Abstract

Based on the experimental results, this paper investigates the shear mechanism of reinforced concrete deep beams without stirrups. By analyzing the kinematics of the critical shear crack, it can be found that the compression of concrete above the critical shear crack causes the crack sliding and that the combined action of the elongation of longitudinal reinforcement and the compression of concrete above the critical shear crack causes the crack opening. Based on the new-found crack kinematics and test data, the aggregate interlock force is calculated by two methods. The dowel action is also calculated. The results reveal that the shear forces transmitted by the aggregate interlock and the dowel action are relatively small, ranging from 0.5% to 9.2%. The uncracked concrete in the compression zone provides the primary resistance. Both the aggregate interlock and the uncracked concrete in the compression zone can cause a size effect. But because of the small proportion of the aggregate interlock, the size effect of shear strength is mainly caused by the size effect of uncracked concrete in the compression zone. A modified strut-and-tie model (STM) is established based on the shear mechanism found in the test. It considers the size effect using the modified size effect law. The modified STM is evaluated by comparing the calculation results with the experimental results of 194 beams. It is shown that the prediction of the modified STM is more accurate than those of the other five models, with a mean value of Vu/Vu,cal of 1.01 and a coefficient of variation value of 0.22. The proposed model well captures the effect of the shear span-to-effective depth ratio and the size effect on the shear strength. The modified STM reflects the actual shear transfer mechanism of deep beams without stirrups and has the advantages of simple calculation and accurate prediction.

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 gratefully acknowledge the financial support provided by the National Natural Science Foundation of China (Nos. 51878260 and 52078201) and the Hunan Provincial Innovation Foundation for Postgraduate No. 541109080046 (CX2017B121). The findings and opinions expressed in this paper are those of the authors and do not necessarily reflect those of the sponsor.

References

AASHTO. 2017. Bridge design specifications. Washington, DC: AASHTO.
ACI (American Concrete Institute). 2019. Building code requirements for structural concrete: Commentary on building code requirements for structural concrete. Farmington Hills, MI: ACI.
Bažant, Z. 1984. “Size effect in blunt fracture: Concrete, rock, metal.” J. Eng. Mech. 110 (4): 518–535. https://doi.org/10.1061/(ASCE)0733-9399(1984)110:4(518).
Bažant, Z. P., and M. T. Kazemi. 1991. “Size effect on diagonal shear failure of beams without stirrups.” ACI Struct. J. 88 (3): 268–276. https://doi.org/10.14359/3097.
Bažant, Z. P., and J. K. Kim. 1984. “Size effect in shear failure of longitudinally reinforced beams.” ACI J. Proc. 81 (5): 456–468. https://doi.org/10.14359/10696.
Bažant, Z. P., Q. Yu, W. Gerstle, J. Hanson, and J. W. Ju. 2007. “Justification of ACI 446 proposal for updating ACI code provisions for shear design of reinforced concrete beams.” Struct. J. 104 (5): 601–610. https://doi.org/10.14359/18862.
Bažant, Z. P., Q. Yu, M. H. Hubler, V. Krístek, and Z. Bittnar. 2011. “Wake-up call for creep, myth about size effect and black holes in safety: What to improve in fib model code draft.” In Proc., fib Symp. PRAGUE 2011: Concrete Engineering for Excellence and Efficiency, 731–746. Prague, Czech Republic: Czech Concrete Society.
Bentz, E. C. 2005. “Empirical modeling of reinforced concrete shear strength size effect for members without stirrups.” ACI Struct. J. 102 (2): 232. https://doi.org/10.14359/14274.
Bentz, E. C., and M. P. Collins. 2018. “The Toronto size effect series.” Spec. Publ. 328 (Sep): 1–12. https://doi.org/10.14359/51711146.
Bentz, E. C., F. J. Vecchio, and M. P. Collins. 2006. “Simplified modified compression field theory for calculating shear strength of reinforced concrete elements.” ACI Struct. J. 103 (4): 614. https://doi.org/10.14359/16438.
Birrcher, D., R. Tuchscherer, M. Huizinga, O. Bayrak, S. Wood, and J. Jirsa. 2009. Strength and serviceability design of reinforced concrete deep beams. Austin, TX: Univ. of Texas.
Brown, M. D., and O. Bayrak. 2008a. “Design of deep beams using strut-and-tie models—Part I: Evaluating U.S. provisions.” ACI Struct. J. 105 (4): 395–404. https://doi.org/10.14359/19853.
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. https://doi.org/10.14359/19854.
CEB-FIP MC (Euro-International Committee for Concrete-International Federation for Prestressing Model Code). 2010. fib model code for concrete structures 2010. Berlin: Ernst & Sohn.
CEN (European Committee for Standardization). 2004. Design of concrete structures—Part 1-1: General rules and rules for buildings. Brussels, Belgium: CEN.
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.
China Architectural and Building Press. 2010. Code for design of concrete structures. Beijing: China Architectural and Building Press.
Choi, K.-K., H.-G. Park, and J. K. Wight. 2007. “Unified shear strength model for reinforced concrete beams—Part I: Development.” ACI Struct. J. 104 (2): 142–152. https://doi.org/10.14359/18526.
Cladera, A., A. Marí, J.-M. Bairán, E. Oller, and C. Ribas. 2017. “One-way shear design method based on a multi-action model.” Concr. Int. 39 (9): 40–46.
Clark, A. P. 1951. “Diagonal tension in reinforced concrete beams.” J. Proc. 48 (10): 145–156. https://doi.org/10.14359/11876.
Collins, M. P., E. C. Bentz, P. T. Quach, and G. T. Proestos. 2015. “The challenge of predicting the shear strength of very thick slabs.” Concr. Int. 37 (11): 29–37.
Collins, M. P., and D. Kuchma. 1999. “How safe are our large, lightly reinforced concrete beams, slabs, and footings?” ACI Struct. J. 96 (4): 482–491. https://doi.org/10.14359/684.
CSA (Canadian Standards Association). 2014. Design of concrete structures. Toronto: CSA.
Daluga, D., K. McCain, M. Murray, and S. Pujol. 2018. “Effect of geometric scaling on shear strength of reinforced concrete beams without stirrups.” ACI Struct. J. 115 (1): 1813–1815. https://doi.org/10.14359/51700947.
El-Sayed, A. K., and A. B. Shuraim. 2016. “Size effect on shear resistance of high strength concrete deep beams.” Mater. Struct. 49 (5): 1871–1882. https://doi.org/10.1617/s11527-015-0619-1.
Foster, S. J., and R. I. Gilbert. 1998. “Experimental studies on high-strength concrete deep beams.” ACI Struct. J. 95 (4): 382–390. https://doi.org/10.14359/554.
Hwang, S.-J., W.-Y. Lu, and H.-J. Lee. 2000. “Shear strength prediction for deep beams.” ACI Struct. J. 97 (3): 367–376. https://doi.org/10.14359/9624.
Kani, G. N. J. 1967. “How safe are our large reinforced concrete beams.” ACI J. 64 (12): 128–141. https://doi.org/10.14359/7549.
Kani, G. N. J. 1979. Kani on shear in reinforced concrete. Toronto: Univ. of Toronto.
Kim, J.-K., and S.-H. Eo. 1990. “Size effect in concrete specimens with dissimilar initial cracks.” Mag. Concr. Res. 42 (153): 233–238. https://doi.org/10.1680/macr.1990.42.153.233.
Kim, J.-K., and Y.-D. Park. 1994. “Shear strength of reinforced high strength concrete beam without web reinforcement.” Mag. Concr. Res. 46 (166): 7–16. https://doi.org/10.1680/macr.1994.46.166.7.
Korol, E., J. Tejchman, and Z. Mróz. 2017. “Experimental and numerical assessment of size effect in geometrically similar slender concrete beams with basalt reinforcement.” Eng. Struct. 141 (Jun): 272–291. https://doi.org/10.1016/j.engstruct.2017.03.011.
Kotsovos, M. D. 1988. “Compressive force path concept: Basis for reinforced concrete ultimate limit state design.” ACI Struct. J. 85 (1): 68–75. https://doi.org/10.14359/2986.
Lemaitre, J. 1971. Evaluation of dissipation and damage in metals submitted to dynamic loading. Kyoto, Japan: ICM.
Leonhardt, F., and R. Walther. 1962. “Beiträge zur Behandlung der Schubprobleme in Stahlbetonbau.” J. Beton-Und Stahlbetonbau 7: 161–173.
Lesley, H. S., and A. R. Julio. 2010. “Influence of effective depth on shear strength of concrete beams—Experimental study.” ACI Struct. J. 107 (5): 554–562. https://doi.org/10.14359/51663906.
Li, J., and X. Ren. 2009. “Stochastic damage model for concrete based on energy equivalent strain.” Int. J. Solids Struct. 46 (11): 2407–2419. https://doi.org/10.1016/j.ijsolstr.2009.01.024.
Li, Y., H. Chen, W.-J. Yi, F. Peng, Z. Li, and Y. Zhou. 2021. “Effect of member depth and concrete strength on shear strength of RC deep beams without transverse reinforcement.” Eng. Struct. 241 (Aug): 112427. https://doi.org/10.1016/j.engstruct.2021.112427.
Li, Y., Z. Li, W.-J. Yi, H. Chen, and W.-X. Zhang. 2022. “Study on size effect in shear strength of reinforced concrete short beams without stirrups.” China Civ. Eng. J. 55 (12): 1–12. https://doi.org/10.15951/j.tmgcxb.21111100.
Lubell, A., T. Sherwood, E. Bentz, and M. P. Collins. 2004. “Safe shear design of large wide beams.” Concr. Int. 26 (1): 67–78.
Manuel, R. F., B. W. Slight, and G. T. Suter. 1971. “Deep beam behavior affected by length and shear span variations.” ACI J. Proc. 68 (12): 954–958.
Matamoros, A. B., and K. H. Wong. 2003. “Design of simply supported deep beams using strut-and-tie models.” ACI Struct. J. 100 (6): 704–712. https://doi.org/10.14359/12836.
Mathey, R. G., and D. Watstein. 1963. “Shear strength of beams without web reinforcement containing deformed bars of different yield strengths.” ACI J. Proc. 60 (2): 183–203. https://doi.org/10.14359/7851.
Mihaylov, B. I., E. C. Bentz, and P. C. Michael. 2010. “Behavior of large deep beams subjected to monotonic and reversed cyclic shear.” ACI Struct. J. 107 (6): 726–734. https://doi.org/10.14359/51664021.
Mihaylov, B. I., E. C. Bentz, and P. C. Michael. 2013. “Two-parameter kinematic theory for shear behavior of deep beams.” ACI Struct. J. 110 (3): 448–456. https://doi.org/10.14359/51685602.
Moody, K. G., I. M. Viest, R. C. Elstner, and E. Hognestad. 1954. “Shear strength of RC beams: Part 1—Tests of simple beams.” ACI J. Proc. 51 (12): 317–332.
Morrow, J., and I. M. Viest. 1957. “Shear strength of reinforced concrete frame members without web reinforcement.” ACI J. Proc. 53 (3): 833–869. https://doi.org/10.14359/11558.
Mphonde, A. G., and G. C. Frantz. 1984. “Shear tests of high- and low-strength concrete beams without stirrups.” ACI J. Proc. 81 (4): 350–357. https://doi.org/10.14359/10690.
Oh, J.-K., and S.-W. Shin. 2001. “Shear strength of reinforced high-strength concrete deep beams.” ACI Struct. J. 98 (2): 164–173. https://doi.org/10.14359/10184.
Park, H.-G., S. Kang, and K.-K. Choi. 2013. “Analytical model for shear strength of ordinary and prestressed concrete beams.” Eng. Struct. 46 (Jan): 94–103. https://doi.org/10.1016/j.engstruct.2012.07.015.
Quintero-Febres, C. G., G. Parra-Montesinos, and J. K. Wight. 2006. “Strength of struts in deep concrete members designed using strut-and-tie method.” ACI Struct. J. 103 (4): 577. https://doi.org/10.14359/16434.
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. https://doi.org/10.14359/12488.
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. https://doi.org/10.14359/51686820.
Rogowsky, D. M., J. G. MacGregor, and S. Y. Ong. 1983. Tests of reinforced concrete deep beams. Edmonton, AB, Canada: Univ. of Alberta.
Rosenbusch, J., and M. Teutsch. 2002. “Trial beams in shear.” In Brite Durham project, 97. Braunschweig, Germany: Univ. of Braunschweig.
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. https://doi.org/10.14359/14414.
Scholz, H. 1994. Ein Querkrafttragmodell für Bauteile ohne Schubbewehrung im Bruchzustand aus normalfestem und hochfestem Beton. Berlin: Univ. bibliothek.
Shioya, T., M. Iguro, Y. Nojiri, H. Akiyama, and T. Okada. 1990. “Shear strength of large reinforced concrete beams.” Spec. Publ. 118 (Jan): 259–280. https://doi.org/10.14359/2978.
Tan, K. H., and G. H. Cheng. 2006. “Size effect on shear strength of deep beams: Investigating with strut-and-tie model.” J. Struct. Eng. 132 (5): 673–685. https://doi.org/10.1061/(ASCE)0733-9445(2006)132:5(673.
Tan, K. H., and H. Y. Lu. 1999. “Shear behavior of large reinforced concrete deep beams and code comparisons.” ACI Struct. J. 96 (5): 836–845. https://doi.org/10.14359/738.
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. Y. 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.
Tan, K.-H., F.-K. Kong, S. Teng, and L.-W. Weng. 1997. “Effect of web reinforcement on high-strength concrete deep beams.” ACI Struct. J. 94 (5): 573–581. https://doi.org/10.14359/506.
Tanaka, Y., T. Shimomura, and M. Watanabe. 2010. “Role of diagonal tension crack in size effect of shear strength of deep beams.” In Proc., Framcos-7, 198–206. Seoul: Korea Concrete Institute.
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.
Teng, S., F. Kong, and S. Poh. 1998. “Shear strength of reinforced and prestressed concrete deep beams. Part II: The supporting evidence.” Proc. Inst. Civ. Eng. Struct. Build. 128 (2): 124–143. https://doi.org/10.1680/istbu.1998.30120.
Trandafir, A. N., G. T. Proestos, and B. I. Mihaylov. 2022. “Detailed crack-based assessment of a 4-m deep beam test specimen.” Struct. Concr. 24 (1): 756–770. https://doi.org/10.1002/suco.202200149.
Tureyen, A. K., and R. J. Frosch. 2003. “Concrete shear strength: Another perspective.” ACI Struct. J. 100 (5): 609–615. https://doi.org/10.14359/12802.
Vecchio, F. J., and M. P. Collins. 1986. “The modified compression-field theory for reinforced concrete elements subjected to shear.” ACI J. Proc. 83 (2): 219–231. https://doi.org/10.14359/10416.
Walraven, J. 1980. Aggregate interlock: A theoretical and experimental analysis. Delft, Netherlands: Delft Univ. of Technology.
Walraven, J., and N. Lehwalter. 1994. “Size effects in short beams loaded in shear.” ACI Struct. J. 91 (5): 585–593. https://doi.org/10.14359/4177.
Walraven, J. C. 1978. Influence of member depth on the shear strength of lightweight concrete beams without shear reinforcement. Delft, Netherlands: Delft Univ. of Technology.
Watstein, D., and R. G. Mathey. 1958. “Strains in beams having diagonal cracks.” ACI J. Proc. 55 (12): 717–728. https://doi.org/10.14359/11384.
Wight, J. K., and J. G. MacGregor. 2011. Reinforced concrete mechanics and design. Upper Saddle River, NJ: Pearson.
Wu, J. Y., J. Li, and R. Faria. 2006. “An energy release rate-based plastic-damage model for concrete.” Int. J. Solids Struct. 43 (3): 583–612. https://doi.org/10.1016/j.ijsolstr.2005.05.038.
Xie, Y., S. H. Ahmad, T. Yu, S. Hino, and W. Chung. 1994. “Shear ductility of reinforced concrete beams of normal and high-strength concrete.” ACI Struct. J. 91 (2): 140–149. https://doi.org/10.14359/4592.
Yang, K.-H., and A. F. Ashour. 2011. “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, E.-T. Lee, and H.-C. Eun. 2003. “Shear characteristics of high-strength concrete deep beams without shear reinforcements.” Eng. Struct. 25 (10): 1343–1352. https://doi.org/10.1016/S0141-0296(03)00110-X.
Yu, Q., J. L. Le, M. H. Hubler, R. Wendner, G. Cusatis, and Z. P. Bažant. 2016. “Comparison of main models for size effect on shear strength of reinforced and prestressed concrete beams.” Struct. Concr. 17 (5): 778–789. https://doi.org/10.1002/suco.201500126.
Zararis, P. D., and G. C. Papadakis. 2001. “Diagonal shear failure and size effect in RC beams without web reinforcement.” J. Struct. Eng. 127 (7): 733–742. https://doi.org/10.1061/(ASCE)0733-9445(2001)127:7(733).
Zhang, N., and K. H. Tan. 2007. “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.

Information & Authors

Information

Published In

Go to Journal of Structural Engineering
Journal of Structural Engineering
Volume 149Issue 11November 2023

History

Received: Jan 4, 2023
Accepted: Jul 19, 2023
Published online: Sep 13, 2023
Published in print: Nov 1, 2023
Discussion open until: Feb 13, 2024

Permissions

Request permissions for this article.

Authors

Affiliations

Ph.D. Candidate, College of Civil Engineering, Hunan Provincial Key Lab on Damage Diagnosis for Engineering Structures, Hunan Univ., Changsha 410082, China. ORCID: https://orcid.org/0000-0001-6593-4371. Email: [email protected]
Ph.D. Candidate, College of Civil Engineering, Hunan Provincial Key Lab on Damage Diagnosis for Engineering Structures, Hunan Univ., Changsha 410082, China. ORCID: https://orcid.org/0000-0002-9022-933X. 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 410082, China (corresponding author). Email: [email protected]
Professor, College of Civil Engineering, Hunan Provincial Key Lab on Damage Diagnosis for Engineering Structures, Hunan Univ., Changsha 410082, China. Email: [email protected]
Professor, College of Civil Engineering, Hunan Provincial Key Lab on Damage Diagnosis for Engineering Structures, Hunan Univ., Changsha 410082, China. ORCID: https://orcid.org/0000-0003-3153-2467. Email: [email protected]
Wang-Xi Zhang [email protected]
Professor, College of Civil Engineering, Hunan Provincial Key Lab on Damage Diagnosis for Engineering Structures, Hunan Univ., Changsha 410082, China. 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.

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