### Abstract

The floor response spectrum is the maximum response of a single degree of freedom oscillator (secondary structure) with varying frequency attached to the degree of freedom (floor) of interest in the primary structure. In general, the two available approaches for calculating floor response spectra, given the ground spectra (or an ensemble of base excitations), are: A) time history (TH) and b) floor spectrum generation (FSG). In the time history approach, one uses a set of base excitations corresponding to a given ground motion spectrum (or uses a given ensemble of base excitations) in a series of time history analyses to find a set of floor response spectra. To find the final floor response spectrum one then averages over this set to obtain a smooth spectrum. The floor spectrum generation approach on the other hand is an efficient method which avoids the time history analysis of the composite system while accounting for the various effects such as tuning, interaction as well as the non-classical damping in the composite system. In this paper we study the variability in the floor response spectra generated using TH approach, both theoretically and numerically.We do this for a special case in which oscillator and structure comprise a perfectly tuned primary-secondary (PS) system. To this end we use Gaussian approximations along with some previously derived expressions for covariances of modal responses (Sinha & Igusa 1995) to derive closed form expressions for the variance of sample correlation coefficient between modal responses. These expressions involve damping and frequency characteristics of the composite system as well as its tuning and the duration of the input excitation.We then combine these expressions with other results on mean square response of structures to random excitations (Der Kiureghian 1980, Sinha & Igusa 1995) to estimate the variability in the floor response spectra.

Original language | English (US) |
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Title of host publication | Safety, Reliability, Risk and Life-Cycle Performance of Structures and Infrastructures - Proceedings of the 11th International Conference on Structural Safety and Reliability, ICOSSAR 2013 |

Pages | 3043-3048 |

Number of pages | 6 |

State | Published - Dec 1 2013 |

Event | 11th International Conference on Structural Safety and Reliability, ICOSSAR 2013 - New York, NY, United States Duration: Jun 16 2013 → Jun 20 2013 |

### Other

Other | 11th International Conference on Structural Safety and Reliability, ICOSSAR 2013 |
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Country | United States |

City | New York, NY |

Period | 6/16/13 → 6/20/13 |

### Fingerprint

### ASJC Scopus subject areas

- Civil and Structural Engineering
- Safety, Risk, Reliability and Quality

### Cite this

*Safety, Reliability, Risk and Life-Cycle Performance of Structures and Infrastructures - Proceedings of the 11th International Conference on Structural Safety and Reliability, ICOSSAR 2013*(pp. 3043-3048)

**Statistical analysis of variability in floor response spectra using random vibration theory.** / Tootkaboni, M.; Louhghalam, A.; Igusa, Takeru.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Safety, Reliability, Risk and Life-Cycle Performance of Structures and Infrastructures - Proceedings of the 11th International Conference on Structural Safety and Reliability, ICOSSAR 2013.*pp. 3043-3048, 11th International Conference on Structural Safety and Reliability, ICOSSAR 2013, New York, NY, United States, 6/16/13.

}

TY - GEN

T1 - Statistical analysis of variability in floor response spectra using random vibration theory

AU - Tootkaboni, M.

AU - Louhghalam, A.

AU - Igusa, Takeru

PY - 2013/12/1

Y1 - 2013/12/1

N2 - The floor response spectrum is the maximum response of a single degree of freedom oscillator (secondary structure) with varying frequency attached to the degree of freedom (floor) of interest in the primary structure. In general, the two available approaches for calculating floor response spectra, given the ground spectra (or an ensemble of base excitations), are: A) time history (TH) and b) floor spectrum generation (FSG). In the time history approach, one uses a set of base excitations corresponding to a given ground motion spectrum (or uses a given ensemble of base excitations) in a series of time history analyses to find a set of floor response spectra. To find the final floor response spectrum one then averages over this set to obtain a smooth spectrum. The floor spectrum generation approach on the other hand is an efficient method which avoids the time history analysis of the composite system while accounting for the various effects such as tuning, interaction as well as the non-classical damping in the composite system. In this paper we study the variability in the floor response spectra generated using TH approach, both theoretically and numerically.We do this for a special case in which oscillator and structure comprise a perfectly tuned primary-secondary (PS) system. To this end we use Gaussian approximations along with some previously derived expressions for covariances of modal responses (Sinha & Igusa 1995) to derive closed form expressions for the variance of sample correlation coefficient between modal responses. These expressions involve damping and frequency characteristics of the composite system as well as its tuning and the duration of the input excitation.We then combine these expressions with other results on mean square response of structures to random excitations (Der Kiureghian 1980, Sinha & Igusa 1995) to estimate the variability in the floor response spectra.

AB - The floor response spectrum is the maximum response of a single degree of freedom oscillator (secondary structure) with varying frequency attached to the degree of freedom (floor) of interest in the primary structure. In general, the two available approaches for calculating floor response spectra, given the ground spectra (or an ensemble of base excitations), are: A) time history (TH) and b) floor spectrum generation (FSG). In the time history approach, one uses a set of base excitations corresponding to a given ground motion spectrum (or uses a given ensemble of base excitations) in a series of time history analyses to find a set of floor response spectra. To find the final floor response spectrum one then averages over this set to obtain a smooth spectrum. The floor spectrum generation approach on the other hand is an efficient method which avoids the time history analysis of the composite system while accounting for the various effects such as tuning, interaction as well as the non-classical damping in the composite system. In this paper we study the variability in the floor response spectra generated using TH approach, both theoretically and numerically.We do this for a special case in which oscillator and structure comprise a perfectly tuned primary-secondary (PS) system. To this end we use Gaussian approximations along with some previously derived expressions for covariances of modal responses (Sinha & Igusa 1995) to derive closed form expressions for the variance of sample correlation coefficient between modal responses. These expressions involve damping and frequency characteristics of the composite system as well as its tuning and the duration of the input excitation.We then combine these expressions with other results on mean square response of structures to random excitations (Der Kiureghian 1980, Sinha & Igusa 1995) to estimate the variability in the floor response spectra.

UR - http://www.scopus.com/inward/record.url?scp=84892406907&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84892406907&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84892406907

SN - 9781138000865

SP - 3043

EP - 3048

BT - Safety, Reliability, Risk and Life-Cycle Performance of Structures and Infrastructures - Proceedings of the 11th International Conference on Structural Safety and Reliability, ICOSSAR 2013

ER -