THE FEATURES OF STOCHASTIC CALCULATON OF THE ECCENTRIC COMPRESSION ELEMENTS
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Keywords:
reliability, coefficient of the critical factor, stability factor under the eccentric compressionAbstract
The paper deals with a stochastic calculation of the coefficient of the critical factor. The elements of steel storage capacities, which operate on the eccentric compression, were calculated. It was considered the compressed elements of a symmetrical solid cross-section, which bending in one of the main planes. Two laws of the distribution of the random value of the generalized effort were taken into account. This was the normal distribution, which is used to describe the pressure of the bulk material on the capacity’s wall, and the double exponential distribution of the Gumbel, which is used to describe the maximums of the snow and wind loads. The simple expressions were obtained to determine the mathematical expectation, the mean square deviation, and the variation coefficient of the critical factor. It is difficult to determine the density of distribution of this parameter for both variants of the loads’ presentation according to the classical theory. It requires the use of special mathematical packages for calculating integral expressions and it could not be an engineering method. A new approach for calculating the coefficient of the critical factor on the basis of numerical simulation and analysis of the distribution function in the area of big values of the argument was proposed. The problem of representing the dependence of the stability coefficient under the eccentric compression from the conditional flexibility and the reduced relative eccentricity was solved. It was proposed the approximated expression for this dependence. The diagrams were made to compare the values of the eccentric compression’s coefficients in accordance with the normative document and the author's approach.
The analysis showed a good consistency of the results. On the basis of approximation, it was obtained simple analytical expressions for the coefficient of the critical factor and its expected value. This expression could be used to determine the actual probability of the construction’s no-failure work.
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