Abstract: The paper deals with the classical fiber bundle model
of equal load sharing, sometimes referred to as the Daniels’ bundle
or the democratic bundle. Daniels formulated a multidimensional
integral and also a recursive formula for evaluation of the
strength cumulative distribution function. This paper describes
three algorithms for evaluation of the recursive formula and also
their implementations with source codes in the Python high-level
programming language. A comparison of the algorithms are provided
with respect to execution time. Analysis of orders of magnitudes of
addends in the recursion is also provided.
Abstract: The presented paper copes with an experimental evaluation of a model based on modified Weibull size effect theory. Classical statistical Weibull theory was modified by introducing a new parameter (correlation length lp) representing the spatial autocorrelation of a random mechanical properties of material. This size effect modification was observed on two different materials used in civil engineering: unreinforced (plain) concrete and multi-filament yarns made of alkaliresistant (AR) glass which are used for textile-reinforced concrete. The behavior under flexural, resp. tensile loading was investigated by laboratory experiments. A high number of specimens of different sizes was tested to obtain statistically significant data which were subsequently corrected and statistically processed. Due to a distortion of the measured displacements caused by the unstiff experiment device, only the maximal load values were statistically evaluated. Results of the experiments showed a decreasing strength with an increasing sample length. Size effect curves were obtained and the correlation length was fitted according to measured data. Results did not exclude the existence of the proposed new parameter lp.