Journal of Engineering Mechanics

A load effect from the traffic load on a large bridge with a large interval of slowly varying nonzero influence on the load effect can be modeled as a Gaussian random process. The mean value function and the covariance function that completely determines the process can be obtained by modeling the traffic load along each lane as a translating white‐noise field. On the basis of a realistic traffic theoretical modeling of instantaneous random positions of single vehicles as represented by their random weights, the paper derives formulas for the mean and intensity of the white‐noise traffic‐load field in terms of traffic parameters and vehicle weight mean and variance. The formulas cover the entire range of traffic from free Poissonian traffic to congested traffic with the full stop queue as a limit case. The standard level crossing rate approximation method, used for the distribution of the maximal load effect over a given period of time due to moving traffic of any type, is taken as an example of an application of the white‐noise traffic‐load model. In a companion paper, Ditlevsen and Madsen (in press, 1994) used the model to obtain the distribution of the maximal load effect during a given period of time due to the formation of standing queues on the bridge.

The elastic lateral postbuckling response of geometrically perfect beams, under simultaneously uniform bending and axial compression, is examined in the vicinity of the critical bifurcational state. The field equations, which include the warping effect of the cross section, are highly nonlinear due to the nonlinear bending‐moment‐curvature relationship. The stability of the critical state associated with a stable bifurcation point is analytically established using a comprehensive approach. Therefore, these beam columns are not sensitive to initial imperfections, exhibiting postbuckling strength. However, the postbuckling equilibrium path is quite shallow (becoming more shallow with the increase of the axial force), so the load‐carrying capacity of such beam columns above the critical state is rather limited. The analysis is supplemented by illustrative examples for I‐beam columns for which the effect of various parameters on the initial postbuckling path is also discussed.

Theoretical models of mechanical properties of fiber reinforced cementitious composites require assumptions of fiber‐cement interfacial behavior. In this paper, strength‐based and fracture‐based fiber debonding criteria are reviewed. To determine whether interfacial debonding is governed by the bond strength or critical energy release rate of the fiber‐matrix interphase, fiber pull‐out experiments were conducted using steel and brass wires of various diameters. The bond properties, including effective bond strength and frictional stress, were interpreted through a theoretical model of fiber pull‐out. It was found that, for the material systems tested, interfacial debonding is dominated by frictional stress which is independent of the fiber diameters. Therefore, the debond mode of these material systems is categorized as strength‐based. In general, the debond mode is a material characteristic and is dependent on the specific fiber and matrix types. In order to precisely predict the mechanical response of a fiber reinforced cementitious composite, it is necessary to determine the debond mode for a particular material system following the methodology proposed in this paper.

This study presents a modified eddy viscosity model for describing vertical distribution of turbulent eddy viscosity in one‐dimensional fully developed asymmetric channel flows, which cannot be obtained by the traditional eddy viscosity model. A two‐power law expression, used to describe vertical distribution of flow velocity, is shown to account quite well for the major characteristics of flow in channels of asymmetric roughness. The modified eddy viscosity model, utilizing the two‐power law expression, enables formulation of a continuous distribution of eddy viscosity with positive magnitudes of turbulent eddy viscosity for asymmetric channel flows. Examples are given showing that the distribution of eddy viscosity obtained by using the modified eddy viscosity model is comparable with that obtained using Launder and Spalding's $k‐\epsilon$ turbulence model. This modified eddy viscosity model can, therefore, provide a relatively simple means for estimation of turbulent eddy viscosity in asymmetric channel flows.

This is the first part of a two‐part investigation of reliability of nonlinear‐truss structures with uncertain system parameters under random excitations. The objective is to develop a method of stochastic finite‐element analysis for obtaining response statistics. The related reliability problem is considered in the companion paper. In this study, random excitations are modeled as filtered Gaussian white noises and uncertain system parameters are modeled as either random fields or random variables. Structural nonlinear behavior due to both large deflection and inelastic deformation is considered. The structure is discretized via a total Lagrangian finite‐element formulation that yields a set of stochastic nonlinear equations of motion. An equivalent linearization method in conjunction with a perturbation method is then developed to solve for the total response statistics. No separate mesh for each random field is necessary in this formulation. Numerical examples indicate that the proposed method yields accurate results with much less computer time compared with the Monte Carlo simulation method. It is found that the system uncertainties contribute significantly to the total response statistics.

This is the second part of an investigation of the reliability of nonlinear‐truss structures with uncertain system parameters under random excitations. It develops a method for efficient reliability evaluation of such structures. A modified version of the fast integration method reported by Wen and Chen in 1987 in conjunction with a second‐order asymptotic method reported by Breitung in 1989 is developed to solve for the overall failure probability. The proposed method is applicable to problems for which the conditional failure probabilities given system parameters are available, for example, by random vibration or other empirical methods. It does not require the transformation of original random variables into standard normal variables; as a result, numerical efforts and mathematical complications associated with this transformation are eliminated. The sensitivity of the failure probability to changes in probability‐distribution parameters can be easily computed. The numerical study indicates that the proposed method yields accurate results with less computer time compared with the Monte Carlo simulation method. The system uncertainties contribute significantly to the overall failure probability.

The lateral cyclic response of a pile foundation is formulated by treating the subgrade as a viscoelastic Winkler model for simplicity. Viscoelastic characterization of the model is convenient for the computation of a cyclic response exhibiting the hysteresis nature. The governing equation of a pile foundation is solved for a cyclic force applied at the pile head with the Laplace transformation. The inverse integration is evaluated on a complex plane using a contour integration. The residue of the integration around the pole is associated with the steady‐state response. With this solution, simple expressions are developed for the maximum responses along the depth and for the spring and dashpot parameters of a pile at its head. Applications of these simple expressions are demonstrated for the evaluation of pile responses observed in shake table tests, in which the soil was liquefied or semiliquefied during the shaking. The responses are evaluated both in a conservative way and in a straightforward manner. The observed responses along the pile shafts are somewhat higher than the computed results but less than those computed in a conservative way.

The fatigue crack growth phenomenon is analyzed by means of postulated damage accumulation theory herein. By considering the plastic component of $J$ integral as a damage factor, the proposed damage accumulation theory successfully leads to a simple formula for the fatigue crack growth rate. This formula covers all three regions of the fatigue crack growth rate and shows a high potential in future application to different groups of materials. This research yields the following results: (1) The crack growth rate is not simply a function of $\Delta K$, but a function of average local yielding strength, fracture toughness, and amplitude of the applied effective stress intensity factor in regions II and III; (2) the behavior of the fatigue crack growth rate (FCGR) near the threshold value is found to be dominated by maximum value of applied effective stress intensity factor instead of its amplitude; (3) the onset instability value of $\Delta K_c$ is a specimen geometrical‐dependent parameter; and (4) the average yielding local strength has a significant influence on the threshold value, $K_{\mathrm{th}}$ that cannot be ignored when one studies the problem of the crack growth properties in region II. Test data reported were compared with the proposed formula and were found to be in reasonably good agreement.

This study investigates the influence of initial curvature on the dynamic behavior of a hinge‐supported thin plate. The large‐deflection theory is used to determine the mid‐plane forces produced by the deflection and the initial curvature. Then, the vertical components of the mid‐plane forces are found as a set of distributive surface loads applied on the plate in the transverse direction. Subsequently, the equilibrium condition of the plate is expressed in a nonlinear differential equation. With proper simplification and linearization the differential equation leads to a special type of eigenvalue problem that can be solved by using a weighted residual method. Hence, the natural frequencies and modes are found. The computational results of examples clearly demonstrate the phenomenon of the natural frequencies moving upward when the plate is preformed into the shape of a specific mode of vibration.

The probability of first‐passage failure affected by nonnormality (or non‐Gaussianity) is investigated through approaches that are more accurate than the commonly used analytical methods. The index used to measure the degree of nonnormality of a random process is the coefficient of excess, which is a normalized fourth‐cumulant function. The techniques are illustrated by consideration of the response nonnormality of a linear secondary system, which is mounted on a nonlinear primary structure subjected to a normally distributed ground acceleration. The nonlinearity considered in the primary structure is bilinear hysteretic yielding. It is shown that first‐passage failure can be significantly affected by the nonnormality in some situations. It is also found that the interaction force of the primary‐secondary system can significantly reduce the nonnormality of secondary response, especially when the frequency of the secondary system is tuned to that of the primary system.

Correlation between fractal dimensions and fracture properties in cementitious material is reported. Wedge splitting tests of specimens as much as 1.52 m (5 ft) long and having 7.62‐cm (3‐in.) maximum size aggregate were first performed to determine fracture toughness $K_{\mathrm{Ic}}$ and fracture energy $G_F$. Subsequently, one of the split parts was mapped using a profilometer to provide detailed one‐dimensional profiles. Finally, the fractal dimension of the profiles was determined by a specially developed computer program. The fracture surfaces are fractal over the measured range of scales, and the fractal dimension is independent of crack trajectory. There is a weak correlation between the fracture properties and the fractal dimensions. The implications of the fractal nature of the cracked surfaces on the fracture energy $G_F$ are discussed, as is the relationship between a fractal analysis and the size effect law.

Analytical development is presented for the theory of conditional random fields involving conditioning deterministic time functions. After discussion of their basic concept and their engineering significance, the probability distribution of the Fourier coefficients for conditioned stochastic processes is derived. Its physical interpretation is presented in terms of harmonic amplitudes and phase angles. On this basis, solutions are obtained for the time‐varying mean values and the variances of conditioned stochastic processes as well as their first‐passage probabilities. Numerical simulation of the conditional random fields is also performed for assumed power spectral density and coherence functions. These results are discussed in terms of the probability theory and engineering application. Specifically, effects of coherency and the number of conditioning deterministic time functions are examined.

The behavior of one‐ply and two‐ply unidirectional cord‐rubber composite plates in pure bending is presented. The model developed takes in account the extension‐twisting coupling of the cord, as well as the exact location of the cord within the composite plate, and the bending stiffness of an individual cord. The Kirchhoff plate assumptions are used as the kinematic relationships for the composite plate. The cord mechanics are based on the work of Costello. The current results are compared to the classical lamination theory results using the material constants of Gough and Tangorra, as well as the constants of Akasaka and Hirano, to show the limits of usefulness for classical lamination theory for this class of composites. The results of the one‐ply composite plate investigations vary significantly from the results of classical lamination theory, especially for cases with large mismatch between the cord and matrix modulus of elasticity.

Examinations are made of the dynamic effects associated with modal responses of deep‐water, wave‐excited offshore structures. Such examinations are intended to assess the influences that variations in several parameters involved have on the dynamic structural response. Variations in the following parameters are considered: the distributions of the structural volume and projected area, the distributions of the inertia and drag force coefficients, the relative magnitude of the inertia and drag force components, the natural modes of vibration of the structure, and the random phase angles used for the generation of the wave loading. The response is examined for a wide range of values of the natural frequencies of the system, and the relative importance of the effects of changes in the parameters considered is elucidated. The results of the study provide valuable insight into the response of offshore structures to wave forces, and may contribute to forming a basis for the development of future, efficient design procedures in the field of offshore engineering.

A linearization method is deduced in which energy is first time averaged over a basic harmonic wave, then assemble averaged over the random amplitude. The method is useful for solving nonlinear narrowband vibration problems of stochastic dynamics in multidegree‐of‐freedom (MDF) systems. Numerical calculation samples are given to show the simplicity, effectiveness, and accuracy of the present method.

Signal transmission losses in optical fibers resulting from wave mode conversion and wave refraction are adversely affected by small radius microbending in the fibers. Attempts to reduce such bending by means of a low‐modulus fiber coating may have the opposite effect of magnifying this bending under certain conditions. A small‐deflection, linear, beam on elastic foundation analysis is used to demonstrate this paradoxical phenomenon. The coating is modelled as a weak elastic foundation of the Winkler type, which supports the fiber beam within a hard outer coating. A 6.7% magnification of the nominal curvature resulting from microbending is possible in the extreme case, accompanied by an undesirable cyclical variation of the curvature near the bending disturbance.