Technical Papers
Jul 17, 2020

Size Effect on Shear Strength of Reinforced Concrete: Is CSCT or MCFT a Viable Alternative to Energy-Based Design Code?

Publication: Journal of Engineering Mechanics
Volume 146, Issue 10

Abstract

After sketching the history of the size effect models for the shear strength of reinforced concrete (RC) in design codes, the energy-based size effect law (SEL), recently incorporated into the American Concrete Institute (ACI) design code articles for beam shear and slab punching, is briefly discussed. A general derivation of the SEL based only on the first principles involving energy conservation and dimensional analysis (or laws of similitude) is presented. Attention is then focused on recent articles that present a severe critique of the SEL and various arguments in support of the Muttoni et al.’s critical shear crack theory (CSCT)—an update of the Collins et al.’s modified compression field theory (MCFT)—that some researchers propose to be introduced into the fib Model Code and the Eurocode as an alternative to the SEL. In a point-by-point analysis, it is shown that this critique and these arguments are incorrect and baseless. It is hoped that the present clarification would lead to progress in design codes, enhancing the safety and efficiency of RC structures.

Get full access to this article

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

Data Availability Statement

Some or all data, models, or code generated or used during the study are available in a repository online in accordance with funder data retention policies. Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.

Acknowledgments

Partial preliminary funding under National Science Foundation (NSF) Grant No. CMMI-2029641 to Northwestern University is gratefully acknowledged.

References

ACI (American Concrete Institute). 2019. Building code requirements for structural concrete and commentary. Farmington Hills, MI: ACI.
Ballarini, R., L. M. Keer, and S. P. Shah. 1987. “An analytical model for the pull-out of rigid anchors.” Int. J. Fract. 33 (2): 75–94.
Ballarini, R., S. Shah, and L. Keer. 1986. “Failure characteristics of short anchor bolts embedded in a brittle material.” Proc. R. Soc. London. Math. Phys. Sci. 404 (1826): 35–54. https://doi.org/10.1098/rspa.1986.0017.
Barenblatt, G. I. 1987. Dimensional analysis. London: CRC Press.
Bažant, Z., and L. Cedolin. 1991. Stability of structures: Elastic, inelastic, fracture and damage theories; 2010. 3rd ed. Singapore: World Scientific Publishing.
Bažant, Z. P. 1976. “Instability, ductility, and size effect in strain-softening concrete.” J. Eng. Mech. Div. 102 (2): 331–344.
Bažant, Z. P. 1983. “Comment on orthotropic models for concrete and geomaterials.” J. Eng. Mech. 109 (3): 849–865. https://doi.org/10.1061/(ASCE)0733-9399(1983)109:3(849).
Bažant, Z. P. 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. 2004. “Probability distribution of energetic-statistical size effect in quasibrittle fracture.” Probab. Eng. Mech. 19 (4): 307–319. https://doi.org/10.1016/j.probengmech.2003.09.003.
Bažant, Z. P., and P. Gambarova. 1980. “Rough cracks in reinforced concrete.” J. Struct. Div. 106 (4): 819–842.
Bažant, Z. P., and M. T. Kazemi. 1990. “Size effect in fracture of ceramics and its use to determine fracture energy and effective process zone length.” J. Am. Ceram. Soc. 73 (7): 1841–1853. https://doi.org/10.1111/j.1151-2916.1990.tb05233.x.
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., and J.-L. Le. 2017. Probabilistic mechanics of quasibrittle structures: Strength, lifetime, and size effect. Cambridge, UK: Cambridge University Press.
Bažant, Z. P., and B. H. Oh. 1983. “Crack band theory for fracture of concrete.” Matériaux et Constr. 16 (3): 155–177. https://doi.org/10.1007/BF02486267.
Bažant, Z. P., and J. Planas. 1998. Fracture and size effect in concrete and other quasibrittle materials. London: CRC Press.
Bažant, Z. P., and A. Yavari. 2005. “Is the cause of size effect on structural strength fractal or energetic–statistical?” Eng. Fract. Mech. 72 (1): 1–31. https://doi.org/10.1016/j.engfracmech.2004.03.004.
Bažant, Z. P., and A. Yavari. 2007. “Response to A. Carpinteri, B. Chiaia, P. Cornetti and S. Puzzi’s comments on ‘Is the cause of size effect on structural strength fractal or energetic-statistical?’” Eng. Fract. Mech. 74 (17): 2897–2910. https://doi.org/10.1016/j.engfracmech.2007.02.026.
Bažant, Z. P., and Q. Yu. 2005. “Designing against size effect on shear strength of reinforced concrete beams without stirrups: I. Formulation.” J. Struct. Eng. 131 (12): 1877–1885. https://doi.org/10.1061/(ASCE)0733-9445(2005)131:12(1877).
Bažant, Z. P., and Q. Yu. 2006. “Reliability, brittleness, covert understrength factors, and fringe formulas in concrete design codes.” J. Struct. Eng. 132 (1): 3–12. https://doi.org/10.1061/(ASCE)0733-9445(2006)132:1(3).
Bažant, Z. P., and Q. Yu. 2008. “Minimizing statistical bias to identify size effect from beam shear database.” ACI Struct. J. 105 (6): 685–691. https://doi.org/10.14359/20096.
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.” ACI Struct. J. 104 (5): 601–610. https://doi.org/10.14359/18862.
Bentz, E. C., and S. J. Foster. 2019. “On shear in members without stirrups and the application of energy-based methods in light of 30 years of test observations.” Struct. Concr. 20 (4): 1481–1489. https://doi.org/10.1002/suco.201900224.
Bhal, N. S. 1968. “Uber den Einfluss der Balkenhöhe auf die Schubtragfähigkeit von Einfeldrigen Stahlbetonbalken mit und ohne Schubbewehrung.” [In German.] Ph.D. thesis, Otto-Graf-Institut, Universität Stuttgart.
Buckingham, E. 1914. “On physically similar systems; illustrations of the use of dimensional equations.” Physical Rev. 4 (4): 345. https://doi.org/10.1103/PhysRev.4.345.
Buckingham, E. 1915. “Model experiments and the form of empirical equations.” Trans. ASME 37 (1487): 263–296.
Caner, F. C., and Z. P. Bažant. 2013. “Microplane model m7 for plain concrete. II: Calibration and verification.” J. Eng. Mech. 139 (12): 1724–1735. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000571.
Carpinteri, A. 1994a. “Fractal nature of material microstructure and size effects on apparent mechanical properties.” Mech. Mater. 18 (2): 89–101. https://doi.org/10.1016/0167-6636(94)00008-5.
Carpinteri, A. 1994b. “Scaling laws and renormalization groups for strength and toughness of disordered materials.” Int. J. Solids Struct. 31 (3): 291–302. https://doi.org/10.1016/0020-7683(94)90107-4.
Carpinteri, A., B. Chiaia, and G. Ferro. 1995. “Size effects on nominal tensile strength of concrete structures: Multifractality of material ligaments and dimensional transition from order to disorder.” Mater. Struct. 28 (6): 311. https://doi.org/10.1007/BF02473145.
Cavagnis, F., M. Fernández Ruiz, and A. Muttoni. 2018. “An analysis of the shear-transfer actions in reinforced concrete members without transverse reinforcement based on refined experimental measurements.” Struct. Concr. 19 (1): 49–64. https://doi.org/10.1002/suco.201700145.
Cavagnis, F., J. T. Simoes, M. Fernández Ruiz, and A. Muttoni. 2020. “Shear strength of members without transverse reinforcement based on development of critical shear crack.” ACI Struct. J. 117 (1): 103–118. https://doi.org/10.14359/51718012.
Cladera, A., and A. R. Mari. 2005. “Experimental study on high-strength concrete beams failing in shear.” Eng. Struct. 27 (10): 1519–1527. https://doi.org/10.1016/j.engstruct.2005.04.010.
Collins, M. P., D. Mitchell, P. Adebar, and F. J. Vecchio. 1996. “A general shear design method.” ACI Struct. J. 93 (1): 36–45. https://doi.org/10.14359/9838.
Dönmez, A., and Z. P. Bažant. 2017. “Size effect on punching strength of reinforced concrete slabs with and without shear reinforcement.” ACI Struct. J. 114 (4): 875. https://doi.org/10.14359/51689719.
Dönmez, A., and Z. P. Bažant. 2019. “Critique of critical shear crack theory for fib model code articles on shear strength and size effect of reinforced concrete beams.” Struct. Concr. 20 (4): 1451–1463. https://doi.org/10.1002/suco.201800315.
Eringen, A. C. 1980. Mechanics of continua. 2nd ed. New York: Oxford University Press.
Fernández Ruiz, M., and A. Muttoni. 2018. “Size effect in shear and punching shear failures of concrete members without transverse reinforcement: Differences between statically determinate members and redundant structures.” Struct. Concr. 19 (1): 65–75. https://doi.org/10.1002/suco.201700059.
Fernández Ruiz, M., A. Muttoni, and J. Sagaseta. 2015. “Shear strength of concrete members without transverse reinforcement: A mechanical approach to consistently account for size and strain effects.” Eng. Struct. 99 (Sep): 360–372. https://doi.org/10.1016/j.engstruct.2015.05.007.
Fung, Y. 1965. Fundamentals of solid mechanics. Englewood Cliffs, NJ: Prentice-Hall.
Griffith, A. A. 1921. “VI. The phenomena of rupture and flow in solids.” Philos. Trans. R. Soc. London, Ser. A 221 (582–593): 163–198. https://doi.org/10.1098/rsta.1921.0006.
Hassan, A., K. Hossain, and M. Lachemi. 2008. “Behavior of full-scale self-consolidating concrete beams in shear.” Cem. Concr. Compos. 30 (7): 588–596. https://doi.org/10.1016/j.cemconcomp.2008.03.005.
Hoover, C. G., and Z. P. Bažant. 2014. “Cohesive crack, size effect, crack band and work-of-fracture models compared to comprehensive concrete fracture tests.” Int. J. Fract. 187 (1): 133–143. https://doi.org/10.1007/s10704-013-9926-0.
Iguro, M., T. Shioya, Y. Nojiri, and H. Akiyama. 1984. “Experimental studies on the shear strength of large reinforced concrete beams under uniformly distributed load.” Doboku Gakkai Ronbunshu 1984 (348): 175–184. https://doi.org/10.2208/jscej.1984.348_175.
Kani, G. N. J. 1967. “How safe are our large reinforced concrete beams?” ACI J. 64 (3): 128–141. https://doi.org/10.14359/7549.
Leonhardt, F., and R. Walther. 1962. “Beitrage zur Behandlung der Schubprobleme im Stahlbetonbau, 4. Fortsetzung des Kapitals II: Versuchsberichte.” [In German.] Beton und Stahlbetonbau 57 (3): 54–64.
Malvern, L. E. 1969. Introduction to the mechanics of a continuous medium. New Jersey: Prentice-Hall.
Muttoni, A. 2008. “Punching shear strength of reinforced concrete slabs without transverse reinforcement.” ACI Struct. J. 4 (1): 440–450. https://doi.org/10.14359/19858.
Muttoni, A., and M. Fernández Ruiz. 2019. “From experimental evidence to mechanical modeling and design expressions: The critical shear crack theory for shear design.” Struct. Concr. 20 (4): 1464–1480. https://doi.org/10.1002/suco.201900193.
Muttoni, A., and J. Schwartz. 1991. “Behavior of beams and punching in slabs without shear reinforcement.” IABSE Colloquium 62: 703–708.
Nguyen, H. T., M. Pathirage, G. Cusatis, and Z. P. Bazant. 2020a. “Gap test of crack-parallel stress effect on quasibrittle fracture and its consequences.” J. Appl. Mech. 87 (Jul). https://doi.org/10.1115/1.4047215.
Nguyen, H. T., M. Pathirage, M. Rezaei, M. Issa, G. Cusatis, and Z. P. Bazant. 2020b. “New perspective of fracture mechanics inspired by gap test with crack-parallel compression.” Proc. Natl. Acad. Sci. 117 (Jun). https://doi.org/10.1073/pnas.2005646117.
Okamura, H., and T. Higai. 1980. “Proposed design equation for shear strength of reinforced concrete beams without web reinforcement.” Proc. Jpn. Soc. Civ. Eng. 1980 (300): 131–141. https://doi.org/10.2208/jscej1969.1980.300_131.
Ospina, C. E., and G. Birkle. 2012. Databank of concentric punching shear tests of two-way concrete slabs without shear reinforcement at interior supports, 1814–1832. Seattle: Structures Congress.
Podgorniak-Stanik, B. A. 1998. “The influence of concrete strength, distribution of longitudinal reinforcement, amount of transverse reinforcement and member size on shear strength of reinforced concrete members.” M.S. thesis, Graduate Dept. of Civil Engineering, Univ. of Toronto.
Reineck, K.-H., E. C. Bentz, B. Fitik, D. A. Kuchma, and O. Bayrak. 2013. “ACI-DAfStb database of shear tests on slender reinforced concrete beams without stirrups.” ACI Struct. J. 110 (5): 867–876. https://doi.org/10.14359/51685839.
Shioya, T., and H. Akiyama. 1994. “Application to design of size effect in reinforced concrete structures.” In Proc., Japan Concrete Institute Int. Workshop, edited by H. M. Sendai, H. Okamura, and Z. P. Bažant, 409–416. London: E. & F.N. Spon Publisher.
Shioya, T., M. Iguro, Y. Nojiri, H. Akiyama, and T. Okada. 1990. “Shear strength of large reinforced concrete beams.” ACI Special Publication 118 (Jan): 259–280.
Syroka-Korol, E., and J. Tejchman. 2014. “Experimental investigations of size effect in reinforced concrete beams failing by shear.” Eng. Struct. 58 (Jan): 63–78. https://doi.org/10.1016/j.engstruct.2013.10.012.
Vaschy, A. 1892. “Sur les lois de similitude en physique.” [In French.] Annales télégraphiques 11 (1-1970): 71–74.
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. 1978. Influence of member depth on the shear strength of lightweight concrete beams without shear reinforcement. 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., and J. Stroband. 1994. “Shear friction in high-strength concrete.” ACI Special Publication 149 (Oct): 311–330. https://doi.org/10.14359/4089.
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.

Information & Authors

Information

Published In

Go to Journal of Engineering Mechanics
Journal of Engineering Mechanics
Volume 146Issue 10October 2020

History

Received: Feb 13, 2020
Accepted: Mar 19, 2020
Published online: Jul 17, 2020
Published in print: Oct 1, 2020
Discussion open until: Dec 17, 2020

Permissions

Request permissions for this article.

Authors

Affiliations

A. Abdullah Dönmez, Ph.D. [email protected]
Postdoctoral Researcher, Dept. of Civil and Environmental Engineering, Northwestern Univ., Evanston, IL 60208; Postdoctoral Scholar, Dept. of Civil Engineering, İstanbul Teknik Üniversitesi, Istanbul 34469, Turkey. Email: [email protected]
Christian Carloni, Ph.D., M.ASCE [email protected]
Chair of Joint ACI/ASCE 446 Committee, Fracture Mechanics; Associate Professor, Dept. of Civil and Environmental Engineering, Case Western Reserve Univ., Cleveland, OH 44106. Email: [email protected]
Gianluca Cusatis, Ph.D., M.ASCE [email protected]
Past Chair of Joint ACI/ASCE 446 Committee, Fracture Mechanics; Professor, Dept. of Civil and Environmental Engineering, Northwestern Univ., Evanston, IL 60208. Email: [email protected]
Zdeněk P. Bažant, Ph.D., Hon.M.ASCE [email protected]
S.E.
McCormick Institute Professor and W.P. Murphy Professor of Civil and Mechanical Engineering and Materials Science, Northwestern Univ., Evanston, IL 60208 (corresponding author). 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