Title:
Redistribution of Internal Forces in Reinforced Concrete Beams Subjected to Combined Load
Author(s):
Jung-Yoon Lee, Na-Yeong Kim, DongIk Shin, Kil-Hee Kim, and Muhammad Haroon
Publication:
Structural Journal
Volume:
120
Issue:
6
Appears on pages(s):
151-165
Keywords:
bending moment; combined load; force redistribution; torsional strength
DOI:
10.14359/51739093
Date:
11/1/2023
Abstract:
In an actual structure, torsion seldom acts alone; rather, a complex
load combination acts together. Members subjected to a complex
loading condition—that is, shear, bending, torsion, and so on—
show lower strength compared to the members under torsion only.
However, when structural members exhibit ductile behavior, the
force-deformation correlation of shear force, bending, and torsional
moment may change due to the redistribution of internal forces. In
this study, the interaction of bending and torsional moments was
evaluated by analyzing the test results of 123 reinforced concrete
(RC) members subjected to combined loading. Additionally, 13 RC
beams subjected to combined actions of bending and torsional
moments were tested to investigate the effect of force redistribution.
The results indicate that the post-yielding behavior of actual
members subjected to combined loading significantly differs from
the theoretically predicted one. This is because the theoretically
induced bending and torsional moment interaction curves are
based on strengths corresponding to the yield point of reinforcement. However, the experimental results show that the force redistribution mechanism develops after the first reinforcement yielding. Consequently, the torsional strength does not decrease as sharply as theoretically assumed, even when the bending moment increases.
Related References:
1. Hsu, T. T. C., “Torsion of Structural Concrete—Behavior of Reinforced Concrete Rectangular Members,” Torsion of Structural Concrete, SP-18, American Concrete Institute, Farmington Hills, MI, 1968, pp. 261-306.
2. McMullen, A. E., and Rangan, B. V., “Pure Torsion in Rectangular Sections—A Re-Examination,” ACI Journal Proceedings, V. 75, No. 10, Oct. 1978, pp. 511-519.
3. Mitchell, D., and Collins, M. P., “The Behaviour of Structural Concrete Beams in Pure Torsion,” Publication 74-06, Department of Civil Engineering, University of Toronto, Toronto, ON, Canada, 1974, 88 pp.
4. MacGregor, J. G., and Ghoneim, M. G., “Design for Torsion,” ACI Structural Journal, V. 92, No. 2, Mar.-Apr. 1995, pp. 211-218.
5. Rahal, K. N., and Collins, M. P., “Effect of Thickness of Concrete Cover on Shear-Torsion Interaction—An Experimental Investigation,” ACI Structural Journal, V. 92, No. 3, May-June 1995, pp. 334-342.
6. Lee, J.-Y., and Kim, S.-W., “Torsional Strength of RC Beams Considering Tension Stiffening Effect,” Journal of Structural Engineering, ASCE, V. 136, No. 11, Nov. 2010, pp. 1367-1378. doi: 10.1061/(ASCE)ST.1943-541X.0000237
7. Rasmussen, L. J., and Baker, G., “Torsion in Reinforced Normal and High-Strength Concrete Beams—Part 1: Experimental Test Series,” ACI Structural Journal, V. 92, No. 1, Jan.-Feb. 1995, pp. 56-62.
8. Koutchoukali, N.-E., and Belarbi, A., “Torsion of High-Strength Reinforced Concrete Beams and Minimum Reinforcement Requirement,” ACI Structural Journal, V. 98, No. 4, July-Aug. 2001, pp. 462-469.
9. Fang, I.-K., and Shiau, J.-K., “Torsional Behavior of Normal- and High-Strength Concrete Beams,” ACI Structural Journal, V. 101, No. 3, May-June 2004, pp. 304-313.
10. Kim, C.; Kim, S.; Kim, K.-H.; Shin, D.; Haroon, M.; and Lee, J.-Y., “Torsional Behavior of Reinforced Concrete Beams with High-Strength Steel Bars,” ACI Structural Journal, V. 116, No. 6, Nov. 2019, pp. 251-263. doi: 10.14359/51718014
11. Lee, J.-Y.; Haroon, M.; Shin, D.; and Kim, S.-W., “Shear and Torsional Design of Reinforced Concrete Members with High-Strength Reinforcement,” Journal of Structural Engineering, ASCE, V. 147, No. 2, Feb. 2021, p. 04020327. doi: 10.1061/(ASCE)ST.1943-541X.0002887
12. Gesund, H., and Boston, L. A., “Ultimate Strength in Combined Bending and Torsion of Concrete Beams Containing Only Longitudinal Reinforcement,” ACI Journal Proceedings, V. 61, No. 11, Nov. 1964, pp. 1453-1472.
13. Collins, M. P.; Walsh, P. F.; Archer, F. E.; and Hall, A. S., “Ultimate Strength of Reinforced Concrete Beams Subjected to Combined Torsion and Bending,” Torsion of Structural Concrete, SP-18, American Concrete Institute, Farmington Hills, MI, 1968, pp. 379-402.
14. Pandit, G. S., and Warwaruk, J., “Reinforced Concrete Beams in Combined Bending and Torsion,” Torsion of Structural Concrete, SP-18, American Concrete Institute, Farmington Hills, MI, 1968, pp. 133-163.
15. Pritchard, R. G., “Torsion Shear Interaction of Reinforced Concrete Beams,” master’s thesis, University of Calgary, Calgary, AB, Canada, 1970, 146 pp.
16. Badawy, H. E. I.; McMullen, A. E.; and Jordaan, I. J., “Experimental Investigation of the Collapse of Reinforced Concrete Curved Beams,” Magazine of Concrete Research, V. 29, No. 99, June 1977, pp. 59-69. doi: 10.1680/macr.1977.29.99.59
17. Ewida, A. A., and McMullen, A. E., “Concrete Members Under Combined Torsion and Shear,” Journal of the Structural Division, ASCE, V. 108, No. 4, Apr. 1982, pp. 911-928. doi: 10.1061/JSDEAG.0005932
18. Elfren, L.; Karlsson, I.; and Losberg, A., “Torsion-Bending-Shear Interaction for Concrete Beams,” Journal of the Structural Division, ASCE, V. 100, No. 8, Aug. 1974, pp. 1657-1676. doi: 10.1061/JSDEAG.0003843
19. Klus, J. P., “Ultimate Strength of Reinforced Concrete Beams in Combined Torsion and Shear,” ACI Journal Proceedings, V. 65, No. 3, Mar. 1968, pp. 210-216.
20. McMullen, A., and Warwaruk, J., “Concrete Beams in Bending, Torsion and Shear,” Journal of the Structural Division, ASCE, V. 96, No. 5, May 1970, pp. 885-903. doi: 10.1061/JSDEAG.0002577
21. Osburn, D. L.; Mayoglou, B.; and Mattock, A. H., “Strength of Reinforced Concrete Beams with Web Reinforcement in Combined Torsion, Shear, and Bending,” ACI Journal Proceedings, V. 66, No. 1, Jan. 1969, pp. 31-41.
22. Li, Q., “Performance of RC Bridge Columns under Cyclic Combined Loading Including Torsion,” PhD dissertation, University of Houston, Houston, TX, 2012, 346 pp.
23. Greene, G. Jr., and Belarbi, A., “Model for Reinforced Concrete Members under Torsion, Bending, and Shear. I: Theory,” Journal of Engineering Mechanics, ASCE, V. 135, No. 9, Sept. 2009, pp. 961-969. doi: 10.1061/(ASCE)0733-9399(2009)135:9(961)
24. Ju, H., “Multi-Potential Capacity Model for Torsion in Reinforced Concrete Members Subjected to Combined Loads,” PhD thesis, University of Seoul, Seoul, South Korea, 2017, 321 pp.
25. Ju, H., and Lee, D., “Nonlinear Analysis of Reinforced Concrete Members Subjected to Combined Torsion and Bending Moment,” ACI Structural Journal, V. 118, No. 4, July 2021, pp. 55-70.
26. ACI Committee 318, “Building Code Requirements for Structural Concrete (ACI 318-19) and Commentary (ACI 318R-19) (Reapproved 2022),” American Concrete Institute, Farmington Hills, MI, 2019, 624 pp.
27. EN 1992, “Eurocode 2: Design of Concrete Structures,” European Committee for Standardization, Brussels, Belgium, 1992.
28. Joint ACI-ASCE Committee 445, “Report on Torsion in Structural Concrete (ACI 445.1R-12) (Reapproved 2021),” American Concrete Institute, Farmington Hills, MI, 2013, 92 pp.
29. CSA A23.3:19, “Design of Concrete Structures,” CSA Group, Toronto, ON, Canada, 2019, 301 pp.
30. Hsu, T. T. C., and Mo, Y.-L., Unified Theory of Concrete Structures, John Wiley & Sons, Ltd., Chichester, UK, 2010, 520 pp.
31. McMullen, A. E., and Warwaruk, J., “The Torsional Strength of Rectangular Reinforced Concrete Beams Subjected to Combined Loading,” Structural Engineering Report No. 2, Department of Civil Engineering, University of Alberta, Edmonton, AB, Canada, 1967, 258 pp.
32. Onsongo, W. M., “The Diagonal Compression Field Theory for Reinforced Concrete Beams Subjected to Combined Torsion, Flexure and Axial Load,” PhD thesis, Department of Civil Engineering, University of Toronto, Toronto, ON, Canada, 1978, 261 pp.
33. Lee, J.-Y.; Haroon, M.; Park, J.; and Kim, C., “Longitudinal Axial Strain in Plastic Hinge Regions of Reinforced-Concrete Columns,” Magazine of Concrete Research, V. 71, No. 20, Oct. 2019, pp. 1043-1069. doi: 10.1680/jmacr.17.00438
34. Lampert, P., “Bruchwiderstand von Stahlbetonbalken unter Torsion und Biegung,” Institut für Baustatik, ETH Zürich, Zürich, Switzerland, 1970, 189 pp. (in German)