1. Reliability analysis of statically indeterminate steel frame (pilot study) David Pustka VŠB – Technical University of Ostrava Faculty of Civil Engineering Ludvíka Podéště 1875, 708 00 Ostrava, Czech Republic

2. Introduction In the last months was performed the pilot study demonstrating the applicability of SBRA method to systems. This study is briefly explained in the following. The first order theory and static and elastic response to the loading was assumed. The calculation of load efects was based on simplified deformation method. All loads acting on structure were assumed as random variables and were described by load duration curves.

3. Example assignment Statically indeterminate planar steel frame made of rolled-sections IPE:

4. Load effects calculation – normal forces

5. Load effects calculation – shear forces

6. Load effects calculation – bending moments

7. Load effects combination calculation, Resistance calculation Load effects combination in any point of the structure (in case of shear forces neglecting) can be expressed by normal stress  x : The resistance of the whole structure from the viewpoint of the safety was related to yield stress f y : The overstep of this reference value in any point of the structure was considered as failure.

8. Reliability assessment The reliability assessment in the critical cross-section of the structure was based on the reliability criterion: where P d is target probability given by codes and P f is probability of failure calculated from the reliability function RF of the critical cross-section :

9. Reliability function calculation Resulting reliability function of critical cross-section:

10. Summary and conclusion The demonstrated simulation based approach SBRA can be used as a tool for reliability analysis of systems. This approach allows to evaluate all possible combinations of all input variables in time due to direct Monte Carlo simulation technique. The calculation is quickly, clearly and leads to balanced reliability level. For details, see dissertation work (Pustka, VŠB-TU Ostrava, 2002).

11. Thank you for attention …