RC Slab Punching Shear Capacity

1 Column & Slab Geometry

Column loaded area (rectangular)

c₁ =mm∥ to eccentricity

c₂ =mm⊥ to eccentricity

Slab

h =mmtotal thickness

d =mmavg. effective depth

Control perimeters

u₀ =2(c₁+c₂)=—mm

u₁ =2(c₁+c₂)+4πd=—mm

Figure 1 — Plan view: column, u₀ (face) & u₁ (2d from face) control perimeters (interactive)

2 Applied Loads at Control Perimeter

V_Ed =kNdesign punching shear force

M_Ed =kN·mdesign moment (eccentricity effect)

c₁ is the column dimension parallel to the eccentricity of the load.
c₂ is the column dimension perpendicular to the eccentricity of the load.
Set M_Ed = 0 for symmetric loading (β = 1.0).

3 Material Properties

Concrete — C30/37

Class:

f_ck =30MPa

γ_c =Table 2.1N

α_cc =§3.1.6

f_cd =20.00MPa= α_cc·f_ck/γ_c

Longitudinal flexural reinforcement

ρ_ly =ratio in y-dir.

ρ_lz =ratio in z-dir.

ρ_l =min(√(ρ_ly·ρ_lz), 0.02)=—

4 Control Perimeter Parameters & Applied Shear Stress

Eccentricity coefficient k (Table 6.1 — EN 1992-1-1)

c₁/c₂	≤ 0.5	1.0	2.0	≥ 3.0
k	0.45	0.60	0.70	0.80
c₁/c₂ =	—			—

W₁ — shear distribution at u₁ (§6.4.3 Eq. 6.41)

W₁ =c₁²/2 + c₁c₂ + 4c₂d + 16d² + 2πdc₁

W₁ =—mm²

Applied shear stress at u₁ (§6.4.4 Eq. 6.51)

v_Ed =V_Ed/(u₁·d) · [1 + k·M_Ed·u₁/(V_Ed·W₁)]

β =—eccentricity factor

v_Ed =—MPa

Figure 2 — Slab cross-section at u₁

5 Punching Shear Resistance — Without Shear Reinforcement

C_Rd,c =0.18/γ_c=—§6.4.4 Note

k_size =min(1+√(200/d), 2.0)=—

v_min =0.035·k³/²·f_ck^½=—MPa

C_Rd,c·k·(100ρ_lf_ck)^⅓ =—MPa

v_Rd,c =—MPa= max of above two values

Face of column — check at u₀ (§6.4.5)

W₀ =c₁²/2 + c₁·c₂=—mm²

β₀ =1+k·M_Ed·u₀/(V_Ed·W₀)=—

v_Ed,max =—MPa

ν =0.6(1−f_ck/250)=—

v_Rd,max =—MPa= 0.5·ν·f_cd

✓

—

✓

—

6 Punching Shear Reinforcement (if required — §6.4.5)

Shear stud / link parameters

φ_sw = mmlink diameter

n_sw =bars per perimeter

A_sw =—mm²area per perimeter

s_r =mmradial spacing

α =°inclination to slab plane

f_yk,sw =MPalink yield strength

γ_s =

f_ywd =—MPa

f_ywd,ef =min(250+0.25d, f_ywd)=—MPa

v_Rd,cs =—MPa

✓

—

7 Outer Perimeter — No Shear Reinforcement Required (§6.4.5(4))

u_out,ef =β·V_Ed/(v_Rd,c·d)=—mm

Dist. from col.= (u_out,ef − 2(c₁+c₂))/(2π)=—mmfrom face of column

Last ring ≤kd = 2d =—mmfrom outer perimeter

Overall Punching Shear Check

—

Utilisation at u₁

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Reference: EN 1992-1-1:2004 — Eurocode 2: Design of concrete structures — Part 1-1: General rules and rules for buildings, Section 6.4

RC Slab — Punching Shear Capacity