Journal of Engineering Mechanics

For approximate estimation of the maximum inelastic roof displacement demand for existing multistory buildings, the current displacement coefficient method uses the maximum linear elastic displacement of the first-mode single-degree-of-freedom (SDOF) system corresponding to the buildings. The statistics of the SDOF system estimate of the roof displacement on the following topics are presented by three SAC steel buildings subjected to 72 earthquake ground motions recorded on firm sites. (a) How uncertain is the first-mode SDOF system estimation of the roof displacement? (b) What are the main sources of uncertainty in the estimation of the roof displacement? (c) How can the uncertainty be reduced? It is shown from the study that the maximum inelastic roof displacement demand of multistory buildings can be more accurately and more directly estimated by the maximum inelastic displacement of the first-mode elastoplastic SDOF system. This is especially true for low-rise buildings.

The issue of structural damage detection is addressed through an innovative multivariate statistical approach in this paper. By invoking principal component analysis, the vibration responses acquired from the structure being monitored are represented by the multivariate data of the sample principal component coefficients (PCCs). A damage indicator is then defined based on a multivariate exponentially weighted moving average control chart analysis formulation, involving special procedures to allow for the effects of the estimated parameters and to determine the upper control limits in the control chart analysis for structural damage detection applications. Also, a data shuffling procedure is proposed to remove the autocorrelation probably present in the obtained sample PCCs. This multivariate statistical structural damage detection scheme can be applied to either the time domain responses or the frequency domain responses. The efficacy and advantages of the scheme are demonstrated by the numerical examples of a five-story shear frame and a shear wall as well as the experimental example of the I-40 Bridge benchmark.

This paper presents an externally reinforced I-beam-to-box-column seismic connection. An inclined rib-plated collar-plated configuration with web plates is used to ensure planar continuity between I-beam and box-column webs; the rib plates, inclined in plan between the beam web and the two column web planes, along with collar-plates encircling the box-column at beam flange levels and web plates in plane with the rib plates at the beam web level constitute the new configuration. This connection configuration relieves stresses on box-column flanges and helps in force transfer to the box-column webs. Performance evaluation of the proposed connection configuration shows that sufficient inelasticity is mobilized in the beam away from the column face with connection elements and welds remaining elastic. The seismic performance of the proposed connection is also found to be better than two state-of-the-art connection schemes in terms of higher strength, stiffness, and higher reserve strength of the welds under cyclic displacement loading.

A method to interrogate changes in transfer matrices regarding damage localization is extended to cases where these changes cannot be experimentally obtained because the input is not known deterministically. The extension is realized by noting that the method does not require the transfer matrix change explicitly, but only vectors from its kernel, and that some of these vectors can be estimated—for a fictive collocated input distribution—from constraints between realization matrices and results of an output-only identification. The interrogation approach, denoted as the stochastic dynamic damage locating vector method, is demonstrated in the context of simulations.

Recent disagreements on the mathematical modeling of fracture and size effect in concrete and other quasi-brittle materials are obstacles to improvements in design practice, and especially in design codes for concrete structures. In an attempt to overcome this impediment to progress, this paper compares the Hu-Duan boundary effect model (BEM) expounded since 2000 to the size-shape effect law (SEL) proposed at Northwestern University in 1984 and extended to the geometry (or shape) effects in 1990. It is found that within a rather limited part of the range of sizes and shapes, the fracture energy values identified by BEM and SEL from the test data on maximum loads are nearly the same. But in other parts of the range the BEM is either inferior or inapplicable. The material tensile strength values identified by BEM have a much larger error than those obtained from the SEL after calibration by the cohesive crack model. From the theoretical viewpoint, several hypotheses of BEM are shown to be unrealistic.

This paper shows that the mechanical behavior of concrete materials can be described by a nonlinear unified strength criterion which requires four independent parameters for model calibration. The criterion covers all the area from spatially mobilized plane curve in the lower bound to Mises circle in the upper bound on the deviatoric plane, with an exponential curve on the meridian plane in principal stress space. Four material parameters in the strength criterion have their clear physical meanings and their determination approaches are also given. Four sets of true triaxial experimental results are compared with the modeling results of the proposed criterion. It shows that the proposed criterion is capable to capture the characteristics of yielding and failure and reasonably calculate the multiaxis strength of concrete materials.

Size effect (SE) on quasi-brittle fracture of concrete and concretelike heterogeneous materials has been commonly demonstrated by the influence of specimen size $D$ on the transition from strength-dominant fracture to toughness-dominant fracture for geometrically similar specimens with a common initial-crack/specimen-size ratio, i.e., $a_0/D=\text{constant}$ . Under such a condition, size $D$ appears to be the single controlling parameter for SE. In this study, we clarify that the primary source of quasi-brittle fracture, the presence of a large fracture process zone (FPZ) in front of a crack-tip, does not follow the condition of geometry similarity even for geometrically similar specimens. This suggests that the role of FPZ is not clearly explained for SE. Therefore, this study emphasizes the interaction between FPZ and the nearest specimen/structure boundary, and the consequent SE phenomenon. The deficiencies associated with the common SE models developed by Bazant and his coworkers are discussed through comparisons with the analysis on the boundary and FPZ interaction, or the boundary effect. It is shown that quasi-brittle fracture and the transition from strength-dominant fracture to toughness-dominant fracture can occur even if specimen/structure size $D$ is constant, i.e., size $D$ is not the dominant factor for SE.

This paper considers the problem of a beam with a small bending stiffness, within the framework of a nonlinear beam model that includes both the classical cable and the linear beam as limiting cases. This problem, treated as a perturbation of the catenary solution, is solved with the multiple scales method. The resulting expressions of the beam deflection and of the internal forces, as well as those obtained with the more commonly applied matched asymptotics method, are compared with numerical results. This comparison indicates that a better accuracy can be achieved with the multiple scales approach, for a similar computational effort. These results also suggest that application of the multiple scales method to the solution of beam problems involving boundary layers extend the range of values of the small parameter, for which accurate analytical solutions can be obtained by a perturbation technique.

The results of laboratory measurements of large focusing wave groups, which were generated using the New Wave theory, are presented. The influences of both the steepness and frequency bandwidth on focused wave characteristics were examined. The influence of frequency bandwidth on focused wave groups with small and moderate steepness was very small. However, for cases with the large steepness, the nonlinearity increased with increasing bandwidth frequency and widened free-wave regimes are identified for those cases with large steepness at the focal location. The underlying nonlinear phase coupling of focused waves was examined using wavelet-based bicoherence and biphase, which can detect nonlinear phase coupling in a short time series. For wave groups with large initial steepness, as wave groups approached the focal location, the values of bicoherence between primary waves and its higher harmonics progressively increased to 1 and the corresponding biphase was gradually close to zero, suggesting that an extreme wave event can be produced by considering Stokes-like nonlinearity to very high-order. Furthermore, the fast change of bicoherence of focused wave groups indicates that the nonlinear energy transfer within focusing waves is faster than that of nonfocusing wave trains.

An efficient model correction method is proposed by using the modal measurement from a structural system. The method corrects/updates the mass and stiffness matrix without imposing any parameterization. It considers the information from both the nominal finite-element model and the measurement of modal frequencies and mode shapes. The method is computationally very efficient and it does not require computation of the complete set of eigenvalues and eigenvectors of the nominal model. Instead, only the nominal eigenvalues and eigenvectors of the modes to be corrected are needed. The Gram-Schmidt orthogonalization process is used to construct a basis that satisfies the mass orthogonality condition. This basis is used to transform the eigenvectors of the nominal model so that the corrected model is compatible with the measurement. A thousand-degree-of-freedom chainlike system and a 1,440-degree-of-freedom structural frame are used to illustrate the proposed method.

This paper presents a unique structural reliability estimation method incorporating structural parameter identification results based on the seismic response measurement. In the shaking table test, a three-bent concrete bridge model was shaken to different damage levels by a sequence of earthquake motions with increasing intensities. Structural parameters, stiffness and damping values of the bridge were identified under damaging seismic events based on the seismic response measurement. A methodology was developed to understand the importance of structural parameter identification in the reliability estimation. Along this line, a set of structural parameters were generated based on the Monte Carlo simulation. Each of them was assigned to the base bridge model. Then, every bridge model was analyzed using nonlinear time history analyses to obtain damage level at the specific locations. Last, reliability estimation was performed for bridges modeled with two sets of structural parameters. The first one was obtained by the nonlinear time history analysis with the Monte Carlo simulated parameters which is called nonupdated structural parameters. The second one was obtained by updating the first set in Bayesian sense based on the vibration-based identification results which is called updated structural parameters. In the scope of this paper, it was shown that residual reliability of the system estimated using the updated structural parameters is lower than the one estimated using the nonupdated structural parameters.

Dam-reservoir dynamic interactions are complex phenomena requiring advanced mathematical and numerical modeling. Although available sophisticated techniques can handle many aspects of these phenomena, simplified procedures are useful and still needed to globally evaluate the dynamic response of dam-reservoir systems. This paper presents and validates an original practical procedure to investigate earthquake induced dam-reservoir interaction in the frequency domain, including the effects of dam flexibility, water compressibility, and reservoir bottom wave absorption. The procedure relates hydrodynamic pressure due to any deflected modal response of a two-dimensional gravity dam on a rigid foundation to hydrodynamic pressure caused by a horizontal rigid body motion. New analytical expressions that can be easily programmed in a spreadsheet package or implemented in a dam structural analysis program are also proposed to conduct simplified fundamental mode earthquake analysis of gravity dams. The techniques presented can be efficiently used to provide valuable insight into the effects and relative importance of the various parameters involved in the dynamic response of dam-reservoir systems. Although the mathematical derivations and closed-form expressions developed were applied to dam-reservoir systems herein, they can be easily adapted to other fluid-structure interaction problems.

The vibration problem of a simply supported beam subjected to a moving elastic structure is investigated. The model consists of two Euler-Bernoulli beams which are assumed to be connected by flexible springs at two discrete points. The dynamic response of the simply supported beam subjected to the moving elastic beam at a constant speed is studied by the modal superposition method. The elastic stiffness and the inertial effect of the moving beam are included in the analysis. By solving the ordinary differential equations governing the motion of the model, some approximate analytical results are derived and influence factors on the dynamic response of the simply supported beam are discussed in details, including the stiffness ratio, which is defined as the stiffness of the moving beam to that of the simply supported beam, the moving velocity and the connection spring stiffness between the two beams. Results of the study imply that the connection stiffness has an apparent influence on the dynamic behavior of the simply supported beam.