This paper discusses the local approach of fracture using damage mechanics concepts to evaluate the seismic response of concrete gravity dams. A constitutive model for plain concrete, subjected to tensile stresses, is presented. The meshdependent hardening technique is adopted such that the fracture energy dissipated is not affected by the finite element mesh size. The model is implemented in conjunction with the Hilber, Hughes Taylor alpha algorithm for time marching. Koyna dam is utilized to validate the proposed formulation. The importance of initial damage prior to the advent of an earthquake is also investigated. A 60 m concrete gravity dam is therefore selected and subjected to ground motion typical of eastern North America. Five scenarios of initial damage are presented and the results confirm the importance of accounting for the initial state for the seismic safety evaluation of an existing dam.

Due to their high lateral flexibility and low inherent damping, stay cables are prone to dynamic excitations. Application of dampers to improve the energy dissipation capacity of stay cables and mitigate their excessive vibrations has been extensively studied, and design tools have been proposed to select the optimum damper size and predict the maximum achievable damping ratio of a cable-damper system. In this study, the effectiveness of external viscous dampers in controlling stay cable vibrations is investigated by considering the negative stiffness behavior of passive dampers. An analytical model is developed to include the damper stiffness effect for further refinement of existing damper design tools, of which the influence of cable sag, cable flexural stiffness, and damper support stiffness has already been considered. The performance of passive negative stiffness dampers (NSDs) and conventional zero or positive stiffness dampers (PSDs) is investigated in detail via parametric studies using the refined design formula. In particular, a criterion is defined for selecting the negative stiffness in NSD based on the stability limits. Two design examples are presented to illustrate the application of the proposed refined damper design tool to the selection of optimum damper size and evaluation of damper performance for a passive viscous PSD and NSD. Results show that compared with the conventional viscous dampers, a passive NSD demonstrates superior performance in stay cable vibration control. Results are also compared and verified with the numerical solution of the proposed analytical model.

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SUMMARYThe evaluation of the fundamental period of shear wall buildings considering the exibility of the base is investigated in this paper. This research is motivated by the discrepancy reported between the formulas used in di erent building codes and the measurement of real buildings. Both experimental and analytical approaches are used to assess the e ect of the base exibility on the fundamental period of shear wall structures. In total, twenty buildings built on di erent types of soil are tested under ambient vibration. The fundamental period is identiÿed using a non-parametric linear model in the frequency domain. The results show that fundamental period formulas used by UBC-97 and NBCC-95 are inadequate since they do not include the e ect of the foundation sti ness. To improve the estimation of the fundamental period of shear wall buildings, an analytical approach is presented. The structure and the foundation are represented by a continuous-discrete system. The sti nesses of the base are represented by translational and rotational discrete springs. The rigidities of these springs are evaluated from the elastic uniform compression of the soil mass and the size of the foundation. The analytical predictions improve the estimation of the fundamental period and keep the computation simple. The error between the measured period and the analytical results is, on average, less than 10%.

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Summary Due to their low inherent damping and high lateral flexibility, stay cables are prone to large amplitude vibrations governed by either a single or multiple cable modes. Among the practical measures, the installation of transverse passive dampers near the cable‐deck anchorage is a popular choice. Compared to conventional positive stiffness and zero stiffness dampers, negative stiffness damper (NSD) manifests superior performance in mitigating cable vibrations, especially in the case of long cables. In this study, a novel design approach is proposed to optimize NSD for multimode cable vibration control. Two design scenarios are considered. In the former, the damper size is optimized for a predetermined negative damper stiffness; whereas in the latter, the size and negative stiffness of the NSD are both optimized to achieve a required damping ratio for the dominant modes. The applicability of the proposed NSD optimum design approach is validated using 15 sample real stay cables. A numerical example is presented, of which a NSD is designed based on the proposed approach to optimize wind‐induced multimode vibration control of a 460‐m stay cable, and the performance is compared with that of a linear‐quadratic regulator (LQR) control. Results show that the selected NSD can effectively suppress the dominant modes and has a controlling effect comparable with an active control using LQR. In addition, it is found that when there exist more than two dominant modes in vibration, designing NSD for the lowest and the highest dominant modes would also adequately control the mid‐range modes.

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