Year 2024,
Volume: 42 Issue: 1, 141 - 152, 27.02.2024
Sema Alacalı
,
Güray Arslan
,
Aydoğan İbiş
References
- REFERENCES
- [1] Gündüz A. Probability, statistics, risk, and reliability in engineering. Istanbul; 1996. (Turkish).
- [2] Ang AHS, Tang WH. Probability concepts in engineering planning and design. Volume II-Decision, risk, and reliability. New York: Wiley; 1984.
- [3] Ranganathan R. Reliability analysis and design of structures. New Delhi: McGraw-Hill; 1990.
- [4] Nowak AS, Collins KR. Reliability of structures. McGraw Hill; 2000.
- [5] Cremona C, Gao Y. The possibilistic reliability theory. Theoretical aspects and applications. Struct Safe 1997;19:173–201. [CrossRef]
- [6] Daniel W. Probability theory: An analytic view. 2nd ed. Cambridge: Cambridge University Press; 2010.
- [7] DerKiureghian A, Haukaas T, Fujimura K. Structural reliability software at the University of California. Struct Safe 2006;28:44–67. [CrossRef]
- [8] Byung-Cheol K, Reinschmidt F. A second moment approach to probabilistic IRR using Taylor series. Eng Economist 2012;57:1–19. [CrossRef]
- [9] Sayan G, Manohar CS. An improved response surface method for the determination of failure probability and importance measures. Struct Safe 2004;26:123–139. [CrossRef]
- [10] Simon MK. Probability distributions involving Gaussian random variables: A handbook for engineers, scientists, and mathematicians. (International Series in Engineering and Computer
Science). Berlin, Heidelberger: Sprigner; 2006.
- [11] Devore JL. Probability and statistics for engineering and the sciences. 8th ed. 2011.
- [12] Smith DJ. Reliability, maintainability, and risk: practical methods for engineers. 8th ed. Amserdam: Elsevier Ltd; 2011.
- [13] Birolini A. Reliability engineering: theory and practice. 6th ed. Berlin, Heidelberger: Sprigner; 2010. [CrossRef]
- [14] Gavin HP, Yau SC. High-order limit state functions in the response surface method for structural reliability analysis. Struct Safe 2008;30:162–179. [CrossRef]
- [15] Shinozuka M. Basic analysis of structural safety. Proceed ASCE 1983;109:721–740. [CrossRef]
- [16] Lee YK, Hwang DS. A study on the techniques of estimating the probability of failure. J Chungcheong Math Soc 2008;21:573–583.
- [17] Bresler B, Scordelis AC. Shear strength of reinforced concrete beams. Structural and Research Series 100. Berlin, Heidelberger: Sprigner; 1961.
- [18] Krefeld WJ, Thurston CW. Studies of the shear and diagonal tension strength of simply supported reinforced concrete beams. ACI J Proc 1966;63:451–476. [CrossRef]
- [19] Placas A, Regan PE. Shear failure of reinforced concrete beams. ACI J Proc 1971;68:763–773. [CrossRef]
- [20] Mattock AH, Wang Z. Shear strength of reinforced concrete members subject to high axial compressive stress. ACI Struct J 1984;11:287–298.
- [21] Leonhardt F, Walter R. Schubversuche an einfeldriegen stahlbeton-balken mit und ohne schubbewehrung zur ermittlung der Schubtragfähigkeit und der Oberen Schubspannungsgrenze, Heft
151. Berlin: Deutscher Ausschuss für Stahlbeton, W. Ernst u. Sohn; 1962.
- [22] Swamy RN, Andriopoulos AD. Contribution of aggregate interlock and dowel forces to the shear resistance of reinforced beams with web reinforcement. Shear in reinforced concrete, SP-42.
ACI 1974:129–166.
- [23] Mphonde AG, Frantz GC. Shear tests of high and low-strength concrete beams without stirrups. ACI J Proc 1984;81:350–357. [CrossRef]
- [24] Adebar P, Collins MP. Shear strength of members without transverse reinforcement. Can J Civil Eng 1996;23:30–41. [CrossRef]
- [25] ASCE-ACI Committee 445 on Shear and Torsion. Recent approaches to shear design of structural concrete. State-of-the-Art-Report. J Struct Eng ASCE 1998;124:1375–1417. [CrossRef]
- [26] American Concrete Institute Committee 318 (ACI 318). Building code requirements for structural concrete (ACI 318M-11) and commentary. Farmington Hills, MI: ACI; 2011.
- [27] Turkish Standards Institute. TS 500 Requirements for design and construction of reinforced concrete structures. Ankara, Turkey; 2000. (Turkish).
- [28] Eurocode 2. Design of Concrete Structures, Part 1-1: General rules and rules for buildings, EN 1992-1-1. Brussels: European Committee for Standardization; 2004.
- [29] Eurocode 2. Design of Concrete Structures Part 1-1, General rules and rules for buildings. ENV 1992-1-1. Brussels: Comité Européen de Normalisation CEN; 1992.
- [30] Zsutty TC. Shear strength prediction for separate categories of simple beam tests. ACI J Proceed 1971;68:138–143. [CrossRef]
- [31] ASCE-ACI 426. The shear strength of reinforced concrete members. Proc Am Soc Civil Eng 1973;99:1091–1187. [CrossRef]
- [32] Turkish Standards Institute-TS 500. Requirements for design and construction of reinforced concrete structures. Turkey; 1984. (Turkish).
- [33] Nowak A, Szerszen M. Calibration of design code for buildings (ACI 318): part 1–statistical models for resistance. ACI Struct 2003;100:377–382. [CrossRef]
- [34] Ribeiro S, Diniz SMC. Reliability-based design recommendations for FRP-reinforced concrete beams. Eng Struct 2013;52:273–283. [CrossRef]
- [35] Hao H, Stewart MG, Li ZX, Shi Y. RC column failure probabilities to blast loads. Int J Protec Struct 2010;1:571–591. [CrossRef]
- [36] Neves RA, Chateauneuf AM, Venturini WS. Component and system reliability analysis of nonlinear reinforced concrete grids with multiple failure modes. Struct Safe 2008;30:183–189.
[CrossRef]
- [37] Val D, Bljuger F, Yankelevsky D. Reliability evaluation in nonlinear analysis of reinforced concrete structures. Struct Safe 1997;19:203–217. [CrossRef]
- [38] Mirza SA. Reliability-based design of reinforced concrete columns. Struct Safe 1996;18:179–194. [CrossRef]
- [39] Mirza SA, Hatzinikolas M, MacGregor JG. Statistical descriptions of strength of concrete. ASCE J Struct Div 1979;105:1021–1037. [CrossRef]
- [40] Mirza SA, MacGregor JG. Variability of mechanical properties of reinforcing bars. ASCE J Struct Div 1979;105:921–937. [CrossRef]
- [41] Mirza SA, MacGregor JG. Variations in dimensions of reinforced concrete members. ASCE J Struct Div 1979;105:751–766. [CrossRef]
- [42] Val DV, Chernin L. Serviceability reliability of reinforced concrete beams with corroded reinforcement. ASCE J Struct Eng 2009;135:896–905. [CrossRef]
- [43] Melchers RE. Structural reliability analysis and prediction. John Wiley & Sons; 1999.
- [44] Ellingwood B. Reliability basis of load and resistance factors for reinforced concrete design. Building Science Series No. 110. Washington, D.C: National Bureau of Standards; 1978. [CrossRef]
- [45] JCSS. Probabilistic model code Part III. Joint Committee on Structural Safety; 2000.
- [46] Low HY, Hao H. Reliability analysis of reinforced concrete slabs under explosive loading. Int J Struct Safe 2001;23:157–178. [CrossRef]
- [47] Ostlund L. An estimation of t-values, In reliability of concrete structures. CEB Bulletin d'Information no. 202. Lausanne, Switzerland; 1991.
- [48] MacGregor JG, Mirza SA, Ellingwood B. Statistical analysis of resistance of reinforced and prestressed concrete members. ACI J 1983;80:167–176. [CrossRef]
- [49] Enright MP, Frangopol DM. Probabilistic analysis of resistance degradation of reinforced concrete bridge beams under corrosion. Eng Struct 1998;20:960–971. [CrossRef]
- [50] Hognestad E. A study of combined bending and axial load in reinforced concrete members. Engineering Experiment Station Bulletin 399. University of Illinois, Urbana; 1951.
Reliability analysis of shear strength equations of RC beams
Year 2024,
Volume: 42 Issue: 1, 141 - 152, 27.02.2024
Sema Alacalı
,
Güray Arslan
,
Aydoğan İbiş
Abstract
Shear strength of a reinforced concrete (RC) member should be larger than its flexural strength, in order to prevent the shear failure, which is sudden and brittle. The reliability of a RC beam against the shear failure is closely related to the reliability of the equation determin-ing its shear strength. In this study, the reliabilities of shear strength equations of RC beams were investigated by constructing the performance function between prediction equations and experimental results using a second-moment approach. It is assumed that the random variables are statistically independent, and the correlation effects are not taken into account. It is observed from the reliability rankings that the equation of EN 1992:2004 yields the lowest failure probability while the equation of Zsutty is the highest failure probability.
References
- REFERENCES
- [1] Gündüz A. Probability, statistics, risk, and reliability in engineering. Istanbul; 1996. (Turkish).
- [2] Ang AHS, Tang WH. Probability concepts in engineering planning and design. Volume II-Decision, risk, and reliability. New York: Wiley; 1984.
- [3] Ranganathan R. Reliability analysis and design of structures. New Delhi: McGraw-Hill; 1990.
- [4] Nowak AS, Collins KR. Reliability of structures. McGraw Hill; 2000.
- [5] Cremona C, Gao Y. The possibilistic reliability theory. Theoretical aspects and applications. Struct Safe 1997;19:173–201. [CrossRef]
- [6] Daniel W. Probability theory: An analytic view. 2nd ed. Cambridge: Cambridge University Press; 2010.
- [7] DerKiureghian A, Haukaas T, Fujimura K. Structural reliability software at the University of California. Struct Safe 2006;28:44–67. [CrossRef]
- [8] Byung-Cheol K, Reinschmidt F. A second moment approach to probabilistic IRR using Taylor series. Eng Economist 2012;57:1–19. [CrossRef]
- [9] Sayan G, Manohar CS. An improved response surface method for the determination of failure probability and importance measures. Struct Safe 2004;26:123–139. [CrossRef]
- [10] Simon MK. Probability distributions involving Gaussian random variables: A handbook for engineers, scientists, and mathematicians. (International Series in Engineering and Computer
Science). Berlin, Heidelberger: Sprigner; 2006.
- [11] Devore JL. Probability and statistics for engineering and the sciences. 8th ed. 2011.
- [12] Smith DJ. Reliability, maintainability, and risk: practical methods for engineers. 8th ed. Amserdam: Elsevier Ltd; 2011.
- [13] Birolini A. Reliability engineering: theory and practice. 6th ed. Berlin, Heidelberger: Sprigner; 2010. [CrossRef]
- [14] Gavin HP, Yau SC. High-order limit state functions in the response surface method for structural reliability analysis. Struct Safe 2008;30:162–179. [CrossRef]
- [15] Shinozuka M. Basic analysis of structural safety. Proceed ASCE 1983;109:721–740. [CrossRef]
- [16] Lee YK, Hwang DS. A study on the techniques of estimating the probability of failure. J Chungcheong Math Soc 2008;21:573–583.
- [17] Bresler B, Scordelis AC. Shear strength of reinforced concrete beams. Structural and Research Series 100. Berlin, Heidelberger: Sprigner; 1961.
- [18] Krefeld WJ, Thurston CW. Studies of the shear and diagonal tension strength of simply supported reinforced concrete beams. ACI J Proc 1966;63:451–476. [CrossRef]
- [19] Placas A, Regan PE. Shear failure of reinforced concrete beams. ACI J Proc 1971;68:763–773. [CrossRef]
- [20] Mattock AH, Wang Z. Shear strength of reinforced concrete members subject to high axial compressive stress. ACI Struct J 1984;11:287–298.
- [21] Leonhardt F, Walter R. Schubversuche an einfeldriegen stahlbeton-balken mit und ohne schubbewehrung zur ermittlung der Schubtragfähigkeit und der Oberen Schubspannungsgrenze, Heft
151. Berlin: Deutscher Ausschuss für Stahlbeton, W. Ernst u. Sohn; 1962.
- [22] Swamy RN, Andriopoulos AD. Contribution of aggregate interlock and dowel forces to the shear resistance of reinforced beams with web reinforcement. Shear in reinforced concrete, SP-42.
ACI 1974:129–166.
- [23] Mphonde AG, Frantz GC. Shear tests of high and low-strength concrete beams without stirrups. ACI J Proc 1984;81:350–357. [CrossRef]
- [24] Adebar P, Collins MP. Shear strength of members without transverse reinforcement. Can J Civil Eng 1996;23:30–41. [CrossRef]
- [25] ASCE-ACI Committee 445 on Shear and Torsion. Recent approaches to shear design of structural concrete. State-of-the-Art-Report. J Struct Eng ASCE 1998;124:1375–1417. [CrossRef]
- [26] American Concrete Institute Committee 318 (ACI 318). Building code requirements for structural concrete (ACI 318M-11) and commentary. Farmington Hills, MI: ACI; 2011.
- [27] Turkish Standards Institute. TS 500 Requirements for design and construction of reinforced concrete structures. Ankara, Turkey; 2000. (Turkish).
- [28] Eurocode 2. Design of Concrete Structures, Part 1-1: General rules and rules for buildings, EN 1992-1-1. Brussels: European Committee for Standardization; 2004.
- [29] Eurocode 2. Design of Concrete Structures Part 1-1, General rules and rules for buildings. ENV 1992-1-1. Brussels: Comité Européen de Normalisation CEN; 1992.
- [30] Zsutty TC. Shear strength prediction for separate categories of simple beam tests. ACI J Proceed 1971;68:138–143. [CrossRef]
- [31] ASCE-ACI 426. The shear strength of reinforced concrete members. Proc Am Soc Civil Eng 1973;99:1091–1187. [CrossRef]
- [32] Turkish Standards Institute-TS 500. Requirements for design and construction of reinforced concrete structures. Turkey; 1984. (Turkish).
- [33] Nowak A, Szerszen M. Calibration of design code for buildings (ACI 318): part 1–statistical models for resistance. ACI Struct 2003;100:377–382. [CrossRef]
- [34] Ribeiro S, Diniz SMC. Reliability-based design recommendations for FRP-reinforced concrete beams. Eng Struct 2013;52:273–283. [CrossRef]
- [35] Hao H, Stewart MG, Li ZX, Shi Y. RC column failure probabilities to blast loads. Int J Protec Struct 2010;1:571–591. [CrossRef]
- [36] Neves RA, Chateauneuf AM, Venturini WS. Component and system reliability analysis of nonlinear reinforced concrete grids with multiple failure modes. Struct Safe 2008;30:183–189.
[CrossRef]
- [37] Val D, Bljuger F, Yankelevsky D. Reliability evaluation in nonlinear analysis of reinforced concrete structures. Struct Safe 1997;19:203–217. [CrossRef]
- [38] Mirza SA. Reliability-based design of reinforced concrete columns. Struct Safe 1996;18:179–194. [CrossRef]
- [39] Mirza SA, Hatzinikolas M, MacGregor JG. Statistical descriptions of strength of concrete. ASCE J Struct Div 1979;105:1021–1037. [CrossRef]
- [40] Mirza SA, MacGregor JG. Variability of mechanical properties of reinforcing bars. ASCE J Struct Div 1979;105:921–937. [CrossRef]
- [41] Mirza SA, MacGregor JG. Variations in dimensions of reinforced concrete members. ASCE J Struct Div 1979;105:751–766. [CrossRef]
- [42] Val DV, Chernin L. Serviceability reliability of reinforced concrete beams with corroded reinforcement. ASCE J Struct Eng 2009;135:896–905. [CrossRef]
- [43] Melchers RE. Structural reliability analysis and prediction. John Wiley & Sons; 1999.
- [44] Ellingwood B. Reliability basis of load and resistance factors for reinforced concrete design. Building Science Series No. 110. Washington, D.C: National Bureau of Standards; 1978. [CrossRef]
- [45] JCSS. Probabilistic model code Part III. Joint Committee on Structural Safety; 2000.
- [46] Low HY, Hao H. Reliability analysis of reinforced concrete slabs under explosive loading. Int J Struct Safe 2001;23:157–178. [CrossRef]
- [47] Ostlund L. An estimation of t-values, In reliability of concrete structures. CEB Bulletin d'Information no. 202. Lausanne, Switzerland; 1991.
- [48] MacGregor JG, Mirza SA, Ellingwood B. Statistical analysis of resistance of reinforced and prestressed concrete members. ACI J 1983;80:167–176. [CrossRef]
- [49] Enright MP, Frangopol DM. Probabilistic analysis of resistance degradation of reinforced concrete bridge beams under corrosion. Eng Struct 1998;20:960–971. [CrossRef]
- [50] Hognestad E. A study of combined bending and axial load in reinforced concrete members. Engineering Experiment Station Bulletin 399. University of Illinois, Urbana; 1951.