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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 83
PROCEEDINGS OF THE EIGHTH INTERNATIONAL CONFERENCE ON COMPUTATIONAL STRUCTURES TECHNOLOGY
Edited by: B.H.V. Topping, G. Montero and R. Montenegro
Paper 187

Probabilistic Reliability Assessment of Structural Systems in the Computer Era

V. Krivý1, L. Václavek2, P. Marek3 and J. Valihrach1

1Faculty of Civil Engineering,
2Faculty of Mechanical Engineering, VSB - Technical University of Ostrava, Ostrava, Czech Republic
3Institute of Theoretical and Applied Mechanics, The Academy of Sciences of the Czech Republic, Prague, Czech Republic

Full Bibliographic Reference for this paper
V. Krivý, L. Václavek, P. Marek, J. Valihrach, "Probabilistic Reliability Assessment of Structural Systems in the Computer Era", in B.H.V. Topping, G. Montero, R. Montenegro, (Editors), "Proceedings of the Eighth International Conference on Computational Structures Technology", Civil-Comp Press, Stirlingshire, UK, Paper 187, 2006. doi:10.4203/ccp.83.187
Keywords: simulation based reliability assessment, stability, steel frames, probability, second order theory, analytical models, numerical models, reliability assessment.

Summary
The common approach to the stability assessment of structural steel components and systems is based so far mainly on the conventional models using buckling lengths, buckling coefficients, compressive strength and other characteristics. This paper is concerned with an alternative reliability assessment of steel structures using the probabilistic simulation based reliability assessment (SBRA) method documented in the book [1]. Advances in computer technology make it possible to utilize the potential of the SBRA method not only for the reliability assessment of simple structures and their components, but also for the reliability assessment of more complex, statically indeterminate frame structures.

In connection with the transition to a probabilistic reliability assessment of systems, it is necessary to select appropriate reference values, which serve to define the resistance limits applied in the calculation of the probability of failure of the structure and its components. Next, it is necessary to evaluate the suitability of particular transformation models serving as tools to transform the loading into the response of the structure to the load with regard to the substance of stochastic methods.

The character and the interaction of imperfections should be also considered and evaluated with regard to the applied transformation model. In this connection attention is paid to the transition from the traditional assessment of buckling strength in compliance with contemporary standards [2,3] (based on determining buckling lengths and buckling factors) to the SBRA based strength stability concept applying the second order theory. A fully probabilistic approach to safety and serviceability assessment of a structural system is demonstrated next using two pilot examples: (a) a planar unbraced steel frame with leaning columns, and (b) a planar six-story two bay steel frame.

The main principles concerning the SBRA reliability assessment of steel frame structures are briefly explained in Section 2 of the paper using an example of the planar unbraced steel frame with leaning columns. The safety and serviceability assessment of the frame is performed, whereas an analytical transformation model applying the second order theory is used. A major part of the input variables (including loadings, temperature differences, imperfections, cross section characteristics and material properties) are considered by using random variables to represent compliance with the SBRA method by corresponding histograms.

In this example, an analytical model was used to calculate the response of the structure to the loading. Such models are very useful to explain the main principles concerning the probabilistic reliability assessment and to demonstrate the potential of SBRA method but the analytical methods can not be generally used to solve more complex frame structures. It is necessary to deal with the possibility of interconnecting the probabilistic approaches with the numerical models of the structural analysis.

These problems are described and discussed in Section 3 of the paper using an example of the probabilistic reliability assessment of a four-story three bay moment resisting steel frame. The results of safety and serviceability assessment are expressed using a plot of "probability of failure curves". To enable a visual control of structural analysis, the scatter of resulting internal forces and bending moments can be illustrated using the set of dots, so called "ants", corresponding to the random combinations of the input variables. The results were obtained using the MCD 1.0 computer program [4].

Additionally, a comparative study was performed, comparing two different support models of the frame. The results show the advantage of the curves approach, which allows easy identification of critical points in the structure design and thus enables both quick and easy comparison of different design alternatives.

References
1
P. Marek, M. Guštar, T. Anagnos, "Simulation-based Reliability Assessment for Structural Engineers", CRC Press, Boca Raton, USA, 1995.
2
European Committee for Standardization, "EN 1990: Basis of Structural Design", CEN, Brussels, Belgium, 2004.
3
European Committee for Standardization, "EN 1993-1-1: Design of Steel Structures. Part 1-1: General Rules and Rules for buildings", CEN, Brussels, Belgium, 2004.
4
V. Krivý, "Computer programme MCD 1.0", VŠB - TUO, Ostrava, 2005.

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