Technical Papers
Aug 22, 2020

Shear-Transfer Mechanisms and Strength Modeling of RC Continuous Deep Beams

Publication: Journal of Structural Engineering
Volume 146, Issue 11

Abstract

Based on experimental results including the crack pattern and maximum applied strut stress, as well as on stress states obtained using a nonlinear finite-element analysis, it is identified that the typical critical shear crack of continuous deep beams is a web-shear crack, which has a large effect on shear-transfer mechanisms of deep beams. By theoretically considering the influence of the web-shear crack on the diagonal strut in a strut-and-tie model (STM) of continuous deep beams, a cracking strut-and-tie model (CSTM) has been developed. Shear-transfer mechanisms including aggregate interlock action, dowel action of longitudinal bars, and tension of web reinforcement are rationally considered. By comparing with a large database including 90 tests, the CSTM is verified to well predict the effect of main parameters including shear span-to-depth ratio, longitudinal reinforcement ratio, stirrup ratio, concrete compressive strength, and effective depth on the shear strength. Moreover, the proposed model is simplified to be used in the practical shear design, which shows a better prediction than the STM of a current standard.

Get full access to this article

View all available purchase options and get full access to this article.

Data Availability Statement

All data, models, and code generated or used during the study appear in the published article.

Acknowledgments

The authors would like to acknowledge the financial support provided for this work by the National Natural Science Foundation of China (Nos. 51338004 and 51878260).

References

AASHTO. 2017. AASHTO LRFD bridge design specifications. Washington, DC: AASHTO.
Abdul-Razzaq, K. S., and S. F. Jebur. 2017. “Experimental verification of strut and tie method for reinforced concrete deep beams under various types of loadings.” J. Eng. Sustainable Dev. 21 (6): 39–55.
ACI (American Concrete Institute). 2014. Building code requirements for structural concrete (ACI 318-14): Commentary on building code requirements for structural concrete 14. ACI 318-14. Farmington Hills, MI: ACI.
Ashour, A. F. 1997. “Tests of reinforced concrete continuous deep beams.” ACI Struct. J. 94 (1): 3–11.
Ashour, A. F., and K. H. Yang. 2008. “Application of plasticity theory to reinforced concrete deep beams: A review.” Mag. Concr. Res. 60 (9): 657–664. https://doi.org/10.1680/macr.2008.00038.
Asin, M. 1999. The behaviour of reinforced concrete continuous deep beams. Delft, Netherlands: Delft Univ. of Technology.
Asin, M., and J. C. Walraven. 1995. “Numerical analysis of reinforced concrete continuous deep beams.” Heron-English Ed. 40 (2): 164–178.
Bazant, Z. P., and B. H. Oh. 1983. “Crack band theory for fracture of concrete.” Matériaux et Constr. 16 (3): 155–177.
Bentz, E. C. 2000. “Sectional analysis of reinforced concrete members.” Ph.D. thesis, Dept. of Civil Engineering, Univ. of Toronto.
Bentz, E. C., F. J. Vecchio, and M. R. Collins. 2006. “Simplified modified compression field theory for calculating shear strength of reinforced concrete elements.” ACI Struct. J. 103 (4): 614–624.
Brown, M. D., and O. Bayrak. 2008a. “Design of deep beams using strut-and-tie models. Part I: Evaluating US provisions.” ACI Struct. J. 105 (4): 395–404.
Brown, M. D., and O. Bayrak. 2008b. “Design of deep beams using strut-and-tie models. Part II: Design recommendations.” ACI Struct. J. 105 (4): 405–413.
BSI (British Standards Institution). 2004. Eurocode 2: Design of concrete structures. Part 1-1: General rules and rules for buildings. London: BSI.
Cervenka, V., J. Cervenka, T. Sajdlova, and R. Pukl. 2017. “Uncertainty of predicting shear strength.” Solid State Phenom. 259: 244–248. https://doi.org/10.4028/www.scientific.net/SSP.259.244.
Cervenka, V., L. Jendele, and J. Cervenka. 2012. ATENA program documentation. Part 1: Theory, 2013. Prague, Czech Republic: Cervenka Consulting.
Červenka, J., and V. K. Papanikolaou. 2008. “Three dimensional combined fracture–plastic material model for concrete.” Int. J. Plast. 24 (12): 2192–2220. https://doi.org/10.1016/j.ijplas.2008.01.004.
Chen, H., W.-J. Yi, and B. Huang. 2016. “Research on shear strength of reinforced concrete continuous deep flexural members based on database.” [In Chinese.] J. Build. Struct. 37 (5): 273–283.
Chen, H., W.-J. Yi, and H.-J. Hwang. 2018. “Cracking strut-and-tie model for shear strength evaluation of reinforced concrete deep beams.” Eng. Struct. 163 (May): 396–408. https://doi.org/10.1016/j.engstruct.2018.02.077.
Chen, H., W.-J. Yi, and Z. J. Ma. 2019a. “Shear size effect in simply supported RC deep beams.” Eng. Struct. 182 (Mar): 268–278. https://doi.org/10.1016/j.engstruct.2018.12.062.
Chen, H., W.-J. Yi, Z. J. Ma, and H.-J. Hwang. 2019b. “Shear strength of reinforced concrete simple and continuous deep beams.” ACI Struct. J. 116 (6): 31–40. https://doi.org/10.14359/51718003.
Chetchotisak, P., J. Teerawong, S. Yindeesuk, and J. Song. 2014. “New strut-and-tie-models for shear strength prediction and design of RC deep beams.” Comput. Concr. 14 (1): 19–40. https://doi.org/10.12989/cac.2014.14.1.019.
CSA (Canadian Standard Association). 2014. Design of concrete structures. CSA A23.3. Mississauga, ON, Canada: CSA.
fib (Fédération Internationale du Béton). 2010. fib model code for concrete structures. Lausanne, Switzerland: Ernst & Sohn.
FIP (Fédération Internationale de la Précontrainte). 1999. Practical design of structural concrete. London: SETO.
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.
Hordijk, D. A. 1991. “Local approach to fatigue of concrete.” Ph.D. thesis, Dept. of Civil Engineering and Geosciences, Delft Univ. of Technology.
Hu, Q., M. T. Ley, and B. W. Russell. 2014. “Determining efficient strut-and-tie models for simply supported beams using minimum strain energy.” ACI Struct. J. 111 (5): 1015–1026. https://doi.org/10.14359/51686824.
Hwang, S.-J., W.-Y. Lu, and H.-J. Lee. 2000. “Shear strength prediction for deep beams.” ACI Struct. J. 97 (3): 367–376.
Ismail, K. S., M. Guadagnini, and K. Pilakoutas. 2018. “Strut-and-tie modeling of reinforced concrete deep beams.” J. Struct. Eng. 144 (2): 04017216. https://doi.org/10.1061/(ASCE)ST.1943-541X.0001974.
Jeli, I., M. N. Pavlović, and M. D. Kotsovos. 1999. “Study of dowel action in reinforced concrete beams.” Mag. Concr. Res. 51 (2): 131–141. https://doi.org/10.1680/macr.1999.51.2.131.
Jendele, L., and J. Cervenka. 2006. “Finite element modelling of reinforcement with bond.” Comput. Struct. 84 (28): 1780–1791. https://doi.org/10.1016/j.compstruc.2006.04.010.
Kani, G. 1964. “The riddle of shear failure and its solution.” ACI J. 61 (4): 441–467.
Laughery, L., and S. Pujol. 2015. “Compressive strength of unreinforced struts.” ACI Struct. J. 112 (5): 838–896. https://doi.org/10.14359/51687711.
Marti, P. 1985. “Basic tools of reinforced concrete beam design.” ACI Struct. J. 82 (1): 46–56.
Matamoros, A. B., and K. Wong. 2003. “Design of simply supported deep beams using strut and tie models.” ACI Struct. J. 100 (6): 704–712.
Mihaylov, B., B. Hunt, E. Bentz, and M. P. Collins. 2015. “Three-parameter kinematic theory for shear behaviour of continuous deep beams.” ACI Struct. J. 112 (1): 47–58. https://doi.org/10.14359/51687180.
Mihaylov, B. I., E. C. Bentz, and M. P. Collins. 2013. “Two-parameter kinematic theory for shear behavior of deep beams.” ACI Struct. J. 110 (3): 447–455.
Nguyen, P. T. 2013. “A study of shear behavior of reinforced concrete deep beams.” Ph.D. thesis, Graduate School, Univ. of Texas at Austin.
Park, J.-W., and D. Kuchma. 2007. “Strut-and-tie model analysis for strength prediction of deep beams.” ACI Struct. J. 104 (6): 657–666.
Paulay, T., R. Park, and M. H. Phillips. 1974. “Horizontal construction joints in cast-in-place reinforced concrete.” ACI Spec. Publ. 42: 599–616.
Reineck, K. H., D. A. Kuchma, K. S. Kim, and S. Marx. 2003. “Shear database for reinforced concrete members without shear reinforcement.” ACI Struct. J. 100 (2): 240–249.
Reineck, K. H., and L. Todisco. 2014. “Database of shear tests for non-slender reinforced concrete beams without stirrups.” ACI Struct. J. 111 (6): 1363–1372.
Rogowsky, D. M. 1990. “Continuous deep beams.” In Reinforced concrete deep beams, edited by F. K. Kong, 288. Glasgow, Scotland: Blackie.
Rogowsky, D. M., and J. G. MacGregor. 1983. Shear strength of deep reinforced concrete continuous beams. Edmonton, AB, Canada: Univ. of Alberta.
Rogowsky, D. M., J. G. MacGregor, and S. Y. Ong. 1986. “Tests of reinforced concrete deep beams.” ACI J. 83 (4): 614–623.
Russo, G., R. Venir, and M. Pauletta. 2005. “Reinforced concrete deep beams-shear strength model and design formula.” ACI Struct. J. 102 (3): 429–437.
Sagaseta, J. 2008. “The influence of aggregate fracture on the shear strength of reinforced concrete beams.” Ph.D. thesis, Dept. of Civil and Environmental Engineering, Imperial College London.
Sagaseta, J. 2013. “The influence of aggregate fracture on the shear strength of reinforced concrete beams: An experimental and analytical research project.” Struct. Concr. 14 (4): 401–414. https://doi.org/10.1002/suco.201200015.
Sagaseta, J., and R. Vollum. 2010. “Shear design of short-span beams.” Mag. Concr. Res. 62 (4): 267–282. https://doi.org/10.1680/macr.2010.62.4.267.
Schlaich, J., K. Schäfer, 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.
Tan, K. H., C. Y. Tang, and K. Tong. 2003. “A direct method for deep beams with web reinforcement.” Mag. Concr. Res. 55 (1): 53–63. https://doi.org/10.1680/macr.2003.55.1.53.
Tan, K. H., K. Tong, and C. Tang. 2001. “Direct strut-and-tie model for prestressed deep beams.” J. Struct. Eng. 127 (9): 1076–1084. https://doi.org/10.1061/(ASCE)0733-9445(2001)127:9(1076).
Tanimura, Y., and T. Sato. 2005. “Evaluation of shear strength of deep beams with stirrups.” Q. Rep. RTRI 46 (1): 53–58. https://doi.org/10.2219/rtriqr.46.53.
Todisco, L., K. H. Reineck, and O. Bayrak. 2015. “Database with shear tests on non-slender reinforced concrete beams with vertical stirrups.” ACI Struct. J. 112 (6): 761–769. https://doi.org/10.14359/51688055.
Tuchscherer, R., D. Birrcher, C. Williams, D. Deschenes, and O. Bayrak. 2014. “Evaluation of existing strut and tie methods and recommended improvements.” ACI Struct. J. 111 (6): 1451–1460. https://doi.org/10.14359/516869926.
Vecchio, F. J., and M. P. Collins. 1986. “The modified compression-field theory for reinforced concrete elements subjected to shear.” ACI J. 83 (2): 219–231.
Walraven, J. C. 1980. “Aggregate interlock: A theoretical and experimental analysis.” Ph.D. thesis, Dept. of Civil Engineering and Geosciences, Delft University Press.
Wight, J. K., and J. G. MacGregor. 2012. Reinforced concrete: Mechanics and design. Upper Saddle River, NJ: Pearson Education.
Yang, K.-H., and A. F. Ashour. 2011a. “Aggregate interlock in lightweight concrete continuous deep beams.” Eng. Struct. 33 (1): 136–145. https://doi.org/10.1016/j.engstruct.2010.09.026.
Yang, K.-H., and A. F. Ashour. 2011b. “Strut-and-tie model based on crack band theory for deep beams.” J. Struct. Eng. 137 (10): 1030–1038. https://doi.org/10.1061/(ASCE)ST.1943-541X.0000351.
Yang, K.-H., H.-S. Chung, and A. F. Ashour. 2007a. “Influence of section depth on the structural behaviour of reinforced concrete continuous deep beams.” Mag. Concr. Res. 59 (8): 575–586. https://doi.org/10.1680/macr.2007.59.8.575.
Yang, K.-H., H.-S. Chung, and A. F. Ashour. 2007b. “Influence of shear reinforcement on reinforced concrete continuous deep beams.” ACI Stbuct. J. 104 (4): 420–429.
Yi, W.-J., B. Huang, and H. Chen. 2017. “Finite element analysis on the effect of web reinforcement on shear failure of reinforced concrete continuous deep beams.” [In Chinese.] Chin. J. Comput. Mech. 34 (2): 175–182.
Zararis, P. D. 2003. “Shear compression failure in reinforced concreted deep beams.” J. Struct. Eng. 129 (4): 544–553. https://doi.org/10.1061/(ASCE)0733-9445(2003)129:4(544).
Zhang, N., and K.-H. Tan. 2007a. “Direct strut-and-tie model for single span and continuous deep beams.” Eng. Struct. 29 (11): 2987–3001. https://doi.org/10.1016/j.engstruct.2007.02.004.
Zhang, N., and K.-H. Tan. 2007b. “Size effect in RC deep beams: Experimental investigation and STM verification.” Eng. Struct. 29 (12): 3241–3254. https://doi.org/10.1016/j.engstruct.2007.10.005.
Zhang, N., and K.-H. Tan. 2010. “Effects of support settlement on continuous deep beams and STM modeling.” Eng. Struct. 32 (2): 361–372. https://doi.org/10.1016/j.engstruct.2009.09.019.

Information & Authors

Information

Published In

Go to Journal of Structural Engineering
Journal of Structural Engineering
Volume 146Issue 11November 2020

History

Received: Aug 12, 2019
Accepted: Jun 1, 2020
Published online: Aug 22, 2020
Published in print: Nov 1, 2020
Discussion open until: Jan 22, 2021

Permissions

Request permissions for this article.

Authors

Affiliations

Postdoctoral Fellow, College of Civil Engineering, Hunan Provincial Key Lab on Damage Diagnosis for Engineering Structures, Hunan Univ., Changsha, Hunan 410082, China. Email: [email protected]
Wei-Jian Yi [email protected]
Professor, College of Civil Engineering, Hunan Provincial Key Lab on Damage Diagnosis for Engineering Structures, Hunan Univ., Changsha, Hunan 410082, China (corresponding author). Email: [email protected]
Professor, Dept. of Civil and Environmental Engineering, Univ. of Tennessee, Knoxville, TN 37996. ORCID: https://orcid.org/0000-0001-8246-7605. Email: [email protected]

Metrics & Citations

Metrics

Citations

Download citation

If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.

Cited by

View Options

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Media

Figures

Other

Tables

Share

Share

Copy the content Link

Share with email

Email a colleague

Share