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Research Papers

Interval Fractile Levels for Stationary Stochastic Response of Linear Structures With Uncertainties

[+] Author and Article Information
Giuseppe Muscolino

Mem. ASME
Department of Civil, Building and Environmental Engineering with Information Technology and Applied Mathematics,
University of Messina,
Villaggio S. Agata, 98166 Messina, Italy
e-mail: gmuscolino@unime.it

Roberta Santoro

Department of Civil, Building and Environmental Engineering with Information Technology and Applied Mathematics,
University of Messina,
Villaggio S. Agata, 98166 Messina, Italy
e-mail: roberta.santoro@unime.it

Alba Sofi

Department of Civil, Energy, Environmental and Materials Engineering,
University “Mediterranea” of Reggio Calabria, Via Graziella, Località Feo di Vito, 89124 Reggio Calabria, Italy
e-mail: alba.sofi@unirc.it

Manuscript received September 23, 2014; final manuscript received March 6, 2015; published online November 20, 2015. Assoc. Editor: Michael Beer.

ASME J. Risk Uncertainty Part B 2(1), 011004 (Nov 20, 2015) (11 pages) Paper No: RISK-14-1058; doi: 10.1115/1.4030455 History: Received September 23, 2014; Accepted April 27, 2015

In the framework of stochastic analysis, the extreme response value of a structural system is completely described by its CDF. However, the CDF does not represent a direct design provision. A more meaningful parameter is the response level which has a specified probability, p, of not being exceeded during a specified time interval. This quantity, which is basically the inverse of the CDF, is referred to as a fractile of order p of the structural response. This study presents an analytical procedure for evaluating the lower bound and upper bound of the fractile of order p of the response of linear structures, with uncertain stiffness properties modeled as interval variables subjected to stationary stochastic excitations. The accuracy of the proposed approach is demonstrated by numerical results concerning a wind-excited truss structure with uncertain Young’s moduli.

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Figures

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Fig. 1

Sketch of the UB and LB of the peak factor CDF and interval fractile of orderp

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Fig. 2

Truss structure under wind excitation

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Fig. 3

Comparison between the exact and proposed bounds of the interval fractilesZU1maxI(p,T) of the horizontal displacement U1maxI(T) of order (a) p=0.5 and (b) p=0.95 versus Δα(T=1000T0)

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Fig. 4

Comparison between the exact and proposed bounds of the interval fractilesZU7maxI(p,T) of the horizontal displacement U7maxI(T) of order (a) p=0.5 and (b) p=0.95 versus Δα(T=1000T0)

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Fig. 5

Absolute PEs affecting the proposed bounds of the interval fractiles (a) ZU1maxI(p,T) and (b) ZU7maxI(p,T) of order p=0.5 and p=0.95 versus Δα(T=1000T0)

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Fig. 6

Comparison between the exact and proposed bounds of the interval fractiles (a) ZU1maxI(p,T) and (b) ZU7maxI(p,T) of order p=0.5 and p=0.95 versus T/T0 (Δα=0.2)

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