Journal of Engineering Mechanics

A stochastic model of traffic excitation on bridges is developed assuming that the arrival of vehicles traversing a bridge (modeled as an elastic beam) follows a Poisson process, and that the contact force of a vehicle on the bridge deck can be converted to equivalent dynamic loads at the nodes of the beam elements. The parameters in this model, such as the Poisson arrival rate and the stochastic distribution of vehicle speeds, are obtained by image processing of traffic video data. The model reveals that traffic excitations on bridges are spatially correlated. This important characteristic is usually incorrectly ignored in most output-only methods for the identification of bridge structural properties using traffic-induced vibration measurement data. In this study, the stochastic traffic excitation model with partial traffic information is incorporated in a Bayesian framework, to evaluate the structural properties and update their uncertainty for condition assessment of the bridge superstructure. The vehicle weights are also estimated simultaneously in this procedure. The proposed structural assessment methodology is validated on an instrumented highway bridge.

An analytical comparison between three techniques for the identification of modal properties of structures when subjected to ambient vibrations is performed. The algorithms examined include the eigensystem realization algorithm with data correlations, the prediction error method through least squares, and the stochastic subspace identification (SSI) technique. Both analytical and experimental data from a four-storey building scaled at 1:3 are used to perform these evaluations. The level of noise added to the simulated data is varied to study the robustness of the techniques. All techniques are fully automated, allowing for assessments to be conducted through Monte Carlo simulations. The results indicate that the SSI technique provides the most accurate identification of natural frequencies and mode shapes even with high noise levels, all while requiring the least amount of experience for implementation.

This paper presents a short review of the state-of-the-art methods to identify bridge deck flutter derivatives and proposes a new algorithm to simultaneously extract the aeroelastic coefficients from free-vibration section-model tests, which is based on the improvement of the unifying least-squares (ULS) method and is therefore called modified unifying least-squares method. The advantages with respect to ULS are the faster and better convergence and the improvement in accuracy due to the introduction of weighting factors in the unifying error function. The method has been validated through numerically simulated noisy signals and experimental heaving and pitching time histories for two different bridge deck cross sections: a single-box and a multiple-box girder section model. The analysis of the artificial signals shows that a few system parameters are very difficult to be identified due to the fact that the problem is strongly ill-conditioned. Nevertheless, all the diagonal and off-diagonal components of the stiffness and damping matrices which significantly contribute to the output of the system are correctly estimated. The improvement with respect to other methods is extensively discussed. For the wind-tunnel test cases the accuracy of the identification procedure is evaluated through the comparison between measured signals and those simulated through the estimated mechanical and aerodynamic system parameters with very satisfactory results. With respect to many previous attempts of validation, this approach clearly shows the degree of accuracy that can be expected from the identification algorithm. Finally, for the considered test cases the linear model which stands behind the method seems to be an acceptable approximation of the physics of the phenomenon.

The weighted-amplitude wave superposition method and the proper orthogonal decomposition (POD) technique are first introduced. Then the POD technique combined with a wind field reconstruction method for a flat roof is studied. In the meantime, wind field extension using B-spline interpolation and the wind field reconstruction are verified. On this basis, a three-step simulation algorithm to generate wind field is presented for roof structures. In the proposed algorithm, the weighted-amplitude wave superposition method, the POD technique, and the B-spline interpolation technique are combined together. In contrast to the existing algorithms in frequency-domain-based simulation, the proposed one can reduce the computation cost remarkably. In order to demonstrate the capability and efficiency of the proposed algorithm, an engineering example, the wind field simulation for a large-scale roof of the Foshan Century Lotus Stadium, is illustrated. The results show that the proposed algorithm is very efficient with sufficient precision. Therefore, it is advantageous in wind resistance analysis for large-scale roofs.

To determine the stress state of a wire rope is tedious although analytical solution of a simple rope subjected to static load is available. While facing the problems involving complex ropes, it is usual practice to take approximations based upon the concepts of an average stress state for the constitutive ropes or for every wire. For a statically loaded cable superimposed with a tensile impulse, practically in sudden lifting of a heavy weight, the coupled axial-shearing strain waves in the cable has rarely been studied and explored through analytical approaches. Based on Costello’s force-deformation relationship and elastic wave propagation theory, analysis procedures and results are presented in this paper. Time-dependent coupled axial-torsional displacements and axial-shearing strain waves in a simple straight wire rope, due to a longitudinal impact at one end, are obtained. At the instance of the strike, a pair of coupled primary axial-torsional waves is created and begins to travel in the cable independently with different speed. Meanwhile, a coupling induced secondary torsional wave and an axial wave were observed to travel with the primary axial wave and the primary torsional wave, respectively. Phenomenon such as the traveling, reflections from ends, and intersections of the primary waves as well as the secondary wave are presented. Information provided in this paper would be useful in the study of unexpected overstress and/or fatigue problems.

Recent trends towards developing increasingly taller and irregularly-shaped buildings imply that these complex structures are potentially more responsive to wind excitation. Making accurate predictions of wind loads and their effects on such structures is therefore a necessary step in the design synthesis process. This paper presents a framework for dynamic analysis of the wind-induced lateral-torsional response of tall buildings with three-dimensional (3D) mode shapes. The cross correlation reflecting the statistical coupling among modal responses under spatiotemporally varying dynamic wind excitations has been investigated in detail. The effects of intermodal correlations on the lateral-torsional response of tall buildings with 3D mode shapes and closely spaced natural frequencies are elucidated and a more accurate method for quantifying intermodal cross correlations is analytically developed. Utilizing the wind tunnel derived synchronous multipressure measurements, a full-scale 60-story asymmetric building of mixed steel and concrete construction is used to illustrate the proposed framework for the coupled dynamic analysis and highlight the intermodal correlation of modal responses on the accurate prediction of coupled building acceleration.

The free vibration analysis of asymmetrical three-dimensional (3D) uniform shear beam-columns with generalized boundary conditions (semirigid flexural and torsional restraints, lateral bracings, and lumped masses at both ends) subjected to an eccentric end axial load in addition to a linearly distributed eccentric axial load along its span is presented in a classic manner. The five coupled governing equations of dynamic equilibrium (i.e., two shear equations, two bending moment equations, and the pure torsion moment equation) are sufficient to determine the natural frequencies and modal shapes. The proposed model which is an extension of a 2D model presented previously by the writer includes the simultaneous 3D coupling effects among the lateral deflections, deformations of the cross section along the member (shear, torsional and rotational), the translational, rotational and torsional inertias of all masses considered, an eccentric end axial load in addition to a linearly distributed axial load along its span, and the end restraints. Deformations caused by shear forces and pure torsion are considered. The effects of axial deformations, warping torsion and torsional stability are not included. The proposed model shows that the dynamic behavior of 3D shear beam-columns is highly sensitive to the coupling effects just mentioned, particularly in members with both ends free to rotate. Analytical results indicate that except for doubly symmetric members with concentric axial loads and with perfectly clamped ends, the natural frequencies and modal shapes of 3D shear beam-columns are determined from the eigenvalues of a full $8\times 8$ matrix, rather than from the uncoupled equations of transverse (or shear-wave equations) and torsional moment equilibrium. Two comprehensive examples are presented that show the effectiveness of the proposed method.

A symmetric Galerkin boundary element method is developed for modeling steady-state Darcy’s flow in three-dimensional porous media. The proposed technique is capable of treating a nonhomogeneous medium that consists of several regions possessing different permeabilities and may contain a surface of discontinuity such as impermeable seals. The key governing equations are established based on a pair of weakly singular weak-form integral equations for the fluid pressure and the fluid flux. The crucial feature of those integral equations are that they are completely regularized such that all involved kernels are only weakly singular and that they are applicable to a medium possessing generally anisotropic permeability. A final system of governing integral equations is obtained in a symmetric form and validity of all involved integrals only requires continuity of the pressure boundary data; as a consequence, continuous interpolations can be employed everywhere in the numerical approximation. To accurately capture the jump of the fluid pressure in the local region near the boundary of the discontinuity surface, special tip elements are employed. To further enhance accuracy and computational efficiency of the method, special integration quadrature is adopted to treat both weakly singular and nearly singular integrals and an interpolation strategy is utilized to evaluate the kernels for anisotropic permeability. As demonstrated by various numerical experiments, the current method yields highly accurate results with only weak dependence on mesh refinement.

Numerical simulations have been performed for three-dimensional flow past a square cylinder. The cylinders are placed normal to the incoming uniform flow. The results are based on higher order spatial and temporal discretization. The computations are carried out for a range of Reynolds number (100-325). The flow is found to be two-dimensional at $\mathsf{R}=160$ while it becomes three-dimensional at $\mathsf{R}=163.5$ . Both Mode-A and Mode- ${\mathrm{A}}^{*}$ are observed to be quite prominent and distinct at $\mathsf{R}=175$ though they are present in a range of Reynolds number. The spanwise wavelength for Mode-A is higher than at $\mathsf{R}=250$ where finer-scale structures are observed called Mode-B. The decay rate for primary vortices in Mode- ${\mathrm{A}}^{*}$ is the fastest and it is the lowest for Mode-B. The magnitude of secondary vortices of Mode- ${\mathrm{A}}^{*}$ is quite high compared to Mode-A, but of comparable magnitude to Mode-B. The effect of transitions on the instantaneous flow and root mean square fluctuations are quite significant while the time-averaged flow does not show any noticeable variation.

The paper applies the power series method to find the dynamic stiffness for the dynamics axial-moment buckling analyses of linear framed structures. Since the formulation is exact in classical sense, one element is good enough for the entire beam. The dynamic stiffness thus obtained can be decomposed into the stiffness, mass and initial stress matrices at a particular frequency, a particular axial force and a particular initial moment. The given axial force and moment can be nonuniformly distributed. The interaction diagrams in classical loading conditions of uniform moment, moment due to concentrated and distributed lateral force are given explicitly. The effects of warping rigidity, torsion rigidity, axial tension and compression are investigated in detail. The static and dynamic interaction buckling of a two-section I-beam structure is studied. Finally, we conclude that the three dimensional interaction diagram of the dynamic biaxial moment buckling can be obtained simply by rotating the three dimensional interaction diagram of the dynamic mono-axial moment buckling about the frequency axis if the bimoments are appropriately scaled. It is shown that application for non-uniform section is not suitable due to convergent problem. The method is very efficient that many interaction diagrams are produced for the first time.

The judicious region-matching technique is adopted to derive a series solution for shear horizontal waves scattering from a truncated semicircular canyon on the ground surface. A circular-arc auxiliary boundary is introduced to divide the analyzed region into two subregions. The antiplane motion of each subregion is represented in terms of an infinite series of cylindrical wavefunctions with unknown coefficients. By employing the Graf’s addition formula, boundary conditions on the curved canyon surface and continuity conditions on the auxiliary boundary, the unknown coefficients can be determined. Two modifications of the present theoretical derivation are done for the semicircular canyon and free surface cases. The plotted results reveal how the surface displacement amplitudes are influenced by varying the truncation depth.

The moisture content in concrete pores is a critical parameter for most of the degradation processes suffered by concrete, such as concrete shrinkage and related cracking. The objective of this paper is to present the formulation of a general moisture distribution model for young-age concrete. In the modeling, both cement hydration and moisture diffusion resulted humidity variations are taken into account synchronously. The effect of initial water distribution (after concrete casting) on the development of moisture distribution is considered by introducing a critical time parameter. The simulation of humidity reduction produced from self-desiccation is based on cement hydration degree that taking the effect of temperature into account by using the equilibrant age concept. During modeling the moisture diffusion, a multilinear model was adopted to simulate the moisture dependent diffusivity. The developed model and finite deferential method can well predict the moisture distribution as well as its variations with time. Good agreement between model predictions and experimental results is found. These results can subsequently be used in shrinkage induced stress field analyses, and further be used for cracking control of concrete structures.

In this paper, wave attenuation and mass transport of a water-mud system due to a solitary wave on the free surface is modeled by using the Chebyshev-Chebyshev collocation spectral method for spatial discretization and a fourth-order multistage scheme for time integration. The governing equations are formulated in Lagrangian coordinates and perturbation equations for shallow water waves are derived. An iteration-by-subdomain technique is introduced to tackle the interface in the two-layer system. The numerical model is tested against available analytical solutions and good agreement has been found. Numerical simulations of the water-mud system with different layer thicknesses suggest that the accuracy of the existing boundary layer theory for fluid-mud interaction is limited when the mud layer is thin because the assumption of irrotational core may not be valid. Although the paper is focused on solitary waves and Newtonian fluid-mud, the methodology can be extended to oscillatory, nonlinear water waves over a non-Newtonian mud bottom.

This paper is concerned with the plastic-buckling of rectangular plates under uniaxial compressive and shear stresses. In the prediction of the plastic-buckling stresses, we have adopted the incremental theory of plasticity for capturing the inelastic behavior, the Mindlin plate theory for the effect of transverse shear deformation, the Ramberg-Osgood stress–strain relation for the plate material, and the Ritz method for the bifurcation buckling analysis. The interaction curves of the plastic uniaxial buckling stress and the plastic shear buckling stress for thin and thick rectangular plates are presented for various aspect ratios. The effect of transverse shear deformation is examined by comparing the interaction curves obtained based on the Mindlin plate theory and the classical thin plate theory.