The Application of Structural Reliability and Sensitivity Analysis in Engineering Practice - Urszula Radoń; Paweł Zabojszcza (Applied Sciences)
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.