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High voltage transformers are essential parts of the electrical distribution grid. Severe failure of entire grids can occur during earthquakes, when transformer bushings fail due to structural dynamic mismatch to the seismic demands. Proper consideration of the fundamental frequency of vibration, which depends on the flexibility of the cover plate of the transformer to which they are connected, is therefore crucial for determining the seismic response of bushings. A simplified method is developed in this work for the evaluation of the “as-installed” fundamental frequency of transformer bushings. Such bushings are modeled as cantilever beams with distributed mass and elasticity, and an additional rotational spring is introduced at the base, to account for the flexibility of the cover plate of the transformer. A simple yet efficient expression is derived for the as-installed frequency, based on the Southwell-Dunkerley method. The solutions require the knowledge of the bending rigidity of the bushing and the (out-of-plane) rotational stiffness of the cover plate. The evaluation of both these quantities is presented. While analytical solutions for the (out-of-plane) rotational stiffness of circular plates are well known, solutions for rectangular plates have not yet been addressed. A semi-empirical-numerical solution is suggested, based on finite element models and analytical expressions derived by force-fitting the “circular plate solution” to the numerical analyses. The results yielded by the proposed method are compared with experiments on real bushings. [ABSTRACT FROM AUTHOR]

This paper proposes a new seismic modification methodology for optimal design of multistory frame structures to avoid damage and attain a robust response to extreme hazards. The methodology determines added damping devices of optimal size at strategic locations and modifies story stiffnesses, by solving a newly formulated constrained optimization problem. The objective is to minimize a cost function representing total energy while satisfying the equations of motion and allowable interstory drifts for given severe ground motions. The proposed methodology combines the classical linear quadratic regulator, which searches for an optimal gain matrix, with an analysis-redesign iterative procedure to produce a robust analysis redesign (RAR) iterative approach. A new algorithm approximates the equivalent stiffness to fit the displacement gains. At convergence, the RAR procedure will yield optimal sizing and new topology for the designed system. The RAR procedure is developed here for shear structures. However, RAR can be utilized for complex structures by modeling them first as equivalent shear-type structures having stiffness properties that yield the same maximum interstory drifts for the given records. Two numerical examples of shear-type structures are examined. These examples use structures already having an 'optimal' configuration, which are further optimized using the methodology developed herein. In addition, a numerical example comprised of a 10-story moment resisting frame structure is presented to illustrate the use of the equivalent shear structure approach. The results of the exemplified retrofitted moment resisting frame structure show great improvements in its dynamic response. [ABSTRACT FROM AUTHOR]

A new passive seismic response control device has been developed, fabricated, and tested by the authors and shown to be capable of producing negative stiffness via a purely mechanical mechanism, thus representing a new generation of seismic protection devices. Although the concept of negative stiffness may appear to be a reversal on the desired relationship between the force and displacement in structures (the desired relationship being that the product of restoring force and displacement is nonnegative), when implemented in parallel with a structure having positive stiffness, the combined system appears to have substantially reduced stiffness while remaining stable. Thus, there is an 'apparent weakening and softening' of the structure that results in reduced forces and increased displacements (where the weakening and softening is of a non-damaging nature in that it occurs in a seismic protection device rather than within the structural framing system). Any excessive displacement response can then be limited by incorporating a damping device in parallel with the negative stiffness device. The combination of negative stiffness and passive damping provides a large degree of control over the expected performance of the structure. In this paper, a numerical study is presented on the performance of a seismically isolated highway bridge model that is subjected to various strong earthquake ground motions. The Negative Stiffness Devices (NSDs) are described along with their hysteretic behavior as obtained from a series of cyclic tests wherein the tests were conducted using a modified design of the NSDs (modified for testing within the bridge model). Using the results from the cyclic tests, numerical simulations of the seismic response of the isolated bridge model were conducted for various configurations (with/without negative stiffness devices and/or viscous dampers). The results demonstrate that the addition of negative stiffness devices reduces the base shear substantially, while the deck displacement is limited to acceptable values. This assessment was conducted as part of a NEES (Network for Earthquake Engineering Simulation) project which included shaking table tests of a quarter-scale highway bridge model. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Abstract: In nonlinear analysis of structures the structural elements exhibiting yielding in its sections are usually modeled using concentrated plastic hinges at the end of the elements or fiber models accounting for yielding along the member. In the last four decades however, alternative models were developed based on spread plasticity formulations which consider an extended inelastic zone in proximity of the critical sections, therefore affecting the stiffness (or the flexibility) matrix of the member. Two flexibility formulations were generally considered to account approximately for the variation of curvature in the plasticized zones, one linear and the other uniform. The linear spread plasticity model assumes that the curvature in the plasticized zone is distributed linearly at the ends of the element while the uniform curvature model considers a constant distribution of plasticity. In this study, a power spread plasticity model is proposed which is able to model more complex or various plasticity distribution patterns, including concentrated plasticity (plastic hinge). The derivation is the same as for the previous spread flexibility formulations, where the flexibility coefficients represent the relation between the end moments and the correspondent plane rotations. Considering both flexural and shear flexibilities, the model is developed and implemented in a nonlinear structural analysis platform, IDARC2D. Several nonlinear analyses are carried out on a previously tested full scale bridge pier and a 10-story structure to show the influence of the power values on the cyclic and dynamic structural response. The results of the analyses show that the high order spread plasticity models produce smaller displacement and higher acceleration responses in the structural system. At the end of the paper, an alternative definition for the selection of the power value (variable power) is suggested and the corresponding results are also investigated. [Copyright &y& Elsevier]

A method is suggested to reduce the structural seismic response using viscous dampers with their effect magnified with mechanical levers (lever arms). The lever arms are used to magnify the drift and the drift velocities transferred from the structure to the dampers thus producing larger energy dissipation in smaller devices. The increase of energy dissipation in each unit results in a reduction of the number of units necessary to achieve the same reduction in structural response, or it results in a reduction of the size of dampers required for the same purpose. The use of the proposed technique permits one to reduce the number of frame bays obstructed by diagonal or Chevron bracing elements. An optimal design procedure, based on the linear quadratic regulator (LQR) technique, is proposed in this study to obtain the initial properties of the viscous dampers. The study presents the amplification and the contribution of the construction details to such amplification. A seven-story structure model with the proposed system was simulated numerically in order to check the damping efficiency. The numerical example shows that using the lever arms for dampers’ connection, it yields significant reduction in the structural response, very close to that designed according to the LQR strategy. [ABSTRACT FROM AUTHOR]