Response Of Secondary Systems Research Articles

Seismic response of secondary systems

The purpose of this paper is to provide a comprehensive review and assessment of the state-of-the-art in the area of research on seismic response of secondary systems (structural and non-structural), which are anchored or attached to primary structural systems. Included are an appraisal of current engineering practice and design, an update of recent advances, and a discussion of possible future research direction.

Seismic analysis of multiply supported secondary systems with dynamic interaction effects

AbstractFor a proper response spectrum analysis of a secondary system with multiple supports, the seismic inputs are required to be defined in terms of the auto and cross floor response spectra. If no feed‐back or interaction effect from the secondary system to its supporting primary structure is suspected, these inputs can be developed by a direct analysis of the supporting structure alone. However, sometimes the effect of the interaction on the secondary system response can be quite significant. Herein, a method is developed to incorporate the feed‐back effect, through proper modification of the interaction‐free floor spectrum inputs. The interaction coefficients are used to effect such modifications in different floor spectral quantities. A procedure for the calculation of the interaction coefficients is proposed. The modified floor spectra when used as inputs to the secondary system do introduce the interaction effect in the secondary system response. A successful application of this method is demonstrated by numerical examples of secondary systems with three different secondary‐to‐primary system mass ratios.

Dynamic response of secondary systems in structures subjected to ground shock or impact

The dynamic responses of a variety of multi-degree of freedom primary-secondary systems subjected to ground shock or impact are presented. The systems are damped and undamped. Completely detuned systems (all frequencies of the subsystems well-spaced) as well as singly tuned systems (a natural frequency of the primary subsytem equal or close to a natural frequency of the secondary subsystem) are investigated. The accuracy of the conventional floor spectrum method when applied to primary-secondary systems is presented determined. A new method for the determination of the dynamic response of multiply-tuned primary-secondary systems is presented.

A new instructure response spectrum (IRS) method for multiply connected secondary systems with coupling effects

A new instructure response spectrum (IRS) method is presented. The new method is capable of accounting for various coupling effects on the response of secondary systems, e.g., interaction between primary-secondary systems (mass effect), correlation between responses from multiple connecting DOF, and the straining effect of multiple connecting DOF displacements including the related correlations. The new IRS method directly uses the displacement and velocity spectra at the base of the primary system as seismic input without converting it into either compatible time history or power spectral density function. It is shown that the new method gives IRS, and secondary system response values very close to those from time history analysis using real earthquake ground motions.

Seismic response of light internal equipment in base‐isolated structures

AbstractThe seismic response of light secondary systems in a building is dependent on the response of the primary structural system to the seismic ground motion with the result that very high accelerations can be induced in such secondary systems. This response can be reduced through the use of aseismic base isolation which is a design strategy whereby the entire building can be decoupled from the damaging horizontal components of seismic ground motion by the use of some form of isolation system.The paper presents a theoretical analysis of the response of light equipment in isolated structures and a parallel experimental programme both of which show that the use of base isolation can not only attenuate the response of the primary structural system but also reduce the response of secondary systems. Thus, the design of equipment and piping in a base‐isolated building is very much simpler than that for a conventionally founded structure: inelastic response and equipment‐structure interaction need not be considered and multiple support response analysis is rendered unnecessary.Although an isolation system with linear elastic bearings can reduce the acceleration of the structure, it may be accompanied by large relative displacements between the structure and the ground. A system using lead‐rubber hysteretic bearings, having a force‐displacement relation which is approximately a bilinear loop, can reduce these displacements. A parallel experimental programme was carried out to investigate the response of light equipment in structures isolated using lead‐rubber bearings. The experimental results show that these bearings can dissipate energy and limit the displacement and acceleration of the structure but are less effective in reducing the accelerations in the internal equipment.The results of both the analysis and the tests show that base isolation is a very effective method for the seismic protection of light equipment items in buildings.

Dynamic Response of Multiply Supported Secondary Systems

An accurate and efficient method for analysis of multiply supported, multi‐degree‐of‐freedom secondary systems is developed. The method accounts for the effects of tuning, interaction, nonclassical damping, and spatial coupling that are intrinsic dynamic characteristics of composite primary‐secondary systems. The method consists of two steps: (1) Synthesis of the modal properties of the composite primary‐secondary system in terms of the known properties of the individual subsystems, and (2) evaluation of secondary system response through modal combination. Concepts from modal synthesis, perturbation theory, and random vibrations are used to produce accurate results. The method is efficient since it avoids large eigenvalue solutions, time‐history analysis and floor spectra computations. It is also general, as it is applicable to a variety of stochastic or deterministic inputs. The responses of an example secondary system to seismic input are obtained directly in terms of the ground response spectrum.

Response of secondary systems in structures subjected to transient excitation

AbstractAn analytical method, based on matrix perturbation theory, is developed whereby a simple estimate can be obtained of the maximum dynamic response of lightly damped, light equipment (modelled as a n(2)‐degree‐of‐freedom system) attached to a structure (modelled as a n(1)‐degree‐of‐freedom system) subjected to ground motion or impact. A natural frequency of the equipment is considered close or equal to a natural frequency of the structure. It is assumed that the information available to the designer is a time history of the ground motion or impact, or an associated design spectrum; the fixed base modal properties of the structure; and the fixed base modal properties of the equipment. The method employed avoids the direct conventional analysis of a n(2) + n(1)‐degree‐of‐freedom system either by modal or by matrix time‐marching methods; as well as errors in estimates of peak response due to the possible unreliability of numerical schemes because of the lightness of the equipment, or due to uncertainty as to the appropriate procedure for summing the contributions of the two closely spaced modes which occur in the system. The proposed procedure is demonstrated for an example equipment‐structure system. Computed results based on the method are in close agreement with results obtained through a Newmark time‐integration scheme.