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59x

001303

2024-01-16

Punching Shear Resistance of Slab Without Shear Reinforcement According to DIN EN 1992-1-1, 6.4.4 (1)

Punching shear resistance of the slab without shear reinforcement according to DIN EN 1992-1-1, 6.4.4 (1)

V_{Rd, c} = C_{Rd, c} \cdot k \cdot {(100 \cdot ρ_{l} \cdot f_{ck})}^{1 / 3} + k_{1} \cdot σ_{cp} \geq (v_{\min} + k_{1} \cdot σ_{cp}) = 0.12 \cdot 2.0 \cdot {(100 \cdot 0.0166 \cdot 35)}^{1 / 3} + 0.10 \cdot 0 = 0.929 MN / m^{2} \geq 0.586 MN / m^{2}

where

v_{\min} = (0.0525 / γ_{c}) \cdot k^{3 / 2} \cdot {f_{ck}}^{1 / 2} = (0.0525 / 1.5) \cdot 2 . 0^{3 / 2} \cdot 35^{1 / 2} = 0.586 MN / m^{2}

ρ_{l} = \sqrt{ρ_{ly} \cdot ρ_{lz}} = \sqrt{\frac{31.42 {cm}^{2} / m \cdot 10^{- 4}}{0.18 m} \cdot \frac{31.42 {cm}^{2} / m \cdot 10^{- 4}}{0.20 m}} = 0.0166 \leq 0.02

C_{Rd, c} = 0.18 / γ_{c} = 0.18 / 1.5 = 0.12

k_{1} = 1 + \sqrt{\frac{200 mm}{190 mm}} = 2.02 \leq 2.0

Eurocode 2

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