Safety Estimation Method for Structures with Cumulative Damage
Publication: Journal of Engineering Mechanics
Volume 124, Issue 11
Abstract
Considering progressive weakening under repetitive events of loading, the proposed method estimates the safety probability for structures with cumulative damage. The structural damage is represented by a finite number of discrete states. The time evolution of damage is described by a Markov chain where the collapse corresponds to an absorbing state. Structural loading is defined as a discrete stochastic process of random events. This stochastic model can describe the seismic phenomenon as well as other environmental loads. A homogeneous Poisson process is used to model the random occurrences of the loading. To illustrate this method, the safety estimation of a masonry structure under seismic loading was performed. The obtained results are checked by a numerical simulation and compared with those of the classical analysis, which did not consider cumulative damage. The main features of the damage time evolution, the safety assessment, and the hazard function are pointed out.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Amin, M., and Ang, A. H.-S.(1968). “Nonstationary stochastic model of earthquake motions.”J. Engrg. Mech. Div., ASCE, 94(2), 559–583.
2.
Augusti, G., Baratta, A., and Casciati, F. (1984). Probabilistic methods in structural engineering. Chapman & Hall, Ltd., London.
3.
Banon, H., and Veneziano, D.(1982). “Seismic safety of reinforced concrete members and structures.”Earthquake Engrg. and Struct. Dyn., 10, 179–193.
4.
Bogdanoff, J. L., and Kozin, F. (1985). Probabilistic models of cumulative damage. John Wiley & Sons, Inc., New York. Design provision for earthquake resistance of structures . (1994). Eurocode 8. Eur. Prestandard, CEN (European Committee for Standardization), Bruxelles, Belgium.
5.
Feller, W. (1968). An introduction to probability theory and its applications. John Wiley & Sons, Inc., New York.
6.
Gumbel, E. J. (1958). Statistic of extreme. Columbia University Press, New York.
7.
Gusella, V.(1991a). “Estimation of extreme winds from short-term records.”J. Struct. Engrg., ASCE, 117(2), 375–390.
8.
Gusella, V.(1991b). “Structural failure and stochastic discrete process of random events: An application to seismic vulnerability analysis of an historic building.”Struct. Safety, Amsterdam, The Netherlands, 11, 13–28.
9.
Kanai, K.(1957). “Seismic-empirical formula for the seismic characteristics of the ground.”Bull. Earthquake Res. Inst., Tokyo Univ., Tokyo, Japan, 35, 309–325.
10.
Krawinkler, H., and Zohrei, M. (1983). “Cumulative damage in steel structures subjected to earthquake ground motion.”Comp. and Struct., 16(1–4), 531–541.
11.
Lomnitz, C.(1973). “Poisson process in earthquake studies.”Bull. Seismological Soc. of Am., 63(2), 735.
12.
Manson, S. S.(1965). “Fatigue: A complex problem subject—some simple approximation.”Experimental Mech., 5, 193–226.
13.
Meli, R. (1973). “Behavior of masonry walls under lateral loads.”Proc., 5th World Conf. on Earthquake Engrg., Edigraf, Rome Italy, Vol. 1, 853–862.
14.
Miner, M. A.(1945). “Cumulative damage in fatigue.”J. Appl. Mech., 12, 159–164.
15.
Newmark, N. M., and Rosenblueth, E. (1974). Fundamentals of earthquake engineering. Prentice-Hall, Inc., Englewood Cliffs, N.J.
16.
Park, Y. J.(1985). “Mechanistic seismic damage model for reinforced concrete.”J. Struct. Engrg., ASCE, 111(4), 722–739.
17.
Park, Y. J., Ang, A. H.-S., and Wen, Y. K.(1985). “Seismic damage of reinforced concrete buildings.”J. Struct. Engrg., ASCE, 111(4), 740–756.
18.
Richter, C. F. (1958). Elementary seismology. Freeman & Co., New York.
19.
Shinozuka, M., and Jan, C. M.(1972). “Digital simulation of random process and its applications.”J. Sound Vibr., 25(1), 111–128.
20.
Soog, T. T., and Grigoriu, M. (1992). Random vibration of mechanical and structural systems. Prentice-Hall, Inc., Englewood Cliffs, N.J.
21.
Tajimi, H. (1960). “A statistical method of determining the maximum response of a building structure during an earthquake.”Proc., 2nd World Conf. on Earthquake Engrg., Gakujutsu Bunken Fukyu-kai, Oh-Okayma, Meguro-ku, Tokyo, Japan, 781–798.
22.
Tassios, T. P. (1988). Meccanica delle murature. 1st Italian Ed., Liguori, Napoli, Italy (in Italian).
23.
Turnsek, V., and Cacovic, F. (1971). “Some experimental results on the strength of brick masonry walls.”Proc., 2nd Int. Brick Masonry Conf., British Ceramic Research Association, Stoke-on-Trent, U.K.,149–156.
24.
Turnsek, V., and Sheppard, P. (1980). “The shear and flexural resistance of masonry walls.”Proc., Int. Res. Conf. on Earthquake Engrg, Institute of Earthquake Engineering and Engineering Seismology, University Kiril and Metodij, Skopje, Macedonia, 121–126.
Information & Authors
Information
Published In
Copyright
Copyright © 1998 American Society of Civil Engineers.
History
Published online: Nov 1, 1998
Published in print: Nov 1998
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.