The paper deals with application of the Gumbel model to evaluation of the environmental loads. According to recommendations of Eurocodes, the conventional method of determining return period and characteristic values of loads utilizes the theory of extremes and implicitly assumes that the cumulative distribution function of the annual or other basic period extremes is the Gumbel distribution. However, the extreme value theory shows that the distribution of extremes asymptotically approaches the Gumbel distribution when the number of independent observations in each observation period from which the maximum is abstracted increases to infinity. Results of calculations based on simulation show that in practice the rate of convergence is very slow and significantly depends on the type of parent results distribution, values of coefficient of variation, and number of observation periods. In this connection, a straightforward purely empirical method based on fitting a curve to the observed extremes is suggested.

The paper presents the method of simplified parametric analysis of the sensitivity of a pre-tensioned concrete beam. The presented approach is based on the DOE (design of experiments) data collection which is simulation technique allowing for identification of variables deciding about the effectiveness and costs of designed structures. Additionally, application of the hyper-surface of the construction response allows designers to the development of multi-dimensional trade-off graphs to facilitate, the assessment of the scope of changes in random state variables permitted due to the adequate criteria and selection of their values close to optimum. Design basics, procedures and results of the presented considerations of sensitivity assessment and reliability of the structure has been shown on the example of a pre-stressed concrete beam designed in accordance with the requirements and procedures of Eurocode 2.