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Punching shear at the basic control perimeter

Basic control perimeter at 2d, punching shear stress with the factor beta, and the resistance without punching reinforcement. Reference: EN 1992-1-1 6.4.2-6.4.4.

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Example only. This sheet shows one way to set out the check. It is not endorsed by the bodies that publish the design codes and does not reproduce them. Check every clause, value and assumption against your own copy of the current edition of Eurocode 2 and its national annex before you use it, and have the result checked by a competent person. See the disclaimer.

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# Inputs
f_ck := 30 MPa
gamma_c := 1.5
c_1 := 400 mm
c_2 := 400 mm
d := 240 mm
rho_ly := 0.009
rho_lz := 0.008
V_Ed := 850 kN
beta := 1.15

# Control perimeter
u_1 := 2*(c_1 + c_2) + 4*pi*d = mm
v_Ed := beta*V_Ed/(u_1*d) = MPa

# Resistance
k := min(1 + sqrt(200 mm/d), 2) =
rho_l := min(sqrt(rho_ly*rho_lz), 0.02) =
C_Rdc := 0.18/gamma_c =
v_min := 0.035*k^1.5*sqrt(f_ck/(1 MPa))*1 MPa =
v_Rdc := max(C_Rdc*k*(100*rho_l*f_ck/(1 MPa))^(1/3)*1 MPa, v_min) =
v_Ed <= v_Rdc =
# Here the check is not met: punching shear reinforcement is needed (see the sheet on punching shear reinforcement), or a deeper slab.

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