Title:
Strength Reduction Factors for ACI 318 Strut-and-Tie Method for Deep Beams
Author(s):
Victor Aguilar, Robert W. Barnes, and Andrzej Nowak
Publication:
Structural Journal
Volume:
119
Issue:
2
Appears on pages(s):
103-112
Keywords:
D-region; design strength; ductility; nodal zone; reinforced concrete; reliability; safety; shear; strut-and-tie model
DOI:
10.14359/51734332
Date:
3/1/2022
Abstract:
The strut-and-tie approach has gained importance in reinforced concrete design practice in the United States in the last two decades. This method has proven suitable for designing shear-critical structural members where beam theory is not applicable. However, the strength reduction factors specified for the ACI 318 strut-and-tie
method have not been calibrated based on the structural reliability approach. Therefore, the reliability of members designed according to these provisions is unknown. In this study, the reliability of deep beams designed using the strut-and-tie method according to ACI 318 building code requirements for structural concrete was determined. Statistical parameters employed for loads, material uncertainty, and fabrication uncertainty were based on published literature. The uncertainty in the analytical model was characterized
based on available test results. The findings indicate that current design practice using the strut-and-tie method promotes the likelihood of a nonductile failure mode relative to a ductile failure mode. Inconsistencies in reliability with respect to concrete strength are highlighted. The following reliability-based strength reduction
factors are suggested: ϕ = 0.65 for struts and nodal zones and ϕ = 0.90 for ties.
Related References:
1. ACI Committee 318, “Building Code Requirements for Structural Concrete (ACI 318-02) and Commentary (ACI 318R-02),” American Concrete Institute, Farmington Hills, MI, 2002, 445 pp.
2. Schlaich, J.; Schafer, K.; and Jennewein, M., “Toward a Consistent Design of Structural Concrete,” PCI Journal, V. 32, No. 3, 1987, pp. 74-150. doi: 10.15554/pcij.05011987.74.150
3. AASHTO, “LRFD Bridge Design Specifications,” first edition, American Association of State Highway and Transportation Officials, Washington, DC, 1994.
4. ACI Committee 318, “Building Code Requirements for Structural Concrete (ACI 318-14) and Commentary (ACI 318R-14),” American Concrete Institute, Farmington Hills, MI, 2014, 503 pp.
5. ACI Committee 318, “Building Code Requirements for Structural Concrete (ACI 318-19) and Commentary (ACI 318R-19),” American Concrete Institute, Farmington Hills, MI, 2019, 624 pp.
6. Schlaich, J., and Schafer, K., “Design and Detailing of Structural Concrete Using Strut-and-Tie Models,” Structural Engineering, V. 69, No. 6, 1991, pp. 113-125.
7. Joint ACI-ASCE Committee 445, “Recent Approaches to Shear Design of Structural Concrete (ACI 445R-99),” American Concrete Institute, Farmington Hills, MI, 1999, 55 pp.
8. Collins, M. P., and Mitchell, D., Prestressed Concrete Structures, Prentice Hall Englewood Cliffs, NJ, 1991.
9. Reineck, K.-H., ed., Examples for the Design of Structural Concrete with Strut-and-Tie Models, SP-208, American Concrete Institute, Farmington Hills, MI, 2002, 250 pp.
10. Reineck, K.-H., and Novak, L. C., eds., Further Examples for the Design of Structural Concrete with Strut-and-Tie Models, SP-273, American Concrete Institute, Farmington Hills, MI, 2010, 288 pp.
11. Kuchma, D. A.; Yindeesuk, S.; and Nagle, T., “Experimental Validation of Strut-and-Tie Method for Complex Regions,” ACI Structural Journal, V. 105, No. 5, Sept.-Oct. 2008, pp. 578-589.
12. Rogowsky, D. M., and MacGregor, J. G., “Design of Reinforced Concrete Deep Beams,” Concrete International, V. 8, No. 8, Aug. 1986, pp. 49-58.
13. Smith, K. N., and Vantsiotis, A. S., “Shear Strength of Deep Beams,” ACI Journal Proceedings, V. 79, No. 3, Mar. 1982, pp. 201-213.
14. Kong, F.-K.; Robins, P. J.; and Cole, D. F., “Web Reinforcement Effects on Deep Beams,” ACI Journal Proceedings, V. 67, No. 12, Dec. 1970, pp. 1010-1017.
15. Clark, A. P., “Diagonal Tension in Reinforced Concrete Beams,” ACI Journal Proceedings, V. 48, No. 10, Oct. 1951, pp. 145-156.
16. Oh, J. K., and Shin, S. W., “Shear Strength of Reinforced High-Strength Concrete Deep Beams,” ACI Structural Journal, V. 98, No. 2, Mar.-Apr. 2001, pp. 164-173.
17. Aguilar, G.; Matamoros, A. B.; and Parra-Montesinos, G., “Experimental Evaluation of Design Procedures for Shear Strength of Deep Reinforced Concrete Beams,” ACI Structural Journal, V. 99, No. 4, July-Aug. 2002, pp. 539-548.
18. Quintero-Febres, C. G.; Parra-Montesinos, G.; and Wight, J. K., “Strength of Struts in Deep Concrete Members Designed Using Strut-and-Tie Method,” ACI Structural Journal, V. 103, No. 4, July-Aug. 2006, p. 577.
19. Tan, K.-H.; Kong, F.-K.; and Teng, S., “High-Strength Concrete Deep Beams with Effective Span and Shear Span Variations,” ACI Structural Journal, V. 92, No. 4, July-Aug. 1995, pp. 395-405.
20. Anderson, N. S., and Ramirez, J. A., “Detailing of Stirrup Reinforcement,” ACI Structural Journal, V. 86, No. 5, Sept.-Oct. 1989, pp. 507-515.
21. Tuchscherer, R.; Birrcher, D.; and Huizinga, M., “Confinement of Deep Beam Nodal Regions,” ACI Structural Journal, V. 107, No. 6, Nov.-Dec. 2010, p. 709
22. Hwang, S.-J.; Lu, W.-Y.; and Lee, H.-J., “Shear Strength Prediction for Deep Beams,” ACI Structural Journal, V. 97, No. 3, May-June 2000, pp. 367-376.
23. Garay-Moran, J. D., and Lubell, A. S., “Behavior of Deep Beams Containing High-Strength Longitudinal Reinforcement,” ACI Structural Journal, V. 113, No. 1, Jan.-Feb. 2016, doi: 10.14359/51687910
24. Ismail, K. S.; Guadagnini, M.; and Pilakoutas, K., “Shear Behavior of Reinforced Concrete Deep Beams,” ACI Structural Journal, V. 114, No. 1, Jan.-Feb. 2016, doi: 10.14359/51689151
25. Chen, H.; Yi, W.-J.; and Hwang, H.-J., “Cracking Strut-and-Tie Model for Shear Strength Evaluation of Reinforced Concrete Deep Beams,” Engineering Structures, V. 163, 2018, pp. 396-408. doi: 10.1016/j.engstruct.2018.02.077
26. Kuchma, D. A.; Wei, S.; Sanders, D. H.; Belarbi, A.; and Novak, L. C., “Development of the One-Way Shear Design Provisions of ACI 318-19 for Reinforced Concrete,” ACI Structural Journal, V. 116, No. 4, July-Aug. 2019, doi: 10.14359/51716739
27. Nowak, A. S., and Szerszen, M. M., “Calibration of Design Code for Buildings (ACI 318) Part I: Statistical Models for Resistance,” ACI Structural Journal, V. 100, No. 3, May-June 2003, pp. 377-382.
28. Szerszen, M. M., and Nowak, A. S. “Calibration of Design Code for Buildings (ACI 318) Part 2: Reliability Analysis and Resistance Factors,” ACI Structural Journal, V. 100, No. 3, May-June 2003, pp. 383-391.
29. Nowak, A. S.; Rakoczy, A. M.; and Szeliga, E. K., “Revised Statistical Resistance Models for R/C Structural Components,” Andy Scanlon Symposium on Serviceability and Safety of Concrete Structures: From Research to Practice, P. H. Bischoff and E. Musselman, eds., American Concrete Institute, Farmington Hills, MI, 2012, pp. 1-16.
30. Breen, J. E., “Anchorage Zone Reinforcement for Post-Tensioned Concrete Girders,” V. 356, Transportation Research Board, Washington, DC, 1994.
31. Nowak, A. S., and Collins, K. R., Reliability of Structures, second edition, CRC Press, Boca Raton, FL, 2013.
32. Nowak, A. S., “NCHRP Report 368: Calibration of LRFD Bridge Design Code,” Transportation Research Board, National Research Council, Washington, DC, 1999.
33. Nowak, A. S., and Lind, N. C., “Practical Code Calibration Procedures,” Canadian Journal of Civil Engineering, V. 6, No. 1, 1979, pp. 112-119. doi: 10.1139/l79-012
34. Cornell, C. A., “Bounds on the Reliability of Structural Systems,” Journal of the Structural Division, V. 93, No. 1, 1967, pp. 171-200. doi: 10.1061/JSDEAG.0001577
35. Cornell, C. A., “A Probability-Based Structural Code,” ACI Journal Proceedings, V. 66, No. 12, Dec. 1969, pp. 974-985.
36. Ellingwood, B.; Galambos, T. V.; MacGregor, J. G. et al., “Development of a Probability Based Load Criterion for American National Standard A 58,” NBS Special Report 577, U.S. Department of Commerce, National Bureau of Standards, 1980.
37. Bartlett, F. M., and MacGregor, J. G. “Variation of In-Place Concrete Strength in Structures,” ACI Materials Journal, V. 96, No. 2, Mar.-Apr. 1999, pp. 261-270.
38. Park, J., and Kuchma, D. A., “Strut-and-Tie Model Analysis for Strength Prediction of Deep Beams,” ACI Structural Journal, V. 104, No. 6, Nov.-Dec. 2007, pp. 657-666.
39. ACI Committee 318, “Building Code Requirements for Structural Concrete (ACI 318-05) and Commentary (ACI 318R-05),” American Concrete Institute, Farmington Hills, MI, 2005, 473 pp.
40. Uribe, C. M., and Alcocer, S. M., “Deep Beam Design in Accordance with ACI 318-2002,” Examples for the Design of Structural Concrete with Strut-and-Tie Models, K.-H. Reineck, ed., American Concrete Institute, Farmington Hills, MI, 2002, pp. 65-80.
41. Shuraim, A. B., and El-Sayed, A. K., “Experimental Verification of Strut and Tie Model for HSC Deep Beams without Shear Reinforcement,” Engineering Structures, V. 117, 2016, pp. 71-85. doi: 10.1016/j.engstruct.2016.03.002
42. Su, R. K. L., and Looi, D. T. W., “Revisiting Unreinforced Strut Efficiency Factor,” ACI Structural Journal, V. 113, No. 2, Mar.-Apr. 2016, doi: 10.14359/51688062
43. Mohamed, K.; Farghaly, A. S.; and Benmokrane, B., “Strut Efficiency-Based Design for Concrete Deep Beams Reinforced with Fiber-Reinforced Polymer Bars,” ACI Structural Journal, V. 113, No. 4, July-Aug. 2016, doi: 10.14359/51688476
44. Ismail, K. S.; Guadagnini, M.; and Pilakoutas, K., “Strut-and-Tie Modeling of Reinforced Concrete Deep Beams,” Journal of Structural Engineering, ASCE, V. 144, No. 2, 2018, p. 04017216 doi: 10.1061/(ASCE)ST.1943-541X.0001974