Journal of Engineering Mechanics

An improved algorithm is introduced in this paper for digital simulation of the stochastic wind velocity field on long-span bridges, when the cross-spectral density matrix of the field is given. The target wind velocity field is assumed to be a one-dimensional, multivariate, homogeneous stochastic process. The basic method of simulation used is the spectral representation method. It is improved by explicitly expressing Cholesky's decomposition of the cross-spectral density matrix in the form of algebraic formulas, then cutting off as many as possible of the cosine terms, so long as the accuracy of results is not affected. The fast Fourier transform technique is used to enhance the efficiency of computation. A numerical example of simulation for buffeting analysis is included in this paper to illustrate the improved method introduced. It is demonstrated that deviations between the simulated correlation functions and the target are sufficiently small and that the simulated power spectra are close to the target.

A time domain approach for predicting the coupled flutter and buffeting response of long span bridges is presented. The frequency dependent unsteady aerodynamic forces are represented by the convolution integrals involving the aerodynamic impulse function and structural motions or wind fluctuations. The aerodynamic impulse functions are derived from experimentally measured flutter derivatives, aerodynamic admittance functions, and spanwise coherence of aerodynamic forces using rational function approximations. A significant feature of the approach presented here is that the frequency dependent characteristics of unsteady aerodynamic forces and the nonlinearities of both aerodynamic and structural origins can be modeled in the response analysis. The flutter and buffeting response of a long span suspension bridge is analyzed using the proposed time domain approach. The results show good agreement with those from the frequency domain analysis. The example used to demonstrate the proposed scheme focuses on the treatment of frequency dependent self-excited and buffeting force effects. Application to nonlinear effects will be addressed in a future publication.

The effects of aerodynamic coupling among modes of vibration on the flutter and buffeting response of long-span bridges are investigated. By introducing the unsteady, self-excited aerodynamic forces in terms of rational function approximations, the equations of motion in generalized modal coordinates are transformed into a frequency-independent state-space format. The frequencies, damping ratios, and complex mode shapes at a prescribed wind velocity, and the critical flutter conditions, are identified by solving a complex eigenvalue problem. A significant feature of this approach is that an iterative solution for determining the flutter conditions is not necessary, because the equations of motion are independent of frequency. The energy increase in each flutter motion cycle is examined using the work done by the generalized aerodynamic forces or by the self-excited forces along the bridge axis. Accordingly, their contribution to the aerodynamic damping can be clearly identified. The multimode flutter generation mechanism and the roles of flutter derivatives are investigated. Finally, the coupling effects on the buffeting response due to self-excited forces are also discussed.

Natural frequencies and buckling stresses of a thick isotropic plate on two-parameter elastic foundations are analyzed by taking into account the effect of shear deformation, thickness change, and rotatory inertia. Using the method of power series expansion of the displacement components, a set of fundamental dynamic equations of a two-dimensional, higher-order theory for thick rectangular plates subjected to in-plane stresses is derived through Hamilton's principle. Several sets of truncated approximate theories are used to solve the eigenvalue problems of a simply supported thick elastic plate. To assure the accuracy of the present theory, convergence properties of the minimum natural frequency and the buckling stress are examined in detail. The distribution of modal transverse stresses are obtained by integrating the three-dimensional equations of motion in the thickness direction. The present approximate theories can accurately predict the natural frequencies and buckling stresses of thick plates on elastic foundations as compared with Mindlin plate theory and classical plate theory.

Concrete is a material that changes volumetrically in response to moisture and temperature variations. Frequently, these volumetric changes are prevented by restraint from the surrounding structure, resulting in the development of tensile stresses. This paper provides a method for computing the stress and displacement fields that develop in response to this restraint by considering the concrete slab as a plate resting on an elastic foundation. The interface between the slab and the foundation is capable of simulating all cases between complete perfect bond and perfect compression/zero tension bond to permit debonding. In addition, stress relaxation is considered in the concrete to account for the reduction in stress due to creep/relaxation-related phenomena. For this reason, the stress-strain relationship and equilibrium equations have been considered in the rate or differential form. The history-dependent equilibrium equations are obtained by integrating the differential equations with respect to time. An example is presented to illustrate the favorable correlation that exists between the predicted behavior of the plate model and finite-element modeling.

This paper presents a committee of neural networks technique, which employs frequency response functions (FRFs), modal properties (natural frequencies and mode shapes), and wavelet transform (WT) data simultaneously to identify damage in structures. The experimental demonstration of the method is obtained by studying the sensitivities of the FRFs, modal properties, and WT data to four types of faults in a cylindrical shell. The experimental results show that different faults affect data in a different manner. The proposed approach is tested on simulated data from a three-degree-of-freedom mass-spring-damper system. The results from the simulated study show that the performance of the approach is not influenced by the noise in the data. Finally, the method is used to identify damage in a population of ten steel seam-welded cylindrical shells. The proposed method is able to identify damage cases better than the three approaches used individually. The committee approach gives results that generally have a lower mean square error (MSE) than the average MSE of the individual methods. It is found that the effectiveness of the method is enhanced when experimentally measured data are used, which is in contrast to many existing methods. This is because the committee approach assumes that the errors given by the three approaches are uncorrelated, a situation that becomes more apparent when using measured data rather than simulated data.

Results are presented from an experimental investigation into the skewed three-dimensional flow around a bridge abutment. Velocity profiles on the plane of symmetry matched the standard log-law only near the bed and revealed a rather uniform flow in the upper layer. The bed shear stress was found to amplify nearly 3.63 times near the nose of the abutment. The flow was deflected least at the midwater depth, exceeded slightly by the upper flow and substantially by the lower flow. The flow was also analyzed using the theories of three-dimensional turbulent boundary layers. None of the crossflow models matched the data. The performance of near-wall similarity models was also poor. However, strong evidence of near-wall similarity was found very near to the bed. Compared to the bridge pier flow, greater skewing was found in abutment flow, especially in the downstream region, showing the limitations of treating the abutment as a half-pier.

The introduction of a crack in a steel structure will cause a local change in the stiffness and damping capacity. The change in stiffness will lead to a change of some of the natural frequencies of the structure and a discontinuity in the associated mode shapes. This paper contains a presentation of the results from experimental and numerical tests with hollow section cantilevers containing fatigue cracks. Two different finite-element (FE) models have been used to estimate the modal parameters numerically. The first FE model consists of beam elements. The second FE model consists of traditional rectangular shell elements and one rectangular shell element with a transverse, internal, open crack. The analytical results from the numerical models are compared with data obtained from experimental tests. The numerical models give good agreements with the experimental data. The beam model takes into account only the first mode of the crack evaluation. In the shell model all three modes of the crack growth are taken into account. Nevertheless, the results obtained for both models are satisfactory because the beam is subjected to bending. It can be concluded that it is sufficient to use crack models for calculating natural frequencies in bending, taking into account the first mode of the crack extension only.

A simple numerical algorithm is proposed for directly generating realizations of weighted integrals (or, similarly, local averages) of non-Gaussian random fields for use in simulation-based stochastic finite-element analyses. The method uses a Gaussian quadrature integration rule to numerically evaluate an individual weighted integral (or local average), thus reducing the computation of the integral to a summation of a small number of properly weighted non-Gaussian random variables. Consequently, the need to generate actual realizations of the non-Gaussian random field is eliminated. The vector of non-Gaussian random variables is obtained from a nonlinear mapping of a vector of properly correlated Gaussian random variables, which in turn is obtained from a vector of uncorrelated Gaussian random variables using modal decomposition. The “proper” correlation structure of the Gaussian random variables is established a priori from the correlation structure of the non-Gaussian random variables, which itself is established a priori from the known or desired correlation structure of the non-Gaussian random field. Numerical results are provided to demonstrate the statistical equivalence of weighted integrals (or local averages) generated using the proposed approach to those computed using conventional numerical integration of actual realizations of the non-Gaussian random field.

This paper presents within the scope of the theory of static elasticity a derivation of soil spring constant in longitudinal direction of a buried pipeline in the seismic design. It is found that the spring constant depends on the shear modulus G of the soil deposits and the ratio λ of the radius of zero displacement over the radius of a buried pipeline structure. When λ increases, the soil spring constant decreases and the decreasing rate reduces remarkably when λ is greater than about 10. The ratio of soil spring constant over G is 2.7 when λ = 10. Furthermore, the dynamic effect of soil spring constants on buried pipeline structures is estimated analytically by the dynamic theory of elasticity. The soil spring constant that is derived, taking into account the boundary condition of ground surface, depends on the shear modulus G of the ground, nondimensional frequency ωb/V_s (ω = circular frequency; b = radius of buried pipeline; V_s = ground shear-wave velocity) and nondimensional depth d/b (d = depth of pipeline).

Conventional design procedures for rigid jointed frames encourage a situation in which more than one buckling mode could occur simultaneously. Even though this practice is known to often give rise to increased sensitivity of buckling loads to small initial imperfections, current design practice is usually lacking in explicit design guidance. This paper seeks to explore the extent to which buckling loads in framed structures are reduced by the effects of modal interactions arising when designs are optimized. It takes, as a specific example, the situation where the buckling and bending planes for a rigid-jointed frame coincide and for which sway and nonsway buckling modes occur at similar load levels. It explores the extent to which elastic-plastic buckling loads may be affected by interactions of sway and nonsway modes and compares predictions with results from a recently conducted test program. It is suggested that the theoretical approach described has the potential to provide an extended and improved alternative to existing design practice.

This paper presents experimental evidence to show that a size/geometry dependence is observed in the shrinkage cracking behavior of restrained concrete structures. A theoretical model is developed to explain this behavior. First, a solution is presented to compute the stress and displacement fields of an aging, linear, viscoelastic cylinder by assuming that a uniformly distributed shrinkage strain is perfectly restrained in the radial direction at the internal surface of the cylinder. Second, a fracture mechanics failure criterion is implemented to develop time and geometry-dependent tensile stress resistance (strength) curves. Third, this model is used to illustrate the role of specimen size/geometry and material composition on the failure response. Finally, experimentally measured ages of cracking are compared with the theoretical modeling predictions.

The following problem is considered: A penny-shaped crack is located in the plane z = 0 of a transversely isotropic elastic space and interacts with two equal tangential forces, acting in the same direction, which are located arbitrarily, but symmetrically with respect to the plane of the crack. An exact closed-form solution is obtained here. Some of the stresses and displacements in the whole space are expressed in terms of elementary functions. Two methods of solution are considered. The first method considers superposition of an uncracked space subjected to two forces and a space weakened by a crack and subjected to a specially defined loading. The second method reduces the problem to that of a half-space, one force is acting inside this half-space, and its surface is loaded by a pressure, providing zero displacements outside the crack. It is shown that both methods give the same results.

Lade's criterion is one of the best criteria for describing the shear yield and failure behavior of soils in 3D stresses, and the original Cam-clay model is the most popular and fundamental elastoplastic model for normally consolidated clays. In this paper, a transformed stress tensor is proposed for combining Lade's criterion and the Cam-clay model. The transformed stress is deduced from what makes the curved surface of Lade's criterion become a cone with the axis being the space diagonal, i.e., Lade's criterion becomes the extended Mises type criterion in the transformed principal stress space. The Cam-clay model revised by Lade's criterion is capable of describing the mechanical behavior of soils in general stresses. It is presented that the revised model can simulate well the drained and undrained behavior of soils, not only under triaxial compression conditions, but also under plane strain, true triaxial, and hollow cylinder conditions. The elastoplastic models for soils, in which only the first and second stress invariants are used, can be extended simply to the model, including the third stress invariant by adopting Lade's criterion.