Evaluation of Load Values Using the Gumbel Model

Open access

Abstract

The paper deals with application of the Gumbel model to evaluation of the environmental loads. According to recommendations of Eurocodes, the conventional method of determining return period and characteristic values of loads utilizes the theory of extremes and implicitly assumes that the cumulative distribution function of the annual or other basic period extremes is the Gumbel distribution. However, the extreme value theory shows that the distribution of extremes asymptotically approaches the Gumbel distribution when the number of independent observations in each observation period from which the maximum is abstracted increases to infinity. Results of calculations based on simulation show that in practice the rate of convergence is very slow and significantly depends on the type of parent results distribution, values of coefficient of variation, and number of observation periods. In this connection, a straightforward purely empirical method based on fitting a curve to the observed extremes is suggested.

References

  • 1. PN-EN 1990 Eurocode: Basis of structural design, PKN, Warsaw 2004.

  • 2. ISO 2394 - 1998 (E). General principles on reliability for structures.

  • 3. PN-EN 1991 Eurocode 1: Actions on structures, PKN, Warsaw 2005.

  • 4. E.J. Gumbel, Statistics of extremes. Columbia Univ. Press, New York, 1958.

  • 5. M. Fisz, Probability and PWN, Warsaw, edition II, 1958.

  • 6. J.R. Benjamin, C.A. Cornell, Probability, Statistics and Decision for Civil Engineers, WNT, Warsaw 1977.

  • 7. B. Ellingwood, R. Redfield, Ground snow loads for structural design. Journal of Structural Engineering, ASCE, 109, 4, 1983, 950-964.

  • 8. PN-EN 1991-1-3 Eurocode 1: Actions on structures. Part 1-3: General actions- Snow loads, PKN, Warsaw 2005.

  • 9. B. Mrozek, Z. Mrozek, Matlab and Simulink. Helion, Gliwice 2004.

  • 10. J. Murzewski, Reliabibility of structures, Arkady, Warsaw, 1989.

  • 11. IMiGW Statistic yearbooks of precipitation 1950-2000.

Archives of Civil Engineering

The Journal of Polish Academy of Sciences

Journal Information


SCImago Journal Rank (SJR): 0.251
Source Normalized Impact per Paper (SNIP): 0.521

Metrics

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 7 7 7
PDF Downloads 3 3 3