Abstract
This chapter presents methods for two significant reliability measures: safety index and probability of failure. Because of the iterative nature of calculating these measures, use of limit-state function approximations is a necessary aspect. However, efficient selection of suitable approximations at different stages of reliability analysis makes these tools practical for many large-scale engineering problems. Also, the physical interpretation of sensitivity factors as used in design is discussed. At the end of the chapter, several engineering problems are presented with corresponding results for use as test cases.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
4.4 References
Arora, J.S., Introduction to Optimum Design, Elsevier Academic Press, London, UK, 2004.
Bleistein, N., and Handelsman, R.A., “Asymptotic Expansions of Integrals,” Holt, Rinehart and Winston, New York, NY, 1975.
Breitung, K., “Asymptotic Approximations for Multinormal Integrals,” Journal of the. Engineering Mechanics Division, ASCE, Vol. 110, No. 3, Mar., 1984, pp 357–366.
Cai, G.Q., and Elishakoff, I., “Refined Second-order Approximations Analysis,” Structural Safety, Vol. 14, No. 4, April, 1994, pp. 267–276.
Der Kiureghian, A., Lin, H.Z., and Hwang, S.J., “Second Order Reliability Approximations,” Journal of Engineering Mechanics, ASCE, Vol. 113, 1987, pp. 1208–1225.
Freudenthal, A. M., Garrelts, J. M., and Shinozuka, M., “The Analysis of Structural Safety,” Journal of the Structural Division, ASCE, Vol. 92, No. ST1, 1966, pp. 267–325.
Grandhi, R.V., and Wang, L.P., Structural Reliability Analysis and Optimization: Use of Approximations, NASA CR-1999-209154, 1999.
Hasofer, A.M., and Lind, N.C., “Exact and Invariant Second-Moment Code Format,” Journal of the Engineering Mechanics Division, ASCE, 100(EM), 1974, pp.111–121.
Hohenbichler, M., and Rackwitz, R., “Improvement of Second-order Reliability Estimates by Importance Sampling,” Journal of the Engineering Mechanics Division, ASCE, Vol. 116, 1990, pp. 1183–1197.
Hohenbichler, M., and Rackwitz, R., “Non-normal Dependent Vectors in Structural Safety,” Journal of the Engineering Mechanics Division, ASCE, Vol. 107, No. EM6, Dec. 1981, pp.1227–1238.
Koyluoglu, H.U., and Nielsen, S.R.K., “New Approximations for SORM Integrals,” Structural Safety, Vol. 13, No. 4, April, 1994, pp. 235–246.
Madsen, H.O., Krenk, S., and Lind, N.C., Methods of Structural Safety, Prentice-Hall, Englewood Cliffs, New Jersey, 1986.
Melchers, R.E., Structural Reliability Analysis and Prediction, Ellis Horwood Limited, UK., 1987.
Millwater, H.R., Wu, Y-.T., and Cardinal, J.W., “Probabilistic Structural Analysis of Fatigue and Fracture,” AIAA-94-1507-CP, Proceedings of the 35th AIAA Structures, Structural Dynamics and Materials Conference, Hilton Head, SC, April, 1994.
Penmetsa, R.C., and Grandhi, R.V., “Adaptation of Fast Fourier Transformations to Estimate Structural Failure Probability,” Finite Elements in Analysis and Design, Vol. 39, No. 5, 2003, pp. 473–485.
Rosenblatt, M., “Remarks on a Multivariate Transformation,” The Annals of. Mathematical Statistics, Vol. 23, No. 3, 1952, pp. 470–472.
Todd, J., Survey of Numerical Analysis, McGraw Hill, NY, 1962.
Tvedt, L., “Two Second-order Approximations to the Failure Probability,” Section on. Structural Reliability, A/S Vertas Research, Hovik, Norway, 1984.
Tvedt, L., “Distribution of Quadratic Forms in Normal Space Applications to Structural Reliability,” Journal of the Engineering Mechanics Division, ASCE, Vol. 116, 1990, pp. 1183–1197.
Wang, L.P., and Grandhi, R.V., “Improved Two-point Function Approximation for Design Optimization,” AIAA Journal, Vol. 32, No. 9, 1995, pp. 1720–1727.
Rights and permissions
Copyright information
© 2007 Springer-Verlag London Limited
About this chapter
Cite this chapter
(2007). Methods of Structural Reliability. In: Reliability-based Structural Design. Springer, London . https://doi.org/10.1007/978-1-84628-445-8_4
Download citation
DOI: https://doi.org/10.1007/978-1-84628-445-8_4
Publisher Name: Springer, London
Print ISBN: 978-1-84628-444-1
Online ISBN: 978-1-84628-445-8
eBook Packages: EngineeringEngineering (R0)