Resistance and Sub-Resistances of RC Beams Subjected to Multiple Failure Modes

Authors: F. Sangiorgio, J. Silfwerbrand, G. Mancini

Abstract:

Geometric and mechanical properties all influence the resistance of RC structures and may, in certain combination of property values, increase the risk of a brittle failure of the whole system. This paper presents a statistical and probabilistic investigation on the resistance of RC beams designed according to Eurocodes 2 and 8, and subjected to multiple failure modes, under both the natural variation of material properties and the uncertainty associated with cross-section and transverse reinforcement geometry. A full probabilistic model based on JCSS Probabilistic Model Code is derived. Different beams are studied through material nonlinear analysis via Monte Carlo simulations. The resistance model is consistent with Eurocode 2. Both a multivariate statistical evaluation and the data clustering analysis of outcomes are then performed. Results show that the ultimate load behaviour of RC beams subjected to flexural and shear failure modes seems to be mainly influenced by the combination of the mechanical properties of both longitudinal reinforcement and stirrups, and the tensile strength of concrete, of which the latter appears to affect the overall response of the system in a nonlinear way. The model uncertainty of the resistance model used in the analysis plays undoubtedly an important role in interpreting results.

Keywords: Modelling, Monte Carlo Simulations, Probabilistic Models, Data Clustering, Reinforced Concrete Members, Structural Design.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1099480

References:

[1] W.J. Krefeld, C.W. Thurston, “Contribution of Longitudinal Steel to Shear Resistance of Reinforced Concrete Beams,” ACI Journal 63, No. 3, 1966, pp. 325-344.
[2] W.J. Krefeld, C.W. Thurston, “Studies of the Shear and Diagonal Tension Strength of Simply Supported Reinforced Concrete Beams,” ACI Journal 63, No. 4, 1966, pp. 451-476.
[3] R. Park, T. Paulay, “Reinforced Concrete Structures,” New York: WILEY, 1975.
[4] B.G. Ang, M.J.N. Priestley, T. Paulay, “Seismic Shear Strength of Circular Reinforced Concrete Columns,” ACI Struct. J. 86, No. 1, 1989, pp. 45-59.
[5] M.J.N. Priestley, V. Ravindra, X. Yan, “Seismic Shear Strength of Reinforced Concrete Columns,” ASCE Journal of Structural Engineering 120, No. 8, 1994, pp. 2310-2329.
[6] F. Sangiorgio, J. Silfwerbrand, G. Mancini, “Statistical Investigation on the Ultimate Load Behaviour of RC Beams Subjected to Multiple Failure Modes,” Nordic Concrete Research 50, 2014, pp. 457-460.
[7] F. Sangiorgio, J. Silfwerbrand, G. Mancini, “Probabilistic Investigation of the Ultimate Load Behaviour of RC Structures Designed According to EN 1992-1-1 and Subjected to Multiple Failure Modes,” Engineering Structures, submitted for publication.
[8] Eurocode 2 (EN 1992-1-1), “Design of concrete structures. Part 1-1: general rules and rules for buildings,” 2004.
[9] Eurocode 8 (EN 1998-1), “Design of structures for earthquake resistance,” 1998.
[10] G. Bertagnoli, L. Giordano, G. Mancini, “Safety Format for the Nonlinear Analysis of Concrete Structures. Studi e ricerche,” Politecnico di Milano, Scuola di specializzazione in costruzioni in cemento armato 25, 2004, pp. 31-56.
[11] V. Červenka, “Global Safety Format for Nonlinear Calculation of Reinforced Concrete,” Beton und Stahlbetonbau 103, 2008, pp. 37-42.
[12] H. Schulne, M. Plos, K. Gylltoft, “Safety Formats for Nonlinear Analysis Tested on Concrete Beams Subjected to Shear Forces and Bending Moments,” Eng. Struct. 33, No. 8, 2011, pp. 2350-2356.
[13] M. Sykora, M. Holicky, “Safety Format for Non-Linear Analysis in the Model Code - Verification of Reliability Level,” Fib Symposium on Concrete engineering for excellence and efficiency, Prague, Czech Concrete Society, 2011, pp. 943-946.
[14] Joint Committee on Structural Safety, “Probabilistic Model Code 2000,” JCSS-OSTL/DIA/VROU-10-11-2000.
[15] T.Vrouwenvelder, “Reliability Based Code Calibration. The Use of the JCSS Probabilistic Model Code,” Joint Committee of Structural Safety Workshop on Code Calibration, 2002, March 21/22, Zurich.
[16] J.K. Kim, T.G. Lee, “Nonlinear Analysis of Reinforced Concrete Beams with Softening,” Computer and structures 44, No. 3, 1992, pp. 567-573.
[17] H.A.S. Rasheed, K.S. Dinno, “An Efficient Nonlinear Analysis of RC Sections,” Computers and Structures 53, No. 3, 1994, pp. 613-623.
[18] H.A.S. Rasheed, K.S. Dinno, “An Improved Nonlinear Analysis of Reinforced Concrete Frames,” Computers and Structures 53, No. 3, 1994, pp. 625-636.
[19] H.G. Kwak, S.P. Kim, “Nonlinear analysis of RC beams based on moment-curvature relation,” Computer and structures 80, 2002, pp. 615- 628.
[20] H.R. Valipour, S.J. Foster, “A Total Secant Flexibility-Based Formulation for Frame Elements with Physical and Geometrical Nonlinearities,” Finite Elements in Analysis and Design 46, 2010, pp. 288-297.
[21] M. Sargin, “Stress-Strain Relationships for Concrete and the Analysis of Structural Concrete Sections,” University of Waterloo, Solid Mechanics Division, SM Study 4, 1971, pp. 23-46.
[22] B. Massicotte, A.E. Elwi, J.G. MacGregor, “Tension-Stiffening Model for Planar Reinforced Concrete Members,” ASCE J. Struct. Eng. 116, vol. 11, 1990, pp. 3039-3058.
[23] E.L. Droguett, A. Mosleh, “Bayesian Methodology for Model Uncertainty Using Model Performance Data,” Risk Analysis 28, No. 5, 2008, pp. 1457-1476.
[24] J.B. MacQueen, “Some Methods for Classification and Analysis of Multivariate Observations,” Proceedings of the 5th Berkeley Symposium on Mathematical Statistics and Probability, 1967, pp. 281-297.
[25] M.R. Anderberg, “Cluster Analysis for Applications,” Academic Press, 1973.
[26] A.K. Jain, R.C. Dubes, “Algorithms for Clustering Data,” Prentice Hall, 1988.
[27] L. Kaufman, P.J. Rousseeuw, “Finding Groups in Data - An Introduction to Cluster Analysis,” Wiley, 1990.
[28] P.N. Tan, M. Steinbach, V. Kumar, “Introduction to Data Mining,” Addison-Wesley, 2006.
[29] P.J. Rousseeuw, “Silhouttes: A Graphical Aid to the Interpretation and Validation of a Cluster Analysis,” J Comput Applied Math 20, 1987, pp. 53-65.
[30] G.W. Snedecor, W.G. Cochran, “Statistical Methods,” 6th ed. Iowa State Univ. Press, Ames, 1967.
[31] E. Garcia, “A Tutorial on Correlation Coefficients,” http://www.miislita.com, 2010 - simmons.edu.
[32] G.E. Dallal, “Correlation Coefficients,” http://www.jerrydallal.com/LHSP/corr.htm, 1999.