Journal of Engineering Mechanics

When a slender beam is transversely loaded in the plane of its greatest flexural rigidity, it may buckle laterally at a critical load. It is common practice to provide web openings in beams for the passage of service ducts and pipings, for inspection purposes in beam structures, and for other reasons. The presence of web openings not only reduces the ultimate strength of beams, but also the lateral‐buckling capacity. This paper presents a numerical method, based on the energy approach, to predict the critical lateral‐buckling loads of slender, doubly symmetric beams containing unreinforced web openings. The beams are either cantilevered or simply supported and contain openings along their centerlines. The critical loads evaluated numerically are compared with the values obtained experimentally. The study shows good agreement between the numerial and experimental values.

Adaptive identification problems on coefficient matrices of an autoregressive model for multivariate and one‐dimensional nonstationary Gaussian random processes are investigated by applying the extended Kalman filter incorporated with a weighted global iteration. The major contributions of the present paper are the use of the extended Kalman filter for estimating time‐varying model parameters recursively, and the development of an effective method in terms of computer time. The results indicate that the coefficients of this recursive equation are identified simply, but extremely well, at the stage of their stable convergence to optimum. It is suggested that the method be applied for the analysis of multiple‐point array data of earthquake ground motion.

During displacement‐controlled compression tests on concrete samples, the force displacement curve present a decreasing part. For many authors this part of the curve represents the homogeneous material behavior. This behavior is called softening. But results of compression tests cast some doubt about whether the strain field is indeed homogeneous on the softening part of the tests. These results can only be explained if strain localization occurs. To analyze the occurrence and development of this strain localization we use stereophotogrammetry. Stereophotogrammetry is among the most accurate optical methods used to study strain localization in civil engineering. After an overview of the method we present an example of its application to the phenomenon of strain localization during a displacement‐controlled compression test of a concrete sample. Our experiment shows that localization occurs when the stress becomes maximal. Thereafter, in the softening regime, the strain field is no longer homogeneous and the stress‐strain constitutive relation cannot be determined solely from knowledge of the force‐displacement curve.

The elastoplastic Mohr‐Coulomb (MC) model is shown to overestimate the inclination of shear bands in granular materials. An extended Mohr‐Coulomb (EMC) model is proposed to get a more accurate analytical expression for the average orientation of shear bands in soils. The EMC model uses an additional plastic mechanism that softens the transverse modulus and promotes strain localization similar to the vertexlike model of Rudnicki and Rice. Its mathematical structure is simple enough to derive analytical expressions for the plastic modulus and shear‐band orientation at the onset of strain localization. The paper also introduces the concept of postcritical localization to account for the scattering of experimental data on the orientation of shear bands in soils. The concept of delayed localization and the EMC model allows us to retrieve the conservative lower and upper bounds of Roscoe and Mohr‐Coulomb and to determine more accurate bounds for the average orientation of shear bands in frictional soils.

A systematic procedure for generating impedance matrices for foundations resting on an elastic half‐space medium is presented. The prescribed harmonic loading due to the foundation is decomposed into an infinite Fourier series with respect to the azimuth. For each Fourier component an analytic solution is found. Then, provided that the interaction stresses due to excitation of the foundation can be assumed to be piecewise linear in the r‐direction of the cylindrical coordinates, the impedance matrix of the foundation can be generated using the variational principle and the reciprocal theorem. A simple example of a rigid circular plate, rigidly attached to the half‐space medium, and subjected to torsional, vertical, rocking, and horizontal exitation is used to demonstrate the effectiveness and efficiency of the procedure.

Three‐dimensional micromechanical anisotropic damage models for microcrack‐weakened brittle solids are presented. The self‐consistent method is employed together with analytical solutions for weakly interacting elliptical microcracks in anisotropic media. The microcrack‐induced inelastic compliances are systematically derived in terms of anisotropic microcrack opening displacements. The sizes, orientations and densities of microcracks are taken as random variables. Both stationary and evolutionary damage models are considered. Microcrack kinetic equations are characterized through the use of fracture mechanics stability criteria and microcrack geometry within a representative volume element. Thus, the proposed models have constitutive predictive capability. This general framework is then applied to analyze the constitutive behavior of concrete under uniaxial or triaxial tension loading/unloading stress paths. Simple and efficient computational algorithm as well as uniaxial experimental validation are given to illustrate the potential capability of the proposed framework. It is emphasized that no fitted phenomenological material parameter is employed in the proposed damage models.

In this sequel, three‐dimensional self‐consistent damage models for brittle solids under compressive triaxial loadings are developed based on micromechanics and microcrack geometry within a representative volume. Due to frictional sliding of closed microcracks under compressive loadings, overall compliances of damaged brittle solids are nonsymmetric and anisotropic. Accordingly, solutions of microcrack opening displacements for a single penny‐shaped microcracks embedded in a general nonsymmetric fully anisotropic elastic medium are derived in this paper. The corresponding damage‐induced inelastic compliances are subsequently constructed. In addition to stationary microcrack formulations, micromechanical evolutionary damage models are presented. Both cleavage 1 and cleavage 2 deformation processes are considered. Computational procedures and micromechanical simulations for uniaxial and triaxial compression tests are presented for both the present and Taylor's models. Finally, these micromechanical model simulations are compared with available experimental data.

The linearization of Morison‐type wave loading is to replace $u\left|u\right|$ by cu, where u is a zero mean, stationary Gaussian random process and c is a constant. The coefficient c is traditionally determined by a use of the statistical least‐square error linearization; that is minimizing $E\left[\right(u\left|u\right|-\mathrm{cu}{)}^2]\text{.}$ In this study, the optimal linearization refers to a coefficient c, chosen in such a way that the statistics of structural response calculated from the linearized force will be identical to that calculated from the originally nonlinear force. To accomplish this, the optimal linearization must not only consider the ocean wave properties, but incorporate the structural properties. While most offshore structural engineers believe that the least‐square linearization may cause significantly nonconservative error only when the fundamental structural frequency is nearly three times the peak wave frequency, this study shows that worse errors may occur for other frequency ratios.

A theoretical procedure is described for the dynamic response analysis of engineering structures composed of interconnected slender members. Each structural member is treated as a multichannel waveguide, and the entire structure is treated as a network of such waveguides. Three types of analytical building blocks are then discussed: an individual waveguide, a junction where several waveguides intersect, and a boundary where either zero displacements or zero forces or their combination must be imposed. It is shown that the properties of each type of building block may be characterized by a wave‐scattering matrix that relates the incoming waves to the structural element in question and the outgoing waves from the structural element. The use of wave‐scattering matrices guarantees that numerical computation is always stable, since the computation follows the direction of wave propagation, and the wave amplitude can only decrease with the propagation distance. The proposed analytical procedure is efficient in computation and it yields very accurate results, especially if motions at specific locations on a structure are required. An example is included for illustration.

A method of analysis for beams with shear‐lag effects from wide flanges or with shear deformations resulting from shear studs in composite beams is presented. The basic idea is to replace the real beam with an analog beam, where all the shear deformation is concentrated in a thin layer. The equivalent stiffness of the shear layer can be related to the properties of the flange and the shear studs connecting the beam and the slab. When this stiffness is assigned to shear layer, the real beam and its analog behave in the same overall manner. The solution to the analog beam problem is directly related to the deformation and stresses in the real beam through simple formulas. The method is more complicated, but also more accurate than the customary effective width method, and could prove a good tool for design purposes.

Nonsingular and singular fracture process zones (FPZ) are used to replicate numerically, dynamic fracture of displacement‐controlled and drop‐weight three‐point bend, concrete specimens and crack‐line wedge‐loaded, double‐cantilever beam (CLWL‐DCB) concrete specimens. An inverse procedure, which is based on dynamic finite element analysis, is used to match the measured load, load‐line displacement and three strain histories of the fracturing specimen. This numerical analysis shows that the singular‐FPZ model provides the most realistic simulation of dynamic fracture of concrete. The resulting constitutive relation between the crack closure stress and crack opening displacement for the sigular FPZ model is geometry and strain rate‐independent. The dynamic stress intensity factor, however, is strain rate‐dependent.

Micromechanics analysis of damage in heterogeneous media and composites cannot ignore the interactions among cracks as well as between cracks and inclusions or voids. Previous investigators can to this conclusion upon finding that states of distributed (diffuse) cracking (damage) cannot be mathematically represented merely as crack systems in a homogeneous medium, even though stable states with distributed damage have been experimentally observed in heterogeneous materials such as concrete. This paper presents a method for modeling interactions between a crack and many inclusions. Based on the Duhamel‐Neuman analogy, the effect of the inclusions is equivalent to unbalanced forces acting on the contour of each inclusion in an infinite homogeneous solid. The problem is solved by superposition; it is decomposed into several standard problems of elasticity for which well‐known solutions are available. The problem is finally reduced to a system of linear algebraic equations similar to those obtained by Kachanov for a system of interacting cracks without inclusions. The calculated estimates of the stress intensity factors differ from some known exact solutions by less than 10% provided the cracks or the inclusions are not very close to each other. Approximately, the problem can be treated as crack propagation in an equivalent homogeneous macroscopic continuum for which the apparent fracture toughness increases or decreases as a function of the crack length. Such variations are calculated for staggered inclusions. They are analogous to R‐curves in nonlinear fracture mechanics. They depend on the volume fraction of the inclusions, their spatial distribution and the difference between the elastic properties of the inclusions and the matrix. Large variations (of the order of 100%) are found depending on the location of the crack and its propagation direction with respect to the inclusions.

A boundary element program based on a fictitious crack‐model (FCM) was used to study the size effect in concrete during mode‐I nonlinear fracturing. Series of numerical parametric studies were performed to examine the effects of specimen size, loading configuration (three‐point beam and double cantilever beam), and initial notch size on the nonlinear fracture characteristics. The results of numerical simulations confirmed the curve‐fitting procedure proposed by Bažant and his coworkers in their size‐effect law method. However, two notable exceptions were observed: (1) Small size specimens where bending strengthening may be pronounced; and (2) specimens with small initial notch. In addition to examining the range of applicability of Bažant's size‐effect law method, this paper provides empirical equations for determination of the maximum process‐zone length under three‐point bending or double cantilever beam (DCB) loading condition. Finally, the normalized R‐curves expressed in terms of the energy release rate versus the normalized effective crack extension have been shown to be independent of specimen size, initial notch size, and loading configurations. Therefore, the normalized R‐curves are recommended as a proper way of representing the nonlinear resistance of beam structures to mode‐I fracture.

The short‐term mechanical behavior of a novel prestressing technique is described. The technique involves external bonding of pretensioned fiber‐reinforced plastic (FRP) composite sheets on the tension zones of structural elements. Analytical models are developed describing the maximum achievable prestress level so that the FRP‐prestressed system does not fail near the anchorage zones. Both adhesive layer and beam material failures are considered. It is found that the method's efficiency is improved by increasing the thickness of the adhesive layer and/ or increasing the area fraction of the composite material, efficiency being defined as the level of prestress at the bottom fiber of the member. Moderate to high prestress levels are achieved depending on whether failure of the system is controlled by the shear strength of the beam material or that of the adhesive layer. The technique is applicable to the rehabilitation/strengthening of existing structures as well as the construction of new ones.