the other can apply when the free boundary, even partially, exists. These methods give a solution in a closed form for a shape represented by the rational mapping function. Uniform bending and torsion are considered as loads. Bending moment distributions before and after crack initiation, and the stress intensity factor are investigated for crack length, stiffened edge length, and the Poisson's ratio.

The interaction of local and overall buckling in thin‐walled columns is considered. A finite strip method in conjunction with the theory of mode interaction is developed to study the problem. The method is applicable to doubly symmetric cross sections carrying uniform stress or monosymmetric cross sections subjected to uniform end compression. Imperfection‐sensitivity surfaces are presented for stiffened panels and I‐section columns. A brief parametric study on I‐section columns is presented to illustrate the effect of flange slenderness and the ratio of local to Euler critical load on the maximum load carried. The effect of dynamic loads in the form of suddenly applied end compression is also investigated. It is found that in the presence of overall imperfections likely to occur in practice, the suddenness of load application can cause a reduction of about 10% of the maximum static load carrying capacity. A test program on I‐section columns carried out in Cornell University is cited for an evaluation of the present theory. There exists fair agreement between the theoretical predicted and experimentally observed collapse loads.

Structural layout theory is based on two underlying concepts, i.e., the Prager‐Shield theory of plastic design and the notion of “structural universe.” In this paper, optimal layout theory is extended to allow for the effect of selfweight (dead load). The proposed extension is of practical importance because in the design of long‐span structures selfweight is a significant load component and the total weight is strongly dependent on the choice of layout. The application of the modified optimality criteria is illustrated with examples of minimum weight grillages (truss grids) as well as plane frames. The degree of economy achieved is then demonstrated through comparisons with nonoptimal solutions. It is also shown that in the preceding examples both primal and dual formulations give the same minimum weight. This comparison is a convenient check on the optimality of the proposed solutions.

An analytical study of the nonlinear finite deformation, buckling, and postbuckling behavior of prebuckled (prestressed) tapered arches is conducted by formulating the problem as a two‐point nonlinear boundary‐value problem. The prebuckled arches studied are different from traditional arches in that they are made by first elastically buckling shallow straight members and then attaching them to their supports. An algorithm based on a shooting method is used to solve the system of governing coupled nonlinear differential equations. Numerical results showed that there is a class of prebuckled arches with tapered sections for which the buckling loads (symmetric limit loads) are higher than the load for the equivalent prismatic prebuckled arch.

Wave damping and motion of clay beds are measured in a wave tank for various soil and wave conditions. The propagator matrix theory for continuously layered plasto‐elastic beds is used to model the wave‐soil interactions. In most cases, the theory agrees well with the experimental results. Wave damping and bed motion increase nonlinearly with wave height. Wave damping mechanism of clay beds is the Coulomb friction between grains. Model‐prototype scaling examples are made for application of the model data to design situations.

A workable expression is developed in the case of bivariate Gaussian variables for the probability density function of one variable conditioned on a range of values for the other variable. Such an expression is useful in evaluating sturctural reliability with correlated modes of collapse. A lengthy expression for trivariate Gaussian variables is also presented.

Lateral and effective stresses obtained by an application of the mixture theory in a fluid saturated porous medium of finite width are compared with those of Boussinesq and Biot theories respectively. The porous medium is assumed to be a binary mixture of water and solid particles. The effects of momentum supply on effective intergranular stresses are illustrated. It is shown that mixture theory predicts higher effective stresses than Biot's theory under the loading and lower stresses at regions close to retaining structures.

It is shown that for long narrow buildings with identical frames and identical walls, the modes that involve in-plane floor deformations are not excited by earthquake ground motion. Therefore, the floors in such buildings can be treated as rigid in their own plane in earthquake analysis without introducing an additional approximation. However, this result presupposes the acceptability of the lumping of masses of the building at the floor-frame intersections. In addition, the result does not necessarily hold for other types of excitation.

The importance of constraining the rate of spatial change of cross-sections in optimal design has been presented in previous studies. In the context of plastically designed beams, a theory is proposed for optimizing structures with bounded spatial gradients. The procedure is based on an extended version of the Prager-Shield condition which replaces the cost extremum statement with an optimal strain-stress relationship and thus converts the considered optimization problem into that of structural analysis. The associated strain field, as in most constrained problems, usually contains strain impulses (concentrated rotations). The procedure is illustrated with three examples of beam design and the results are verified by independent methods.