Measures of Structural Safety Under Imperfect States of Knowledge
Publication: Journal of Structural Engineering
Volume 115, Issue 5
Abstract
In assessing structural safety, the state of knowledge is imperfect when uncertainties arise from estimation error or model imperfection. The nature of these uncertainties is fundamentally different from those arising from inherent variabilities. A reliability index under such conditions is a point estimator of safety. Motivated by needs in structural code development, a set of fundamental requirements on the point‐estimator reliability index are formulated. Existing definitions of the reliability index are examined in this light and are found to be deficient in satisfying one or more of the requirements. Based on concepts from Bayesian statistical decision theory, a new reliability index is introduced which satisfies all the stipulated requirements. The index recognizes the fundamental difference between the sources of uncertainty and provides a rational basis for the assessment of structural safety and for development of reliability‐based codes under arbitrary states of knowledge. Methods are also developed for quantifying the uncertainty in the measure of safety arising from the imperfect state of knowledge. Existing reliability methods can be used to compute the probability distribution or variance of the safety measure. A simple example illustrates the main concepts of the paper.
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References
1.
Ang, A. H‐S., and Cornell, C. A. (1974). “Reliability bases of structural safety and design.” J. Struct. Engrg., ASCE, 100(9), 1755–1769.
2.
Ang, A. H‐S., and Tang, W. H. (1975). Probability concepts in engineering planning and design. Vol. I, John Wiley & Sons, Inc., New York, N.Y.
3.
Ang, A. H‐S., and Tang, W. H. (1984). Probability concepts in engineering planning and design. Vol. II, John Wiley & Sons, Inc., New York, N.Y.
4.
Bjerager, P. (1988). “Probability integration by directional simulation.” J. Engrg. Mech., ASCE, 114(8), 1285–1302.
5.
Box, G. E. P., and Tiao, G. C. (1973). Bayesian inference in statistical analysis. Addison‐Wesley Pub. Co., Inc., Reading, Mass.
6.
Brown, C. B. (1979). “A fuzzy safety measure.” J. Engrg. Mech., ASCE, 105(5), 855–872.
7.
“Common unified rules for different types of construction and material.” (1978). Bulletin D'Information No. 124E. Comite Euro‐International du Beton (CEB), Paris, France.
8.
Cornell, C. A. (1969). “A probability‐based structural code.” J. of Am. Concrete Inst., 66(12), 974–985.
9.
Der Kiureghian, A., and Liu, P.‐L. (1986). “Strutural reliability under incomplete probability information.” J. Engrg. Mech., ASCE, 112(1), 85–104.
10.
Der Kiureghian, A., Lin, H.‐Z., and Hwang, S.‐J. (1987). “Second‐order reliability approximations.” J. Engrg. Mech., ASCE, 113(8), 1208–1225.
11.
Ditlevsen, O. (1973). “Structural reliability and the invariance problem.” Research Report No. 22, Solid Mech. Div., Univ. of Waterloo, Waterloo, Canada.
12.
Ditlevsen, O. (1979). “Generalized second moment reliability index.” J. Struct. Mech., 7(4), 435–451.
13.
Ditlevsen, O. (1981). Uncertainty modeling. McGraw‐Hill, New York, N.Y.
14.
Ditlevsen, O. (1982). “Model uncertainty in structural reliability.” Struct. Safety, 1(1), 73–86.
15.
Greimann, L. F., Knapp, W. J., and Yeung, J. Y. (1984). “Propagation of certainty levels.” J. Struct. Engrg., ASCE, 110(9), 1935–1948.
16.
Hasofer, A. M., and Lind, N. C. (1974). “Exact and invariant second‐moment code format.” J. Engrg. Mech., ASCE, 100(1), 111–121.
17.
Liu, P‐L., and Der Kiureghian, A. (1986). “Optimization algorithms for structural reliability analysis.” Report No. UCB/SESM‐86/09, Dept. of Civ. Engrg., Univ. of Calif., Berkeley, Calif.
18.
Madsen, H. O., Krenk, S., and Lind, N. C. (1986). Methods of structural safety, Prentice‐Hall, Inc., Englewood Cliffs, N.J.
19.
Ravindra, M. K., and Galambos, T. V. (1978). “Load and resistance factor design for steel.” J. Struct. Engrg., ASCE, 104(9), 1337–1353.
20.
Schueller, G. I., Bucher, C. G., Bourgund, U., and Ouypomprasert, W. (1987). “On efficient computational schemes to calculate structural failure probabilities.” Stochastic structural mechanics, Y. K. Lin and G. I. Schueller, eds., Lecture notes in engineering, Springer Verlag, 31, 388–410.
21.
Shinozuka, M. (1983). “Basic analysis of structural safety.” J. Struct. Engrg., ASCE, 109(3), 721–740.
22.
Veneziano, D. (1979). “New index of reliability.” J. Engrg. Mech., ASCE, 105(5), 277–296.
23.
Winterstein, S., and Bjerager, P. (1987). “The use of higher moments in reliability estimation.” Proc. of the 5th Int. Conf. on Appl. of Stat, and Prob. in Soil and Struct. Engrg., Vancouver, B.C., Canada, 2, 1027–1036.
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Copyright © 1989 ASCE.
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Published online: May 1, 1989
Published in print: May 1989
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