Title:
Macroelement for Complete Shear Behavior of Continuous Deep Girders
Author(s):
Jian Liu and Boyan I. Mihaylov
Publication:
Structural Journal
Volume:
115
Issue:
4
Appears on pages(s):
1089-1099
Keywords:
crack widths; deep beam; deformation patterns; kinematic model; macroelement
DOI:
10.14359/51702047
Date:
7/1/2018
Abstract:
The evaluation of the serviceability, safety, and resilience of deep girders in bridges and buildings requires accurate models for their pre- and post-peak shear behavior. This paper purposes such a model formulated as a macroelement for deep shear spans under single and double curvature. The element has two nodes with two degrees of freedom per node (translation and rotation). The paper discusses the formulation of the macroelement based on a three parameter kinematic theory and provides comparisons with tests. It is shown that the macroelement captures the redistribution of forces in continuous members, and in this way predicts their enhanced ductility as compared to simply supported beams. It is also shown that the model captures the opening of the critical shear cracks under loading. The crack predictions can be compared with field measurements to accurately evaluate the safety of the structure, and in this way to avoid potential costly strengthening measures.
Related References:
1. Birrcher, D. B., “Design of Reinforced Concrete Deep Beams for Strength and Serviceability,” doctoral thesis, University of Texas at Austin, Austin, TX, 2009.
2. Liu, J., and Mihaylov, B. I., “A Comparative Study of Models for Shear Strength of Reinforced Concrete Deep Beams,” Engineering Structures, V. 112, Apr. 2016, pp. 81-89. doi: 10.1016/j.engstruct.2016.01.012
3. 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.
4. Matamoros, A. B., and Wong, K. H., “Design of Simply Supported Deep Beams using Strut-and-Tie Models,” ACI Structural Journal, V. 100, No. 6, Nov.-Dec. 2003, pp. 704-712.
5. Tang, C. Y., and Tan, K. H., “Interactive Mechanical Model for Shear Strength of Deep Beams,” Journal of Structural Engineering, ASCE, V. 130, No. 10, 2004, pp. 1534-1544. doi: 10.1061/(ASCE)0733-9445(2004)130:10(1534)
6. Russo, G.; Venir, R.; and Pauletta, M., “Reinforced Concrete Deep Beams—Shear Strength Model and Design Formula,” ACI Structural Journal, V. 102, No. 3, May-June 2005, pp. 429-437.
7. Tan, K. H., and Cheng, G. H., “Size Effect on Shear Strength of Deep Beams: Investigating with Strut-and-Tie Model,” Journal of Structural Engineering, ASCE, V. 132, No. 5, 2006, pp. 673-685. doi: 10.1061/(ASCE)0733-9445(2006)132:5(673)
8. Yang, K. H., and Ashour, A. F., “Strut-and-Tie Model based on Crack Band Theory for Deep Beams,” Journal of Structural Engineering, ASCE, V. 137, No. 10, 2011, pp. 1030-1038. doi: 10.1061/(ASCE)ST.1943-541X.0000351
9. Foster, S. J., “Design of Non-Flexural Members for Shear,” Cement and Concrete Composites, V. 20, No. 6, 1998, pp. 465-475. doi: 10.1016/S0958-9465(98)00029-8
10. Foster, S. J., and Gilbert, R. I., “The Design of Non-Flexural Members with Normal and High-Strength Concretes,” ACI Structural Journal, V. 93, No. 1, Jan.- Feb. 1996, pp. 3-10.
11. Garber, D. B.; Gallardo, J. M.; Huaco, G. D.; Samaras, V. A.; and Breen, J. E., “Experimental Evaluation of Strut-and-Tie Model of Indeterminate Deep Beam,” ACI Structural Journal, V. 111, No. 4, July-Aug. 2014, pp. 873-880. doi: 10.14359/51686738
12. Salem, H. M., and Maekawa, K., “Computer-Aided Analysis of Reinforced Concrete Using a Refined Nonlinear Strut and Tie Model Approach,” Journal of Advanced Concrete Technology, V. 4, No. 2, 2006, pp. 325-336. doi: 10.3151/jact.4.325
13. Ashour, A., and Yang, K. H., “Application of Plasticity Theory to Reinforced Concrete Deep Beams: A Review,” Magazine of Concrete Research, V. 60, No. 9, 2008, pp. 657-664. doi: 10.1680/macr.2008.00038
14. CSA A23.3-05, “Design of Concrete Structures,” Canadian Standards Association, Mississauga, ON, Canada, 2005.
15. European Committee for Standardization, “EN 1992-1-1 Eurocode 2: Design of Concrete Structures – Part 1-1: General Rules and Rules for Buildings,” CEN, Brussels, Belgium, 2004.
16. ACI Committee 318, “Building Code Requirements for Structural Concrete (ACI 318-11) and Commentary,” American Concrete Institute, Farmington Hills, MI, 2011, 503 pp.
17. AASHTO, “AASHTO LRFD Bridge Design Specifications,” fourth edition, American Association of State Highway Officials, Washington, DC, 2007, 1526 pp.
18. Wong, P. S., and Vecchio, F. J., “VecTor2 and FormWorks User’s Manual,” University of Toronto, Toronto, ON, Canada, 2002.
19. Červenka, J., “ATENA Program Documentation Part 4-1: Tutorial for Program ATENA 2D,” Červenka Consulting s.r.o., Prague, Czech Republic, 2015.
20. Manie, J., “DIANA-9.5 User’s Manual - Release 9.5,” TNO DIANA BV, Delft, the Netherlands, 2014.
21. Mihaylov, B. I.; Hunt, B.; Bentz, E. C.; and Collins, M. P., “Three-Parameter Kinematic Theory for Shear Behavior of Continuous Deep Beams,” ACI Structural Journal, V. 112, No. 1, Jan.-Feb. 2015, pp. 47-57. doi: 10.14359/51687180
22. Mihaylov, B. I.; Bentz, E. C.; and Collins, M. P., “Two-Parameter Kinematic Theory for Shear Behavior of Deep Beams,” ACI Structural Journal, V. 110, No. 3, Mar.-Apr. 2013, pp. 447-456.
23. Mihaylov, B. I., “Five-Spring Model for Complete Shear Behavior of Deep Beams,” Structural Concrete, V. 16, No. 1, 2015, pp. 71-83. doi: 10.1002/suco.201400044
24. Vecchio, F. J., and Collins, M. P., “The Modified Compression Field Theory for Reinforced Concrete Elements Subjected to Shear,” ACI Journal Proceedings, V. 83, No. 2, Mar.-Apr. 1986, pp. 219-231.
25. Popovics, S., “A Review of Stress-Strain Relationships for Concrete,” ACI Journal Proceedings, V. 67, No. 3, Mar. 1970, pp. 243-248.
26. Li, B.; Maekawa, K.; and Okamura, H., “Contact Density Model for Stress Transfer across Cracks in Concrete,” Journal of the Faculty of Engineering,” 40, No. 1, University of Tokyo, Tokyo, Japan, 1989, pp. 9-52.
27. Vecchio, F. J., “Towards Cyclic Load Modeling of Reinforced Concrete,” ACI Structural Journal, V. 96, No. 2, Mar.-Apr. 1999, pp. 193-202.
28. Mihaylov, B. I.; Bentz, E. C.; and Collins, M. P., “Behavior of Large Deep Beam Subjected to Monotonic and Reversed Cyclic Shear,” ACI Structural Journal, V. 107, No. 6, Nov.-Dec. 2010, pp. 726-734.