Seismic design response by an alternative SRSS rule

Singh, M. P.; Mehta, K. B.

doi:10.1002/eqe.4290110605

Cited by 29 publications

(7 citation statements)

References 14 publications

(1 reference statement)

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“…62) can also be expressed in terms of the deformation function, Dj(t), as or in terms of the pseudo-acceleration function, Aj(t), as in which by and b; are participation factors defined by and Summary of procedure summarized as follows.The steps involved in the analysis of the transient response of a non-classically damped system may be 1. Evaluate the characteristic values, r j , and the associated characteristic vectors, {I,!Ij }; and from equations (5),(7) and(8), determine the damped and pseudo-undamped natural frequencies of the system, pj and pj, and the modal damping factors, cj. From equation (43), compute the participation factors, B j .…”

mentioning

confidence: 99%

Modal analysis of non‐classically damped linear systems

Veletsos

Ventura

1986

Earthq Engng Struct Dyn

218

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A critical, textbook-like review of the generalized modal superposition method of evaluating the dynamic response of nonclassically damped linear systems is presented, which it is hoped will increase the attractiveness of the method to structural engineers and its application in structural engineering practice and research. Special attention is given to identifying the physical significance of the various elements of the solution and to simplifying its implementation. It is shown that the displacements of a nonclassically damped n-degree-of-freedom system may be expressed as a linear combination of the displacements and velocities of n similarly excited single-degree-of-freedom systems, and that once the natural frequencies of vibration of the system have been determined, its response to an arbitrary excitation may be computed with only minimal computational effort beyond that required for the analysis of a classically damped system of the same size. The concepts involved are illustrated by a series of exqmples, and comprehensive numerical data for a three-degree-offreedom system are presented which elucidate the effects of several important parameters. The exact solutions for the system are also compared over a wide range of conditions with those computed approximately considering the system to be classically damped, and the interrelationship of two sets of solutions is discussed.function of time and then combined to yield the response history of the system; and (2) the response spectrum version, in which first the maximum values of the modal responses are determined, usually from the response spectrum applicable to the particular excitation and damping under consideration, and the maximum response of the system is then computed by an appropriate combination of the modal maxima.When damping is of the form specified by Caughey and OKelly,' the natural modes of vibration of the system are real-valued and identical to those of the associated undamped system. Systems satisfying this condition are said to be classically damped, and the modal superposition method for such systems is referred to as the classical modal method.The classical modal method has found widespread application in civil engineering practice because of its conceptual simplicity, ease of application and the insight it provides into the action of the system. The response spectrum variant of the method, which makes it possible to identify and consider only the dominant terms in the solution, is particularly useful for making rapid estimates of maximum response values.Viscously damped systems that do not satisfy the Caughey-OKelly condition generally have complexvalued natural modes. Such systems are said to be non-classically damped, and their response may be evaluated by a generalization of the modal superposition method due to Foss. ' Although well e~tablished,'-~ the generalized modal method has found only limited application in structural engineering practice. Several factors appear to have contributed to this: (a) the generalized method is Bro...

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confidence: 99%

Modal analysis of non‐classically damped linear systems

Veletsos

Ventura

1986

Earthq Engng Struct Dyn

218

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“…The difficulty lies in determining the frequency threshold above which modal-combination should be considered rigid and hence perfectly correlated. Saigal and Gupta (2007) presented a closed-form formulation to this problem, as well as a comprehensive summary of earlier efforts such as those of Kennedy (1979), Lindley and Yow (1980), Hadjian (1981), Singh and Mehta (1983), Gupta (1990), Singh and Maldonado (1991) and Der Kiureghian and Nakamura (1993), and interested readers are referred to that article for further information.…”

Section: Modal-combination Rulesmentioning

confidence: 97%

The use of modal-combination rules with cable-stayed bridges

Walker¹,

Stafford²

2010

Proceedings of the Institution of Civil Engineers - Bridge Engi

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Modal superposition techniques such as the responsespectrum method (RSM) can be used to quickly estimate the peak response of a structure to earthquake-induced vibration and, as such, are widely used in preliminary design. Modal-combination rules for use with the RSM are typically founded on assumptions of linear structural behaviour, well-separated natural modes, classical damping and stationary excitation. By contrast, the response of cable-stayed bridges is known to be nonlinear with three-dimensional orthogonal mode shapes that can be coupled and closely spaced. Furthermore, it is widely known that the use of stationary stochastic processes for modelling earthquake excitation is a firstorder approximation and there is thus sufficient reason to doubt the validity of the RSM for estimating the response of cable-stayed bridges. This paper critiques the historical development and theoretical consistency of popular modal-combination rules with a view to assessing their suitability for estimating the response of cable-stayed bridges and their relative performance is investigated using an example finite-element model. In many cases, the more sophisticated modal-combination rules can be reliably employed; however, numerous scenarios are envisaged where such rules are likely to be inaccurate and caution is advised against their use under these circumstances.

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“…Since the first formulation of the response spectrum concept by Biot and subsequent contributions by Housner, Housner et al, Hudson, several response spectrum‐based formulations have been proposed to estimate the peak linear response of structural systems to base excitation. These include the development of modal combination rules to directly combine various response spectrum ordinates (eg,) and the development of stochastic methods to account for the uncertainty associated with the time history of the excitation (eg,). These formulations involve the ordinates of the SA and SD spectra of the input ground motion most of the times, while there are a few formulations where the ordinates of the RSA (eg, see) and SV (eg, see) spectra may also be needed.…”

Section: Introductionmentioning

confidence: 99%

A new model for spectral velocity ordinates at long periods

Samdaria

Gupta

2017

Earthq Engng Struct Dyn

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SummaryThe estimation of peak linear response via elastic design (response) spectra continues to form the basis of earthquake-resistant design of structural systems in various codes of practice all over the world. Many response spectrum-based formulations of peak linear response require an additional input of the spectral velocity (SV) ordinates consistent with the specified seismic hazard. SV ordinates have been conventionally approximated by pseudo spectral velocity (PSV) ordinates, which are close to the SV ordinates only over the intermediate frequency range coinciding with the velocity-sensitive region. At long periods, PSV ordinates underestimate the SV ordinates, and this study proposes a formulation of a correction factor (>1) that needs to be multiplied by the PSV ordinates in order to close the gap between the two sets of ordinates. A simple model is proposed in the form of a power function in oscillator period to estimate this factor in terms of two governing parameters which are in turn estimated from two single-parameter scaling equations. The parameters considered for the scaling equations are (1) the period at which the PSV spectrum is maximized and (2) the rate of decay of the pseudo spectral acceleration (PSA) amplitudes at long periods. For a given damping ratio, four regression coefficients are determined for the scaling equations with the help of 205 ground motions recorded in western USA. A numerical study undertaken with the help of several design PSA spectra and ensembles of spectrum-compatible ground motions illustrates the effectiveness of the proposed correction factor, together with the proposed scaling models, in comparison with the PSV approximation in a variety of design situations. Both the input parameters mentioned above can be easily obtained from the specified design spectrum, and thus the proposed model is convenient to use. KEYWORDS design spectrum, pseudo spectral velocity, response spectrum method, scaling models, spectral velocity

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Seismic design response by an alternative SRSS rule

Cited by 29 publications

References 14 publications

Modal analysis of non‐classically damped linear systems

Modal analysis of non‐classically damped linear systems

The use of modal-combination rules with cable-stayed bridges

A new model for spectral velocity ordinates at long periods

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