Finite Element Analysis of the Bearing Capacity of Beamless Floor Slabs under Punching, Taking into Account the Design Parameters of the Contacting Elements
Abstract
:1. Introduction
1.1. Fracture Behavior of Monolithic Floor Slabs during Punching
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- numerous experimental and theoretical studies of the nodal zones of reinforced concrete slabs point to a link between the nature of a node’s performance and the structural design of its reinforcement;
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- stress concentrations from the punching pressure in the load-bearing pylons;
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- pylons are almost always subjected to significant damage when subjected to the punching shear force.
1.2. Analytical Method for the Punching Calculation of Monolithic Reinforced Concrete Floor Slabs
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- strength limit (related to load-bearing capacity);
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- the limit states of suitability for normal operation (related to deformation).
- F—stress function;
- aik—stiffness properties of the slab under plane stress conditions.
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- for bending and torsional moments:
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- for transverse forces:
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- for longitudinal forces:
- Мх—bending moment along the x-axis;
- Му—bending moment along the y-axis;
- Мху—torsional moment in the xy plane;
- Мх,ult—ultimate bending moment along the x-axis;
- Мy,ult—ultimate bending moment along the y-axis;
- —ultimate bending moment in concrete in the x- and y-axis;
- —ultimate bending moment of the reinforcement in the x- and y-axis;
- Nх—longitudinal forces along the x-axis;
- Nу—longitudinal forces along the y-axis;
- Nх,y—shear forces;
- —ultimate longitudinal force along the x-axis;
- —ultimate longitudinal force along the y-axis;
- Qult, Qb, Qsw—transverse forces (ultimate, in concrete, in transverse reinforcement);
- Rbt—tensile strength of concrete;
- Rs—reinforcement tensile strength;
- Аb—cross-sectional area of concrete;
- Asx, Asy—reinforcement cross-sectional areas (x- and y-axis)
- qsw—transverse reinforcement intensity;
- b, h—width and height of the design cross-section of the support structure (pylon);
- h0—effective height of the element section;
- indexes (x, y)—belonging to calculation planes;
- index b—single concrete element;
- index s—single reinforcement element.
- —coefficient, taking into account the (strength) class of the concrete element;
- —average value of the upper and lower perimeters of the punching pyramid.
- —tensile strength of concrete for the limit states of the second group;
- —area of the design cross-section of the concrete at a distance of 0.5 h0 from the boundary of the application area of the concentrated force F with the working height of section h0, which is determined by the equation:
- —contour perimeter of the design cross-section;
- —working section height of the reinforced concrete slab.
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- from the action of a concentrated load:
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- from the combined action of a concentrated load and a bending moment:
- Рр—punching force (kN);
- h0—working section height of the reinforced concrete slab (cm);
- a—side dimension of a square column (cm);
- Mu—ultimate bending moment;
- ls—width of the bottom of the punching pyramid.
- S—perimeter of the perforation contour of the calculated section;
- —numerical coefficient equal to the ratio of the breaking loads in pushing and in bending;
- —cylindrical concrete strength.
1.3. Analysis of Experimental Results
1.3.1. Deformations of Concrete and Reinforcement
- БВ—deformations of the concrete of the top zone,
- БН—deformation of the concrete of the bottom zone,
- AB—deformation of the reinforcement of the top zone,
- AH—deformation of the reinforcement of the bottom zone.
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- The mean values of the maximum deformations for the compressed concrete were 163 × 10−5;
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- The mean values of the maximum deformations for the stretched concrete were 61 × 10−5. It should be noted here that the sensors continued to operate after the first cracks formed;
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- The average values of the maximum deformations for the compressed reinforcement were 30 × 10−5;
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- The average maximum deformation values for the tensile reinforcement were 248 × 10−5.
1.3.2. Stresses on Concrete and Reinforcement
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- in the presence of longitudinal reinforcement, the destruction of the sample during the formation of cracks in the tensile zone does not occur, but a pair of forces is formed that forms a compressed zone of concrete within the apex of the punching pyramid and a tensile one from the lower reinforcement;
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- resistance to vertical load is exerted by the compressed zone of concrete formed by the surface of the reduced punching pyramid.
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- the summation on the edges of the punching pyramid of the tensile concrete and transverse reinforcement bearing capacity does not correspond to the actual fracture pattern;
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- the assumption of a uniform distribution of shear stresses in concrete over the entire area of the design cross-section is inconsistent with the experimental data;
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- the normative calculation method for concretes of classes C40 and C45 in some cases shows a significant increase in the load-bearing capacity of the concrete punching compared to the experimental;
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- the analysis does not take into account the longitudinal reinforcement of the reinforced concrete slab, the asymmetric stress state at the different faces of the columns, or the loading mode;
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- the bending moments acting in the columns cannot affect the floor slabs’ stress–strain state outside the limits of their cross-sections.
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- tangential stresses are only uniformly distributed within the working height of the cross-section, not along the height of the concrete compression zone;
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- the bearing capacity of the slab obtained by analytical calculations in some cases exceeds those obtained from experiments;
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- there is unreasonable consideration of column forces from bending moments in the punching calculation of slabs;
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- the failure mechanism of the punching failure depends more on the distribution of internal forces (moments), the height of the concrete compression zone, and the reaching of the yield point of the longitudinal tensile reinforcement (see Figure 11).
2. Materials and Methods
Finite Element Modeling of Flat Reinforced Concrete Floor Slabs
3. Results
3.1. Calculation Results for the Pylon Punching Shear of the Monolithic Slab
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- the pylon sides’ ratio is taken as 1/4;
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- the minimum size of the support pylon is 200 mm;
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- the cross-sectional dimensions of the pylons are assumed to be 200 × 800, 200 × 1000, 200 × 1200, 200 × 1400, and 200 × 1600 mm;
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- the pylon spacing is assumed to be 6000 mm;
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- in order to avoid eccentricities and to simplify the investigations, a uniformly distributed load is applied to the slab, and the calculation model is assumed to be symmetrical.
3.2. Influence of the Design Parameters of the Contacting Elements in Beamless Floor Slabs on the Calculation of the Punching Pressure
4. Discussion
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- As the length and the ratio of the sides of the pylon cross-section increase, the concentration of forces increases proportionally, which lowers the load-carrying capacity of the floor slab. For the concrete classes C25 and C40 and the slab thickness of 200 mm, the increase of the pylon side length from 800 mm to 1000 mm leads to the increase of the bearing capacity safety factor by 14–15%, and the increase of the pylon side length from 1400 mm to 1600 mm leads to the increase of the bearing capacity safety factor by 7–8%. For reinforced concrete floor slabs with a thickness of 1000 mm, the safety factors are 8% and 4%.
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- The force concentration graph in the design cross-section of a 400 mm-thick slab has a maximum value, irrespective of the concrete class and the cross-sectional dimensions of the pylon. As the slab thickness increases, there is a sharp decrease in the concentration of forces in the design cross-section, followed by a damping. There is also a tendency of convergence of the graphs for different pylons with increasing slab thickness. Thus, for concrete of class C25, the difference in concentration values for pylons with sides of 800 mm and a slab thickness of 200 mm is 53%, and for 1600 mm, it is 30%. For concrete C40, these values were 53% and 31%.
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- The concrete class has a significant influence on the load-bearing capacity of the floor slab, but it has little influence (up to 10%) on the load-bearing capacity safety factor.
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- In the presence of longitudinal reinforcement, there is no fracture of the specimen when cracks form in the tensile zone, but a pair of forces forms from the compressed zone of the concrete within the apex of the punching pyramid and the tensile zone from the lower reinforcement.
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- The load is resisted by the compressed zone of the punching pyramid.
5. Conclusions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
- Code of Practice 63.13330.2018 Concrete and Reinforced Concrete Structures. Basic Provisions. SNiP 52-01-2003 (with Amendment N 1): SP (Code of Practice) [SP 63.13330.2018 Gelezobetonniye i kamenniye konstrukcii. Osnovnie polozheniya. SNiP 52-01-2003 (s izmeneniyem № 1)]. Ministry of Construction and Housing and Communal Services of the Russian Federation. Official edition. M.: Standartinform. 2019. Available online: docs.cntd.ru (accessed on 29 June 2019).
- Klovanich, S.F.; Shehovtsov, I.V. Pressing of Reinforced Concrete Slabs. Full-Scale and Numerical Experiments; ONMU: Odessa, Russia, 2011; p. 119. [Google Scholar]
- EN 1992-1-1:2004; Eurocode 2: Design of Concrete Structures. Part 1-1: General Rules and Rules for Buildings. The European Standard. European Committee for Standardization: Brussels, Belgium, 2004. Available online: eurocodes.jrc.ec.europa.eu (accessed on 29 June 2019).
- Muttoni, A. Punching shear strength of reinforced concrete slabs without transverse reinforcement. ACI Struct. J. 2008, 105, 440–450. [Google Scholar]
- ACI Committee 318. Building Code Requirements for Structural Concrete (ACI 318-19) and Commentary (ACI 318R-19); American Concrete Institute: Farmington Hills, MI, USA, 2019; 624p. [Google Scholar]
- Whitney, C.S. Ultimate Shear Strength of Reinforced Concrete Flat Slabs. J. ACI 1957, 54, 57–63. [Google Scholar]
- Moe, J. Shearing Strength of Reinforced Concrete Slabs and Foatings under Concentrated Loads; Portland Cement Association: Washington, DC, USA, 1961; pp. 117–124. [Google Scholar]
- ACI Committee 318. Building Code Requirements for Structural Concrete (ACI 318-05); American Concrete Institute: Farminton Hills, MI, USA, 2005; p. 70. [Google Scholar]
- Zalesov, A.S.; Gundar, V.A.; Chizhevsky, V.V. Edge piercing. Concr. Reinf. Concr. 1990, 36–38. [Google Scholar]
- Alexander, S.D.B.; Simmonds, S.H. Moment transfer at interior slab-column connections. ACI Struct. J. 2003, 100, 197–202. [Google Scholar]
- Chalioris, C.E.; Kosmidou, P.-M.K.; Papadopoulos, N.A. Investigation of a New Strengthening Technique for RC Deep Beams Using Carbon FRP Ropes as Transverse Reinforcements. Fibers 2018, 6, 52. [Google Scholar] [CrossRef]
- Chalioris, C.E.; Kytinou, V.K.; Voutetaki, M.E.; Papadopoulos, N.A. Repair of Heavily Damaged RC Beams Failing in Shear Using U-Shaped Mortar Jackets. Buildings 2019, 9, 146. [Google Scholar] [CrossRef]
- Dönmez, A.; Bažant, Z.P. Size effect on punching strength of reinforced concrete slabs with and without shear reinforcement. ACI Struct. J. 2017, 114, 875–886. [Google Scholar] [CrossRef]
- Einpaul, J.; Bujnak, J.; Ruiz, M.F.; Muttoni, A. Study on influence of column size and slab slenderness on punching strength. ACI Struct. J. 2016, 113, 135–145. [Google Scholar] [CrossRef]
- Fernández Ruiz, M.; Muttoni, A. Size effect in shear and punching shear failures of concrete members without transverse reinforcement: Differences between statically determinate members and redundant structures. Struct. Concr. 2017, 19, 65–75. [Google Scholar] [CrossRef]
- Filatov, V.; Galyautdinov, Z.; Suvorov, A. Elaboration of testing technique of flat slabs on punching shear strength using finite element modeling. MATEC Web Conf. 2018, 196, 02048. [Google Scholar] [CrossRef]
- Hawkins, N.M.; Falssen, H.B.; Hinojosa, R.C. Influence of column rectangularity on the behavior of flat plate structures. ACI Spec. Publ. 1971, SP-30, 127–146. [Google Scholar]
- Heinzmann, D.; Etter, S.; Villiger, S.; Jaeger, T. Punching tests on reinforced concrete slabs with and without shear reinforcement. ACI Struct. J. 2012, 109, 787–794. [Google Scholar]
- Kueres, D.; Siburg, C.; Herbrand, M.; Classen, M.; Hegger, J. Uniform design method for punching shear in flat slabs and column bases. Eng. Struct. 2017, 136, 149–164. [Google Scholar] [CrossRef]
- Setiawan, A.; Vollum, R.L.; Macorini, L.; Izzuddin, B.A. Punching of RC slabs without transverse reinforcement supported on elongated columns. Structures 2020, 27, 2048–2068. [Google Scholar] [CrossRef]
- Stein, T.; Ghali, A.; Dilger, W. Distinction between punching and flexural failure modes of flat plates. ACI Struct. J. 2007, 104, 357–365. [Google Scholar]
- Teng, S.; Cheong, H.K.; Kuang, K.L.; Geng, J.Z. Punching shear strength of slabs with openings and supported on rectangular columns. ACI Struct. J. 2004, 101, 678–687. [Google Scholar]
- Lyudkovsky, A.M.; Sokolov, B.S. Experience of designing and testing reinforced nodes of monolithic reinforced concrete slab support on columns. MSUCE Bull. 2018, 13, 33–43. [Google Scholar]
- Official Website of LIRA-SAPR. Official Website of LIRA-SAPR Software Package. Available online: liraland.ru (accessed on 29 June 2019).
- Tamrazyan, A.G. Calculation of reinforced concrete plates with hole at long-term loading. IOP Conf. Ser. Mater. Sci. Eng. 2018, 365, 052021. [Google Scholar] [CrossRef]
- Tamrazyan, A.G. The Assessment of Reliability of Punching Reinforced Concrete Beamless Slabs under the Influence of a Concentrated Force at High Temperatures. Procedia Eng. 2016, 153, 715–720. [Google Scholar] [CrossRef]
- Sagaseta, J.; Tassinari, L.; Ruiz, M.F.; Muttoni, A. Punching of flat slabs supported on rectangular columns. Eng. Struct. 2014, 77, 17–33. [Google Scholar] [CrossRef]
Specimen | ||||||||
---|---|---|---|---|---|---|---|---|
56.9 | 47.7 | - | - | 2.9 | 3.9 | 1140 | 40 | |
98.9 | - | - | - | 1979 | - | |||
45.9 | 10.1 | - | 4.9 | 920 | 9.2 | |||
55.5 | 5.3 | - | - | 1110 | 4.9 | |||
277.9 | 115.6 | - | - | 5.4 | 3.3 | 5000 | 102.7 | |
124.2 | 90.9 | - | 2.9 | 2483 | 84.3 | |||
92.6 | 73.7 | - | 2.6 | 1853 | 70.2 | |||
84.6 | 81.5 | - | 2.2 | 1693 | 76.7 | |||
237.8 | 112.5 | 2.86 | 2.6 | 3.7 | 5.0 | 3628 | 97.4 | |
- | 100.9 | 2.33 | 6.6 | 5000 | 75.3 | |||
- | 82.9 | - | 4.9 | 4308 | 88.3 | |||
- | 91.2 | - | 4.8 | 3684 | 77.2 | |||
254.4 | 105 | 2.51 | 2.45 | 5.4 | 4.0 | 4346 | 79.9 | |
234.2 | 103.9 | 2.52 | 2.7 | 4038 | 149.9 | |||
268.8 | 120.3 | 2.55 | - | 3874 | - | |||
275.3 | 120.9 | 2.2 | 3.9 | 3070 | 78.2 |
Concrete C25 | ||||||
---|---|---|---|---|---|---|
Side Ratios of the Pylon | 200 mm | 400 mm | 600 mm | 800 mm | 1000 mm | |
Plate Thickness | ||||||
b/h = 1/4 | 1.210 | 1.880 | 1.466 | 1.309 | 1.088 | |
b/h = 1/5 | 1.393 | 2.066 | 1.615 | 1.447 | 1.176 | |
b/h = 1/6 | 1.558 | 2.213 | 1.723 | 1.559 | 1.266 | |
b/h = 1/7 | 1.711 | 2.372 | 1.826 | 1.657 | 1.345 | |
b/h = 1/8 | 1.852 | 2.509 | 1.915 | 1.700 | 1.421 | |
Concrete C40 | ||||||
b/h = 1/4 | 1.221 | 1.885 | 1.448 | 1.283 | 1.047 | |
b/h = 1/5 | 1.401 | 2.082 | 1.598 | 1.412 | 1.135 | |
b/h = 1/6 | 1.564 | 2.241 | 1.717 | 1.5290 | 1.223 | |
b/h = 1/7 | 1.727 | 2.389 | 1.821 | 1.623 | 1.307 | |
b/h = 1/8 | 1.866 | 2.524 | 1.914 | 1.720 | 1.383 |
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Matseevich, T. Finite Element Analysis of the Bearing Capacity of Beamless Floor Slabs under Punching, Taking into Account the Design Parameters of the Contacting Elements. Buildings 2023, 13, 1221. https://doi.org/10.3390/buildings13051221
Matseevich T. Finite Element Analysis of the Bearing Capacity of Beamless Floor Slabs under Punching, Taking into Account the Design Parameters of the Contacting Elements. Buildings. 2023; 13(5):1221. https://doi.org/10.3390/buildings13051221
Chicago/Turabian StyleMatseevich, Tatiana. 2023. "Finite Element Analysis of the Bearing Capacity of Beamless Floor Slabs under Punching, Taking into Account the Design Parameters of the Contacting Elements" Buildings 13, no. 5: 1221. https://doi.org/10.3390/buildings13051221