The document summarizes the calculation of foundations and reinforcement for a trapezoidal pad foundation supporting a column. Soil properties, foundation geometry, loads, and limit states are defined. Calculations are presented for bearing capacity, sliding resistance, uplift, bending moments, required reinforcement, and punching shear. The foundation dimensions were optimized, resulting in a wider and longer foundation with increased depths. All limit states checks passed requirements.

1. Calculation of foundation: Ultimate Limit State 1
Calculation according to EN 1997-1:2008
Foundation geometry - Trapezoidal pad for one column
Width of foundation B = 2.00 m
Length of foundation L = 3.00 m
Height of foundation H = 0.80 m
Width of top platform B1 = 1.00 m
Length of top platform L1 = 2.00 m
Height of step H1 = 0.50 m
Dimensions of column l1 = 0.50 m
b1 = 0.50 m
Column position ex1 = -0.50 m
ey = 0.20 m
Soil input
Nr Name Z
[m]
H
[m]
γsoil
[kN/m3
]
γs
[kN/m3
]
γd
[kN/m3
]
φ'
[deg]
C'
[kPa]
Cu
[kPa]
MOi
[kPa]
Mi
[kPa]
1 inorganic
high plasticy
clays
-4.00 4.00 11.66 26.60 20.50 0.33 0.00 100.00 20192.31 20192.31
2 clayey
gravels
-7.00 3.00 11.67 26.50 20.50 0.56 0.00 9.50 30000.00 30000.00
Foundation formation level zFL = -1.00 m
Ground water level zWL = -3.00 m
Foundation cast-in-situ
Bearing pressure check Critical ULS2 qmax / qult = 100% Pass
Sliding check Critical ULS3 Hxd / Rxres = 14% Pass
Sliding check Critical ULS3 Hyd / Ryres = 8% Pass
Uplift check (UPL) Critical ULS1 Vdst,d / Gstb,d = 0% Pass

2. Dimensions after optimization
Width of foundation B = 5.80 m
Length of foundation L = 6.80 m
Height of foundation H = 1.50 m
Width of top foundation B1 = 1.00 m
Length of top foundation L1 = 2.00 m
Height of down stepped foundation h1 = 0.50 m
Height of top stepped foundation h2 = 1.00 m
Loads
Design load combinations:
Name Limit state VA
[kN]
HxA
[kN]
HyA
[kN]
MxA
[kNm]
MyA
[kNm]
q
[kPa]
ULS1 ULS 450.00 85.00 50.00 25.00 150.00 3.00
ULS2 ULS 800.00 25.00 25.00 250.00 50.00 3.00
ULS3 ULS 500.00 100.00 55.00 30.00 10.00 5.00
Bearing pressure check
Critical ULS2 qmax / qult = 100% Pass
q1= 52.92 kN/m2
q2= 76.39 kN/m2
q3= 38.93 kN/m2
q4= 62.41 kN/m2
Maximum pressure
qmax = 76.39 kN/m2
Minimum pressure
qmin = 38.93 kN/m2
A = B * L = 39.44 m2
V = VA + VB + F = 2274.22 kN
eTx=(VA * ex1 + VB * ex2 + MxA + MxB + (HxA + HxB) * H) / V = -0.14 m
eTy=(VA * ey + VB * ey + MyA + MyB + (HyA + HyB) * H) / V = 0.20 m
Base reaction acts within combined middle third of base

3. abs(eTy) / B < 1/3
abs(eTx) / L < 1/3
B = B - 2 * 0.10 m = 5.80 m
L = L - 2 * 0.10 m = 6.80 m
B' = min(B - 2 * abs(eTy), L - 2 * abs(eTx)) = 6.39 m
L' = max(B - 2 * abs(eTy), L - 2 * abs(eTx)) = 7.38 m
Bearing pressure for drained conditions
Soil layer - clayey gravels
Nq = eπ*tan(φ')
*tan2
(45 + φ' / 2) = 23.18
Nc = (Nq - 1) * ctg(φ') = 35.49
Ny = 2 * (Nq - 1) * tan(φ') = 27.72
bq = by = (1 - α * tan(φ'))2
= 1.00
bc = bq - (1 - bq) / (Nc * tan(φ')) = 1.00
sq = 1 + (B' / L') * sin(φ') = 1.46
sy = 1 - 0.3 * (B' / L') = 0.74
sc = (sq * Nq - 1) / (Nq - 1) = 1.48
mB = [2 + (B' / L')] / [1 + (B' / L')] = 1.54
mL = [2 + (L' / B')] / [1 + (L' / B')] = 1.46
θ = atan(Hx / Hy) = 0.79
m = mL * cos2
θ + mB * sin2
θ = 1.50
iq = [1 - H / (V + A' * c' * ctg(φ'))]m
= 0.99
ic = iq - (1 - iq) / (Nc * tan(φ')) = 0.99
iy = [1 - H / (V + A' * c' * ctg(φ'))]m+1
= 0.99
q' = 20.50 kPa
Allowable bearing pressure qultD = c' * Nc * bc * sc * ic + q' * Nq * bq * sq * iq + 0,5 * γi' * B' * Nγ * bγ * sγ
* iγ = 2014.38 kN/m2
Bearing pressure for undrained conditions
Soil layer - clayey gravels
bc = 1 - 2 * α / (π + 2) = 1.00
sc = 1 + 0.2 * (B' / L') = 1.17
ic = 1 / 2 *[1 + sqrt(1 - H / (A' * cu))] = 0.98
q = 20.50 kPa
qultUD = (π + 2) * cu * bc * sc * ic + q = 76.65 kN/m2
Allowable bearing pressure qult = min (qultD, qultUD ) / γR,v = 76.65 kN/m2
Sliding check
Critical ULS3 Hxd/ Rxres = 14% Pass
Total horizontal load Hxd = HxA + HxB + Rxa = 100.00 kN
Minimum vertical load VG,min = [VGA + VGB + A * (qGsur + qswt + qsoil)] * γFG.pos = 2059.00 kN
Bearing pressure for drained conditions RdD = VG,min * tan(δk) / γR,h = 708.97 kN
Bearing pressure for undrained
conditions
RdUD = A' * cu / γR,h = 4718.70 kN
Total resistance to sliding Rxres = min(RdD, RdUD) + Rxp,d + Rd.add = 708.97 kN
Critical ULS3 Hyd/ Ryres = 8% Pass
Total horizontal load Hyd = HyA + HyB + Rya = 55.00 kN
Minimum vertical load VG,min = [VGA + VGB + A * (qGsur + qswt + qsoil)] * γFG.pos = 2059.00 kN
Bearing pressure for drained conditions RdD = VG,min * tan(δk) / γR,h = 708.97 kN

4. Bearing pressure for undrained
conditions
RdUD = A' * cu / γR,h = 4718.70 kN
Total resistance to sliding Ryres = min(RdD, RdUD) + Ryp,d + Rd.add = 708.97 kN
Uplift check (UPL)
Critical ULS1 Vdst,d / Gstb,d = 0% Pass
Stabilizing vertical actions Gstb,d = VG,min * γGstb = 1476.63 kN
Destabilizing permanent and variable
vetical actions
Vdst,d = max(-V + γw * min(hFL - hWL, 0) * A; γw * max(hFL - hWL, 0) * A) =
0.00 kN
Calculation of foundation: Reinforcement 1
Calculation according to EN 1997-1:2008
Foundation geometry - Trapezoidal pad for one column
Width of foundation B = 2.00 m
Length of foundation L = 3.00 m
Height of foundation H = 0.80 m
Width of top platform B1 = 1.00 m
Length of top platform L1 = 2.00 m
Height of step H1 = 0.50 m
Dimensions of column l1 = 0.50 m
b1 = 0.50 m
Column position ex1 = -0.50 m
ey = 0.20 m
Soil input
Nr Name Z
[m]
H
[m]
γsoil
[kN/m3
]
γs
[kN/m3
]
γd
[kN/m3
]
φ'
[deg]
C'
[kPa]
Cu
[kPa]
MOi
[kPa]
Mi
[kPa]

5. 1 inorganic
high plasticy
clays
-4.00 4.00 11.66 26.60 20.50 0.33 0.00 100.00 20192.31 20192.31
2 clayey
gravels
-7.00 3.00 11.67 26.50 20.50 0.56 0.00 9.50 30000.00 30000.00
Foundation formation level zFL = -1.00 m
Ground water level zWL = -3.00 m
Foundation cast-in-situ
Bending in direction x - Bottom reinforcement Critical ULS3 As.xreq / As.xprov = 47% Pass
Bending in direction y - Bottom reinforcement Critical ULS3 As.yreq / As.yprov = 49% Pass
Punching shear check Critical ULS3 VEd / VRd.c = 30% & VEd' / VRd.c max =
12% Pass
Dimensions after optimization
Width of foundation B = 4.70 m
Length of foundation L = 5.70 m
Height of foundation H = 1.20 m
Width of top foundation B1 = 1.00 m
Length of top foundation L1 = 2.00 m
Height of down stepped foundation h1 = 0.50 m
Height of top stepped foundation h2 = 0.70 m
Loads
Design load combinations:
Name Limit state VA
[kN]
HxA
[kN]
HyA
[kN]
MxA
[kNm]
MyA
[kNm]
q
[kPa]
ULS1 ULS 450.00 85.00 50.00 25.00 150.00 3.00
ULS2 ULS 800.00 25.00 25.00 250.00 50.00 3.00
ULS3 ULS 500.00 100.00 55.00 30.00 10.00 5.00
Foundation properties
d1x = 0.053 m
d2x = 0.053 m
Concrete C20/25
fck = 20.00 MPa
γc = 1.50
fcd = 13.33 MPa
Steel B 400 B
fyk = 400.00 MPa
γs = 1.15
fyd = 347.83 MPa

6. minimum reinforcement ratio ρmin = 0.12 %
maximum reinforcement ratio ρmax = 4.00 %
Reinforcement ratio ρ = 0.00 %
Bending in direction x - Bottom reinforcement
ULS3 As.xreq / As.xprov = 47% Pass
Design bending moment in direction x My = 132.88 kNm
Theoretical area of reinforcement in
direction x
As.xreq = 3.76 cm2
/m
Provided area of reinforcement in
direction x
As.xprov = 8.04 cm2
/m
Bending in direction y - Bottom reinforcement
ULS3 As.yreg / As.yprov = 49% Pass
Design bending moment in direction y Mx = 52.73 kNm
Theoretical area of reinforcement in
direction y
As.yreg = 3.91 cm2
/m
Provided area of reinforcement in
direction y
As.yprov = 8.04 cm2
/m
Punching shear check
ULS3 VEd VRd.c = 30% & VEd' VRd.c max = 12% Pass
β = 1.38
u1 = min(4 * π * d + 2 * l1 + 2 * b1, 2 * (B + L)) = 12.05 m
u0 = 2 * l1 + 2 * b1 = 2.00 m
Net applied force VEd = β * VEd,red / (u1 * d) = 71.55 kN
VEd' = β * VEd,red / (u0 * d) = 431.18 kN
CRd.c = 0.18 / γc = 0.12
k = min(1 + sqrt(200 / d), 2) = 1.50
ρL = min(sqrt(ρx * ρy), 2) = 0.07 %
Vmin = 0.035 * k3 /2
* fck
1 /2
= 234.79 kN

7. Punching shear capacity at control
perimeter at distance 2*d from column
edge
VRd.c = min(C Rd.c * k * (100 * ρL * f ck)1/3
, V min) * 2 * d / a = 234.79 kN
ν = 0.6 * (1 - f ck / 250 MPa) = 0.55
Maximum punching shear capacity
column perimeter
VRd.c max = 0.5 * ν * f cd = 3680.00 kN