Specimen length effect on parameter estimation in modelling fatigue strength by Weibull distribution

Abstract The paper deals with the problem of estimating the S–N field based on samples with different lengths and testing the hypothesis of length independence of fatigue lifetimes. A Weibull model developed by Castillo et al. is used to discuss the problem and analyze two data samples of prestressing wires and prestressing strands. The analysis shows that in the first case the length independence assumption cannot be accepted while for the second case length independence seems to be a reasonable assumption. This shows that every case must be analyzed separately and that assuming length independence can lead to unsafe design.

[1]  J. Aczél,et al.  Lectures on Functional Equations and Their Applications , 1968 .

[2]  C. L. Hulsbos,et al.  Fatigue Properties of Prestressing Strand , 1966 .

[3]  Ali S. Hadi,et al.  Modeling lifetime data with application to fatigue models , 1995 .

[4]  Enrique Castillo,et al.  Lifetime regression models based on a functional equation of physical nature , 1987, Journal of Applied Probability.

[5]  W. Ames.  Mathematics in Science and Engineering , 1999 .

[6]  Bradford D. Allen.  Building and solving mathematical programming models inengineering and science by Enrique Castillo, Antonio J. Conejo,Pablo Pedregal, Ricardo Garcia, and Natalia Alguacil , 2002 .

[7]  R. H. R. Tide,et al.  A statistical study of the static and fatigue properties of high strength prestressing strand, M.S. Thesis, Lehigh University, 1966 , 1966 .

[8]  Ali S. Hadi,et al.  Extreme Value and Related Models with Applications in Engineering and Science , 2004 .

[9]  F. Massey,et al.  Introduction to Statistical Analysis , 1970 .

[10]  Alfonso Fernández-Canteli,et al.  A general regression model for lifetime evaluation and prediction , 2001 .

[11]  Enrique Castillo,et al.  Functional Equations in Applied Sciences , 2004 .

[12]  A D Edwards,et al.  FATIGUE CHARACTERISTICS OF PRESTRESSING STRAND. , 1972 .

[13]  Enrique Castillo,et al.  Building and Solving Mathematical Programming Models in Engineering and Science , 2001 .

[14]  Ali S. Hadi,et al.  On fitting a fatigue model to data , 1999 .

[15]  M. Chernick.  Wiley Series in Probability and Statistics , 2007 .

[16]  Anthony C. Davison,et al.  Bootstrap Methods and Their Application , 1998 .

[17]  Bruno Thürlimann,et al.  Ermüdungsfestigkeit von Bewehrungs- und Spannstählen , 1984 .

[18]  S. T. Buckland,et al.  An Introduction to the Bootstrap. , 1994 .