### Abstract

Design for a specific ductile failure mode is assuming a rǒle of increasing importance for earthquake‐resistant structures. This necessitates an accurate assessment of the distribution of overstrength in the structure, in order that the predefined failure mode can be realized. Consequently, the variability of the response for a given variability in the salient material properties, such as yield strength for steel structures, should be assessed and accounted for. In this paper an analytical method is proposed for the evaluation of the probability density function of the response of a single‐degree‐of‐freedom hysteretic system with random parameters subject to a variable amplitude cyclic load history. A simple algorithm is derived which may be used to obtain the system response as a function of the system parameters. This response function may then be used to evaluate the displacement response probability density function when given the probability density function of the system parameters. Results derived from this procedure are verified against Monte Carlo simulation. It is shown that accurate response statistics are obtained at a fraction of the computing cost of simulation techniques.

Original language | English (US) |
---|---|

Pages (from-to) | 489-506 |

Number of pages | 18 |

Journal | Earthquake Engineering & Structural Dynamics |

Volume | 23 |

Issue number | 5 |

DOIs | |

State | Published - May 1994 |

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### All Science Journal Classification (ASJC) codes

- Geotechnical Engineering and Engineering Geology
- Earth and Planetary Sciences (miscellaneous)

### Cite this

*Earthquake Engineering & Structural Dynamics*,

*23*(5), 489-506. https://doi.org/10.1002/eqe.4290230503

}

*Earthquake Engineering & Structural Dynamics*, vol. 23, no. 5, pp. 489-506. https://doi.org/10.1002/eqe.4290230503

**An analytical solution for the probabilistic response of sdof non‐linear random systems subjected to variable amplitude cyclic loading.** / Manzocchi, G. M.E.; Chryssanthopoulos, M.; Elnashai, A. S.

Research output: Contribution to journal › Article

TY - JOUR

T1 - An analytical solution for the probabilistic response of sdof non‐linear random systems subjected to variable amplitude cyclic loading

AU - Manzocchi, G. M.E.

AU - Chryssanthopoulos, M.

AU - Elnashai, A. S.

PY - 1994/5

Y1 - 1994/5

N2 - Design for a specific ductile failure mode is assuming a rǒle of increasing importance for earthquake‐resistant structures. This necessitates an accurate assessment of the distribution of overstrength in the structure, in order that the predefined failure mode can be realized. Consequently, the variability of the response for a given variability in the salient material properties, such as yield strength for steel structures, should be assessed and accounted for. In this paper an analytical method is proposed for the evaluation of the probability density function of the response of a single‐degree‐of‐freedom hysteretic system with random parameters subject to a variable amplitude cyclic load history. A simple algorithm is derived which may be used to obtain the system response as a function of the system parameters. This response function may then be used to evaluate the displacement response probability density function when given the probability density function of the system parameters. Results derived from this procedure are verified against Monte Carlo simulation. It is shown that accurate response statistics are obtained at a fraction of the computing cost of simulation techniques.

AB - Design for a specific ductile failure mode is assuming a rǒle of increasing importance for earthquake‐resistant structures. This necessitates an accurate assessment of the distribution of overstrength in the structure, in order that the predefined failure mode can be realized. Consequently, the variability of the response for a given variability in the salient material properties, such as yield strength for steel structures, should be assessed and accounted for. In this paper an analytical method is proposed for the evaluation of the probability density function of the response of a single‐degree‐of‐freedom hysteretic system with random parameters subject to a variable amplitude cyclic load history. A simple algorithm is derived which may be used to obtain the system response as a function of the system parameters. This response function may then be used to evaluate the displacement response probability density function when given the probability density function of the system parameters. Results derived from this procedure are verified against Monte Carlo simulation. It is shown that accurate response statistics are obtained at a fraction of the computing cost of simulation techniques.

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U2 - 10.1002/eqe.4290230503

DO - 10.1002/eqe.4290230503

M3 - Article

AN - SCOPUS:0028184453

VL - 23

SP - 489

EP - 506

JO - Earthquake Engineering and Structural Dynamics

JF - Earthquake Engineering and Structural Dynamics

SN - 0098-8847

IS - 5

ER -