Probability calculation of building structures considering asymmetry of random values and functions distribution

Abstract

Introduction. The calculation of structures by the semi-probability method of limit states does not answer the question how reliable the construction is. Probabilistic methods are still imperfect, and attempts to use them to evaluate structures reliability calculated with limit states sometimes lead to contradictory results. A possible reason for this is the lack of research on the influence of the asymmetry of variable distribution functions on the theoretical reliability of structures. The purpose of the research is to develop a practical method for calculating the reliability of structures with considering the asymmetry of the functions distribution and to test the method for evaluating the reliability of bent reinforced concrete elements.Materials and methods. The reliability of structures is estimated by the variability of the strength reserve function based on the methods of moments and design points. A method is proposed for approximating the reliability of fairly complex compositions of random variables using statistical parameters (expectation, standard deviation, and skewness coefficient) of two-element functions approximated by a lognormal three-parameter distribution.Conclusions. Considering the coefficient of the values system asymmetry in the probability calculation allows to justify the reliability of the bent reinforced concrete element designed according to the limit states. On the example of the calculation with the proposed method shown that the availability of the calculation values of the bearing strength of the reinforce concrete element in normal cross section is equal despite the values of the forces in the pressed reinforce concrete or positive reinforcement are indicated. If there is a positive asymmetry, the calculation results using the normal distribution may be significantly underestimated. It is concluded that the value of the asymmetry coefficient of the system of variables can be a justification for the use of normal or lognormal distribution for evaluating the reliability of structures. Ignoring the asymmetry of variables in probabilistic calculations can significantly distort the assessment of the reliability of structures.

Keywords

• reliability
• limit state
• design point
• lognormal distribution asymmetry
• probability calculation