Journal of Engineering Mechanics

A special beam‐column element is developed for the finite element inelastic buckling analysis of reinforcing bars in concrete columns. The material considered is elastic‐plastic‐strain hardening. A strain reversal rule is also included to model the unloading from compression once buckling occurs. The element is used to trace the post‐buckling load‐deflection path of a reinforcing bar supported laterally by sufficiently stiff ties of the column and initially loaded axially to the yielding load. The post‐buckling load‐deflection path depends on the slenderness ratio of the bar. For a very small slenderness ratio, an interesting [straightening] phenomenon is present after the buckling at the yielding load, followed by a second buckling at a higher load. For a larger slenderness ratio, the post‐buckling load carrying capacity may or may not exceed the yielding load. A critical slenderness ratio is found by equating the maximum load to the yielding load.

The present paper examines the problem of a flat circular anchoring region that is embedded at an elastic medium‐rigid surface interface. The compliance of the anchor is enhanced by the presence of a debonded region. The paper develops a mathematical analysis of the ensuing elastostatic contact problem. A numerical scheme coupled with a bounding technique is used to develop a set of bounds for the elastic stiffness of the anchor region. The numerical results presented in the paper illustrate the manner in which the elastic stiffness of the anchor is influenced by the extent of the cracked region and Poisson's ratio of the elastic medium.

A hysteretically nonlinear column subjected to earthquake excitations is considered. The horizontal and vertical earthquake ground accelerations are modeled by segments of stationary and nonstationary Gaussian white noise and filtered white noise processes. The method of equivalent linearization is used, and the time‐dependent equivalent parameters in terms of response moments are evaluated. The Fokker‐Planck equation governing the transition probability density of the response is described, and the associated second moment equations are derived. The transient and nonstationary response statistics for a range of values of parameters are obtained. A Monte Carlo digital simulation study is also performed. The results are compared with the theoretical findings and good agreement is observed. Particular attention is given to the amplification effects of the vertical ground acceleration. It is shown that the effect of the vertical ground motion is usually insignificant, unless the load coefficient is quite large.

A synthesis approach is presented for calculating the complex eigen‐properties of a nonclassically damped structure from the complex eigenproperties of the constituent substructures which are also nonclassically damped. In this approach, the substructures are successively coupled, one degree of freedom at a time. At each stage of coupling, the eigenvalues are obtained as the solution of a simple characteristic equation, defined in closed form. For each calculated eigenvalue, the corresponding eigenvector is then obtained from the closed‐form expressions without solving any simultaneous equations. The approach provides exact eigenproperties. These properties can be used in the calculations of dynamic response of a structure subjected to deterministic or stochastic loads. The numerical results illustrating the application of the proposed approach are presented.

Members of framed structures which are influenced by the dynamic torsional moment from other members connected to the end of the member and structural members like the rotor of a helicopter which experience a twisting moment due to flow are studied. The dynamic stability of those members with a thin‐walled cross section under periodic follower and unidirectional axial torques is investigated. The basic equation of motion of these members becomes a Hill equation, and the parametrically excited unstable vibration occurs in this system. Stability maps of simple parametric resonance are illustrated by using the Bolotin method, and the dynamic stability of various types of members may be estimated from numerical results. The analytical method presented can be applied to analysis members with various boundary conditions and various load conditions.

A fabric tensor $F_{\mathrm{ij}}$ for three‐dimensional assemblies of granular soils is introduced as an index showing the anisotropy due to the preferred orientation of constituent particles and is actually determined by using data derived from a material science approach of soils. Using the fabric tensor, a Drucker‐Prager type of yield function is extended so as to take into account the anisotropic yielding behavior of granular soils. Plane strain tests on Toyoura sand are analyzed with a result that the anisotropic shear strength is well fitted by the extended Drucker‐Prager yield function. Based on this, it is concluded that this study provides a step to link the material science approach of soils, in which the spatial arrangement of particles and associated voids plays an important role, to the continuum theory of plasticity.

Continuum damage models are presented within the framework of elastic‐damage theory for cement paste and mortar. Basic elements of continuum damage mechanics are given, and various types of extensions of elastic‐damage models are proposed. The limitations and possible extensions of these models when applied to concrete are also presented. To facilitate model implementation, a simple and efficient computational update procedure for damage variable is also considered. To assess the applicability of the damage models proposed, well‐documented experimental programs are performed through the use of a data acquisition system developed in the University of California, Berkeley. In particular, through the use of a systematic parameter estimation algorithm, the effects of porosity and sand concentration on the initiation and growth of microcracks are clearly demonstrated.

A one‐dimensional medium consisting of two alternating material states is studied. The occurrences of the states as well as their respective durations are assumed random according to a renewal process. The properties associated with the two materials could be drastically different; they are also subject to uncertainties and spatial variation. Satisfactory performance of a system associated with such medium could depend on the spatial average over some domain within the medium. The domain may consist of a random number of nonoverlapping segments of the two materials. Based on the proposed model, statistics of the domain average property are derived. These statistics may serve as inputs to reliability evaluation, including the determination of exceedance probability of a given threshold by some local spatial average property. Extensive sensitivity analysis reveals the implication of probable presence of another material within an otherwise statistically homogeneous medium. Besides application to geotechnical problems, results could be also useful to any problem involving a random two‐state medium.

The steady‐state vibration of a subway‐soil‐building system is determined using an appropriate finite element model. The vibration level in the podium block of the building is obtained for two different track support systems: direct fixation and a floating slab. A pair of unit harmonic loads is used to simulate the wheel loading from a single train. Because the subway consists of twin double boxes, different loading combinations are used to determine the maximum velocity response in the podium for the frequency range of interest. It is found that the vibration levels for the floating slab track system exceed those of the direct fixation track system in the low frequency range. However, in the high frequency range, the floating slab track system behaves as an effective vibration isolator.

Two‐dimensional rigid‐link models have been used often in the study of elastic stability to provide insight into the behavior of engineering structures; the buckling modes of such models take only planar shapes. Many engineering structures, however, possess three‐dimensional buckling characteristics, so it is important to have models with three‐dimensional buckling characteristics. A three‐dimensional three‐link model that initially assumes either a straight‐line or a planar zigzag configuration is studied and both in‐plane and out‐of‐plane buckling modes are found in each case. The model is formulated in terms of the total potential energy and differentiation is carried out using the MACSYMA program. This structure may deflect continuously with increasing load, buckle in a plane, or buckle out of plane, depending on the angle between the adjoining links and the relative stiffness between the bending springs and the internal rotation springs. We find that in the case of in‐plane buckling, the buckling load is greater than the lowest buckling load of the perfect structure.

A linearized deterministic model is proposed for the coupled lateral and torsional motions of a tall, slender structure in turbulent atmospheric boundary layer. The resultant force acting on the structure is represented as a vector sum of the aerodynamic excitation forces due to atmospheric turbulent and wake‐excitation force due to vortex shedding. The turbulence velocity and the wake‐excited acrosswind force are modeled by cosinusoidal functions of closely spaced frequencies and random phase angles, using the appropriate power spectra. The proposed analytical model predicts the longitudinal, lateral, and torsional motions of a slender structure using the predetermined lift, drag, and moment coefficients of a given geometric shape. The predicted peak displacement and acceleration responses are found to compare reasonably well with the published experimental results. Using the proposed model, the effects of angle of incidence on the peak displacements and accelerations are investigated for various reduced velocities.

Static-kinematic optimality criteria are introduced for plastically designed structures having segments of prescribed length such that the variation of the cross sectional area is (1) Segmentwise linear; and (2) continuous across segment boundaries. It is shown that, compared to other geometrical constraints suggested in the past, these constraints have the following advantages: (1) Stress concentrations due to cross-sectional discontinuities are avoided; (2) unlike some unconstrained optimal solutions, the underlying assumptions of simple structural theories are not violated; and (3) a high degree of design flexibility, an easier fabrication (due to linear segments), and a greater material economy are achieved. The optimality criteria, which turn out to be similar to those of Foulkes, are derived in a general form and then they are applied to a clamped beam with four segments. This theory is being extended to (1) Elastic design; and (2) other types of structures (e.g., plates).

A dimensionless finite-difference equation for predicting the pressure distribution between narrowly-spaced disks is presented. The flow region is bounded by two curves corresponding to creeping and potential flows.

In order to establish relatively simple, accurate formulas for the calculation of torsional rigidities and stresses, the Rayleigh direct (approximate) energy method is combined with the Euler indirect variational method in the analysis of an elastic parallelpiped (i.e., a shaft of rectangular cross section) subjected to end torques. The formula obtained for the calculation of the maximal sharing stress is then improved by an iteration. The single set of formulas derived is valid for both the narrow and bulky cross sections, in contrast to the two different sets of formulas obtained by Timoshenko and Goodier. The numerical values of the torque and shearing stress are calculated and compared with other known results. The accuracy achieved herein is such as to obviate the need for an evaluation of the infinite series in the exact analysis (significant errors do not exceed one percent even in the case of a square cross section).