Peak Factor–Based Modal Combination Rule of Response-Spectrum Method for Peak Floor Accelerations

Pal, Ashish; Gupta, Vinay K.

doi:10.1061/(asce)st.1943-541x.0003044

Cited by 8 publications

(5 citation statements)

References 22 publications

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“…However, it should be noted that 12 showed that this approximation is not always adequate and for those cases they proposed empirical correction factors. A similar observation was more recently made by Pal and Gupta 18 . Assuming the ratios of peak factors to be equal to one, Equation () reduces to

\begin{equation} \left\{ {{r_{max}}\left( t \right)} \right\} = \left[ {{{\left\{ {re{s^2}} \right\}}_{\left( n \right)}}PG{A^2} + \mathop \sum \limits_{i = 1}^n \mathop \sum \limits_{j = 1}^n {{\left\{ {{r^{st}}} \right\}}_i} \circ {{\left\{ {{r^{st}}} \right\}}_j}{\rho _{i,j}}\ {S_{a,i}}\ {S_{a,j}}\ + \ 2{{\left\{ {res} \right\}}_{\left( n \right)}} \circ PGA\mathop \sum \limits_{i = 1}^n {{\left\{ {{r^{st}}} \right\}}_i}\ {\rho _{i,g}}\ {S_{a,i}}\ } \right]^{1/2} \end{equation}

…”

Section: Formulationsupporting

confidence: 88%

“…also developed a similar RSA for estimating peak absolute acceleration but using nonlinear optimization techniques in combination with regression methods. More recently, Pal and Gupta 18 developed a modal combination rule based on the extended version of CQC to estimate PFA very similar to that of Taghavi and Miranda and similarly to the work of those authors, they also studied the influence ratio of peak factor arriving to similar conclusions.…”

Section: Introductionmentioning

confidence: 82%

“…A similar observation was more recently made by Pal and Gupta. 18 Assuming the ratios of peak factors to be equal to one, Equation ( 16) reduces to…”

Section: Formulationmentioning

confidence: 99%

“…𝜌 𝑖,𝑗 = 1 − (1 − 1.1𝜉) 𝑒 −(0.001+0.033𝜉) min (𝑓𝑖 ,𝑓 𝑗 ) 1.97 (18) For modes whose frequencies are well separated, one can use the blue lower bound curve shown in Figure 3A to get a fairly good estimate of the correlation between them. This blue curve is the average of the maximum and minimum envelope of all the lower-bound correlation curves and is represented by Equation ( 18) which is similar to that proposed by [11][12][13] but now based on the frequency content of vertical components as opposed to horizontal components used in that study and for the range of frequencies of interest (0.1 to 50 Hz).…”

Section: Empirical Correlations Using Recorded Ground Motionsmentioning

confidence: 99%

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Response spectrum method for structures subjected to vertical ground motions: Absolute acceleration method

Acosta

Miranda

Deierlein

2023

Earthq Engng Struct Dyn

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Although a wide variety of response spectrum methods have been developed to estimate peak horizontal building responses, much less attention has been devoted to study the applicability of those methods for the vertical direction or to develop new methods to estimate peak vertical building responses. Vertical building responses can be significant for structures located close to the earthquake rupture, and for buildings with fundamental period of vibration within the range of most energy content of the vertical component of the ground motion (typically 0.05 to 0.15 s). The frequency content of the vertical component is significantly different to that in the horizontal components; thus, it is not clear if previous methods are applicable. We present a new alternative response spectrum analysis (RSA) method to estimate absolute accelerations in the vertical direction, which is a modified version of a previously studied modal combination rule developed for the horizontal components of motion. This formulation is derived based on the use of modal absolute accelerations, and we compare it to the traditional complete quadratic combination (CQC). In the proposed method, we develop simplified equations to estimate the necessary correlation coefficients for the vertical direction which are calibrated to fit empirical correlations computed from the vertical response of single degree of freedom systems subjected to a set of 90 vertical components of recorded ground motions. We also compute these correlations by using an improved power spectral density (PSD) function, which is as an enhanced version of the modified Kanai‐Tajimi PSD to represent the frequency content in the vertical direction which differs from that in the horizontal direction. To evaluate the proposed modal combination rule, we compare the RSA results to those obtained using response history analyses (RHA) of peak responses for a simplified model consisting of a prismatic bar fixed only at one end, as well as for 2D frames. We show that the proposed modal combination rule can estimate peak building responses with higher accuracy than the commonly used CQC modal combination rule, for any general building configuration at any structural location.

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\begin{equation} \left\{ {{r_{max}}\left( t \right)} \right\} = \left[ {{{\left\{ {re{s^2}} \right\}}_{\left( n \right)}}PG{A^2} + \mathop \sum \limits_{i = 1}^n \mathop \sum \limits_{j = 1}^n {{\left\{ {{r^{st}}} \right\}}_i} \circ {{\left\{ {{r^{st}}} \right\}}_j}{\rho _{i,j}}\ {S_{a,i}}\ {S_{a,j}}\ + \ 2{{\left\{ {res} \right\}}_{\left( n \right)}} \circ PGA\mathop \sum \limits_{i = 1}^n {{\left\{ {{r^{st}}} \right\}}_i}\ {\rho _{i,g}}\ {S_{a,i}}\ } \right]^{1/2} \end{equation}

…”

Section: Formulationsupporting

confidence: 88%

Section: Introductionmentioning

confidence: 82%

“…A similar observation was more recently made by Pal and Gupta. 18 Assuming the ratios of peak factors to be equal to one, Equation ( 16) reduces to…”

Section: Formulationmentioning

confidence: 99%

Section: Empirical Correlations Using Recorded Ground Motionsmentioning

confidence: 99%

See 2 more Smart Citations

Response spectrum method for structures subjected to vertical ground motions: Absolute acceleration method

Acosta

Miranda

Deierlein

2023

Earthq Engng Struct Dyn

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show abstract

“…It is likely that a few of the 16 strong‐motion duration definitions considered here would be close contenders in meeting these objectives, and therefore it will be useful to consider a quantitative measure to arrive at the most appropriate strong‐motion duration definition in the present context. To this end, the parameter

{E}_{d}

proposed by Pal and Gupta 14 to quantify the nonstationarity of a ground motion is considered here. This parameter measures the RMS deviation of the temporal variation of cumulative energy in the given motion from that in a fictitious stationary motion of the same total duration

{T}_{t}

.…”

Section: Comparison Of Strong‐motion Duration Definitionsmentioning

confidence: 99%

Duration and damping for ground motion characterization in frequency‐domain damage estimation of SDOF structures

Naqvi,

Gupta

2023

Earthquake Engineering and Resilience

Self Cite

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In estimating the damage to a single‐degree‐of‐freedom (SDOF) structure due to multiple earthquake events, it may be convenient to use a frequency‐based approach, in which the anticipated ground motions are characterized through power spectral density functions (PSDFs) compatible with the specified design spectra for those motions. Since a spectrum‐compatible PSDF corresponds to a fictitious stationary ground motion process of a specified duration, the duration of this process should preferably be same as the length of the stationary segment in the actual ground acceleration process for a meaningful computation of the stochastic response. On assuming the strong‐motion segment of a given ground motion to represent its stationary segment, the nonstationarity of the strong‐motion segment is evaluated for the existing strong‐motion duration definitions. It is found that the Trifunac‐Brady definition is the most reasonable strong‐motion duration definition in respect of consistently giving the longest strong‐motion segment with least nonstationarity. Further, a spectrum‐compatible PSDF can be used for estimating the stochastic response of a linear system, provided the system has the same damping ratio as that of the design spectrum from which the PSDF has been computed. This causes errors in estimating the peak response of an equivalent linear system due to its damping ratio being higher than the initial damping ratio of the nonlinear system. To address this, an empirical expression is developed for the modified damping ratio of a linear system, which would lead to the correct peak response of the system on using the PSDF obtained from the 5%‐damping design spectrum.

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Estimation of inelastic displacement ratio spectrum for existing RC structures via displacement response spectrum

Dadheech,

Gupta

2024

Earthq Engng Struct Dyn

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In the present seismic design philosophy, the structures are designed to remain within the specified displacement limits for multiple earthquake hazard levels expected during their design life. Accordingly, the estimation of maximum inelastic displacement demand in a structure consistent with a given hazard level is of primary importance. Considering the complexity and inconvenience associated with the nonlinear response history analyses for a suite of hazard‐consistent ground motions, it is preferred to estimate the maximum inelastic displacement demand by using the scaling models available for the inelastic displacement ratio in the single‐degree‐of‐freedom (SDOF) structures. In this study, a new scaling model is developed for the inelastic displacement ratio spectrum for a given response reduction factor R in the case of 5%‐initial damping Bouc‐Wen‐Baber‐Noori (BWBN) oscillators with stiffness and strength degradations and pinching. This model is based on the observed similarities between the spectrum and the reciprocal of given displacement response SD() spectrum in most cases, and thus, this indirectly accounts for the effects of seismological and site parameters. A new strong‐motion duration definition is also proposed to identify shorter strong‐motion segments of comparable relevance, and on using this definition, it is shown that the dependence of the mean spectrum on strong‐motion duration may be considered negligible. Accordingly, the regression parameters of the proposed scaling model for spectrum are estimated as the exponential functions of only five governing BWBN parameters. The best‐fit estimates of the regression coefficients of the resulting prediction equations are obtained for three values of R. The residual error spectra are also modeled to estimate the spectrum for a given confidence level. The proposed scaling model can be applied to a wide range of existing reinforced concrete (RC) structures with 5% initial damping by using the input of the design displacement spectrum and BWBN parameters.

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Peak Factor–Based Modal Combination Rule of Response-Spectrum Method for Peak Floor Accelerations

Cited by 8 publications

References 22 publications

Response spectrum method for structures subjected to vertical ground motions: Absolute acceleration method

Response spectrum method for structures subjected to vertical ground motions: Absolute acceleration method

Duration and damping for ground motion characterization in frequency‐domain damage estimation of SDOF structures

Estimation of inelastic displacement ratio spectrum for existing RC structures via displacement response spectrum

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