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Publication# Random field-based modeling of size effect on the longitudinal tensile strength of clear timber

Thomas Keller, Anastasios Vassilopoulos, Alireza Farajzadeh Moshtaghin, Steffen Franke

2016

Journal paper

2016

Journal paper

Abstract

In the current study, a random field-based size effect model has been proposed for the longitudinal tensile strength of clear timber. Since the failure mode is brittle, the problem is basically an extreme value problem of finding the distribution of minima of strength fields for specimens of different volumes. The stochastic response has been evaluated based on the Monte Carlo method along with the weakest link theory. Within the framework of the spectral representation method, the Weibull distribution has been considered as the marginal distribution to generate realizations of the strength as a 3D random field. The squared exponential autocorrelation function has been used for the description of spatial variability. The error resulting from this model, as compared to existing experimental data in the literature, is much lower than that of the classical Weibull law. The results show that when one of the specimen's dimensions decreases to less than 10 times the correlation length of the strength field, the size effect starts to deviate from the classical size effect law. Moreover, a simple analytical approximation, which includes the correlation length as length scale, has been presented that facilitates the application of the proposed model. (C) 2015 Elsevier Ltd. All rights reserved.

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Strength of materials

The field of strength of materials (also called mechanics of materials) typically refers to various methods of calculating the stresses and strains in structural members, such as beams, columns, and shafts. The methods employed to predict the response of a structure under loading and its susceptibility to various failure modes takes into account the properties of the materials such as its yield strength, ultimate strength, Young's modulus, and Poisson's ratio.

Effect size

In statistics, an effect size is a value measuring the strength of the relationship between two variables in a population, or a sample-based estimate of that quantity. It can refer to the value of a statistic calculated from a sample of data, the value of a parameter for a hypothetical population, or to the equation that operationalizes how statistics or parameters lead to the effect size value. Examples of effect sizes include the correlation between two variables, the regression coefficient in a regression, the mean difference, or the risk of a particular event (such as a heart attack) happening.

Random variable

A random variable (also called random quantity, aleatory variable, or stochastic variable) is a mathematical formalization of a quantity or object which depends on random events. The term 'random variable' can be misleading as it is not actually random nor a variable, but rather it is a function from possible outcomes (e.g., the possible upper sides of a flipped coin such as heads and tails ) in a sample space (e.g., the set ) to a measurable space (e.g., in which 1 corresponding to and −1 corresponding to ), often to the real numbers.

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