Dimensionless Formulae for Punching Shear Strengthof Reinforced Concrete Slabs
doi: 10.11858/gywlxb.2016.04.005
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摘要: 冲剪研究对钢筋混凝土平板和柱连接之间承载能力的评估以及核电厂中安全壳的安全计算和安全评估有重要意义。先前研究都忽略了跨深比对冲剪强度的影响，且现有设计准则中所用的方程量纲不一致，故大大限制了其使用范围和精度。给出了一个新的无量纲公式，考虑了钢筋数量、钢筋间距和跨深比的影响，可用于预测钢筋混凝土平板在冲头作用下的冲剪强度。结果表明, 新方程与已有实验结果吻合得很好，且优于现有设计准则。Abstract: Punching shear plays a very important role in assessing the load carrying capacities of connections between slabs and columns or slabs loaded by flat-faced punches, especially in the safety calculation and assessment of containment structures in nuclear power plants.For many years this has been examined by researchers and the influences of the span-to-depth ratio on punching shear strengths are often neglected, and all the equations employed in the current codes are dimensionally inconsistent.We proposed a dimensionless new empirical equation to predict the punching shear strengths of reinforced concrete circular slabs without shear reinforcement which are loaded quasi-statically by flat-faced circular indentors.In the present formulation, we took into consideration various effects such as rebar quantity, rebar spacing and span-to-depth ratio.It is shown that the present equation is in good correlation with available experimental results.It is also shown that the present equation is applicable to square punches as well as square slabs.
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Figure 1. Failure criterion for concrete (α0 is theangle of tangent to yield line with vertical)
Figure 2. Control perimeters of concrete slabs loaded by circular column as specified inACI 318-11, Euro-code 2, JSCE and BS8110-97
Figure 3. Schematic showing punching shear failure(L is the side length of a square reinforcedconcrete slab)
Figure 5. Dimensionless punching shear strengthvs. slab thickness to column diameter ratio
Figure 6. Comparison of the present empirical model(Eq.(13)) with available experimental data
Figure 7. Comparison of the present empiricalmodel with the experimental results forsquare reinforced concrete slabsloaded by a circular punch
Figure 8. Comparison of the present empiricalmodel with the experimental resultsfor the reinforced concrete slabsloaded by a square punch
Table 1. Comparisons of various formulae with available experimental results
Exp.No. L/(mm) S/(mm) H/(mm) de/(mm) d/(mm) fc′/(MPa) ζ/(%) Pu/(kN)(Exp.) Pu/Pm Ref. ACI318-11 BS8110-97 JSCE(2002) Euro-code2 (2004) Eq.(11) IA15b-7 1840 1710 153 124 150 28.0 2.03 247.2 1.33 1.25 0.88 0.84 1.03 IA15b-8 1840 1710 153 121 150 27.5 2.03 247.2 1.39 1.30 0.92 0.88 1.05 IA15b-9 1840 1710 150 117 150 25.5 2.18 274.6 1.68 1.51 1.08 1.02 1.27 IA15b-10 1840 1710 150 117 150 25.5 2.18 274.6 1.68 1.51 1.08 1.02 1.27 IA15c-11 1840 1710 153 121 150 31.5 2.16 333.5 1.75 1.64 1.14 1.11 1.24 [9] IA15c-12 1840 1710 154 122 150 30.4 2.16 331.5 1.75 1.63 1.14 1.10 1.27 IA30a-22 1840 1710 154 128 300 27.8 1.01 254.0 0.85 1.08 0.81 0.85 0.79 IA30a-23 1840 1710 151 125 300 26.7 1.04 207.9 0.73 0.91 0.68 0.72 0.68 IA30e-34 1840 1710 150 120 300 26.9 1.00 331.5 1.22 1.54 1.15 1.22 1.14 IA30e-35 1840 1710 153 122 300 24.6 0.98 331.5 1.25 1.57 1.19 1.24 1.23 2A 127 101.6 25.4 127 21.437 47.7 3.36 22.46 3.13 1.75 1.13 0.99 0.71 2B 254 203.2 50.8 254 42.545 47.7 3.07 78.73 2.77 1.90 1.22 1.16 0.88 2C 508 406.4 101.6 508 85.09 47.7 3.07 309.6 2.72 2.22 1.43 1.42 0.86 [16] 3A 127 101.6 25.4 127 21.437 45.3 2.74 16.32 2.33 1.38 0.90 0.78 0.75 3B 254 203.2 50.8 254 42.545 45.3 2.43 60.63 2.19 1.61 1.05 0.98 1.08 3C 508 406.4 101.6 508 85.09 45.3 2.43 228.9 2.07 1.80 1.17 1.16 1.02 F1 203.2 200 101.6 83 101.6 39.3 1.75 479.5 4.86 4.60 3.07 1.97 1.16 F2 406.4 400 101.6 83 101.6 39.3 1.75 204.2 2.07 1.96 1.30 1.26 1.01 F3 609.6 600 101.6 83 101.6 39.3 1.75 149.0 1.51 1.43 0.95 0.94 1.20 [19] F4 812.8 800 101.6 83 101.6 39.3 1.75 129.0 1.31 1.24 0.83 0.82 1.04 F5 1500 1200 101.6 83 101.6 39.3 1.75 138.8 1.41 1.33 0.89 0.88 1.12 S12 960 674 275 250 250 28.2 0.42 1049 1.60 2.97 2.07 1.53 0.85 [14] S13 960 674 275 250 250 19.8 0.42 803 1.45 2.53 1.87 1.30 0.93 9-1 2750 2600 180 143 300 37.3 1.48 628 1.57 1.88 1.32 1.44 0.97 [1] 9-2 2750 2600 191 171 300 28.5 1.18 626 1.40 1.79 1.29 1.31 1.14 12-1 2900 2650 280 240 500 29.3 1.3 1662 1.67 2.28 1.66 1.75 0.94 [1] 12-2 1400 1200 127 109 226 33.3 1.2 326 1.66 1.95 1.39 1.48 1.21 S1 850 600 275 242 250 39.8 0.40 1363 1.75 3.49 2.30 1.68 0.81 S2 850 600 277 243 250 28.4 0.40 1015 1.53 2.90 2.02 1.39 0.83 S3 850 600 278 250 250 29.8 0.39 1008 1.43 2.75 1.90 1.30 0.78 [14](Squareslabs) S7 850 600 277 246 250 14.4 0.40 622 1.30 2.19 1.71 1.04 1.01 S8 850 600 277 245 250 31.4 0.25 915 1.30 2.92 2.00 1.39 1.19 S9 850 600 277 244 250 25.5 0.40 904 1.43 2.66 1.89 1.27 0.83 S11 850 600 274 235 250 28.2 0.41 1190 1.90 3.53 2.47 1.71 1.00 S14 850 600 273 240 250 21.4 0.41 1100 1.95 3.48 2.54 1.67 1.23 
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Table 2. Comparisons of various formulae through the statistical method
Equation Pu/Pm Mean Standard deviation Coefficient of variation 95% confidence interval ACI 318-11 1.83 0.82 44.90 1.83±0.32 BS8110-97 1.80 0.72 39.78 1.80±0.28 JSCE (2002) 1.25 0.48 38.72 1.25±0.19 Euro-code 2 (2004) 1.15 0.31 26.50 1.15±0.12 Eq.(11) 1.03 0.18 17.45 1.03±0.07
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