抄録
The present paper discusses on the relationship between the reliability index and global load factor which are both key factors in design for anti-buckling of single layer reticular domes. The load is restricted in this study to dead and uniform snow loads. First an approximate formula for nominal buckling load is presented, then followed by a proposal for reliability performance function to evaluate the failure probability. The performance function is solved to derive the relationship between the reliability index and snow load factor for design. The relationship is then transformed to the relationship between the reliability index and a single global load factor. Several discussions about the results are given from a viewpoint of anti-buckling design with focusses on the effect of the imperfection for design. Chapter 1 is an overview of the past studies on buckling load, elasto-plastic buckling load in other words, then followed by the aim of the present study for reliability analysis of buckling under dead and heavy snow loads. The present study aims at a proposal of relationship between a single global design load factor γn and corresponding reliability index β for design usage. Chapter 2 concerns, first the geometry of fourteen typical shallow domes with 100m for a span, respectively with respect to pin-support and roller support conditions at a tension ring position. The domes are analyzed under a uniform load based on geometrically and materially nonlinear FEM considering related parameters. Second based on the FEM results an explicit mathematical formulation for elasto-plastic buckling load is presented in terms of the related parameters; subtended half angle of member θ0, member slenderness ratio λ0eq, sectional area of members A, and Young's modulus Es, and geometrical imperfection wi0. Chapter 3 concerns member sections A of the domes to be analyzed for reliability under dead and snow loads. Dead load pd0(n), as nominal, is assumed 1.15 kN/m2, while three snow fall depth hs (n), as nominal, of 0.3m, 0.5m and 0.7m with constant snow density 2.83 kN/m3 per unit volume. The value A varies depending on member slenderness ratio, subtended half angle of member, and design snow load factor γs. Chapter 4 concerns a mathematical presentation and its solution of performance function Z, defined by resistance Pcr minus (D +S), where Pcr denotes elasto-plastic buckling load, D and S denote respectively dead load and snow load. In this solution, the geometric imperfection is assumed as δ function around a certain value wio. The variables θ0, λ 0eq, A, Es, and D are assumed as log-normal with their certain coefficient variations, and geometrical imperfection wi0, while S is assumed as a Gumbel distribution with 0.23 as its coefficient of variation considering 100 year reference period. Based on the results, the relationship between a global load factor γn and reliability index β is numerically obtained. Chapter 5 concerns the relationship between γn-β in the case where the probability distribution is arbitrary, and an integral formula is presented for the relationship of γn to β. Some examples are presented in the case of a step type probabilistic distribution. Chapter 6 is a conclusion on the importance and effectiveness of the obtained relationships between γn and β, then followed by a proposal for some future research targets.
