Title:
Generation of Optimal Load Paths for Corroded Reinforced Concrete Beams Part II: Multi-Angle Truss Model
Author(s):
Lei Wang, Ping Yuan, and Royce W. Floyd
Publication:
Structural Journal
Volume:
120
Issue:
4
Appears on pages(s):
115-126
Keywords:
corroded reinforced concrete (CRC) beams; multi-angle truss model; multiple variable-inclination struts; optimal load paths; shear capacity
DOI:
10.14359/51738751
Date:
7/1/2023
Abstract:
A multi-angle truss model is proposed based on the optimal load paths of corroded reinforced concrete (CRC) beams. The load paths of CRC beams at the ultimate limit state, considering various corrosion levels, shear span-depth ratios, stirrup ratios, and loading methods are first studied. The load paths incorporating multiple variable-inclination struts can realistically describe the force-transfer mechanisms of CRC beams under flexure-shear interaction. The limiting failure criteria of the proposed truss model are then presented to estimate the shear capacity of CRC beams. Finally, the proposed model is verified by comparing with the experimental results of uncorroded and corroded reinforced concrete (RC) beams. Results show that the proposed model can reasonably predict the shear capacity and failure mode of CRC beams. For CRC beams at the ultimate limit state, corrosion damage has a negligible influence on the trajectory of load paths.The load paths change with the increase of the shear span-depth ratios of CRC beams.
Related References:
1. He, Z.; Liu, Z.; and John Ma, Z., “Simplified Shear Design of Slender Reinforced Concrete Beams with Stirrups,” Journal of Structural Engineering, ASCE, V. 142, No. 2, 2016, p. 06015003. doi: 10.1061/(ASCE)ST.1943-541X.0001394
2. Zhang, T.; Visintin, P.; and Oehlers, D. J., “Shear Strength of RC Beams with Steel Stirrups,” Journal of Structural Engineering, ASCE, V. 142, No. 2, 2016, p. 04015135. doi: 10.1061/(ASCE)ST.1943-541X.0001404
3. Li, B., and Tran, C., “Determination of Inclination of Strut and Shear Strength Using Variable Angle Truss Model for Shear-Critical RC Beams,” Structural Engineering and Mechanics, V. 41, No. 4, 2012, pp. 459-477. doi: 10.12989/sem.2012.41.4.459
4. Ritter, W., “Die Bauweise Hennebique (Construction Techniques of Hennebique),” Schweizerische Bauzeitung, V. 33, No. 7, 1899, pp. 59-66. (in German)
5. Mörsch, E., Der Eisenbetonbau—Seine Theorie und Anwendung, Wittwer, Stuttgart, Germany, 1908.
6. ACI Committee 318, “Building Code Requirements for Structural Concrete (ACI 318-19) and Commentary (ACI 318R-19),” American Concrete Institute, Farmington Hills, MI, 2019, 623 pp.
7. ENV 1992-1-1: “Eurocode 2 - Design of Concrete Structures - Part 1-1: General Rules and Rules for Buildings,” European Committee for Standardization, Brussels, Belgium, 1991.
8. Bernardo, L.; Andrade, J.; and Lopes, S., “Modified Variable Angle Truss-Model for Torsion in Reinforced Concrete Beams,” Materials and Structures, V. 45, No. 12, 2012, pp. 1877-1902. doi: 10.1617/s11527-012-9876-4
9. Tran, N. C., and Vu, S. N., “Shear Deformations Based on Variable Angle Truss Model for Concrete Beams Reinforced with FRP Bars,” Structural Engineering and Mechanics, V. 79, No. 3, 2021, pp. 337-345.
10. Vecchio, F. J., and Collins, M. P., “The Modified Compression-Field Theory for Reinforced Concrete Elements Subjected to Shear,” ACI Structural Journal, V. 83, No. 2, July-Aug. 1986, pp. 219-231.
11. Collins M. P.; Mitchell, D.; Adebar, P.; and Vecchio, F. J., “A General Shear Design Method,” ACI Structural Journal, V. 93, No. 1, Jan.-Feb. 1996, pp. 36-45.
12. Bentz, E. C.; Vecchio, F. J.; and Collins, M. P., “Simplified Modified Compression Field Theory for Calculating Shear Strength of Reinforced Concrete Elements,” ACI Materials Journal, V. 103, No. 4, July-Aug. 2006, pp. 614-624.
13. UNI EN 1992-1-1:2005, “Eurocode 2 - Design of Concrete Structures - Part 1-1: General Rules and Rules for Buildings,” European Committee for Standardization, Brussels, Belgium, 2005.
14. Nielsen, M. P., and Hoang, L. C., Limit Analysis and Concrete Plasticity, second edition, CRC Press, Boca Raton, FL, 1999.
15. Wang, T.; Dai, J. G.; and Zheng, J. J., “Multi-Angle Truss Model for Predicting the Shear Deformation of RC Beams with Low Span-Effective Depth Ratios,” Engineering Structures, V. 91, Mar. 2015, pp. 85-95. doi: 10.1016/j.engstruct.2015.02.035
16. De Domenico, D., and Ricciardi, G., “Shear Strength of RC Beams with Stirrups Using an Improved Eurocode 2 Truss Model with Two Variable-Inclination Compression Struts,” Engineering Structures, V. 198, June 2019, p. 109359. doi: 10.1016/j.engstruct.2019.109359
17. Teo, W., and Hor, Y., “Suitability of Optimized Truss Model to Predict the FRP Contribution to Shear Resistance for Externally Bonded FRP Strengthened RC Beams without Internal Stirrups,” Composites. Part B: Engineering, V. 80, May 2015, pp. 385-398. doi: 10.1016/j.compositesb.2015.05.004
18. Li, B., and Ngoc Tran, C. T., “Reinforced Concrete Beam Analysis Supplementing Concrete Contribution in Truss Models,” Engineering Structures, V. 30, No. 11, 2008, pp. 3285-3294. doi: 10.1016/j.engstruct.2008.05.002
19. Zhu, W.; François, R.; Cleland, D.; and Coronelli, D., “Failure Mode Transitions of Corroded Deep Beams Exposed to Marine Environment for Long Period,” Engineering Structures, V. 96, Apr. 2015, pp. 66-77. doi: 10.1016/j.engstruct.2015.04.004
20. Higgins, C., and Farrow, W. C., “Tests of Reinforced Concrete Beams with Corrosion-Damaged Stirrups,” ACI Materials Journal, V. 103, No. 1, Jan.-Feb. 2006, pp. 133-141.
21. Xia, J.; Jin, W.; and Li, L., “Shear Performance of Reinforced Concrete Beams with Corroded Stirrups in Chloride Environment,” Corrosion Science, V. 53, No. 5, 2011, pp. 1794-1805. doi: 10.1016/j.corsci.2011.01.058
22. Bhargava, K.; Mori, Y.; and Ghosh, A. K., “Time-Dependent Reliability of Corrosion-Affected RC Beams—Part 1: Estimation of Time-Dependent Strengths and Associated Variability,” Nuclear Engineering and Design, V. 241, No. 5, 2011, pp. 1371-1384. doi: 10.1016/j.nucengdes.2011.01.005
23. Val, D. V., “Deterioration of Strength of RC Beams Due to Corrosion and Its Influence on Beam Reliability,” Journal of Structural Engineering, ASCE, V. 133, No. 9, 2007, pp. 1297-1306. doi: 10.1061/(ASCE)0733-9445(2007)133:9(1297)
24. Potisuk, T.; Higgins, C.; Miller, T. H.; and Yim, S. C., “Finite Element Analysis of Reinforced Concrete Beams with Corrosion Subjected to Shear,” Advances in Civil Engineering, V. 2011, Mar. 2011, pp. 1-14. doi: 10.1155/2011/706803
25. Coronelli, D., and Gambarova, P., “Structural Assessment of Corroded Reinforced Concrete Beams: Modeling Guidelines,” Journal of Structural Engineering, ASCE, V. 130, No. 8, 2004, pp. 1214-1224. doi: 10.1061/(ASCE)0733-9445(2004)130:8(1214)
26. Lu, Z.; Li, H.; Li, W.; Zhao, Y. G.; and Dong, W., “An Empirical Model for the Shear Strength of Corroded Reinforced Concrete Beam,” Construction and Building Materials, V. 188, Sept. 2018, pp. 1234-1248. doi: 10.1016/j.conbuildmat.2018.08.123
27. Alaskar, A.; Alqarni, A. S.; Alfalah, G.; El-Sayed, A. K.; Mohammadhosseini, H.; and Alyousef, R., “Performance Evaluation of Reinforced Concrete Beams with Corroded Web Reinforcement: Experimental and Theoretical Study,” Journal of Building Engineering, V. 35, Nov. 2021, p. 102038. doi: 10.1016/j.jobe.2020.102038
28. Higgins, C.; Farrow, W. C.; and Turan, O. T., “Analysis of Reinforced Concrete Beams with Corrosion Damaged Stirrups for Shear Capacity,” Structure and Infrastructure Engineering, V. 8, No. 11, Nov. 2012, pp. 1080-1092.
29. El-Sayed, A. K., “Shear Capacity Assessment of Reinforced Concrete Beams with Corroded Stirrups,” Construction and Building Materials, V. 134, Dec. 2017, pp. 176-84.
30. Yang, Y.; Liu, Z.; Tang, H.; and Peng, J., “Deflection-Based Failure Probability Analysis of Low Shrinkage-Creep Concrete Structures in Presence of Non-Stationary Evolution of Shrinkage and Creep Uncertainties,” Construction and Building Materials, V. 376, May 2023, p. 131077.
31. Zhang, W.; Ye, Z.; and Gu, X., “Effects of Stirrup Corrosion on Shear Behaviour of Reinforced Concrete Beams,” Structure and Infrastructure Engineering, V. 13, No. 8, 2017, pp. 1081-1092. doi: 10.1080/15732479.2016.1243563
32. Vidal, T.; Castel, A.; and François, R., “Analyzing Crack Width to Predict Corrosion in Reinforced Concrete,” Cement and Concrete Research, V. 34, No. 1, 2004, pp. 165-174. doi: 10.1016/S0008-8846(03)00246-1
33. González, J.; Andrade, C.; Alonso, C.; and Feliu, S., “Comparison of Rates of General Corrosion and Maximum Pitting Penetration on Concrete Embedded Steel Reinforcement,” Cement and Concrete Research, V. 25, No. 2, 1995, pp. 257-264. doi: 10.1016/0008-8846(95)00006-2
34. Zhang, T.; Oehlers, D.; and Visintin, P., “Shear Strength Of FRP RC Beams And One-Way Slabs Without Stirrups,” Journal of Composites for Construction, ASCE, V. 18, No. 5, 2014, p. 04014007. doi: 10.1061/(ASCE)CC.1943-5614.0000469
35. Chabib, H. E.; Nehdi, M.; and Said, A., “Predicting the Effect of Stirrups on Shear Strength of Reinforced Normal-Strength Concrete (NSC) and High-Strength Concrete (HSC) Slender Beams Using Artificial Intelligence,” Canadian Journal of Civil Engineering, V. 33, No. 8, 2006, pp. 933-944. doi: 10.1139/l06-033
36. Lee, J. Y.; Choi, I. J.; and Kim, S. W., “Shear Behavior of Reinforced Concrete Beams with High-Strength Stirrups,” ACI Structural Journal, V. 108, No. 5, Sept.-Oct. 2011, pp. 620-629.
37. Cladera, A., and Mari, A. R., “Experimental Study on High-Strength Concrete Beams Failing in Shear,” Engineering Structures, V. 27, No. 10, 2005, pp. 1519-1527. doi: 10.1016/j.engstruct.2005.04.010
38. Rahal, K. N., “Shear Behavior of Reinforced Concrete Beams with Variable Thickness of Concrete Side Cover,” ACI Materials Journal, V. 103, No. 2, Mar.-Apr. 2006, pp. 171-177.
39. Rahal, K. N., and Al-Shaleh, K. S., “Minimum Transverse Reinforcement in 65 MPa Concrete Beams,” ACI Structural Journal, V. 101, No. 6, Nov.-Dec. 2004, pp. 872-878.
40. Clark, A. P., “Diagonal Tension in Reinforced Concrete Beams,” ACI Journal Proceedings, V. 48, No. 10, Oct. 1951, pp. 145-156.
41. Kong, P. Y., “Shear Strength of High Performance Concrete Beams,” doctoral dissertation, Curtin University, Perth, Australia, 1996.
42. Li, H.; Wu, J.; and Wang, Z., “Shear Performance of Reinforced Concrete Beams with Corroded Stirrups Strengthened with Carbon Fiber-Reinforced Polymer,” ACI Structural Journal, V. 113, No. 1, Jan.-Feb. 2016, pp. 51-61. doi: 10.14359/51687913
43. Ye, Z.; Zhang, W.; and Gu, X., “Deterioration of Shear Behavior of Corroded Reinforced Concrete Beams,” Engineering Structures, V. 168, May 2018, pp. 708-720. doi: 10.1016/j.engstruct.2018.05.023
44. Suffern, C.; El-Sayed, A.; and Soudki, K., “Shear Strength of Disturbed Regions with Corroded Stirrups in Reinforced Concrete Beams,” Canadian Journal of Civil Engineering, V. 37, No. 8, 2010, pp. 1045-1056. doi: 10.1139/L10-031
45. Rodriguez, J.; Ortega, L.; and Casal, J., “Load Carrying Capacity of Concrete Structures with Corroded Reinforcement,” Construction and Building Materials, V. 11, No. 4, 1997, pp. 239-248. doi: 10.1016/S0950-0618(97)00043-3