The failure criterion of structural serviceability is often fuzzy, which has a direct impact on the results of structural reliability analysis. Membership function is a basic mathematical tool to describe the fuzziness of failure criteria. At present, the fuzzy statistical method for generating the fuzzy set membership function is to take the numerical interval of the fuzzy set as a sample, and directly generate the membership function through statistics. However, this kind of sample will cover the uncertainty of the individual’s understanding of fuzzy boundaries to a certain extent, and its statistical results are difficult to truly reflect the characteristics of fuzzy sets. The fuzzy boundary is described by the membership density function, and the numerical interval covering the fuzzy boundary is taken as the sample. The fuzzy statistical method for generating the membership density function is proposed, and the indirect statistical method for generating the membership function is established. The comparative analysis results show that the membership functions generated by the two statistical methods are different. The membership function generated by indirect statistical method can fully reflect the uncertainty of the individual’s understanding of the fuzzy boundary, more truly reflect the characteristics of the fuzzy set, and provide a more solid foundation for the fuzzy probability analysis of structural serviceability.

This study investigated the loading mechanism of SPFRC shear walls by conducting low-cycle repeated loading tests on two steel-polypropylene hybrid fiber reinforced concrete (SPFRC) shear walls and one reinforced concrete (RC) shear wall. Furthermore, this study analyzed the impact of fiber content and axial compression ratio on the failure mode, shear carrying capacity, ductility, and energy dissipation capacity of the shear walls. The test results show that hybrid fibers effectively restrain the development of cracks in shear walls, and improve the shear carrying capacity, deformation capacity, and energy dissipation capacity of the shear walls. Considering the contributions of hybrid fibers, horizontal and vertical distributed steel reinforcement, concrete diagonal struts, and concealed columns to shear carrying capacity, a calculation formula for the shear carrying capacity of SPFRC shear walls has been established based on the truss-diagonal brace mechanism. This formula has been validated using data from this study and relevant domestic literature. The average ratio of measured shear carrying capacity to calculated values is 1.01, with a standard deviation of 0.17, indicating a good agreement between them.

At present, the design method of components is still a partial factor design method, and the partial factor value is related to the load value. Because the partial factor has a great influence on the safety of engineering structure, it has been adjusted many times in the process of organization of the code. In order to be basically equivalent to European and American reliability standards and to conform to China’s national conditions and national policies, the Unified standard for reliability design of building structures is revised (i.e., the partial factor of permanent action and variable action was adjusted). Although the concept of factor of safety is commonly used in structure design practice to cover all the unexpected risks, there are some disadvantages to its direct use in structural reliability analysis. For example, the eccentricity of compression members is random, which will lead to the change in resistance parameters of compression members, rather than the fixed value specified in the code. However, the random variation in eccentricity is not considered in the code. So, in this paper, the partial factors of eccentrically loaded members are studied by considering the statistical parameter information of members with random eccentricity. This paper studies the partial factors of different types of components in different ratios of live load effect to dead load effect, and some recommendations are proposed to obtain safer designs. Finally, Monte Carlo simulation method is used to analyze the reliability of the eccentric member. The research results show that the value of partial factors of structure proposed in this paper is reasonable.