Numerical Evaluation of the Punching Shear Strength of Flat Slabs Subjected to Balanced and Unbalanced Moments
Abstract
:1. Introduction
2. Experimental Test
3. Numerical Models
3.1. Geometrics Parameters
3.2. Boundary Conditions and Reference Points
3.3. Load Conditions
3.4. Reinforcement Bars and Concrete
3.5. Finite Element Mesh
4. Validation of the F.E. Models
4.1. Concrete Parameters
4.2. Symmetry Conditions
4.3. Ultimate Shear Force and Rotation
4.4. Crack Distribution
4.4.1. Slab LS05
4.4.2. Slab LS06
4.5. Steel Strains
4.5.1. Slab LS05
4.5.2. Slab LS06
4.6. Concrete Strains
4.6.1. Slab LS05
4.6.2. Slab LS06
5. Parametric Study and Design Codes Comparison
5.1. Ultimate Shear Forces and Rotations
5.2. Cracking Pattern
5.3. Desing Codes Comparison
6. Conclusions and Remarks
- The numerical results of both loading cases (non-eccentric and eccentric) agreed well with the experimental results. The most significant discrepancy between the ultimate experimental and computational shear forces was 11%, referring to the LS06 model (eccentric load) with one plane of symmetry.
- Regarding cracking, all F.E. models exhibited cracking patterns identical to those found experimentally by the reference authors.
- The strains in the concrete slab were the parameters that showed the most significant discrepancies. Such differences can be attributed to several factors, including the proximity between the strain gauge sensors and the column, uncertainties associated with the mechanical properties of the material, numerical errors generated from approximations in the analysis of F.E. models, the size and conditions of adherence of the strain gauges during the application of the load, the boundary conditions, and characteristics of the loading process.
- All aspects allow us to conclude that the F.E. models developed are valid and capable of adequately representing the mechanical behaviour of smooth slabs subjected to balanced and unbalanced moments.
- The parametric study results confirmed that the increase in the unbalanced moment negatively impacts the punching strength of the slab–column connections.
- In summary, the unbalanced moment results in an increase in shear stress in the slab–column connection, a phenomenon observed by all numerical models in Groups 1, 2, and 3, and corroborated by the design codes.
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A. Punching Shear Provisions in Design Codes
Crushing of compression strut: |
Diagonal tension: |
Examples of control perimeters: |
Crushing of compression strut: |
Diagonal tension: |
Example of control perimeter: |
Stress corresponding to the nominal shear strength without shear reinforcement: |
Examples of control perimeters: |
Maximum shear force resistance: |
without shear reinforcement: |
Examples of control perimeters: |
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Load Step | Experimental Response | Displacement Increment (Each Rigid Plate—Figure 4) | |||||||
---|---|---|---|---|---|---|---|---|---|
Jack 01 L1 (kN) | Jack 02 L2 (kN) | Jack 03 L3 (kN) | Jack 04 L4 (kN) | Total Load TL (kN) | L1/TL | L2/TL | L3/TL | L4/TL | |
1 | 12.5 | 3.8 | 8.0 | 7.4 | 69.2 | 0.090 | 0.027 | 0.058 | 0.053 |
2 | 24.1 | 6.0 | 15.1 | 15.3 | 98.0 | 0.123 | 0.031 | 0.077 | 0.078 |
3 | 36.1 | 9.5 | 22.6 | 22.9 | 128.6 | 0.140 | 0.037 | 0.088 | 0.089 |
4 | 48.0 | 12.0 | 29.9 | 29.8 | 157.2 | 0.153 | 0.038 | 0.095 | 0.095 |
5 | 59.9 | 15.0 | 37.2 | 37.4 | 187.0 | 0.160 | 0.040 | 0.099 | 0.100 |
6 | 72.1 | 18.0 | 44.8 | 44.6 | 217.0 | 0.166 | 0.041 | 0.103 | 0.103 |
7 | 83.8 | 21.5 | 54.7 | 53.2 | 250.7 | 0.167 | 0.043 | 0.109 | 0.106 |
8 | 96.8 | 25.0 | 60.0 | 59.8 | 279.1 | 0.173 | 0.045 | 0.107 | 0.107 |
9 | 107.9 | 27.3 | 67.4 | 67.5 | 307.6 | 0.175 | 0.044 | 0.110 | 0.110 |
10 | 121.0 | 32.0 | 76.7 | 76.0 | 343.2 | 0.176 | 0.047 | 0.112 | 0.111 |
11 | 132.2 | 33.0 | 83.0 | 83.0 | 368.7 | 0.179 | 0.045 | 0.113 | 0.113 |
12 | 144.1 | 36.5 | 90.0 | 90.0 | 398.1 | 0.181 | 0.046 | 0.113 | 0.113 |
13 | 156.7 | 39.5 | 98.4 | 98.0 | 430.1 | 0.182 | 0.046 | 0.114 | 0.114 |
14 | 168.5 | 42.5 | 105.1 | 105.8 | 459.4 | 0.183 | 0.046 | 0.114 | 0.115 |
15 | 181.0 | 47.5 | 112.5 | 114.0 | 492.5 | 0.184 | 0.048 | 0.114 | 0.116 |
Mean displacement of each hydraulic jack [mm] | 0.163 | 0.042 | 0.103 | 0.103 |
Model | ||||||
---|---|---|---|---|---|---|
LS05 | 779.0 | 735.6 | 1.06 | 9.76 | 10.62 | 0.92 |
LS06 (symmetrical model) | 528.0 | 475.1 | 1.11 | 8.61 | 7.00 | 1.23 |
LS06 (complete model) | 528.0 | 480.4 | 1.10 | 8.61 | 6.50 | 1.32 |
Position | Mean Value (1) | Group 1 | Group 2 | Group 3 | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|
N1 | N2 | N3 | N4 | S1 | S2 | S3 | S4 | EW1 | EW2 | ||
North | 0.163 | 0.170 | 0.180 | 0.190 | 0.200 | 0.163 | 0.163 | 0.163 | 0.163 | 0.163 | 0.163 |
South | 0.042 | 0.042 | 0.042 | 0.042 | 0.042 | 0.030 | 0.020 | 0.010 | 0.005 | 0.042 | 0.042 |
East/West | 0.103 | 0.103 | 0.103 | 0.103 | 0.103 | 0.103 | 0.103 | 0.103 | 0.103 | 0.120 | 0.130 |
Model | [kN] | ||||
---|---|---|---|---|---|
Group 1 | N1 | 443.85 | 1.07 | 6.27 | 1.12 |
N2 | 440.97 | 1.08 | 6.04 | 1.16 | |
N3 | 434.89 | 1.09 | 5.77 | 1.21 | |
N4 | 411.86 | 1.15 | 5.20 | 1.35 | |
Group 2 | S1 | 469.37 | 1.01 | 6.28 | 1.12 |
S2 | 412.71 | 1.15 | 6.45 | 1.09 | |
S3 | 399.47 | 1.19 | 6.50 | 1.08 | |
S4 | 393.95 | 1.21 | 6.76 | 1.04 | |
Group 3 | EW1 | 444.93 | 1.07 | 6.89 | 1.02 |
EW2 | 450.20 | 1.06 | 7.46 | 0.94 |
Pmáx | ACI 318 | Pmáx/ PACI | Eurocode 2 | Pmáx/ PEC2 | Model Code | Pmáx/ PMC | FprEN | Pmáx/ PFprEN | ABNT NBR 6118 | Pmáx/ PNBR | |
---|---|---|---|---|---|---|---|---|---|---|---|
Experimental Test | 528.0 | 354.2 | 1.49 | 416.6 | 1.27 | 258.9 | 2.04 | 404.9 | 1.30 | 300.8 | 1.76 |
LS06 (symmetrical model) | 475.1 | 354.2 | 1.49 | 416.6 | 1.27 | 288.7 | 1.83 | 333.0 | 1.59 | 300.8 | 1.76 |
N1 | 443.9 | 277.9 | 1.60 | 426.4 | 1.04 | 352.5 | 1.26 | 338.4 | 1.31 | 307.9 | 1.44 |
N2 | 441.0 | 278.9 | 1.58 | 415.1 | 1.06 | 336.5 | 1.31 | 336.8 | 1.31 | 299.8 | 1.47 |
N3 | 434.9 | 281.0 | 1.55 | 404.4 | 1.08 | 323.6 | 1.34 | 335.2 | 1.30 | 292.1 | 1.49 |
N4 | 411.9 | 289.2 | 1.42 | 394.2 | 1.04 | 322.5 | 1.28 | 333.5 | 1.23 | 284.7 | 1.45 |
S1 | 469.4 | 269.6 | 1.74 | 420.7 | 1.12 | 327.5 | 1.43 | 353.4 | 1.33 | 303.8 | 1.54 |
S2 | 412.7 | 288.9 | 1.43 | 409.7 | 1.01 | 346.5 | 1.19 | 351.3 | 1.17 | 295.9 | 1.39 |
S3 | 399.5 | 293.8 | 1.36 | 399.3 | 1.00 | 338.8 | 1.18 | 349.2 | 1.14 | 288.4 | 1.39 |
S4 | 394.0 | 295.9 | 1.33 | 394.2 | 1.00 | 334.5 | 1.18 | 350.2 | 1.12 | 284.7 | 1.38 |
EW1 | 444.9 | 277.6 | 1.60 | 389.5 | 1.14 | 294.7 | 1.51 | 351.2 | 1.27 | 281.3 | 1.58 |
EW2 | 450.2 | 275.8 | 1.63 | 434.6 | 1.04 | 361.6 | 1.25 | 383.4 | 1.17 | 313.9 | 1.43 |
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Mendes, R.P.; Mesquita, L.C.; Ferreira, M.P.; Trautwein, L.M.; Marvila, M.T.; Marques, M.G. Numerical Evaluation of the Punching Shear Strength of Flat Slabs Subjected to Balanced and Unbalanced Moments. Buildings 2024, 14, 985. https://doi.org/10.3390/buildings14040985
Mendes RP, Mesquita LC, Ferreira MP, Trautwein LM, Marvila MT, Marques MG. Numerical Evaluation of the Punching Shear Strength of Flat Slabs Subjected to Balanced and Unbalanced Moments. Buildings. 2024; 14(4):985. https://doi.org/10.3390/buildings14040985
Chicago/Turabian StyleMendes, Roberta Prado, Leonardo Carvalho Mesquita, Maurício Pina Ferreira, Leandro Mouta Trautwein, Markssuel Teixeira Marvila, and Marília Gonçalves Marques. 2024. "Numerical Evaluation of the Punching Shear Strength of Flat Slabs Subjected to Balanced and Unbalanced Moments" Buildings 14, no. 4: 985. https://doi.org/10.3390/buildings14040985