Abstract
The non-linear analysis of the performance of engineering structures requires in general a huge computational effort. Moreover, in some cases a model updating procedure is needed. In this contribution, a model updating procedure has been applied for the simulation of pre-stressed reinforced concrete (RC) beams. The combined ultimate shear and flexure capacity of the beams is affected by many complex phenomena, such as the multi-axial state of stress, the anisotropy induced by diagonal concrete cracking, the interaction between concrete and reinforcement (bond), and the brittleness of the failure mode. Spatial distribution of material properties may be considered by random fields. Furthermore, statistical and energetic size effects may influence the analysis. To incorporate all the mentioned affects within a probabilistic analysis by using Monte Carlo simulation, feasibility limits are achieved quickly. Therefore, the aim was to improve the sampling technique for the generation of the realizations of the basic variables for, a general, computationally complex analysis tasks. The target was to develop a method similar to a simplified probabilistic method e.g. Estimation of Coefficient of Variation (ECoV). Therefore the so-called fractile based sampling procedure (FBSP) by using Latin Hypercube Sampling (LHS) has been developed. It allows a drastic reduction in the computational effort and allows the consideration of correlations between the individual basic variables (BV). However, fundamental aspect of the presented procedure is the appropriate selection of a leading basic variable (LBV). The appropriate choice of the LBV among the defined BVs is essential for mapping the correct correlation. Three methods for the determination of the LBV were investigated in this paper.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Vořechovská, D., Teplý, B., & Chromá, M. (2010). Probabilistic assessment of concrete structure durability under reinforcement corrosion attack. Journal of Performance of Constructed Facilities, 24(6), 571–579.
Belletti, B., Damoni, C., Hendriks, M. A. N., & De Boer, A. (2014). Analytical and numerical evaluation of the design shear resistance of reinforced concrete slabs. Structural Concrete, 15(3), 317–330.
Belletti, B., Pimentel, M., Scolari, M., & Walraven, J. C. (2015). Safety assessment of punching shear failure according to the level of approximation approach. Structural Concrete, 16(3), 366–380.
Schlune, H., Plos, M., & Gylltoft, K. (2011). Comparative study of safety formats for nonlinear finite element analysis of concrete structures. In Applications of Statistics and Probability in Civil Engineering, Proceedings of the 11th International Conference on Applications of Statistics and Probability in Civil Engineering (pp. 2542–2548).
Cervenka, V. (2013). Reliability-based non-linear analysis according to fib Model Code 2010. Structural Concrete, 14(1), 19–28.
Holický, M., & Sykora, M. (2010). Global resistance factors for reinforced concrete structures. In Advances and Trends in Structural Engineering, Mechanics and Computation - Proceedings of the 4th International Conference on Structural Engineering, Mechanics and Computation, SEMC (pp. 771–774).
Holický, M. (2006). Global resistance factors for reinforced concrete members. Presented at the ACTA POLYTECHNICA.
Schlune, H., Plos, M., & Gylltoft, K. (2011). Safety formats for nonlinear analysis tested on concrete beams subjected to shear forces and bending moments. Engineering Structures, 33(8), 2350–2356.
Hurd, C. C. (1985). A note on early Monte Carlo computations and scientific meetings. Annual History Computing, 7(2), 141–155.
McKay, M. D., Beckman, R. J., & Conover, W. J. (1979). Comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics, 21(2), 239–245.
Vořechovský, M., & Novák, D. (2003). Efficient random fields simulation for stochastic FEM analyses. Computational Fluid and Solid Mechanics, 2003, 2383–2386.
Strauss, A., Krug, B., Slowik, O., & Novák, D. (2017). Combined shear and flexure performance of prestressing concrete T-shaped beams: Experiment and deterministic modeling. Structural Concrete, 19(1), 16–35.
Zimmermann, T., & Lehký, D. (2015). Fracture parameters of concrete C40/50 and C50/60 determined by experimental testing and numerical simulation via inverse analysis. Journal of Fractional, 192(2), 179–189.
Novák, D., Vořechovský, M., & Teplý, B. (2014). FReET: Software for the statistical and reliability analysis of engineering problems and FReET-D: Degradation module. Advances in Engineering Software, 72, 179–192.
Keramat, M., & Kielbasa, R. (1997). Efficient average quality index estimation of integrated circuits by modified Latin hypercube sampling Monte Carlo (MLHSMC). In Proceedings—IEEE International Symposium on Circuits and Systems (Vol. 3, pp. 1648–1651).
Huntington, D. E., & Lyrintzis, C. S. (1998). Improvements to and limitations of Latin hypercube sampling. Probabilistic Engineering Mechanics, 13(4), 245–253.
Acknowledgments
Austrian Research Promotion Agency (FFG) and the National Foundation for Research, Technology and Development supported this work by the project OMZIN [FFG-N° 836472]. This paper also reports on the scientific results obtained by the University of Parma within the project PRIN (Project of Prominent National Interest, Italian Research) and financially co-supported by MIUR (the Italian Ministry of Education, University and Research). Finally, the support of DASSAULT SYSTEMES is also strongly acknowledged.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Strauss, A., Belletti, B., Zimmermann, T. (2021). Fractile Based Sampling Procedure for the Effective Analysis of Engineering Structures. In: Matos, J.C., et al. 18th International Probabilistic Workshop. IPW 2021. Lecture Notes in Civil Engineering, vol 153. Springer, Cham. https://doi.org/10.1007/978-3-030-73616-3_27
Download citation
DOI: https://doi.org/10.1007/978-3-030-73616-3_27
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-73615-6
Online ISBN: 978-3-030-73616-3
eBook Packages: EngineeringEngineering (R0)