Journal of Engineering Mechanics

A simple theory is developed for the coupled warping and cross‐sectional distortion at joints between thin‐walled I‐beams. Continuity of the joined flanges and the local character of the cross‐sectional distortion permit the distortion deformation to be expressed in terms of the warping parameters of the two beams at the joint. Four types of joints are treated. The unstiffened joint has two independent warping parameters, the two partially stiffened joints each have a single warping parameter, while the fully stiffened joint prevents warping. The distortion mode acts as a local spring stiffness. The formulation is fully compatible with classical thin‐walled beam theory, and detailed three‐dimensional finite element analyses demonstrate high accuracy of the theory.

A new form of a capillary potential/temperature formulation of heat and mass transfer in unsaturated soil is presented. Moisture transfer in both the vapor and liquid phases and heat transfer by means of conduction and latent heat of vaporization effects are accommodated in a one‐dimensional approach. A numerical solution of the complete formulation is then developed, based on the use of the finite‐element method, to describe spatial variations and a finite‐difference time‐stepping scheme to model transient behavior. The application of the model is then presented, making use of material parameters that have been independently established for all the soil properties specified in the formulation. A comprehensive, consistent approach is therefore claimed to be proposed. The results obtained are shown to be qualitatively correct throughout, conforming with physically realistic behavior. For a number of aspects of the work, it proved possible to examine precisely the validity of the results achieved, and in all those cases the model was found to be valid. Comparisons of the solutions with those obtained from other numerical approaches yield excellent correlations.

This paper extends the recent work of Ari‐Gur and Elishakoff on shear‐flexural buckling of columns with overhang to include the effect of axial shortening. The combined effects of axial and shear deformations on buckling of columns have been investigated by Ziegler and more recently by Wang et al.. Their governing equations and results defer slightly due to different assumptions made on the constitutive relation for the shearing force. Closed‐form analytical buckling solutions for columns with overhang, derived from both formulations, are presented. These new results are compared to those obtained by Ari‐Gur and Elishakoff so as to determine the importance of axial deformation effect on such buckling problems. It was found that the inclusion of axial shortening increases the critical loads by, at most, several percent for colunns with short overhang. For columns with long overhang, the effect of axial shortening is almost negligible and thus can be overlooked.

Various analogies between the Saint Venant‐type torsion of prismatic bars with solid cross sections of polygonal planform and the problem of bending of simply supported, thin plates are discussed. The analogous plate has the same planform as the cross section of the bar and is bent by imposed thermal curvatures, or by lateral force loadings, respectively. Those plate loadings are proportional to the rate of torsional twist. The analogies are based on a reduction of the fourth‐order problem of bending of thin plates to a second‐order Poisson differential equation with Dirichlet boundary conditions, which is possible in the case of simply supported, polygonal plates. As a main result, a direct correspondence between the torsional shear stresses and the shear forces in the analogous plate loaded by uniformly distributed forces is established. In this sense, numerical routines for fourth‐order plate‐bending problems can be used, or checked, respectively, in the context of the second‐order Saint Venant torsion problem.

A structural analysis method based on a combined use of the boundary element and transfer matrix method is applied to static problems of plated structures. In this paper, a transfer matrix is evaluated by combining two transfer matrices for in‐plane and plate‐bending problems, which are derived from the systems of equations based on the ordinary boundary element method for in‐plane and plate‐bending problems, respectively. Furthermore, an extended transfer matrix is proposed for the structures with complicated cross section such as T‐ and I‐section members. This method permits the use of a large number of elements, without getting involved with large matrices. Some numerical examples of plated structures subjected to various loads are proposed and their results are compared with those obtained by the finite element method.

This paper is concerned with the investigation of the forced time‐harmonic vertical vibration of a rigid disc embedded at an arbitrary depth in a semi‐infinite medium. By virtue of transform methods, the generalized mixed boundary‐value problem is formulated as a set of dual integral equations, which, in turn, are reduced to a Fredholm equation of the second kind. With the aid of contour integration, the governing integral equation is solved numerically. Selected results for the complex compliance are presented to illustrate the various effects of embedment on the dynamic response. In addition to furnishing a unified view of the static and dynamic solutions for zero and infinite embedments, the present analysis reveals a dynamic boundary‐layer phenomenon, which is apt to be of interest to this class of problems in general.

With the higher modes being considered in structural vibration control, practical problems such as the effect of the time delay between sensing the structural motion and applying the control force become more pronounced. Instability due to time delay is observed experimentally using a carefully calibrated model of a typical single‐span bridge modeled as a continuous system. The control action is applied using an accelerometer, analog integrator, cable, post, and hydraulic actuator in conjunction with an on‐line digital microcomputer. A practical scheme for time‐delay compensation based on response sampling, curve fitting, and extrapolation is employed. The purposed scheme has the advantage of eliminating the observation spillover that may cause instability in the control system on one hand, and may serve as an almost perfect state estimator on the other hand. The correlation between the analytical and experimental results is presented.

The present study deals with the dynamic behavior of cable‐stayed bridges when the vibration characteristics of the stay cables are taken into consideration. Such complex vibrations are strongly coupled with the bridge deck and tower motions and were either overlooked or treated independently in previous dynamic analyses. By discretizing each stay cable into small elements, there results new and numerous very complex pure cable vibration modes, as well as new deck‐tower bridge modes. It would be impossible to predict such motions by using, analytically, the linearized natural frequency expressions for the individual inclined cables. The multiple‐element cable system also provides coupled deck‐cable motions involving lateral bending and torsional motions of the deck as well as vertical and swinging cable motions; such motions cannot be predicted using a one‐element cable discretization system. The effect of these modes on the participation factors of any earthquake‐response calculation is significant.

New results are presented in the area of hysteretic modeling and experimental characterization of shape memory alloys (SMAs). A stress‐induced micromechanical phase transition occurs in SMAs that causes inelastic deformation and gives rise to a large energy‐absorbing capacity. Because it is possible to achieve large hysteretic deformation in SMAs without incurring plastic deformation, SMAs have potential for use in earthquake‐engineering passive damping schemes. In order to represent such energy‐absorbing behavior, an existing one‐dimensional model of hysteresis is modified to include the macroscopic characteristics of SMAs. Also, the results of cyclic material‐characterization tests applied to a nickel‐titanium SMA known as Nitinol are presented. Hysteretic behavior closely resembling that of the superelastic material was obtained in the laboratory for cyclic strain levels up to 4.5%. The model of SMA behavior is also compared to the cyclic responses of Nitinol.

The classical applications of Weibull statistical theory of size effect in quasi‐brittle structures such as reinforced concrete structures, rock masses, ice plates, or tough ceramic parts are being reexamined in light of recent results. After a brief review of the statistical weakest‐link model, distinctions between structures that fail by initiation of macroscopic crack growth (metal structures) and structures that exhibit large macroscopic crack growth prior to failure (quasi‐brittle structures) are pointed out. It is shown that the classical Weibull‐type approach ignores the stress redistributions and energy release due to stable large fracture growth prior to failure, which causes a strong deterministic size effect. Further, it is shown that, according to this classical theory, every structure is equivalent to a uniaxially loaded bar of variable cross section, which means that the mechanics of the failure process is ignored. Discrepancies with certain recent test data on the size effect are also pointed out. Modification of the Weibull approach that can eliminate these shortcomings is left for a subsequent paper.

The failure probability of structures must be calculated from the stress field that exists just before failure, rather than the initial elastic field. Accordingly, fracture‐mechanics stress solutions are utilized to obtain the failure probabilities. This leads to an amalgamated theory that combines the size effect due to fracture energy release with the effect of random variability of strength having Weibull distribution. For the singular stress field of linear elastic fracture mechanics, the failure‐probability integral diverges. Convergent solution, however, can be obtained with the nonlocal‐continuum concept. This leads to nonlocal statistical theory of size effect. According to this theory, the asymptotic size‐effect law for very small structure sizes agrees with the classical‐power law based on Weibull theory. For very large structures, the asymptotic size‐effect law coincides with that of linear elastic fracture mechanics of bodies with similar cracks, and the failure probability is dominated by the stress field in the fracture‐process zone while the stresses in the rest of the structure are almost irrelevant. The size‐effect predictions agree reasonably well with the existing test data. The failure probability can be approximately calculated by applying the failure‐probability integral to spatially averaged stresses obtained, according to the nonlocal‐continuum concept, from the singular stress field of linear elastic fracture mechanics. More realistic is the use of the stress field obtained by nonlinear finite element analysis according to the nonlocal‐damage concept.

The effect of interphases on the mechanical behavior of fiber‐reinforced composites is studied. The interphase is modeled as distributed continuous shear and normal springs. Two problems, a fiber pulled out of a matrix and a cracked fiber in a matrix, are discussed. An analytical solution is developed in terms of simultaneous integral equations. An asymptotic analysis reveals singularities in the stress and strain functions. Numerical results are obtained to study the effect on the micromechanical behavior of a composite as a function of relative mechanical properties of the fiber, the matrix and interphase regions, and the ratio of the interphase thickness to the fiber width.

The research reported herein is concerned with the finite deformations and snap‐through buckling behavior of slender symmetrical uniform and nonuniform elastic circular arches with clamped end supports at large deflection under a vertical downward concentrated load at the crown. Values of height‐to‐span ratios equal to 0.2, 0.25, 0.3, 0.4, and 0.5 for each value of the depth of the section at support to the depth of the section at crown equal to 1.0,1.5, and 2.0 are considered. Comparison between the results obtained and the results calculated by others is carried out.

An acoustic emission (AE) is a localized rapid release of strain energy in a stressed material. Quantitative acoustic emission measurement techniques have recently been developed to estimate the location, size, orientation, and fracture mode of individual microcracks. Quantitative AE techniques were applied to a laboratory study of plain concrete beams under four point loading. Center‐notched and off‐center‐notched beams were loaded in order to produce, respectively, mode I and mixed mode failure. Using AE seismic moment tensor representation, mi‐crocracking was characterized as mode I, mode II, or mixed mode. The mode of microcracking was compared to the mode of the visible crack. Most microcrack planes were in a direction normal to the tensile stress for a mode I macrocrack (center‐notched), whereas microcrack planes were relatively uniformly distributed for a mixed‐mode macrocrack (off‐center notched). A large number of mixed‐mode microcracks were observed even for the center‐notched beam indicating that fracture mechanisms of microcracks may differ from the main macromechanical crack. It is shown that AE measurements can provide a potentially powerful tool in assessing damage.

Examination of previous research on the collapse behavior of conventional plate girders with slender webs in shear indicates that the major contributions to the ultimate load capacity of component panels are provided by the characteristic postbuckling diagonal tension field and the flange plastic moment capacity. An open‐web plate girder, in which the contribution of the web critical strength in shear is replaced by engineered inclined tendons providing a reinforced tension field, is proposed and discussed. It is found that for every particular girder configuration, there is an optimal inclination of the tendons in order to maximize the overall ultimate shear load capacity. Parametric studies using computer‐based mathematical models are conducted and verified with subsequent experimentation in the laboratory with small‐scale physical models. It is concluded that open‐web plate girders with inclined tension bars have the potential to offer an attractive design alternative to slender conventional plate girders when the overall strength is controlled by the shear capacity of the girder and lighter stuctural elements are desired.

Conditions for snap-through (limit-point instability) of a clamped-free beam column from a buckled configuration to a second stable equilibrium state are examined. In particular, the relationships between a compressive load and the magnitude and location of a transverse force that produce a reversal in curvature are investigated. Approximate analytical solutions for stable equilibria are found by minimizing the structure's total potential energy. An incremental load approach is employed for the prediction of snap-through. For verification of the approximate solutions obtained using the energy method, predicted equilibrium configurations are compared with results calculated by numerical integration.