Worked Example to Eurocode 2: Design of Pad Footing
Basic Steps
01. Calculate the size of the footing considering allowable bearing pressure and service load.
02. Calculate the bearing pressure for ultimate loads
03. Check the vertical line shear (shear at face of the column)
04. Check for punching shear
05. Calculate reinforcement for bending
06. Check shear at critical section
Design Example
- Live load 400kN
- Dead load 900kN
- Allowable bearing pressure 175kN
- fck 30N/mm2
- fyk 500N/mm2
- Size of column 400mm
- Assume 150kN as footing weight
Calculation of Base Area
Design service load = 1.0Gk + 1.0Qk
= 900 +150 + 400
= 1450kN
Required footing area = 1450/175
= 8.3m2
Hence, provide 2.9m square footing (area 8.41m2)
Calculate Ultimate Loads
Axial load = 1.35Gk + 1.5Gk
= 1.35*900 + 1.5*400
= 1815kN
Ultimate pressure = 1815/(2.9*2.9)
= 216kN/m2
Check for the adequacy of footing thickness
Check for Maximum Shear
Assume, footing thickness 500mm, 16mm diameter bars at base and cover to the reinforcement as 40mm
d = 500-40-16/2
= 452mm
Max. Shear resistance
VRD,max = 0.5ud[0.6(1-fck/250)](fck/1.5)
= 0.5*(4*400)*452*0.6*(1-30/250)*(30/1.5)*10^-3
= 3818.5kN
Hence, VRd,max > VEd = 1815kN
- Punching Shear
Critical section is considered at 2d from the face of the column
Critical Perimeter = Column Perimeter + 4πd
= 4*400 + 4π*452
= 7280mm
Area with the perimeter = (400-4d)^2 -(4-π)(2d)^2
= (400+4*452)^2 -(4-π)(2*452)^2
= 4.17*10^6 mm
Punching Shear Force = 216*(2.9^2-4.17)
= 915.84kN
Shear Stress = VEd/(perimeter * d)
= 915.84*E3/ (7280* 452)
= 0.28
Shear stress is not that large so 500mm thickness can be used
Bending Reinforcements
Consider critical section (at column face)
MEd = 216*2.9*(2.9/2-0.4/2)*(2.9/2-0.4/2)/2
= 490kNm
K = M/[b*(d^2)*fck]
K = 490*E6/[1000*(452^2)*30]
K = 0.08
Kbal = 0.167 (balance codition is taken based on x = 0.45d)
Therefore
K<Kbal
Compression reinforcement is not required
z = d[0.5+(0.25-K/1.134)^0.5]
z = 452[0.5+(0.25-0.08/1.134)^0.5]
z = 417.5mm (Z/d = 0.92<0.95)
As = M/(0.87*fyk*z)
As = 490*E6/(0.87*500*417.5
= 2698mm2
Provide T25@175mm spacing (As Provided = 2804mm2)
OR you may increase the depth of the footing in order to reduce the reinforcement area.
Check for Punching Shear
As/(bd) = 2698/(1000*452)
= 0.006
= 0.6% < 2%
Therefore,
Shear stress = 0.4N/mm2
VRd,c = 0.4*7280*542
= 1316.2kN > 915.84kN
Hence, punching shear is ok.
Check for Maximum Shear
Consider 1.0d form face of the column
Design Shear Force = 216*2.9*0.798
= 499.9kN
As above
VRd,c @ 1.0d = 0.4*1000*452
= 180.8kN < 499.9kN
Hence,
Shear reinforcement is required.
Normally, Shear reinforcements are not provided for pad footings. Therefore, the thickness of the footing may be increased and re-do the design as done above.
