Abstract
The compatibility strut-and-tie method (C-STM) is a well-established nonlinear modeling tool to efficiently and accurately predict the overall load–deformation response of shear-critical RC members subjected to combined bending and shear. Such a high-performance tool, however, is computationally demanding. In this paper, a simplified limit analysis model based on C-STM is presented to predict the load-carrying capacity of RC beams. Amenable for hand methods of analysis, the approach is called the truss-arch model unified (TAMU). The TAMU approach accounts for the failure mechanism of the diagonal concrete strut that is softened because of the transverse tensile strain. Instead of providing overall force–deformation behavior, this model focuses on evaluating the ultimate load-carrying capacity by assuming the failure mechanism occurs when the principal diagonal strut reaches its softened strength in shear-critical beams. An explicit equation for the principal strain ratio is derived to evaluate the softened concrete strength and is used to develop formulas for the ultimate load-carrying capacity. The validity of the formulas is verified through a comparison of the predicted ultimate load-carrying capacities with maximum measured strengths from previous experimental results on large-scale physical tests representing bridge piers. The TAMU approach is then compared with other code-based strength analysis methods and shows better predictions of the maximum load-carrying capacity.
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Data Availability Statement
Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.
References
AASHTO. 2017. AASHTO LRFD bridge design specifications. 8th ed. Washington, DC: AASHTO.
ACI (American Concrete Institute). 2019. Building code requirements for structural concrete. Farmington Hills, MI: ACI.
Birely, A. C., K. J. Yole, J. D. Lee, C. D. McKee, and J. B. Mander. 2020. “Experimental behavior of reinforced concrete and pretensioned concrete bent caps.” J. Bridge Eng. 25 (2): 04019137. https://doi.org/10.1061/(ASCE)BE.1943-5592.0001392.
Birrcher, D. B., R. G. Tuchscherer, M. Huizinga, and O. Bayrak. 2014. “Depth effect in deep beams.” ACI Struct. J. 111 (4): 731–740. https://doi.org/10.14359/51687002.
Bracci, J. M., P. B. Keating, and M. B. D. Hueste. 2000. Cracking in RC bent caps. College Station, TX: Texas Transportation Institute.
Brown, M. D., and O. Bayrak. 2008. “Design of deep beams using strut-and-tie models—Part I: Evaluating US provisions.” ACI Struct. J. 105 (4): 395–404.
Fenwick, R. C., and T. Paulay. 1968. “Mechanisms of shear resistance of concrete beams.” J. Struct. Div. 94 (10): 2325–2350. https://doi.org/10.1061/JSDEAG.0002092.
FIP (International Federation for Structural Concrete). 1996. Practical design of structural concrete. London: FIP.
He, Z.-Q., Z. Liu, and Z. J. Ma. 2012. “Investigation of load-transfer mechanisms in deep beams and corbels.” ACI Struct. J. 109 (4): 467–476.
Hwang, S.-J., W.-Y. Lu, and H.-J. Lee. 2000. “Shear strength prediction for deep beams.” ACI Struct. J. 97 (3): 367–376.
Karthik, M. M., J. B. Mander, and S. Hurlebaus. 2016. “Displacement-based compatibility strut-and-tie method and application to monotonic and cyclic loading.” Eng. Struct. 142 (6): 04016010. https://doi.org/10.1061/(ASCE)ST.1943-541X.0001457.
Karthik, M. M., J. B. Mander, and S. Hurlebaus. 2020. “Simulating behaviour of large reinforced concrete beam-column joints subject to ASR/DEF deterioration and influence of corrosion.” Eng. Struct. 222 (Jan): 111064. https://doi.org/10.1016/j.engstruct.2020.111064.
Kim, J. H., and J. B. Mander. 1999. Truss modeling of reinforced concrete shear-flexure behavior. New York: State Univ. of New York at Buffalo.
Kim, J. H., and J. B. Mander. 2000a. “Cyclic inelastic strut-tie modeling of shear-critical reinforced concrete members.” ACI Spec. Publ. 193 (5): 707–728.
Kim, J. H., and J. B. Mander. 2000b. “Seismic detailing of reinforced concrete beam-column connections.” Struct. Eng. Mech. 10 (6): 589–601. https://doi.org/10.12989/sem.2000.10.6.589.
Lee, J. D. 2020. “Development of a truss-arch model unified for flexure and shear-critical interaction of structural concrete members.” Ph.D. dissertation, Dept. of Civil and Environmental Engineering, Texas A&M Univ.
Liu, S.-H., J. M. Bracci, J. B. Mander, and S. Hurlebaus. 2017. “Performance of D-regions affected by alkali-silica reaction: Experimental and analytical study.” J. Struct. Eng. 143 (9): 04017109. https://doi.org/10.1061/(ASCE)ST.1943-541X.0001847.
Marti, P. 1985. “Basic tools of reinforced concrete beam design.” ACI J. Proc. 82 (1): 46–56.
Matsumoto, E. E., M. C. Waggoner, G. Sumen, M. E. Kreger, S. L. Wood, and J. E. Breen. 2001. Development of a precast bent cap system. Austin, TX: Univ. of Texas at Austin.
McKee, C. D., J. D. Lee, A. C. Birely, and J. B. Mander. 2020. “Experimental behavior of pretensioned bent caps with internal voids for weight reduction.” J. Bridge Eng. 25 (1): 04019110. https://doi.org/10.1061/(ASCE)BE.1943-5592.0001410.
Park, R., and T. Paulay. 1975. Reinforced concrete structures. New York: Wiley.
Paulay, T. 1971. “Coupling beams of reinforced concrete shear walls.” J. Struct. Div. 97 (3): 843–862. https://doi.org/10.1061/JSDEAG.0002848.
Sahoo, D. K., M. S. V. Sagi, B. Singh, and P. Bhargava. 2010. “Effect of detailing of web reinforcement on the behavior of bottle-shaped struts.” J. Adv. Concr. Technol. 8 (3): 303–314. https://doi.org/10.3151/jact.8.303.
Schlaich, J., K. Schaefer, and M. Jennewein. 1987. “Toward a consistent design of structural concrete.” PCI J. 32 (3): 74–150. https://doi.org/10.15554/pcij.05011987.74.150.
Scott, R. M., J. B. Mander, and J. M. Bracci. 2012a. “Compatibility strut-and-tie modeling: Part I—Formulation.” ACI Struct. J. 109 (5): 635–644.
Scott, R. M., J. B. Mander, and J. M. Bracci. 2012b. “Compatibility strut-and-tie modeling: Part II—Implementation.” ACI Struct. J. 109 (5): 645–653.
Vecchio, F. J. 2000. “Analysis of shear-critical reinforced concrete beams.” ACI Struct. J. 97 (1): 102–110.
Young, B. S., J. M. Bracci, P. B. Keating, and M. B. D. Hueste. 2002. “Cracking in reinforced concrete bent caps.” ACI Struct. J. 99 (4): 488–498.
Zhu, R. R. H., W. Wanichakorn, T. T. C. Hsu, and J. Vogel. 2003. “Crack width prediction using compatibility-aided strut-and-tie model.” ACI Struct. J. 100 (4): 413–421.
Information & Authors
Information
Published In
Journal of Structural Engineering
Volume 148 • Issue 7 • July 2022
Copyright
© 2022 American Society of Civil Engineers.
History
Received: Aug 19, 2021
Accepted: Feb 23, 2022
Published online: Apr 22, 2022
Published in print: Jul 1, 2022
Discussion open until: Sep 22, 2022
ASCE Technical Topics:
- Beams
- Business management
- Concrete
- Concrete beams
- Decision making
- Decision support systems
- Engineering materials (by type)
- Foundation design
- Foundations
- Geotechnical engineering
- Load bearing capacity
- Material mechanics
- Material properties
- Materials engineering
- Practice and Profession
- Reinforced concrete
- Shear strength
- Strength of materials
- Structural behavior
- Structural engineering
- Structural members
- Structural strength
- Structural systems
- Struts
- Trusses
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