Standard safety assessments of civil engineering systems are conducted using safety factors. An alternative method to this approach is the assessment of the engineering system using reliability analysis of the structure. In reliability analysis of the structure, both the uncertainty of the load and the properties of the materials or geometry are explicitly taken into account. The uncertainties are described in a probabilistic manner. After defining the ultimate and serviceability limit state functions, we can calculate the failure probability for each state. When assessing structural reliability, it is useful to calculate measures that provide information about the influence of random parameters on the failure probability. Classical measures are vectors, whose coordinates are the first partial derivatives of reliability indices evaluated in the design point. These values are obtained as a by-product of the First-Order Reliability Method. Furthermore, we use Sobol indices to describe the sensitivity of the failure probability to input random variables. Computations of the Sobol indices are carried out using the classic Monte Carlo method. The aim of this article is not to define new sensitivity measures, but to show the advantages of using structural reliability and sensitivity analysis in everyday design practice. Using a simple cantilever beam as an example, we will present calculations of probability failure and local and global sensitivity measures. The calculations will be performed using COMREL modules of the STRUREL computing environment. Based on the results obtained from the sensitivity analysis, we can conclude that in the case of the serviceability limit state, the most significant influence on the results is exerted by variables related to the geometry of the beam under consideration. The influence of changes in Young’s modulus and load on the probability of failure is minimal. In further calculations, these quantities can be treated as deterministic. In the case of the ultimate limit state, the influence of changes in the yield strength is significant. The influence of changes in the load and length of the beam is significantly smaller. The authors present two alternative ways of designing with a probabilistic approach, using the FORM (SORM) and Monte Carlo simulation. The approximation FORM cannot be used in every case in connection with gradient determination problems. In such cases, it is worth using the Monte Carlo simulation method. The results of both methods are comparable.

The concept of fire safety covers an extremely vast scope of issues. To ensure an adequate fire safety level, it is necessary to combine research and actions in several fields, such as the mathematical, physical, or numerical modelling of a fire phenomenon. Another problem is to design different types of fire protection, including alarm systems, sprinkler systems, and also roads and evacuation systems, in a manner that ensures maximum safety for the building’s users. A vital issue is the analysis of the static-strength response of the structure under fire conditions. This study, concerned with such analyses, is limited to steel truss structures. In technical approvals, manufacturers of fire-proofing materials do not account for the character of the performance of individual structural members. The components in compression need thicker insulation than those in tension. This phenomenon is related to the fact that under fire conditions, the flexural buckling coefficient in compressed members is abruptly reduced with an increase in temperature. In turn, this increase in temperature leads to a fast reduction in resistance. In addition, members in tension have much higher resistance than those in compression in the basic design situation, i.e., at the instant of t = 0 min. Consequently, even a considerable decrease in the resistance of tension members is not as dangerous as that of compression members. Therefore, due to the nature of the performance of individual elements, fire-proofing insulation of every steel structure should be computationally verified. Additionally, in this paper, the influence of the type of fire insulation on the mechanical response of the structure was investigated. Calculations were carried out for different types of sprayed-on insulation, and also for contour and box insulation panels. The graphs show the behaviour of the elastic modulus, the yield point, and the resistance of the elements in the successive minutes of the fire for the different methods of fire protection used. The best results were obtained for vermiculite and gypsum spray.

The paper presents a proposal for the assessment of the reliability of steel truss (both statically determinate and indeterminate) in the persistent and accidental design situation. In the analysis, a probabilistic approach was used. The global Hasofer-Lind reliability index was employed, computed in successive time steps for the whole structure, not for individual elements. The statically determinate truss was modelled as a serial system from the reliability standpoint. For the statically indeterminate truss, kinematically admissible failure mechanisms were determined by means of the examination of the singularity of the stiffness matrix of the structure, converting the truss into a geometrically variable system. For the problem thus formulated, a serial-parallel reliability model was constructed. Monitoring the reliability index in the successive minutes of the fire makes it possible to estimate the probability of the structure failure, and to decide whether the required safety level is maintained.

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.

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...