Worked example combined footing design as per Eurocode
- Footing has two columns
- 300mm square column has 100kN and 500kN live and dead loads respectively
- 400mm square column has 200kN and 800kN live and dead loads respectively
- Spacing of columns 3m
- fck = 30N/mm2
- fyk = 500N/mm2
- Assumed footing thickness 500mm
- Allowable bearing pressure 200N/mm2
- Assume effective depth 440mm for initial calculations
Calculation of required footing area
Net bearing pressure = 200-25*.500
= 187.5N/mm2
Service load = 100 + 500 + 200 + 800
= 1600kN
Required footing area = 1600/187.5
= 8.53m2
Select footing dimensions as 4.3m X 2m
(550mm offset from 300mm square column and 750mm offset from 400mm square column)
Take moment about center of 300mm square column
x = (200+800)*3/(100+500+200+800)
= 1.875m
Calculation of Bearing Pressure
Design Load = (1.35*800+1.5*200) + 1.35*500+1.5*100)
= 2205kN
Pressure = 2205/(4.3*2)
= 257N/mm2
Check for Punching Shear
Max. Shear Resistance = 0.5ud[0.6(1-fck/250)](fck/1.5)
At 300mm column face
= 0.5*300*4*440*0.6*(1-30/250)*(30/1.5)
= 2788kN > (1.35*500+1.5*100 = 825kN)
At 400mm column face
= 0.5*400*4*440*0.6*(1-30/250)*(30/1.5)
= 3717kN > (1.35*800+1.5*200 = 1380kN)
Hence, Punching Shear is OK
Maximum bending was calculated
It was 209kNm, and it occurred at1.05m from 300mm square column
Design for Bending
Longitudinal reinforcements
MEd = 209kNm
K = M/[b*(d^2)*fck]
K = 209*E6/[1000*(440^2)*30]
K = 0.04
Kbal = 0.167 (balance condition 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 = 440[0.5+(0.25-0.04/1.134)^0.5]
z = 424mm (Z/d = 0.96>0.95)
Therefore
Z = 0.95*440
= 418mm
As = M/(0.87*fyk*z)
As = 209*E6/(0.87*500*418)
= 1150mm2
As min. = 0.15*b*d/100
= 0.15*1000*440/100
= 660mm2
Therefore,
Proved T16@150mm spacing
Transverse reinforcements
Bending Moment = 257*(1^2)/2
MEd = 128.5kNm
K = M/[b*(d^2)*fck]
K = 128.5*E6/[1000*(440^2)*30]
K = 0.022
Kbal = 0.167 (balance condition 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 = 440[0.5+(0.25-0.022/1.134)^0.5]
z = 431mm (Z/d = 0.97>0.95)
Therefore
Z = 0.95*431
= 409.5mm
As = M/(0.87*fyk*z)
As = 128.5*E6/(0.87*500*409.5)
= 722mm2
As min. = 0.15*b*d/100
= 0.15*1000*440/100
= 660mm2
Provide T12@150mm spacing