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The log-normal distribution: A better fitness for the results of mechanical testing of materials

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Abstract

According to present regulations, the characteristic value of a property of a material is calculated assuming the population is normally distributed. Here it is shown that this assumption is only a good approximation to the real distribution of values when coefficients of variation are low, but that it fails when that coefficient is higher than 0.25, if the variable ranges between 0 and +∞. It is also shown that the log-normal distribution is an accurate approach to the true distribution of values, both for low and high coefficients of variation. An analysis of the relevant features of both the normal and log-normal distribution functions is performed. Likewise both functions are applied to six different sets of experimental results of materials tests and the characteristic values obtained are compared. An easy method developed to compute the characteristic value under the assumption of a log-normal distribution is finally presented.

Résumé

Selon les règlements actuels, la valeur caractéristique d'une propriété d'un matériau est évaluée sur l'hypothèse que la population est normalement distribuée. On montre ici que ce n'est là qu'une bonne approximation de la distribution réelle des valeurs si les coefficients de variation sont faibles, mais qui cesse d'être effective avec un coefficient supérieur à 0,25 lorsque les variables sont comprises entre 0 et +∞. On montre aussi que la distribution lognormale serre de plus près la distribution réelle des valeurs tant pour les coefficients de variation faibles qu'élevés.

Il a été procédé à une analyse des caractéristiques significatives des fonctions de distribution normales et log-normales. L'une et l'autre fonctions ont été appliquées à six séries différentes de résultats d'essais de matériaux et les valeurs caractéristiques ont été comparées. Enfin, on a mis au point une ,éthode pratique de calcul de la valeur caractéristique dans l'hypothèse d'une distribution log-normale.

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Authors and Affiliations

  1. Building Materials Division, National Institute of Industrial Technology (INTI), Buenos Aires, Argentina

    R. J. Torrent (Civil Engineer)

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  1. R. J. Torrent
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Torrent, R.J. The log-normal distribution: A better fitness for the results of mechanical testing of materials. Mat. Constr. 11, 235–245 (1978). https://doi.org/10.1007/BF02551768

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  • DOI: https://doi.org/10.1007/BF02551768

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