First-order second-moment approximation in reliability of structural systems: Critical review and alternative approach

Abstract The objective of the paper is to present and discuss the methods originated from the first-order second-moment approximation that are commonly used in the reliability analysis of structural systems. The approach is formulated as an optimization problem. The consequences of this formulation and some objections concerning the methods are investigated and illustrated on the examples. The lack of uniqueness and some difficulties with error estimation are considered as the main disadvantages of the approach. An alternative approach is given for the independent random variables. The approach yields the upper and lower bounds for the structural reliability. Its application is presented in the case of the linear conditions of structural failure. It is shown that the bounds remain sometimes a sole verification of the correctness of the first-order second-moment approximation.

[1]  C. Cornell.  Bounds on the Reliability of Structural Systems , 1967 .

[2]  N. Lind.  Optimal Reliability Analysis by Fast Convolution , 1979 .

[3]  Alfred M. Freudenthal,et al.  SAFETY AND THE PROBABILITY OF STRUCTURAL FAILURE , 1956 .

[4]  harald Cramer,et al.  Stationary And Related Stochastic Processes , 1967 .

[5]  R. Rackwitz,et al.  Non-Normal Dependent Vectors in Structural Safety , 1981 .

[6]  Niels C. Lind,et al.  FORMULATION OF PROBABILISTIC DESIGN , 1977 .

[7]  O. Ditlevsen.  Narrow Reliability Bounds for Structural Systems , 1979 .

[8]  R. Rackwitz,et al.  Quadratic Limit States in Structural Reliability , 1979 .

[9]  A. Ang,et al.  Analysis of Activity Networks under Uncertainty , 1975 .

[10]  O. Ditlevsen.  Generalized Second Moment Reliability Index , 1979 .

[11]  Ove Ditlevsen,et al.  Principle of Normal Tail Approximation , 1981 .

[12]  G. I. Schuëller,et al.  Benchmark study on methods to determine collapse failure probabilities of redundant structures , 1982 .

[13]  Z. Šidák.  ON MULTIVARIATE NORMAL PROBABILITIES OF RECTANGLES: THEIR DEPENDENCE ON CORRELATIONS' , 1968 .

[14]  A. M. Hasofer,et al.  Exact and Invariant Second-Moment Code Format , 1974 .

[15]  M. Rosenblatt.  Remarks on a Multivariate Transformation , 1952 .

[16]  A. H-S. Ang,et al.  Reliability Analysis of Redundant Ductile Structural Systems , 1981 .

[17]  C. Dunnett,et al.  Approximations to the probability integral and certain percentage points of a multivariate analogue of Student's t-distribution* , 1955 .