Numerical and Experimental Investigation on Concrete Splitting Failure of Anchor Channels
Abstract
:1. Introduction
2. Design Provisions for the Concrete Splitting Failure Due to Loading
- The edge distance in all directions is c ≥ 1.2ccr,sp, and the member thickness is h ≥ hmin with hmin corresponding to ccr,sp.
- The characteristic resistances for concrete breakout failure and pull out failure are calculated for cracked concrete and reinforcement resists the splitting forces and limits the crack width to wk ≤ 0.3 mm.
3. FE Models and Experimental Validation
3.1. Validation of the Numerical Model
3.2. Definition of the Support and Boundary Conditions
4. Numerical Parametric Study
5. Numerical Results and Evaluation
5.1. Influence of Member Thickness
5.2. Influence of Edge Distance
5.3. Influence of Anchor Spacing
5.4. Modifications of the Current Design Model for Concrete Splitting of EN 1992-4
6. Experimental Results
7. Conclusions
- The 3D FE code employed in the numerical investigation, which is based on the microplane model for concrete, the smeared crack approach and the crack band regularization method, was able to replicate the experimentally obtained ultimate capacities and failure modes. However, the load-bearing behavior in numerical simulations was stiffer than in experiments resulting in smaller displacements at the ultimate capacity. The possible reason could be the local crushing of concrete around the anchor head that cannot be properly accounted for in macroscopic analyses.
- The influence of member thickness should be considered in the design model for concrete splitting. It was found that the existing factor of EN 1992-4 is relatively accurate at predicting the influence of member thickness. An improvement for the modification factor to take the slab thickness into account is proposed. The value hmin (chosen by the manufacturer for qualification testing) should be replaced by the embedment depth hef (physical dimension) together with a different calibrating factor of 1.15. The experimental results also showed that the influence of member thickness is present for anchor channels without edge influence, which is consistent with the findings of Nilforoush [8] for headed studs, although with slightly different results.
- Currently, the characteristic edge distance for splitting is set to ccr,sp = 3hef. According to the numerical and experimental results, a larger value is required to attain the capacity without edge influence, especially when the concrete member is relatively thin. In addition, it was found that the influence of edge distance can be well approximated by a linear function that yields to the limit value for c1 = 6hef.
- The numerical results indicated that the proportion between the characteristic edge distance and characteristic anchor spacing should be scr,sp = 2ccr,sp = 12hef.
- The doubling of the critical edge and spacing distances may seem excessive but, together with the other proposed modifications, results in the splitting failure only being decisive for small slab thicknesses compared to the concrete breakout failure.
- The experimental results showed that the modified design model for splitting is able to accurately predict the tensile capacity of anchor channels in thin slabs. This is very important as a basis for future work on the design of anchor channels in composite slabs, where an additional reduction factor should be applied to account for complex geometry of the concrete above the metal deck.
- In the prospective harmonization of the US and European verifications, the authors recommend keeping the two verifications for splitting and concrete breakout separately as per EN 1992-4, accordingly modifying the splitting verification, as this approach was proven to provide an overall excellent accuracy.
Outlook
- The influence of corners on the capacity of anchor channels in thin members should be clarified.
- The influence of reinforcement should be studied in detail since the presence of adequate reinforcement is considered to be a condition when the splitting verification can be omitted.
- Further numerical and experimental investigations for anchor channels without edge influence are required to determine how to consider the influence of member thickness in the verification for concrete breakout.
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A
c1 [mm] | hef [mm] | h [mm] | s [mm] | Nu [kN] | Nu,CB1 [kN] | Nu,proposal2 [kN] | Nu/Nu,decisive3 [−] |
---|---|---|---|---|---|---|---|
100 | 60 | 75 | 250 | 33.46 | 40.20 | 28.47 | 1.18 |
100 | 60 | 90 | 250 | 39.38 | 40.20 | 32.15 | 1.22 |
100 | 60 | 105 | 250 | 43.25 | 40.20 | 35.63 | 1.21 |
100 | 60 | 130 | 250 | 45.91 | 40.20 | 41.09 | 1.14 |
100 | 60 | 150 | 250 | 46.29 | 40.20 | 42.67 | 1.15 |
100 | 60 | 180 | 250 | 46.16 | 40.20 | 42.67 | 1.15 |
100 | 100 | 110 | 250 | 66.39 | 76.87 | 59.82 | 1.11 |
100 | 100 | 125 | 250 | 69.39 | 76.87 | 65.15 | 1.07 |
100 | 100 | 150 | 250 | 77.51 | 76.87 | 73.56 | 1.05 |
100 | 100 | 175 | 250 | 82.40 | 76.87 | 81.53 | 1.07 |
100 | 100 | 200 | 250 | 84.09 | 76.87 | 89.12 | 1.09 |
100 | 100 | 250 | 250 | 85.26 | 76.87 | 93.03 | 1.11 |
200 | 100 | 110 | 250 | 79.71 | 108.72 | 67.80 | 1.18 |
200 | 100 | 125 | 250 | 81.87 | 108.72 | 73.83 | 1.11 |
200 | 100 | 150 | 250 | 90.93 | 108.72 | 83.37 | 1.09 |
200 | 100 | 175 | 250 | 94.40 | 108.72 | 92.40 | 1.02 |
200 | 100 | 200 | 250 | 104.47 | 108.72 | 101.00 | 1.03 |
200 | 100 | 250 | 250 | 105.80 | 108.72 | 105.43 | 1.00 |
100 | 120 | 130 | 250 | 80.20 | 93.66 | 76.13 | 1.05 |
100 | 120 | 150 | 250 | 86.72 | 93.66 | 83.75 | 1.04 |
100 | 120 | 180 | 250 | 98.72 | 93.66 | 94.58 | 1.05 |
100 | 120 | 210 | 250 | 101.96 | 93.66 | 104.81 | 1.09 |
100 | 120 | 240 | 250 | 102.00 | 93.66 | 114.57 | 1.09 |
100 | 175 | 193 | 250 | 129.21 | 153.06 | 129.24 | 1.00 |
100 | 175 | 220 | 250 | 149.80 | 153.06 | 141.27 | 1.06 |
100 | 175 | 260 | 250 | 154.79 | 153.06 | 157.91 | 1.01 |
100 | 175 | 306 | 250 | 158.54 | 153.06 | 176.03 | 1.04 |
100 | 175 | 350 | 250 | 157.74 | 153.06 | 181.85 | 1.03 |
c1 [mm] | hef [mm] | h [mm] | s [mm] | Nu [kN] | Nu,CB1 [kN] | Nu,proposal2 [kN] | Nu/Nu,decisive3 [−] |
---|---|---|---|---|---|---|---|
60 | 60 | 75 | 250 | 31.04 | 31.14 | 26.15 | 1.19 |
100 | 60 | 75 | 250 | 33.46 | 40.20 | 28.47 | 1.18 |
150 | 60 | 75 | 250 | 36.07 | 47.90 | 31.38 | 1.15 |
180 | 60 | 75 | 250 | 38.06 | 47.90 | 33.12 | 1.15 |
240 | 60 | 75 | 250 | 44.29 | 47.90 | 36.61 | 1.21 |
360 | 60 | 75 | 250 | 47.38 | 47.90 | 43.58 | 1.09 |
∞ | 60 | 75 | 250 | 49.37 | 47.90 | / | 1.03 |
60 | 60 | 130 | 250 | 36.85 | 31.14 | 37.73 | 1.18 |
100 | 60 | 130 | 250 | 45.91 | 40.20 | 41.09 | 1.14 |
150 | 60 | 130 | 250 | 50.33 | 47.90 | 45.28 | 1.11 |
180 | 60 | 130 | 250 | 50.78 | 47.90 | 47.79 | 1.06 |
240 | 60 | 130 | 250 | 52.53 | 47.90 | 52.82 | 1.10 |
∞ | 60 | 130 | 250 | 53.88 | 47.90 | / | 1.12 |
50 | 100 | 125 | 250 | 57.55 | 54.36 | 60.80 | 1.06 |
100 | 100 | 125 | 250 | 69.39 | 76.87 | 65.15 | 1.07 |
150 | 100 | 125 | 250 | 75.83 | 94.15 | 69.49 | 1.09 |
200 | 100 | 125 | 250 | 81.87 | 108.72 | 73.83 | 1.11 |
300 | 100 | 125 | 250 | 91.89 | 110.81 | 82.52 | 1.11 |
∞ | 100 | 125 | 250 | 114.12 | 110.81 | / | 1.03 |
50 | 100 | 150 | 250 | 63.43 | 54.36 | 68.66 | 1.17 |
100 | 100 | 150 | 250 | 77.51 | 76.87 | 73.56 | 1.05 |
150 | 100 | 150 | 250 | 86.29 | 94.15 | 78.47 | 1.10 |
200 | 100 | 150 | 250 | 90.93 | 108.72 | 83.37 | 1.09 |
∞ | 100 | 150 | 250 | 114.12 | 110.81 | / | 1.03 |
50 | 100 | 200 | 250 | 65.74 | 54.36 | 83.18 | 1.21 |
100 | 100 | 200 | 250 | 84.09 | 76.87 | 89.12 | 1.09 |
150 | 100 | 200 | 250 | 90.43 | 94.15 | 95.06 | 0.96 |
200 | 100 | 200 | 250 | 104.47 | 108.72 | 101.00 | 1.03 |
300 | 100 | 200 | 250 | 109.84 | 110.81 | 112.88 | 0.99 |
∞ | 100 | 200 | 250 | 123.06 | 110.81 | / | 1.11 |
100 | 175 | 193 | 250 | 129.21 | 153.06 | 129.24 | 1.00 |
350 | 175 | 193 | 250 | 173.13 | 250.95 | 155.34 | 1.11 |
∞ | 175 | 193 | 250 | 264.75 | 250.95 | / | 1.06 |
100 | 175 | 350 | 250 | 157.74 | 153.06 | 181.85 | 1.03 |
262 | 175 | 350 | 250 | 193.99 | 247.74 | 205.66 | 0.94 |
∞ | 175 | 350 | 250 | 255.28 | 250.95 | / | 1.02 |
c1 [mm] | hef [mm] | h [mm] | s [mm] | Nu [kN] | Nu,CB1
[kN] | Nu,proposal2 [kN] | Nu/Nu,decisive3 [−] |
---|---|---|---|---|---|---|---|
100 | 60 | 75 | 100 | 29.72 | 27.51 | 24.17 | 1.23 |
100 | 60 | 75 | 200 | 33.20 | 36.06 | 26.95 | 1.23 |
100 | 60 | 75 | 250 | 33.46 | 40.20 | 28.47 | 1.18 |
100 | 60 | 75 | 300 | 35.34 | 41.86 | 30.09 | 1.17 |
100 | 60 | 75 | 500 | 40.66 | 41.86 | 37.21 | 1.09 |
100 | 60 | 75 | 720 | 44.56 | 41.86 | 43.49 | 1.06 |
100 | 60 | 75 | 840 | 44.83 | 41.86 | 43.49 | 1.07 |
100 | 60 | 130 | 100 | 33.20 | 27.51 | 34.88 | 1.21 |
100 | 60 | 130 | 200 | 41.98 | 36.06 | 38.89 | 1.16 |
100 | 60 | 130 | 250 | 45.91 | 40.20 | 41.09 | 1.14 |
100 | 60 | 130 | 300 | 47.17 | 41.86 | 43.41 | 1.13 |
100 | 60 | 130 | 500 | 49.29 | 41.86 | 53.69 | 1.18 |
100 | 100 | 125 | 100 | 64.63 | 57.89 | 59.13 | 1.12 |
100 | 100 | 125 | 200 | 66.53 | 70.04 | 63.06 | 1.05 |
100 | 100 | 125 | 250 | 69.39 | 76.87 | 65.15 | 1.07 |
100 | 100 | 125 | 300 | 72.72 | 83.90 | 67.31 | 1.08 |
100 | 100 | 200 | 100 | 60.90 | 57.89 | 80.89 | 1.05 |
100 | 100 | 200 | 200 | 77.84 | 70.04 | 86.27 | 1.11 |
100 | 100 | 200 | 250 | 84.09 | 76.87 | 89.12 | 1.09 |
100 | 100 | 200 | 300 | 92.13 | 83.90 | 92.08 | 1.10 |
200 | 100 | 125 | 100 | 73.66 | 81.88 | 67.02 | 1.10 |
200 | 100 | 125 | 200 | 78.37 | 99.05 | 71.47 | 1.10 |
200 | 100 | 125 | 250 | 81.87 | 108.72 | 73.83 | 1.11 |
200 | 100 | 125 | 300 | 83.40 | 118.66 | 76.29 | 1.09 |
100 | 91 | 130 | 150 | 59.34 | 57.32 | 58.43 | 1.04 |
100 | 91 | 130 | 200 | 64.51 | 63.43 | 60.55 | 1.07 |
100 | 91 | 130 | 250 | 67.98 | 69.95 | 62.76 | 1.08 |
100 | 91 | 130 | 300 | 73.96 | 76.52 | 65.06 | 1.14 |
100 | 106 | 130 | 150 | 68.21 | 68.09 | 65.51 | 1.04 |
100 | 106 | 130 | 200 | 73.19 | 74.65 | 67.53 | 1.08 |
100 | 106 | 130 | 250 | 73.45 | 81.70 | 69.63 | 1.05 |
100 | 106 | 130 | 300 | 74.28 | 89.01 | 71.81 | 1.03 |
100 | 120 | 130 | 150 | 76.13 | 79.01 | 72.15 | 1.06 |
100 | 120 | 130 | 200 | 78.46 | 86.06 | 74.11 | 1.06 |
100 | 120 | 130 | 250 | 80.20 | 93.66 | 76.13 | 1.05 |
100 | 120 | 130 | 300 | 86.79 | 101.64 | 78.22 | 1.11 |
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Author | Characteristic Member Thickness | Modification Factor |
---|---|---|
Asmus | ||
Hüer | ||
Nilforoush | 1 |
Strength Class | CEM II/B-M (S-LL) 42.5 N [kg/m3] | Aggregate (Dmax = 16 mm) [kg/m3] | Water [kg/m3] |
---|---|---|---|
C16/20 | 290 | 1870 | 208 (w/c = 0.72) |
Slab Type | c1 [mm] | hef [mm] | h [mm] | Nu,m [kN] | σ [kN] | CoV [%] | Nu,sim [kN] | Nu,sim/Nu,m [−] |
---|---|---|---|---|---|---|---|---|
plain | 100 | 106 | 130 | 79.00 | 0.90 | 1.14 | 74.48 | 0.94 |
composite | 100 | 106 | 130 | 52.22 | 2.95 | 5.66 | 51.08 | 0.98 |
c1 [mm] | hef [mm] | h [mm] | Nu,m [kN] | n [−] | σ [kN] | CoV [%] | Nu,sim [kN] | Nu,sim/Nu,m [−] |
---|---|---|---|---|---|---|---|---|
100 | 65 | 70 | 28.89 | 4 | 4.10 | 14.20 | 31.46 | 1.09 |
100 | 65 | 130 | 45.72 | 2 | 1.97 | 4.31 | 45.16 | 0.99 |
c1 [mm] | hef [mm] | h/hef [−] |
---|---|---|
100 | 100, 120, 175 | 1.10 |
100 | 60, 100, 120, 175 | 1.25 |
100 | 60, 100, 120, 175 | 1.50 |
100 | 60, 100, 120, 175 | 1.75 |
100 | 60, 100, 120, 175 | 2.00 |
100 | 60, 100 | 2.50 |
100 | 60 | 3.00 |
200 | 100 | 1.10–2.50 |
c1/hef [−] | hef [mm] | h [mm] |
---|---|---|
1.00, 1.67, 2.50, 3.00, 4.00, 6.00, in-field | 60 | 75 |
1.00, 1.67, 2.50, 3.00, 4.00, in-field | 60 | 130 |
0.50, 1.00, 1.50, 2.00, 3.00, in-field | 100 | 125 |
0.50, 1.00, 1.50, 2.00, in-field | 100 | 150 |
0.50, 1.00, 1.50, 2.00, 3.00, in-field | 100 | 200 |
0.50, 2.00, in-field | 175 | 193 |
0.50, 1.50, in-field | 175 | 350 |
s [mm] | c1 [mm] | hef [mm] | h [mm] |
---|---|---|---|
150, 200, 250, 300 | 100 | 91 | 130 |
150, 200, 250, 300 | 100 | 106 | 130 |
150, 200, 250, 300 | 100 | 120 | 130 |
100, 200, 250, 300, 500, 720, 840 | 100 | 60 | 75 |
100, 200, 250, 300, 500 | 100 | 60 | 130 |
100, 200, 250, 300 | 100 | 100 | 125 |
100, 200, 250, 300 | 100 | 100 | 200 |
100, 200, 250, 300 | 200 | 100 | 125 |
h [mm] | Nu,m [kN] | Nu,m/Nu,m,Ref (h = 130 mm) [−] | σ [kN] | CoV [%] | Nu,code [kN] | Nu,Grosser [kN] | (h/2hef)0.25 [−] |
---|---|---|---|---|---|---|---|
70 | 40.51 | 0.71 | 1.26 | 2.81 | 24.27 | 50.37 | 0.86 |
100 | 49.71 | 0.87 | 1.63 | 2.96 | 24.27 | 50.37 | 0.94 |
130 | 57.44 | 1.00 | 4.69 | 7.38 | 24.27 | 50.37 | 1.00 |
c1 [mm] | hef [mm] | h [mm] | Nu,m [kN] | ntest [−] | σ [kN] | CoV [%] | Nu,proposal [kN] | Nu,m/Nu,proposal [kN] |
---|---|---|---|---|---|---|---|---|
100 | 65 | 70 | 26.08 | 4 | 4.10 | 14.20 | 25.09 | 1.04 |
100 | 65 | 100 | 31.20 | 1 | - | - | 31.82 | 0.98 |
100 | 65 | 130 | 41.27 | 2 | 1.97 | 4.31 | 37.90 | 1.09 |
150 | 65 | 100 | 36.06 | 4 | 2.04 | 5.10 | 34.86 | 1.03 |
200 | 65 | 100 | 36.19 | 4 | 3.56 | 8.89 | 37.91 | 0.95 |
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Bogdanić, A.; Casucci, D.; Ožbolt, J. Numerical and Experimental Investigation on Concrete Splitting Failure of Anchor Channels. CivilEng 2021, 2, 502-522. https://doi.org/10.3390/civileng2020028
Bogdanić A, Casucci D, Ožbolt J. Numerical and Experimental Investigation on Concrete Splitting Failure of Anchor Channels. CivilEng. 2021; 2(2):502-522. https://doi.org/10.3390/civileng2020028
Chicago/Turabian StyleBogdanić, Anton, Daniele Casucci, and Joško Ožbolt. 2021. "Numerical and Experimental Investigation on Concrete Splitting Failure of Anchor Channels" CivilEng 2, no. 2: 502-522. https://doi.org/10.3390/civileng2020028
APA StyleBogdanić, A., Casucci, D., & Ožbolt, J. (2021). Numerical and Experimental Investigation on Concrete Splitting Failure of Anchor Channels. CivilEng, 2(2), 502-522. https://doi.org/10.3390/civileng2020028