Description
In this verification example the punching shear resistance of an inner column of a flat slab is examined. The column has a circular secton with a 30cm diameter.
| Material | Concrete C30/37 | Modulus of Elasticity | E | 33000 | N/mm2 |
| Design value of concrete compressive strength | fcd | 17.000 | N/mm2 | ||
| Reinforcing Steel B500S(A) | Design yield strength | fyd | 434.783 | N/mm2 | |
| Geometry | Flat slab | Slab thickness | h | 240 | mm |
| Span of a panel in y-direction | leff,y | 7.000 | m | ||
| Span of a panel in x-direction | leff,x | 5.000 | m | ||
| Column | length | lColumn | 4.000 | m | |
| Cross-section diameter | d | 300 | mm | ||
| Loads | Permanant loads | Reinforced concrete slab | p | 36.680 | kN/m2 |
Concrete Design Ultimate Configurations
- The used punching load is a single force from the column
- The applied method for determining the factor β: Constant factors according to figure 6.21N
Results
In the following, the RFEM 6 shear punching results are compared to the results of the reference.
| Punching Shear Desgin Acc. to DIN EN 1992-1-1 | |||||
| Parameter | Symbole | Unit | RFEM | Analytical solution | Ratio |
| Design Shear Force | VEd | kN | 500.850 | 500.000 | 1.002 |
| Mean effective depth | d | mm | 210 | 210 | 1.000 |
| Factor β | β | [-] | 1.10 | 1.10 | 1.000 |
| Length of basic control perimeter | u1 | m | 3.581 | 3.581 | 1.000 |
| Applied maximum shear stress | νEd | kN/m2 | 732.530 | 731.000 | 1.002 |
| Parameter CRd,c | CRd,c | [-] | 0.12 | 0.12 | 1.000 |
| Factor k for calculation of design value for shear resistance | k(6.47) | [-] | 1.980 | 1.976 | 1.002 |
| Reinforcement ratio for longitudinal reinforcement | ρl,1,-z(top) | % | 0.499 | 0.500 | 0.998 |
| Characteristic cylinder compressive strength of concrete | fck | N/mm2 | 30 | 30 | 1.000 |
| Normal concrete stresses in critical section | σcp | N/mm2 | 0 | 0 | 1.000 |
| Basic shear resistance | νRd,c,calc,1(2d) | kN/m2 | 584.290 | 585.000 | 0.999 |
| Minimum shear strength of plain concrete | νmin | kN/m2 | 532.450 | 532.000 | 1.001 |
Punching shear reinforcement is necessary.
| Punching Shear Reinforcement | |||||
| Parameter | Symbole | Unit | RFEM | Analytical solution | Ratio |
| Maximum shear resistance | νRd,u1,max | kN/m2 | 818.020 | 819.000 | 0.999 |
| Basic shear resistance with required longitudinal reinforcement | νRd,c,req,out | kN/m2 | 486.910 | 487.500 | 0,999 |
| Outermost control perimeter | uout,ef | m | 5.388 | 5.372 | 1.003 |
| Distance between loaded area and outermost control perimeter | lw,out | m | 0.708 | 0.705 | 1.004 |
| Designed number of perimeters | n | 3 | 3 | 1.000 | |
| Required punching reinforcement area of one perimeter | Asw,stat,i | cm2 | 3.350 | 3.600 | 0.931 |
| Required punching reinforcement area of 1st perimeter | Asw,req,1st | cm2 | 8.360 | 9.100 | 0.919 |
| Required punching reinforcement area of 2nd perimeter | Asw,req,2nd | cm2 | 4.680 | 5.100 | 0.918 |
| Required punching reinforcement area of 3rd perimeter | Asw,req,3rd | cm2 | 3.350 | 3.600 | 0.931 |
| Required punching reinforcement area of 3rd perimeter | Asw,req,3rd | cm2 | 3.350 | 3.600 | 0.931 |
| Distance from loaded area to 1st perimeter of punching reinforcement | lw,1st,req | m | 0.105 | 0.105 | 1.000 |
| Distance from loaded area to 2nd perimeter of punching reinforcement | lw,2nd,req | m | 0.249 | 0.262 | 0.950 |
| Distance from loaded area to 3rd perimeter of punching reinforcement | lw,3nd,req | m | 0.393 | 0.420 | 0.936 |
Overall, the results from RFEM 6 show a high level of agreement with the reference data, with most ratios between 0.910 and 1.000.
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