# The Impact of Node Location Imperfections on the Reliability of Single-Layer Steel Domes
## 4 Conclusions  
Building the mathematical model of a problem, the designer must make a decision as to which design parameters should be treated as deterministic or random. It must be remembered that, in reality, every physical quantity is a random variable; however, for computational purposes, a part of them are assumed as deterministic parameters. Identification of variables determines the solution of the problem in a significant way; therefore, it is essential to investigate the elasticity index. In this paper, the examination of the elasticity index E\({}_{\beta}\)(p\({}_{i}\)) indicates a uniform increment of the index value for all random variables taken into account. Such a change in the elasticity index shows that when \begin{table}
\begin{tabular}{c c c c c} \hline  & **Case 1** & **Case 2** \\ \hline  & \(\mu\) = 7,07 & \(\mu\) = 23,85 & \(\mu\) = 7,07 & \(\mu\) = 23,85 \\ \hline P & 0,060838 & 0,00047 & 0,683858 & 0,00588722 \\ \(Z_{1}\) & 0,075018 & 0,003919 & 0,0575702 & 0,00598635 \\ \(Z_{2}\) & 0,010806 & 0,00056 & 0,00792583 & 0,00085315 \\ \(Z_{3}\) & 0,01099 & 0,000565 & 0,0107745 & 0,00085699 \\ \(Z_{4}\) & 0,010546 & 0,000567 & 0,0085271 & 0,000851656 \\ \(Z_{5}\) & 0,010921 & 0,000561 & 0,00969135 & 0,000852898 \\ \(Z_{6}\) & 0,010715 & 0,000568 & 0,00941762 & 0,000848981 \\ \(Z_{7}\) & 0,011342 & 0,000566 & 0,00963334 & 0,000856157 \\ \(Z_{8}\) & 0,010686 & 0,000568 & 0,00871643 & 0,000851986 \\ \(Z_{9}\) & 0,011073 & 0,00057 & 0,0106294 & 0,000841353 \\ \(Z_{10}\) & 0,011552 & 0,000533 & 0,00893249 & 0,000836612 \\ \(Z_{11}\) & 0,011284 & 0,000534 & 0,00910208 & 0,000821875 \\ \(Z_{12}\) & 0,011468 & 0,000533 & 0,00917403 & 0,000820686 \\ \(Z_{13}\) & 0,011429 & 0,000542 & 0,00910028 & 0,000835488 \\ \(Z_{14}\) & 0,01147 & 0,000528 & 0,0090027 & 0,000833421 \\ \(Z_{15}\) & 0,011286 & 0,000534 & 0,00901152 & 0,000836247 \\ \(Z_{16}\) & 0,011275 & 0,000534 & 0,00912094 & 0,000832002 \\ \(Z_{17}\) & 0,011464 & 0,000528 & 0,00919437 & 0,000820104 \\ \hline \end{tabular}
\end{table} 
Table 5: Values of the elasticity index E\({}_{\beta}\)(p\({}_{i}\)) with respect to the standard deviation, depending on the load multiplier applied. conducting the reliability analysis of the lattice dome, it is necessary to consider all random variables adopted in the description. After considering the randomness of a given parameter, it is necessary to carefully determine the description of distribution parameters. These parameters have an effect on the results of analysis. In this article, to describe all random variables, the normal type of distribution is used, described by the mean value and standard deviation. Two cases of the variation coefficient, namely 10% and 5%, for random variables of \(Z_{1}\) to \(Z_{17}\) were taken into account. Changing the standard deviation of random variables \(Z_{i}\) reflects the imperfections of the nodes position in the probabilistic description. A constant variation coefficient of 10% for the random variable \(P\) was adopted, which corresponds to the assumed unit load. For the cases of concern, a major difference in the reliability index values was observed (Figure 7). On the basis of the analyses conducted for the paper, it can be stated that adequate probabilistic description of the node location significantly affects the structure reliability. With the growth of the degree of complication that occurs in practical issues of designing, explicit reliability methods lose their functionality. In connection with the above, the present study proposes the possibility of the use of interface between methods, dealing with reliability analysis and the numerical methods of the calculation of engineering structures, e.g., Finite Element Method. Introduction was prepared by [PERSON] and [PERSON]. Definition and properties of analysis were written by [PERSON] and [PERSON]. Results were obtained by [PERSON] and [PERSON]. The analysis of the results and conclusions were written by [PERSON] and [PERSON]. This research received no external funding.