Figure 1
Examples of structural reinforced concrete members where shear or punching shear can be the governing design criterion.
Figure 2
Research on the development of the critical shear crack and associated kinematics: (a) original measurements [2727 A. Muttoni and B. Thürlimann, Shear Tests on Beams and Slabs Without Shear Reinforcement. Zürich, Switzerland: Inst. Baustatik Konstruk., 1986.], [2828 A. Muttoni, “The applicability of the theory of plasticity in the design of reinforced concrete,” Doctoral dissertation, ETHZ: Zürich, Switzerland, 1990 [in German].] and (b) recent measurements with refined techniques [2929 F. Cavagnis, M. Fernández Ruiz, and A. Muttoni, “Shear failures in reinforced concrete members without transverse reinforcement: an analysis of the critical shear crack development on the basis of test results,” Eng. Struct., vol. 103, pp. 157–173, 2015.].
Figure 3
First conceptual ideas and experimental evidence grounding the CSCT for shear in beams and slabs without shear reinforcement: (a) original cardboard model from 1985 with (a1) flexural crack in Mode I and (a2) flexural crack in combined mode I-II; (b) figure from reference [2828 A. Muttoni, “The applicability of the theory of plasticity in the design of reinforced concrete,” Doctoral dissertation, ETHZ: Zürich, Switzerland, 1990 [in German].] presenting the experimental results by Mörsch [3030 E. Mörsch, The Reinforced Concrete Construction, Ist Theory and Ist Application, 6th ed., Vol. 1.2. Stuttgart: Konrad Wittwer Ed., 1929 [in German].], whose interpretation supports the idea that the location and shape of the CSC influences the failure load (theoretical direct struts carrying shear shown in blue).
Figure 4CSCT for punching shear between 1985 to 1991, with: (a) assumptions on the shape and kinematics of the CSC to calculate the interlocking stresses between crack lips (opening in Mode I due to flexure shown in blue, combined Mode I-II due to shear shown in red); (b) adoption of an analytical failure criterion calibrated on the basis of experimental results; (c) calculated normalized punching resistance with the proposed model for different flexural reinforcement ratios as a function of the effective depth (figures (a) adapted from [
3434 A. Muttoni, M. Fernández Ruiz, and J. T. Simões, “The theoretical principles of the critical shear crack theory for punching shear failures and derivation of consistent closed-form design expressions,” Struct. Concr., vol. 19, pp. 174–190, 2018, http://dx.doi.org/10.1002/suco.201700088.
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], (b) and (c) adapted from [
3232 A. Muttoni and J. Schwartz, “Behaviour of beams and punching in slabs without shear reinforcement,” in 62 IABSE Colloq., Stuttgart, Germany, 1991, pp. 703–708.]).
Figure 5
Critical shear crack theory for shear in one-way members between 2000 to 2003, with: (a) adoption of an analytical failure criterion calibrated on the basis of experimental results (adapted from [3737 A. Muttoni, “Shear and punching strength of slabs without shear reinforcement,” Bet. Stahlbetonbau, vol. 98, pp. 74–84, 2003 [in German].], [9393 A. Muttoni, “Shear in Members Without Shear Reinforcement”, in Introduction to the Swiss Code SIA 262, Zürich, Switzerland: Swiss Eng. Archit. Document., 2003, pp. 47-55.[in French and German] [D0182].]); (b) calculated shear resistance varying the value of the effective depth (according to [3737 A. Muttoni, “Shear and punching strength of slabs without shear reinforcement,” Bet. Stahlbetonbau, vol. 98, pp. 74–84, 2003 [in German].], [9393 A. Muttoni, “Shear in Members Without Shear Reinforcement”, in Introduction to the Swiss Code SIA 262, Zürich, Switzerland: Swiss Eng. Archit. Document., 2003, pp. 47-55.[in French and German] [D0182].]).
Figure 6
Application of DIC to investigate the cracking development and associated kinematics in specimen SC70 by Cavagnis et al. [101101 F. Cavagnis, M. Fernández Ruiz, and A. Muttoni, “An analysis of the shear transfer actions in reinforced concrete members without transverse reinforcement based on refined experimental measurements,” Struct. Concr., vol. 19, pp. 49–64, 2018.]: (a) crack pattern at Vmax; (b) measured crack lips displacements and compressive strains in the shear critical region at Vmax; (c) acting forces in the critical shear crack at Vmax; (d) evolution of relative contribution of each shear-transfer action during loading. Figure adapted from [102102 F. Cavagnis, J. T. Simões, M. Fernández Ruiz, and A. Muttoni, “Shear strength of members without transverse reinforcement based on development of critical shear crack,” ACI Struct. J., vol. 117, no. 1, pp. 103–118, 2020.].
Figure 7
Mechanical model based on the development of a critical shear crack according to [102102 F. Cavagnis, J. T. Simões, M. Fernández Ruiz, and A. Muttoni, “Shear strength of members without transverse reinforcement based on development of critical shear crack,” ACI Struct. J., vol. 117, no. 1, pp. 103–118, 2020.], [108108 F. Cavagnis, M. Fernández Ruiz, and A. Muttoni, “A mechanical model for failures in shear of members without transverse reinforcement based on development of a critical shear crack,” Eng. Struct., vol. 157, pp. 300–315, 2018.]. Figure adapted from [102102 F. Cavagnis, J. T. Simões, M. Fernández Ruiz, and A. Muttoni, “Shear strength of members without transverse reinforcement based on development of critical shear crack,” ACI Struct. J., vol. 117, no. 1, pp. 103–118, 2020.].
Figure 8
Failure criterion calculated with the refined formulation of the mechanical model of the CSCT obtained varying (a) ρ or (b) d and comparison with the analytical power-law failure criterion (values when not varied: d=0.55 m; fc=40 MPa; dg=16 mm). Figure adapted from [102102 F. Cavagnis, J. T. Simões, M. Fernández Ruiz, and A. Muttoni, “Shear strength of members without transverse reinforcement based on development of critical shear crack,” ACI Struct. J., vol. 117, no. 1, pp. 103–118, 2020.].
Figure 9
Considering the effects of (a) centered axial forces, (b) prestressing forces and (c) eccentric normal forces on the calculation of the effective shear span. Figure adapted from [105105 A. Muttoni, M. Fernández Ruiz, and F. Cavagnis, “Shear in members without transverse reinforcement: from detailed test observations to a mechanical model and simple expressions for codes of practice,” in Fib Int. Workshop on Beam Shear, Zurich, Switzerland, Sep. 5-6 2016.].
Figure 10
Mechanical model of Simões et al. [
8585 J. T. Simões, M. Fernández Ruiz, and A. Muttoni, “Validation of the Critical Shear Crack Theory for punching of slabs without transverse reinforcement by means of a refined mechanical model,” Struct. Concr., vol. 19, pp. 191–216, 2018, http://dx.doi.org/10.1002/suco.201700280.
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]: (a) main assumptions; (b) different regions of the slab; (c) kinematics; (d) geometry, displacements normal and parallel to the CSC, normal and shear stresses and integration of stresses along the CSC. Figure adapted from [
8585 J. T. Simões, M. Fernández Ruiz, and A. Muttoni, “Validation of the Critical Shear Crack Theory for punching of slabs without transverse reinforcement by means of a refined mechanical model,” Struct. Concr., vol. 19, pp. 191–216, 2018, http://dx.doi.org/10.1002/suco.201700280.
http://dx.doi.org/10.1002/suco.201700280...
], [
8686 A. Muttoni, M. Fernández Ruiz, and J. T. Simões, “Recent improvements of the critical shear crack theory for punching shear design and its simplification for code provisions,” in Proc. 2018 Fib Congr.: Better, Smarter, Stronger, 2019, pp. 116–129.].
Figure 11
Results of the refined mechanical model of the CSCT for punching [
8585 J. T. Simões, M. Fernández Ruiz, and A. Muttoni, “Validation of the Critical Shear Crack Theory for punching of slabs without transverse reinforcement by means of a refined mechanical model,” Struct. Concr., vol. 19, pp. 191–216, 2018, http://dx.doi.org/10.1002/suco.201700280.
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]: (a) normalized punching resistance calculated for selected tests (databases from [
3434 A. Muttoni, M. Fernández Ruiz, and J. T. Simões, “The theoretical principles of the critical shear crack theory for punching shear failures and derivation of consistent closed-form design expressions,” Struct. Concr., vol. 19, pp. 174–190, 2018, http://dx.doi.org/10.1002/suco.201700088.
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]) as a function of the calculated normalized rotation; (b) calculated normalized crack opening at
d/2 from the soffit of the slab as a function of the normalized rotation. Figure adapted from Simões et al. [
8585 J. T. Simões, M. Fernández Ruiz, and A. Muttoni, “Validation of the Critical Shear Crack Theory for punching of slabs without transverse reinforcement by means of a refined mechanical model,” Struct. Concr., vol. 19, pp. 191–216, 2018, http://dx.doi.org/10.1002/suco.201700280.
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].
Figure 12
Normalized punching resistance as a function of the normalized rotation calculated with the refined mechanical model [
8585 J. T. Simões, M. Fernández Ruiz, and A. Muttoni, “Validation of the Critical Shear Crack Theory for punching of slabs without transverse reinforcement by means of a refined mechanical model,” Struct. Concr., vol. 19, pp. 191–216, 2018, http://dx.doi.org/10.1002/suco.201700280.
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] and comparison with simplified power-law failure criterion [
3434 A. Muttoni, M. Fernández Ruiz, and J. T. Simões, “The theoretical principles of the critical shear crack theory for punching shear failures and derivation of consistent closed-form design expressions,” Struct. Concr., vol. 19, pp. 174–190, 2018, http://dx.doi.org/10.1002/suco.201700088.
http://dx.doi.org/10.1002/suco.201700088...
], [
104104 A. Muttoni, M. Fernández Ruiz, and F. Cavagnis, “Shear in members without transverse reinforcement: from detailed test observations to a mechanical model and simple expressions for codes of practice,” in fib Bulletin No. 85: Towards a Rational Understanding of Shear in Beams and Slabs, International Federation for Structural Concrete, Ed., Lausanne, Switzerland: FIB, 2018, pp. 7–23.] for different: (a) column size-to-effective depth ratios; (b) slenderness-to-effective depth ratios. Figure adapted from [
8686 A. Muttoni, M. Fernández Ruiz, and J. T. Simões, “Recent improvements of the critical shear crack theory for punching shear design and its simplification for code provisions,” in Proc. 2018 Fib Congr.: Better, Smarter, Stronger, 2019, pp. 116–129.].
Figure 13
Comparison of the results of the refined mechanical model of the CSCT for punching [
8585 J. T. Simões, M. Fernández Ruiz, and A. Muttoni, “Validation of the Critical Shear Crack Theory for punching of slabs without transverse reinforcement by means of a refined mechanical model,” Struct. Concr., vol. 19, pp. 191–216, 2018, http://dx.doi.org/10.1002/suco.201700280.
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] against experimental results (from [
127127 J. Einpaul, “Punching strength of continuous flat slabs,” Ph.D. dissertation, EPFL, Lausanne, Switzerland, 2016.]) in terms of shear and flexural deformations.
Figure 14
Results of the refined mechanical model of the CSCT for punching [
8585 J. T. Simões, M. Fernández Ruiz, and A. Muttoni, “Validation of the Critical Shear Crack Theory for punching of slabs without transverse reinforcement by means of a refined mechanical model,” Struct. Concr., vol. 19, pp. 191–216, 2018, http://dx.doi.org/10.1002/suco.201700280.
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]: relationship between load, rotation and shear deformation during loading and at failure.
Figure 15
Graphical representation of the analytical derivation of simplified punching shear design formulae for FprEN 1992-1-1:2023 [118118 European Committee for Standardization, Eurocode 2 - Design of Concrete Structures - Part 1-1: General Rules - Rules for Buildings, Bridges and Civil Engineering Structures, Final Draft FprEN 1992-1-1:2023, 2023.] based on the CSCT: (a) closed-form for members without shear reinforcement; (b) activation of shear reinforcement; (c) members with shear reinforcement.
Figure 16
Investigation of the required amount of shear reinforcement by varying the location of the control section as allowed in FprEN 1992-1-1:2023 [118118 European Committee for Standardization, Eurocode 2 - Design of Concrete Structures - Part 1-1: General Rules - Rules for Buildings, Bridges and Civil Engineering Structures, Final Draft FprEN 1992-1-1:2023, 2023.].
Figure 17
Considerations on the control perimeter: (a) location according to different codes of practice [122122 European Committee for Standardization, Eurocode 2. Design of Concrete Structures - Part 1-1: General Rules and Rules for Buildings, EN 1992-1-1:2004, 2004.], [118118 European Committee for Standardization, Eurocode 2 - Design of Concrete Structures - Part 1-1: General Rules - Rules for Buildings, Bridges and Civil Engineering Structures, Final Draft FprEN 1992-1-1:2023, 2023.], [116116 International Federation for Structural Concrete, fib Model Code for Concrete Structures 2010. Berlin, Germany: Ernst & Sohn, 2013.], [131131 American Concrete Institute Committee, Building Code Requirements for Structural Concrete and Commentary, ACI Code 318-19 (22) (Reapproved 2022), 2022.]; influence of the column size-to-effective depth ratio on the punching resistance for (b) round and (c) square columns (accounting for stresses concentrations); (d) reduction of control perimeter in square stiff support areas due to stresses concentrations considered in [116116 International Federation for Structural Concrete, fib Model Code for Concrete Structures 2010. Berlin, Germany: Ernst & Sohn, 2013.] and [118118 European Committee for Standardization, Eurocode 2 - Design of Concrete Structures - Part 1-1: General Rules - Rules for Buildings, Bridges and Civil Engineering Structures, Final Draft FprEN 1992-1-1:2023, 2023.].
Figure 18
Definition of control perimeter according to [118118 European Committee for Standardization, Eurocode 2 - Design of Concrete Structures - Part 1-1: General Rules - Rules for Buildings, Bridges and Civil Engineering Structures, Final Draft FprEN 1992-1-1:2023, 2023.]: (a) large stiff square support area; (b) corner of wall; (c) wall end; (d) interior column with column penetration.
Figure 19
Overview of the framework of the mechanical model of the CSCT for punching.