Reinforced Concrete: Punching¶

CalcpadCE worksheets in this section integrate the punching shear verification of flat slabs around column heads according to Eurocode EN 1992-1-1, with the basic control perimeter \(u_1\) traced at \(2d\) from the column face and the eccentricity factor \(\beta\) applied to the design shear stress.

Each worksheet returns the punching shear strength of the slab without shear reinforcement, the maximum strength at the column face, and the area of stirrups, studs or bent-up bars required to bridge the gap when the demand exceeds the slab capacity. The geometry of the perimeter changes with the column position: the internal column sees a closed perimeter, the edge column loses one side and the corner column loses two sides, with the eccentricity factor adjusted accordingly.

Corner Column¶

Punching shear verification of a flat slab around a corner column: control perimeter on two sides only, eccentricity factor for a corner support and required punching reinforcement when the slab capacity is exceeded.

Code:

'<small>According to <strong>Eurocode</strong>: EN 1992-1-1</small>
'<div style="max-width:180mm">
'<img class="side" style="width:225pt;" src="../../Images/structures/rc/design/punching-corner-column.png" alt="punching-corner-column.png">
'<h4>Input data</h4>
'<p><b>Column</b></p>
'Dimensions - 'c_1 = ?'mm, 'c_2 = ?'mm
'<p><b>Design loads</b></p>
'Support reaction -'V_Ed = ?'kN
'<p><b>Slab</b></p>
'Depth -'h = ?'mm
'Concrete cover -'c = ?'mm
'Longitudinal bars diameter -'d_bL = ?'mm
'Links diameter -'d_w = ?'mm
#post
'Effective slab depth
d = h - c - d_bL'mm
#show
'Longitudinal reinforcement area
A_sx = ?'mm²/m, 'A_sy = ?'mm²/m
#post
'Reinforcement ratio
ρ_lx = A_sx/(1000*d)
ρ_ly = A_sy/(1000*d)
ρ_l = sqr(ρ_lx*ρ_ly)
#show
'<p><b>Material properties</b></p>
'<p><b>Concrete</b> [EN 1992-1-1, Table 3.1]</p>
'Characteristic compressive cylinder strength -'f_ck = ?'MPa
'Partial safety factor for concrete -'γ_c = 1.5','α_cc = ?
#post
'Design compressive cylinder strength -'f_cd = α_cc*f_ck/γ_c'MPa
#show
'<p><b>Steel</b></p>
'Characteristic yield strength -'f_yk = ?'MPa
#post
'Partial safety factor for steel -'γ_s = 1.15
'Design yield strength -'f_ywd = f_yk/γ_s'MPa
#show
'</td></tr></table>
#post
'Basic control perimeter length
u_1 = c_1 + c_2 + π*d'mm
'<p class="ref">[EN 1992-1-1, Figure 6.21N]</p>
'<p><b>β factor</b> -'β = 1.50'</p>
'<div class="fold">
'<h4>Punching shear resistance without reinforcement</h4>
k = min(1 + sqr(200/d);2)
C_Rd_c = 0.18/γ_c
'<p class="ref">[EN 1992-1-1 (6.47)]</p>
'Punching shear resistance
v_Rd_c_ = C_Rd_c*k*(100*ρ_l*f_ck)^(1/3)'MPa
'<p class="ref">[EN 1992-1-1 (6.2b)]</p>
'Minimum shear resistance
v_min = 0.035*k^(3/2)*sqr(f_ck)'MPa
v_Rd_c = max(v_min;v_Rd_c_)'MPa
'<p class="ref">[EN 1992-1-1 (6.38)]</p>
'Design shear stress
v_Ed = β*V_Ed*10^3/(u_1*d)'MPa
'</div>
'<p class="ref">[EN 1992-1-1, §6.4.3 (2,b)]</p>
#if v_Ed ≤ v_Rd_c
    v_Ed'MPa &le; 'v_Rd_c'MPa. Shear reinforcement is NOT required.
#else
    v_Ed'MPa &gt;'v_Rd_c'MPa. Shear reinforcement is required.
    '<div class="fold">
    '<h4>Check at column edge</h4>
    'Column perimeter
    u_0 = min(c_1 + c_2;3*d)'mm
    '<p class="ref">[EN 1992-1-1 (6.53)]</p>
    'Punching shear resistance at column edge
    v_Ed_max = β*V_Ed*10^3/(u_0*d)'MPa
    'Maximum punching shear stress
    ν = 0.6*(1 - f_ck/250)
    '<p class="ref">[BS EN 1992-1-1, Table NA.1, §6.4.5 (3)]</p>
    v_Rd_max = 0.5*ν*f_cd'MPa
    '</div>
    '<p class="ref">[EN 1992-1-1, §6.4.3 (2,a)]</p>
    #if v_Ed_max ≤ v_Rd_max
        v_Ed_max' MPa &le; 'v_Rd_max'MPa. Design check is satisfied.
    #else
        '<p class="err">'v_Ed_max' MPa &gt; 'v_Rd_max'MPa. Design check is NOT satisfied!</p>
        '<p class="err">Increase slab thickness, column dimensions or concrete grade.</p>
    #end if
    '<p class="ref">[BS EN 1992-1-1, Table NA.1, §6.4.5 (3)]</p>
    'Limitation of punching stress at basic control perimeter
    #if v_Ed ≤ 2*v_Rd_c
        v_Ed' MPa &le; '2*v_Rd_c'MPa. Design check is satisfied.
    #else
        '<p class="err">'v_Ed' MPa &gt; '2*v_Rd_c'MPa. Design check is NOT satisfied!</p>
    #end if
    '<div class="fold">
    '<h4>Punching resistance with shear reinforcement</h4>
    'Effective yield strength of shear reinforcement
    f_ywd_ef = min(250 + 0.25*d;f_ywd)'MPa
    'Area of one shear link
    A_sw_1 = π*d_w^2/4'mm²
    '<p class="ref">[EN 1992-1-1, §9.4.3 (1)]</p>
    'Radial link spacing - 's_r = 0.75*d'mm
    'Required shear reinforcement
    A_sw_req = (v_Ed - 0.75*v_Rd_c)*u_1*s_r/(1.5*f_ywd_ef)'mm²
    'Tangential link spacing - 's_t = floor(u_1*A_sw_1/A_sw_req)'mm
    '<p class="ref">[EN 1992-1-1, §9.4.3 (1)]</p>
    #if s_t ≤ 1.5*d
        'Check:'s_t'mm &le; '1.5*d'mm. Check is satisfied.
    #else
        'Check:'s_t'mm &gt;'1.5*d'mm.
        '<p class="err">Distance exceeds the maximum value.</p>
        'Accepted value: 's_t = 1.5*d'mm
    #end if
    '<p class="ref">[EN 1992-1-1, §9.4.3 (2)]</p>
    'Minimum shear reinforcement
    A_sw_min = 0.08*sqr(f_ck)/f_yk*s_r*s_t/1.5'mm²
    #if A_sw_1 ≥ A_sw_min
        A_sw_1'mm² &ge;'A_sw_min'mm². The calculated reinforcement is greater than the minimum.
    #else
        '<p class="err">'A_sw_1'mm² &lt;'A_sw_min'mm². The calculated reinforcement is lower than the minimum!</p>
    #end if
    '</div>
    'Total shear reinforcement for each perimeter
    A_sw = A_sw_1*u_1/s_t'mm²
    '<p class="ref">[EN 1992-1-1 (6.52)]</p>
    'Punching resistance with shear reinforcement
    v_Rd_cs = 0.75*v_Rd_c + 1.5*d/s_r*A_sw*f_ywd_ef/(u_1*d)
    #if v_Ed ≤ v_Rd_cs
        v_Ed'MPa &le;'v_Rd_cs'MPa. Check is satisfied!
        '<p class="ref">[EN 1992-1-1 (6.54)]</p>
        'Outer control perimeter at which shear reinforcement is not required
        u_out = β*V_Ed*10^3/(v_Rd_c*d)'mm
        'Distance to outer control perimeter
        a_out = 2*(u_out - c_1 - c_2)/π'mm
        'Required number of perimeters
        n = ceiling(max((a_out - 2*d)/(0.75*d) + 1;2))
    #else
        '<p class="err">'v_Ed'MPa &gt;'v_Rd_cs'MPa. Check is NOT satisfied. Increase shear reinforcement area.</p>
    #end if
    '<img style="width:225pt;" style="display:inline;" src="../../Images/structures/rc/design/punching-corner-column-reinf-plan.png" alt="punching-corner-column-reinf-plan.png">
    '<img style="width:195pt;" src="../../Images/structures/rc/design/punching-corner-column-reinf-section.png" alt="punching-corner-column-reinf-section.png">
#end if
#show
'</div>600  300 125 200 20  10  6   1200    600 25  1   500

Edge Column¶

Punching shear verification of a flat slab around an edge column: open control perimeter on three sides, eccentricity factor for an edge support and design of the punching reinforcement.

Code:

'<small>According to <strong>Eurocode</strong>: EN 1992-1-1</small>
'<div style="max-width:180mm">
'<img class="side" style="width:225pt;" src="../../Images/structures/rc/design/punching-edge-column.png" alt="punching-edge-column.png">
'<h4>Input data</h4>
'<p><b>Column</b></p>
'Dimensions - 'c_1 = ?'mm, 'c_2 = ?'mm
'<p><b>Design loads</b></p>
'Support reaction -'V_Ed = ?'kN
'<p><b>Slab</b></p>
'Depth -'h = ?'mm
'Concrete cover -'c = ?'mm
'Longitudinal bars diameter -'d_bL = ?'mm
'Links diameter -'d_w = ?'mm
#post
'Effective slab depth
d = h - c - d_bL'mm
#show
'Longitudinal reinforcement area
A_sx = ?'mm²/m, 'A_sy = ?'mm²/m
#post
'Reinforcement ratio
ρ_lx = A_sx/(1000*d)
ρ_ly = A_sy/(1000*d)
ρ_l = sqr(ρ_lx*ρ_ly)
#show
'<p><b>Material properties</b></p>
'<p><b>Concrete</b> [EN 1992-1-1, Table 3.1]</p>
'Characteristic compressive cylinder strength -'f_ck = ?'MPa
'Partial safety factor for concrete -'γ_c = 1.5','α_cc = ?
#post
'Design compressive cylinder strength -'f_cd = α_cc*f_ck/γ_c'MPa
#show
'<p><b>Steel</b></p>
'Characteristic yield strength -'f_yk = ?'MPa
#post
'Partial safety factor for steel -'γ_s = 1.15
'Design yield strength -'f_ywd = f_yk/γ_s'MPa
#show
'</td></tr></table>
#post
'Basic control perimeter length
u_1 = c_2 + 2*c_1 + 2*π*d'mm
'<p class="ref">[EN 1992-1-1, Figure 6.21N]</p>
'<p><b>β factor</b> -'β = 1.40'</p>
'<div class="fold">
'<h4>Punching shear resistance without reinforcement</h4>
k = min(1 + sqr(200/d);2)
C_Rd_c = 0.18/γ_c
'<p class="ref">[EN 1992-1-1 (6.47)]</p>
'Punching shear resistance
v_Rd_c_ = C_Rd_c*k*(100*ρ_l*f_ck)^(1/3)'MPa
'<p class="ref">[EN 1992-1-1 (6.2b)]</p>
'Minimum shear resistance
v_min = 0.035*k^(3/2)*sqr(f_ck)'MPa
v_Rd_c = max(v_min;v_Rd_c_)'MPa
'<p class="ref">[EN 1992-1-1 (6.38)]</p>
'Design shear stress
v_Ed = β*V_Ed*10^3/(u_1*d)'MPa
'</div>
'<p class="ref">[EN 1992-1-1, §6.4.3 (2,b)]</p>
#if v_Ed ≤ v_Rd_c
    ''v_Ed'MPa &le; 'v_Rd_c'MPa. Shear reinforcement is NOT required.
#else
    v_Ed'MPa &gt;'v_Rd_c'MPa. Shear reinforcement is required.
    '<div class="fold">
    '<h4>Check at column edge</h4>
    'Column perimeter
    u_0 = min(2*c_1 + c_2;3*d + c_2)'mm
    '<p class="ref">[EN 1992-1-1 (6.53)]</p>
    'Punching shear resistance at column edge
    v_Ed_max = β*V_Ed*10^3/(u_0*d)'MPa
    'Maximum punching shear stress
    ν = 0.6*(1 - f_ck/250)
    '<p class="ref">[BS EN 1992-1-1, Table NA.1, §6.4.5 (3)]</p>
    v_Rd_max = 0.5*ν*f_cd'MPa
    '</div>
    '<p class="ref">[EN 1992-1-1, §6.4.3 (2,a)]</p>
    #if v_Ed_max ≤ v_Rd_max
        v_Ed_max' MPa &le; 'v_Rd_max'MPa. Design check is satisfied.
    #else
        '<p class="err">'v_Ed_max' MPa &gt; 'v_Rd_max'MPa. Design check is NOT satisfied!</p>
        '<p class="err">Increase slab thickness, column dimensions or concrete grade.</p>
    #end if
    '<p class="ref">[BS EN 1992-1-1, Table NA.1, §6.4.5 (3)]</p>
    'Limitation of punching stress at basic control perimeter
    #if v_Ed ≤ 2*v_Rd_c
        v_Ed' MPa &le; '2*v_Rd_c'MPa. Design check is satisfied.
    #else
        '<p class="err">'v_Ed' MPa &gt; '2*v_Rd_c'MPa. Design check is NOT satisfied!</p>
    #end if
    '<div class="fold">
    '<h4>Punching resistance with shear reinforcement</h4>
    'Effective yield strength of shear reinforcement
    f_ywd_ef = min(250 + 0.25*d;f_ywd)'MPa
    'Area of one shear link
    A_sw_1 = π*d_w^2/4'mm²
    '<p class="ref">[EN 1992-1-1, §9.4.3 (1)]</p>
    'Radial link spacing - 's_r = 0.75*d'mm
    'Required shear reinforcement
    A_sw_req = (v_Ed - 0.75*v_Rd_c)*u_1*s_r/(1.5*f_ywd_ef)'mm²
    'Tangential link spacing - 's_t = floor(u_1*A_sw_1/A_sw_req)'mm
    '<p class="ref">[EN 1992-1-1, §9.4.3 (1)]</p>
    #if s_t ≤ 1.5*d
        'Check:'s_t'mm &le; '1.5*d'mm. Check is satisfied.
    #else
        'Check:'s_t'mm &gt;'1.5*d'mm.
        '<p class="err">Distance exceeds the maximum value.</p>
        'Accepted value: 's_t = 1.5*d'mm
    #end if
    '<p class="ref">[EN 1992-1-1, §9.4.3 (2)]</p>
    'Minimum shear reinforcement
    A_sw_min = 0.08*sqr(f_ck)/f_yk*s_r*s_t/1.5'mm²
    #if A_sw_1 ≥ A_sw_min
        A_sw_1'mm² &ge;'A_sw_min'mm². The calculated reinforcement is greater than the minimum.
    #else
        '<p class="err">'A_sw_1'mm² &lt;'A_sw_min'mm². The calculated reinforcement is lower than the minimum!</p>
    #end if
    '</div>
    'Total shear reinforcement for each perimeter
    A_sw = A_sw_1*u_1/s_t'mm²
    '<p class="ref">[EN 1992-1-1 (6.52)]</p>
    'Punching resistance with shear reinforcement
    v_Rd_cs = 0.75*v_Rd_c + 1.5*d/s_r*A_sw*f_ywd_ef/(u_1*d)
    #if v_Ed ≤ v_Rd_cs
        v_Ed'MPa &le;'v_Rd_cs'MPa. Check is satisfied!
        '<p class="ref">[EN 1992-1-1 (6.54)]</p>
        'Outer control perimeter at which shear reinforcement is not required
        u_out = β*V_Ed*10^3/(v_Rd_c*d)'mm
        'Distance to outer control perimeter
        a_out = (u_out - 2*c_1 - c_2)/π'mm
        'Required number of perimeters
        n = ceiling(max((a_out - 2*d)/(0.75*d) + 1;2))
    #else
        '<p class="err">'v_Ed'MPa &gt;'v_Rd_cs'MPa. Check is NOT satisfied. Increase shear reinforcement area.</p>
    #end if
    '<img style="width:225pt;" style="display:inline;" src="../../Images/structures/rc/design/punching-edge-column-reinf-plan.png" alt="punching-edge-column-reinf-plan.png">
    '<img style="width:195pt;" src="../../Images/structures/rc/design/punching-edge-column-reinf-section.png" alt="punching-edge-column-reinf-section.png">
#end if
#show
'</div>600  300 200 200 20  10  6   1200    600 25  1   500

Internal Column¶

Punching shear verification of a flat slab around an internal column: closed control perimeter, slab strength without and with shear reinforcement, and required area of stirrups, studs or bent-up bars.

Code:

'<small>According to <strong>Eurocode</strong>: EN 1992-1-1</small>
'<div style="max-width:180mm">
'<img class="side" style="width:260pt;" src="../../Images/structures/rc/design/punching.png" alt="punching.png">
'<h4>Input data</h4>
'<p><b>Column</b></p>
'Dimensions - 'c_1 = ?'mm, 'c_2 = ?'mm
'<p><b>Design loads</b></p>
'Support reaction -'V_Ed = ?'kN
'Bending moments
M_x_Ed = ?'kNm,'M_y_Ed = ?'kNm
'<p><b>Slab</b></p>
'Depth -'h = ?'mm
'Concrete cover -'c = ?'mm
'Longitudinal bars diameter -'d_bL = ?'mm
'Links diameter -'d_w = ?'mm
#post
'Effective slab depth
d = h - c - d_bL'mm
#show
'Longitudinal reinforcement area
A_sx = ?'mm²/m, 'A_sy = ?'mm²/m
#post
'Reinforcement ratio
ρ_lx = A_sx/(1000*d)
ρ_ly = A_sy/(1000*d)
ρ_l = sqr(ρ_lx*ρ_ly)
#show
'<p><b>Material properties</b></p>
'<p><b>Concrete</b> [EN 1992-1-1, Table 3.1]</p>
'Characteristic compressive cylinder strength -'f_ck = ?'MPa
'Partial safety factor for concrete -'γ_c = 1.5','α_cc = ?
#post
'Design compressive cylinder strength -'f_cd = α_cc*f_ck/γ_c'MPa
#show
'<p><b>Steel</b></p>
'Characteristic yield strength -'f_yk = ?'MPa
#post
'Partial safety factor for steel -'γ_s = 1.15
'Design yield strength -'f_ywd = f_yk/γ_s'MPa
'Basic control perimeter length
u_1 = 2*(c_1 + c_2) + 4*π*d'mm
'<p><b>Calculation of the β factor</b></p>
#if M_y_Ed ≡ 0
    #if M_x_Ed ≡ 0
        '<p class="ref">[EN 1992-1-1, Figure 6.21N]</p>
        β = 1.15
    #else
        '<p class="ref">[EN 1992-1-1 (6.41)]</p>
        'Critical perimeter modulus
        W_1 = c_1^2/2 + c_1*c_2 + 4*c_2*d + 16*d^2 + 2*π*d*c_1'mm²
        k_c = c_1/c_2
        '<p class="ref">[EN 1992-1-1, Table 6.1]</p>
        #if k_c ≤ 0.5
            k = 0.45
        #else if k_c < 1
            k = 0.45 + (k_c - 0.5)*0.15
        #else if k_c < 2
            k = 0.6 + (k_c - 1)*0.1
        #else if k_c < 3
            k = 0.7 + (k_c - 2)*0.1
        #else
            k = 0.8
        #end if
        '<p class="ref">[EN 1992-1-1 (6.39)]</p>
        β = 1 + k*1000*M_x_Ed/V_Ed*u_1/W_1
    #end if
#else
    #if M_x_Ed ≡ 0
        '<p class="ref">[EN 1992-1-1 (6.41)]</p>
        'Critical perimeter modulus
        W_1 = c_2^2/2 + c_1*c_2 + 4*c_1*d + 16*d^2 + 2*π*d*c_2'mm²
        k_c = c_2/c_1
        '<p class="ref">[EN 1992-1-1, Table 6.1]</p>
        #if k_c ≤ 0.5
            k = 0.45
        #else if k_c < 1
            k = 0.45 + (k_c - 0.5)*0.15
        #else if k_c < 2
            k = 0.6 + (k_c - 1)*0.1
        #else if k_c < 3
            k = 0.7 + (k_c - 2)*0.1
        #else
            k = 0.8
        #end if
        '<p class="ref">[EN 1992-1-1 (6.39)]</p>
        β = 1 + k*1000*M_y_Ed/V_Ed*u_1/W_1
    #else
        e_x = 1000*M_x_Ed/V_Ed
        e_y = 1000*M_y_Ed/V_Ed
        b_x = c_1 + 4*d
        b_y = c_2 + 4*d
        '<p class="ref">[EN 1992-1-1 (6.43)]</p>
        β = 1 + 1.8*sqr((e_x/b_x)^2 + (e_y/b_y)^2)
    #end if
#end if
#if β < 1.15
    '<p class="ref">[EN 1992-1-1, Figure 6.21N]</p>
    β'&lt; 1.15. The relevant value is assumed:'β = 1.15
#end if
'<div class="fold">
'<h4>Punching shear resistance without reinforcement</h4>
k = min(1 + sqr(200/d);2)
C_Rd_c = 0.18/γ_c
'<p class="ref">[EN 1992-1-1 (6.47)]</p>
'Punching shear resistance
v_Rd_c_ = C_Rd_c*k*(100*ρ_l*f_ck)^(1/3)'MPa
'<p class="ref">[EN 1992-1-1 (6.2b)]</p>
'Minimum shear resistance
v_min = 0.035*k^(3/2)*sqr(f_ck)'MPa
v_Rd_c = max(v_Rd_c_; v_min)'MPa
'<p class="ref">[EN 1992-1-1 (6.38)]</p>
'Design shear stress
v_Ed = β*V_Ed*10^3/(u_1*d)'MPa
'</div>
'<p class="ref">[EN 1992-1-1, §6.4.3 (2,b)]</p>
#if v_Ed ≤ v_Rd_c
    v_Ed'MPa &le; 'v_Rd_c'MPa. Shear reinforcement is NOT required.
#else
    v_Ed'MPa &gt;'v_Rd_c'MPa. Shear reinforcement is required.
    '<div class="fold">
    '<h4>Check at column edge</h4>
    'Column perimeter
    u_0 = 2*(c_1 + c_2)'mm
    '<p class="ref">[EN 1992-1-1 (6.53)]</p>
    'Punching shear resistance at column edge
    v_Ed_max = β*V_Ed*10^3/(u_0*d)'MPa
    'Maximum punching shear stress
    ν = 0.6*(1 - f_ck/250)
    '<p class="ref">[BS EN 1992-1-1, Table NA.1, §6.4.5 (3)]</p>
    v_Rd_max = 0.5*ν*f_cd'MPa
    '</div>
    '<p class="ref">[EN 1992-1-1, §6.4.3 (2,a)]</p>
    #if v_Ed_max ≤ v_Rd_max
        v_Ed_max' MPa &le; 'v_Rd_max'MPa. Design check is satisfied.
    #else
        '<p class="err">'v_Ed_max' MPa &gt; 'v_Rd_max'MPa. Design check is NOT satisfied!</p>
        '<p class="err">Increase slab thickness, column dimensions or concrete grade.</p>
    #end if
    '<p class="ref">[BS EN 1992-1-1, Table NA.1, §6.4.5 (3)]</p>
    'Limitation of punching stress at first control perimeter
    #if v_Ed ≤ 2*v_Rd_c
        v_Ed' MPa &le; '2*v_Rd_c'MPa. Design check is satisfied.
    #else
        '<p class="err">'v_Ed' MPa &gt; '2*v_Rd_c'MPa. Design check is NOT satisfied!</p>
    #end if
    '<div class="fold">
    '<h4>Punching resistance with shear reinforcement</h4>
    'Effective yield strength of shear reinforcement
    f_ywd_ef = min(250 + 0.25*d;f_ywd)'MPa
    'Area of one shear link
    A_sw_1 = π*d_w^2/4'mm²
    '<p class="ref">[EN 1992-1-1, §9.4.3 (1)]</p>
    'Radial link spacing - 's_r = 0.75*d'mm
    'Required shear reinforcement
    A_sw_req = (v_Ed - 0.75*v_Rd_c)*u_1*s_r/(1.5*f_ywd_ef)'mm²
    'Tangential link spacing - 's_t = floor(u_1*A_sw_1/A_sw_req)'mm
    '<p class="ref">[EN 1992-1-1, §9.4.3 (1)]</p>
    #if s_t ≤ 1.5*d
        'Check:'s_t'mm &le; '1.5*d'mm. Check is satisfied.
    #else
        'Check:'s_t'mm &gt;'1.5*d'mm.
        '<p class="err">Distance exceeds the maximum value.</p>
        'Accepted value: 's_t = 1.5*d'mm
    #end if
    '<p class="ref">[EN 1992-1-1, §9.4.3 (2)]</p>
    'Minimum shear reinforcement
    A_sw_min = 0.08*sqr(f_ck)/f_yk*s_r*s_t/1.5'mm²
    #if A_sw_1 ≥ A_sw_min
        A_sw_1'mm² &ge;'A_sw_min'mm². The calculated reinforcement is greater than the minimum.
    #else
        '<p class="err">'A_sw_1'mm² &lt;'A_sw_min'mm². The calculated reinforcement is lower than the minimum!</p>
    #end if
    '</div>
    'Total shear reinforcement for each perimeter
    A_sw = A_sw_1*u_1/s_t'mm²
    '<p class="ref">[EN 1992-1-1 (6.52)]</p>
    'Punching resistance with shear reinforcement
    v_Rd_cs = 0.75*v_Rd_c + 1.5*d/s_r*A_sw*f_ywd_ef/(u_1*d)
    #if v_Ed ≤ v_Rd_cs
        v_Ed'MPa &le;'v_Rd_cs'MPa. Check is satisfied!
        '<p class="ref">[EN 1992-1-1 (6.54)]</p>
        'Outer control perimeter at which shear reinforcement is not required
        u_out = β*V_Ed*10^3/(v_Rd_c*d)'mm
        'Distance to outer control perimeter
        a_out = (u_out/2 - c_1 - c_2)/π'mm
        'Required number of perimeters
        n = ceiling(max((a_out - 2*d)/(0.75*d) + 1;2))
    #else
        '<p class="err">'v_Ed'MPa &gt;'v_Rd_cs'MPa. Check is NOT satisfied. Increase shear reinforcement area.</p>
    #end if
    '<img style="width:225pt;" style="display:inline;" src="../../Images/structures/rc/design/punching-reinf-plan.png" alt="punching-reinf-plan.png">
    '<img style="width:260pt;" src="../../Images/structures/rc/design/punching-reinf-section.png" alt="punching-reinf-section.png">
#end if
#show
'</div>600  300 500 0   0   200 20  10  6   1200    1200    25  1   500

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