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Elevators in buildings serve a very important function and are among the critical components of an essential facility. They have several mechanical and electrical components that are known to be susceptible to damage during earthquake occurrences. The counterweights, being the heaviest, are among their most vulnerable components. The ASME code has made several provisions to improve the performance of the counterweights in seismic events. To evaluate their performance under code-mandated provisions, it is necessary that a comprehensive and realistic analytical model is used. This paper uses a detailed model of a counterweight of a traction elevator to study its in-plane and out-of-plane dynamic behavior. The model incorporates the multiple support inputs and flexibilities of the counterweight guidance system along with their non-linearities caused by the clearance limitations. The study examines the effect of changing clearances, variability of input motions, and the use of tie brackets on the system response, and evaluates the impact of some of the code provisions on the dynamic behavior of the system.

The rail-counterweight systems in building elevators are known to be susceptible to earthquake-induced ground motions. Besides avoiding costly repairs and economic disruptions, it is of special interest to maintain the functionality of the elevators in critical facilities such as hospitals during, and especially after, a strong earthquake event. This paper presents an approach to develop a realistic analytical model of these vulnerable systems to study their seismic response behaviour. The model includes the flexibilities of the guidance and supporting components of the counterweights in a systematic manner. Currently only the linear response behaviour is considered; however, the sources of non-linearities in the flexible components are clearly identified. The model considers the effect of the differential support motions from the building. Both the out-of-plane and in-plane responses of the rail-counterweight are studied and included in the stress calculations. Several sets of numerical results considering simultaneous action of the two orthogonal components of historic earthquakes are obtained to study the seismic response characteristics of the rail-counterweight system.

Considerable effort has been devoted to develop passive and active methods for reducing structural response under seismic excitations. Passive control approaches have already found application in practice. Active control methods, on the other hand, are being vigorously examined for application to civil structures. This paper investigates the application of active and semi-active control schemes to structures subjected to seismic excitations, and it focuses on the use of the sliding-mode control approach for the development of the control algorithms. The possibility of control redundancy with respect to the number of sliding constraints is taken into account in the controller design. Several sets of numerical results are obtained for a realistic 10-storey shear building, subjected to earthquake-induced ground motions and controlled by active or semi-active control schemes. It is observed that both active and semi-active control schemes can be used to reduce the dynamic response. Active control performs very effectively in reducing the structural response, but the required control force values can be quite large to limit its practical application in the case of large and massive buildings. Active regulation of linear viscous dampers was found unnecessary for this type of structural system, as it did not induce any significantly more reduction in the response than the dampers acting passively. On the other hand, it is shown that active regulation of stiffness can be used with advantage to reduce the response. © 1997 by John Wiley & Sons, Ltd.

The equations of motion of a rotor finite element subjected to six components of base excitation are developed by applying variational principles. The equations contain speed dependent gyroscopic terms, base rotation dependent parametric terms and several forcing function terms which depend upon the linear accelerations, rotational accelerations and a combination of linear and rotational velocities. To evaluate the importance of various terms, seismic response characteristics of a rotating machine subjected to simulated base excitations are studied. It is observed that even for strong rotational inputs the parametric terms in the equation of motion can be ignored without affecting the response. The rotational input terms in the forcing function, however, are quite important and can be ignored only when they are not very strong. Since the problematic parametric terms can be ignored, one can use a generalied modal analysis approach.

A mode synthesis-based direct approach is presented to calculate seismic response of equipment supported on structures. The approach incorporates the effect of the dynamic interaction between the equipment and the supporting structure. The modal properties of the combined structure–equipment system are obtained by synthesizing the modal properties of the individual structures. The seismic input defined in terms of smoothed ground response spectra can be directly utilized in this approach. Both heavy and light equipment can be considered by the approach equally effectively. Numerical examples demonstrating the effectiveness of the proposed approach are presented.

A method is presented to obtain the exact complex-valued eigenproperties of a classically damped structure and equipment system. The non-classically damped character of the combined system as well as the effect of dynamic interaction between primary structure and equipment are properly included in the calculation of these eigenproperties. It is necessary only to know the classical modal properties of the structure and, of course, the equipment characteristics. The eigenvalues are obtained as the solution of a non-linear equation which can be easily solved by the Newton–Raphson algorithm. Once the eigenvalues are known, the corresponding eigenvectors are obtained from simple closed-form expressions. The method can be used equally effectively with light as well as heavy equipment. Numerical results demonstrating the effectiveness of the method are presented. A procedure which utilizes the complex-valued eigenproperties is developed for calculating the floor response spectra directly from the ground spectra. Numerical results of floor response spectra obtained from this procedure are presented. The floor spectra calculated by this approach include the structure–equipment interaction effect.

Closed-form expressions are obtained to calculate the approximate complex eigenvalues and eigenvectors of a system composed of a non-classically damped primary structure and a single degree of freedom oscillator. The expressions are obtained through a systematic second order perturbation analysis of a transformed eigenvalue problem of the combined system. The possibility of tuning between the structure and equipment is considered. The dynamic properties of the combined system are derived in terms of the complex eigenvalues and eigenvectors of the supporting structure and the frequency, mass and damping ratio of the equipment. Examples demonstrating the accuracy of the expressions for the eigenvalues and eigenvectors are presented. These eigenproperties are used for generation of floor response spectra for non-classically damped structures to incorporate the dynamic interaction effects between the structure and equipment.

The paper presents a method for synthesizing the modal properties of substructures to obtain the exact modal properties of a combined structure. Unlike the currently available modal synthesis approaches, the proposed approach does not require the solution of any transformed eigenvalue problem of the combined structure by conventional means. The substructures are assumed to be coupled by connecting elements and the coupling is done sequentially with one element at a time. The eigenvalues at each stage of coupling are obtained by solving a non-linear characteristic equation. A simple Newton-Raphson solution scheme is adequate for this purpose. Once the eigenvalues are determined, the eigenvectors can be calculated in closed form. Several examples demonstrating the applicability of the proposed approach are presented.