Probabilistic Analysis of Shear Resistance due to Concrete Tension

Abstract:

The aim of the work was to assess the safety margin of reinforced rectangular concrete cross-sections subjected to shear. In the performed analyses models of shear resistance based on concrete tension strength was taken into account. Assessment was performed with use of Monte Carlo method. Utilized models of shear resistance were taken from formerly used Polish standards: PN-84/B-03264, PN-B-03264:2002 and the European standard EN-1992-1-1:2004. From the same standard necessary assumptions related with the models were taken. The safety margin and influence of the differences in assumptions on the obtained results were analyzed. The selected models was also evaluated in terms of their “sensitivity” to changes of basic parameters of distribution functions of selected random variables. Results showed that average shear resistance differs about 3 times depending of assumed model of the shear resistance and the reliability level, measured with the partial reliability exponent Δ_R, differs 4-7 times.

• Periodical: Applied Mechanics and Materials (Volume 797)
• Pages: 35-44
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.797.35
• Online since: November 2015
• Authors: Roman Jaskulski*, Piotr Wiliński
• Keywords: Concrete Tension, Monte Carlo Simulation, Reinforced Concrete, Reliability, Shear

References

[1] P. Marek, M. Gustar, T. Anagnos, Simulation Based Reliability Assessment for Structural Engineers. Boca Raton, FL: CRC Press, (1996).

[2] G.I. Schuëller, Efficient Monte Carlo simulation procedures in structural uncertainty and reliability analysis - recent advances. Journal of Structural Engineering and Mechanics, 32(1) (2009): 1-20.

DOI: 10.12989/sem.2009.32.1.001

[3] M. Di. Sciuva, D. Lomario, A comparison between Monte Carlo and FORMs in calculating the reliability of a composite structure, Composite Structures, 59(1) (2003): 155-162.

DOI: 10.1016/s0263-8223(02)00170-8

[4] A. Naess, B.J. Leira, O. Batsevych, System reliability analysis by enhanced Monte Carlo simulation, Structural Safety, 31(5) (2009): 349-355.

DOI: 10.1016/j.strusafe.2009.02.004

[5] S. Mahadevan, A. Dey, Adaptive Monte Carlo Simulation for Time-Variant Reliability Analysis of Brittle Structures, AIAA Journal, 35(2) (1997): 321-326.

DOI: 10.2514/3.13505

[6] M.G. Stewart, D.V. Rosowsky, Time-dependent reliability of deteriorating reinforced concrete bridge decks, Structural Safety, 20(1) (1998): 91-109.

DOI: 10.1016/s0167-4730(97)00021-0

[7] K. Wróbel, Reliability assessment of reinforced concrete beams under shear reinforced with vertical and diagonal stirrups, (in Polish) in: XLIX Sci. Conf. of Civ. and Wat. Eng. Comm. of PAS and Sci. Comm. of PACET Krynica 2003, Warsaw-Krynica, 14-19 September, vol. III: Concr. Struct., Build. Mat. (2003).

[8] M.S. Borishanskii, Calculation of bent bars and stirrups in bent reinforced concrete elements in the destruction stage, (in Russian), Stroyizdat, Moscow, (1946).

[9] T. Godycki-Ćwirko, Concrete mechanics, (in Polish), Arkady, Warsaw, (1982).

[10] T. Godycki-Ćwirko, Shear in concrete, (in Polish), Arkady, Warsaw, (1968).

[11] W. Kukulski (Ed. ) et al., Calculation of reinforced and pre-stressed concrete structures with the limit states method according to PN-76/B-03264, (in Polish), Arkady, Warsaw, (1976).

[12] B. Lewicki (Ed. ) et al., Concrete, reinforced concrete and pre-stressed concrete structures. Scientific comment to Polish standard PN-B-03264: 2002 (in Polish), vol. I, Building Research Institute, Warsaw (2005).

[13] A. Łapko, B.C. Jensen, Basis of design and algorithms for the calculation of reinforced concrete structures, (in Polish), Arkady, Warsaw, (2005).

[14] M. Knauf (Ed. ) et al.: Basis of design of concrete reinforced and pre-stressed structures according to Eurocode 2, (in Polish), DWE, Wrocław, (2006).

[15] F. Casciati, I. Negri, R. Rackwitz, Geometrical Variability in Structural Members and Systems, JCSS Working Document, (1991).

[16] General Principles on the Specification on Safety Requirements for Structures, German Institute for Standardisation DIN, Beuth, (1981).

[17] R. Jaskulski, Influence of selected calculation assumptions on the safety margin of bent and compressed reinforced concrete rod elements, determined using Monte Carlo method, (in Polish), PhD thesis, Warsaw University of Technology, Płock, (2005).

[18] W. Koper: Determination of basic mechanical properties of modern construction concrete, (in Polish), PhD thesis, Warsaw University of Technology, Płock, (1999).

[19] J. Pawlikowski, P. Wiliński, R. Jaskulski: A new probability density distribution for statistical interpretation of test results, (in Polish), Inżynieria i Budownictwo, 9 (2005): 496-499.

[20] P. Wiliński, R. Jaskulski, J. Pawlikowski, Probabilistic analysis of safety margin shear cross-sections of reinforced concrete elements. The report of the statutory research No. 504G/7701/0250/001, (in Polish, unpublished), Warsaw University of Technology, Płock, (2007).