This study is an attempt to assess the effect of node location imperfections on the reliability dome. The analysis concerns a single-layer steel lattice dome that is very sensitive to node snap-through. The load-displacement path of the structure was determined using the program, Finite Element Method-Krata. To determine the failure probability, reliability index, and elasticity index, the first-order reliability method approximation method was employed. The reliability analysis was conducted with Numpress Explore software, developed at the Institute of Fundamental Technological Research of the Polish Academy of Sciences, Warsaw. In this paper, it is shown how large differences in the assessment of the safety of a structure can appear when we incorrectly estimate the standard deviation of the random variable responsible for the imperfections of node locations.

In this paper, Numpress Explore software, developed at the Institute of Fundamental Technological Research of the Polish Academy of Sciences (IPPT PAN), was used to conduct reliability analyses. For static-strength calculations, the MES3D module, designed by the authors, was employed. Ultimate limit state was defined as condition of non-exceedance of the capacity value, resulting from the stability criterion of the bent and compressed element. The serviceability limit state was defined as the condition of non-exceedance of allowable vertical displacement. The above conditions constitute implicit forms of random variable functions; therefore, it was necessary to build an interface between the Numpress Explore and MES3D programs. In the study, a comparative analysis of two cases was carried out. As regards the first case, all adopted random variables had a normal distribution. The second case involved a more accurate description of the quantities mentioned. A normal distribution can be adopted for the description of, e.g., the randomness in the location of the structure nodes, and also the randomness of the multiplier of permanent loads. In actual systems, the distribution of certain loads deviates substantially from the Gaussian distribution. Consequently, adopting the assumption that the loads have a normal distribution can lead to gross errors in the assessment of structural safety. The distribution of loads resulting from atmospheric conditions is decidedly non-Gaussian in character. The Gumbel distribution was used in this study to describe snow and wind loads. The modulus of elasticity and cross-sectional area were described by means of a log-normal distribution. The adopted random variables were independent. Additionally, based on an analysis of the elasticity index, the random variables most affect the failure probability in the ultimate limit state and serviceability limit state were estimated.

The paper shows the application of the Monte Carlo method to the stability analysis of a single-layer shallow (h/d = 0.04) dome modelled with frame elements. Structures of this type are characterized by strong nonlinearity, consequently, they are extremely susceptible to stability loss resulting from the node snap-through. It is necessary to perform a nonlinear stability analysis that allows determination of limit points related to that mode of stability failure. This paper shows that with the reliability analysis methods, it is possible to trace the failure probability level while moving along the load-displacement path towards the limit point.

The main purpose of the paper was the assessment of the effect of wind load on the load capacity of a single-layer bar dome. Additionally, which numerical method is appropriate for low-rise single-layer bar domes was checked. In order to explain the effect of the height-to-span ratio on the selection of the appropriate calculation model and method of analysis of the bar dome, an example of the known von Mises truss was proposed. Two cases of von Mises truss differing in the height-to-span ratio were considered. For the shallow structure, a significant change in the value of the stiffness matrix determinant and the current stiffness parameter was observed. A similar tendency in the behavior of the structure can be observed on fragments of larger structures, including shallow single-layer steel domes. These problems are described on the basis of the dome, which is located on top of the building housing the restaurant. This structure is subjected to large displacement gradients and the actual configuration is taken into account in analysis. The analysis showed that there is a change in stiffness for these structures, and, therefore, that such structures should be designed according to geometric nonlinear analysis (GNA).

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