Journal of Engineering Mechanics

This paper presents a theoretical model for analyzing shear-flexible steel-concrete composite beams in partial interaction. Both concrete slab and steel beam are modeled according to Timoshenko’s theory, and a continuous linear-behaving shear connection is considered between the two connected members. Simplified kinematic assumptions have been considered for the displacement fields of the two connected members to derive a model, which is at one time rather general, but even simple enough to be easily handled and actually solved in closed-form. The analytical formulation of both stiffness matrix and vector of equivalent nodal forces is the key achievement of the present paper. They completely define an “exact” finite element for the mentioned model and can be easily employed for carrying out computationally efficient analyses of steel-concrete composite beams looking after the effect of both shear flexibility of the structural members and slips occurring at the interface between the two connected members. Simple applications are finally proposed for demonstrating that the present “exact” finite element can be employed for analyzing shear-flexible steel-concrete composite beams by using just one element-per-member. Thus, it is more efficient than both alternative numerical solutions already available in the scientific literature and commercial finite element packages.

A computational model is developed to analyze the hydrodynamic behavior of dam reservoirs during earthquakes. The mathematical model is based on the solution of two-dimensional (2D) Navier-Stokes equations in a vertical, semi-infinite domain truncated by a far-end boundary condition. A depth integrated continuity equation is used to track the deforming free-surface and ensure global mass conservation. A combination of Sommerfeld nonreflecting boundary and dissipation zone methods is implemented at the far end of the reservoir to prevent any back-reflections of pressure and free-surface waves. Nondimensionalized equations are used to compare contributions of each type of force to the development of the hydrodynamic pressure field and to the maximum run-up of free-surface waves on the dam face. Sinusoidal ground accelerations are applied to an idealized dam-reservoir system to analyze the system response. It is observed that the acoustic wave equation solution gives satisfactory results for the pressure field unless the contributions from the free-surface waves become significant at low reservoir depths. The surface wave run-up on the dam face is found to depend on the ground velocity, oscillation period, and the water depth. On the basis of numerical experiments, an expression for the wave run-up to predict conditions of overtopping from probable earthquake characteristics is proposed.

This study focuses on how to exploit long-term monitoring data of structural strain for analytical modeling of multimodal rainflow-counted stress spectra by use of the method of finite mixture distributions in conjunction with a hybrid mixture parameter estimation algorithm. The long-term strain data acquired from an instrumented bridge carrying both highway and railway traffic is used to verify the procedure. A wavelet-based filtering technique is first applied to eliminate the temperature effect inherent in the measured strain data. The stress spectrum is obtained by extracting the stress range and mean stress from the stress time histories with the aid of a rainflow counting algorithm. By synthesizing the features captured from daily stress spectra, a representative sample of stress spectrum accounting for multiple loading effects is derived. Then, the modeling of the multimodal stress range is performed by use of finite mixed normal, lognormal, and Weibull distributions, with the best mixed distribution being determined by the Akaike’s information criterion (AIC). The joint probability density function (PDF) of the stress range and the mean stress is also estimated by means of a mixture of multivariate distributions. It turns out that the obtained PDFs favorably fit the measurement data and reflect the multimodal property fairly well. The analytical expressions of PDFs resulting from this study would greatly facilitate the monitoring-based fatigue reliability assessment of steel bridges instrumented with structural health monitoring (SHM) system.

The characteristics of the recirculation zone structure behind an impulsively started circular cylinder for Reynolds number $R_e$ ranging from 500 to 2,000 and nondimensional time $T$ ranging from 0.5 to 5.0 are investigated experimentally using particle image velocimetry (PIV) and flow visualization techniques. On the basis of the flow visualization pictures and velocity maps, both obtained by a reference frame with a moving coordinate system, the evolution of the recirculation zone structure is studied with special emphasis on the negative velocity subzone. The negative velocity subzone is enveloped by the boundary consisting of the zero-velocity points inside the recirculation zone, and the streamwise velocity profile inside and near the negative velocity subzone is characterized by a jetlike flow moving toward the cylinder. During the evolution of the recirculation zone, the representative dimensions of the vortical structure both in the streamwise and vertical directions, including the recirculation zone length and the center-to-center distance between two primary vortex cores, are found to increase rapidly with time. Characteristic length and velocity scales are proposed first in the literature not only to demonstrate the similarity profile for streamwise velocity within and near the negative velocity subzone, but also to exhibit the similarity for geometric shape of the negative velocity subzone via the ratio of the width of the negative velocity subzone (i.e., the vertical distance between two zero-velocity points) to the center-to-center distance between two primary vortex cores. The very important observation is that the similarities of velocity profile and geometric shape represent promising self-preservation for the jetlike flow enclosed by the zero-velocity points forming the boundary of the negative velocity subzone. In addition, time variation of the nondimensional circulation of two primary vortices in the recirculation zone is studied and found to increase with an increase in the nondimensional time.

Due to the difficulties of fracture mechanics in dealing with multicrack problems, the continuum-based numerical methods always encounter mathematical problems when modeling rock fragmentation, so the alternative discontinuum-based numerical approaches are worth trying. This paper presents a new two-dimensional contact constitutive model for the discontinuous deformation analysis (DDA) method to simulate the fragmentation of jointed rock. This contact constitutive model consists of a two-phase force-displacement relation in the nomal direction and the Mohr-Coulomb criterion in the shear direction. The two-phase force-displacement relation is imposed in the normal direction of the block interface, instead of the penalty contacting spring. The first phase functions as the original penalty spring, and the second phase serves as a cohesive component. This new contact constitutive model was incorporated into the original DDA code, and four examples were computed for verification. The simulated results agree favorably with those obtained from physical tests and other numerical simulation, showing that the proposed method can simulate the whole process of rock fragmentation and can deal with cases of intact rock, rock mass with nonpenetrative joints, and even blocky rock structures. Furthermore, due to the nature of the triangular block shape, the proposed model can avoid the mesh dependence problem.

This paper uses the transfer matrix method (TMM) to analyze the interfacial behavior of a fiber-reinforced polymer (FRP)–plated beam with flexural cracks. The adhesive layer between the beam and the FRP sheet is simulated by the cohesive zone model (CZM) of a general interfacial bond-slip law. The flexural cracks are modeled by rotational springs whose rigidity is dependent on the relative depth of the cracks. The transfer matrix of the FRP-plated beam is then derived, and the joint coupling matrix (JCM) method is introduced to solve the stress resultants, displacements, interfacial shear stress, and axial force of the FRP sheet. Finally, some numerical examples are given, and the results are compared with the available analytical solutions to validate the present method.

The paper presents theoretical and numerical analyses of random wave attenuation attributable to vegetation. Existing models based on Rayleigh distribution of wave heights are critically examined followed by the development of two new models for random waves over vegetation. The first model is derived on the basis of Hasselmann and Collins’ treatment of energy dissipation of random waves attributable to the bottom friction. The second model is derived on the basis of Longuet-Higgins’ probability density function for the joint distribution of wave heights and wave periods, which recovers to the model that uses the Rayleigh distribution of wave heights if the spectrum becomes narrow banded. Such a model allows for quantifying the effects of the spectral width on the model performances. Comparisons of the modeled and measured root-mean-square wave heights over vegetation show good agreement. Moreover, the Joint distribution-based model provides insight into the spectral distribution of the energy dissipation, which is different from other dissipation models that follow exactly the wave energy spectrum.

Considered in this paper is a special case relating to the large deflection of a thin beam. One end of the beam is fixed (i.e., clamped) to a rigid wall, whereas the other end is placed on a flat surface of arbitrary orientation. In previous studies, unique and non-unique solutions to the deflected shape were derived for cases in which the curvature of the beam experiences at least one change in sign. In this paper, a special case is examined in which the curvature of the beam does not change sign. Experimental results from photographs of deflected beams are presented to support the numerical predictions. An excellent agreement was found between the photographed and the predicted shapes.