# DESIGN OF FOOTING

DESIGN OF  FOOTING
Size of the column 600mm×600mm
Add  10% for  self  wt of footing
=131125kN
Assume SBC  of soil  =200kN/M²
Area =P/SBC
=1250/200
=6.25m²
Select 2.5×2.5 square footing
Side of the increase bed square in column
= 600/√2.5
=379mm
Net upward pressure    =(1125/2.5×2.5)
=180 kN/m²
Max.B.M at the side  of the inscribed square
=2.0×180×1.9×1.9/2
=649.8kN.m
M=0.138bd²
Effective depth req= √M/fckbd2
=433.72mm
Considering effects of shear provide the depth of 600mm for top of layers .assume  16mmdia bars with cover 50mm
Total thickness
Eff depth  provided  = 400+50-16/2+16
=658mm
M =0.87 ×fyAstd[1-(fyAst/fckbd)]
649.8 =0.87×415×Ast×600[1-(415×Ast/25×1000×600)]
Ast=2327mm2
Provide 10 nos of 16mm φ bars
Minimum Ast=201 mm2.
DEVELOPMENT  LENGTH:
Ld=φσs/4τbd
= 16×0.87×415/4×1.4
=1031.57mm
The projection of footing  from the face of column =1900mm
Length of bar beyond the column face  =1900mm>1031.57mm
Hence ok
CHECK FOR  TRANSVERSE SHEAR:
The Crtical section  for transverse shear will  be at a distance d=658mm  from the face of column
Length of footing beyond the critical section,
yy   =1900-658
=1242mm
Transverse shear,
Vy=180×2.5×1.24
=558kN
Nominal shear stress,
τvy=0.37N/mm²
Permissible shear stress
Pt=100Ast/bd
=1.03
τcy=0.39N/mm²
τv< τc
Hence safe
CHECK FOR PUNCHING  SHEAR :
The critical section  for punching shear is at a distance of 300mm  {1/2 effective depth around  the face of the column }
= 600+2×300
=1200mm
Punching shear across section -Z
Net up ward pressure  = 180kN/M²
Punching  shear= 180[2.5×2.5-{0.72×0.72}
Vz = 865.8kN
τvz =Vz/bd
=865.8×10³/4.0×1200×600
=0.3 N/mm²
As per IS 456-2000 - 31.6.3.1
Permissible shear stress in concrete =ks τcz
For square ks =1
ks τcz =0.2√fck
=1×0.25×√25
=1.25 N/mm²
τvz <  ks τcz
Hence ok

CHECKING FOR BEARING STRESS:
Base of frustum of pyramid
=700+4×600
=2900mm
Supporting area of bearing of footing
A1= 6.25m²
Loaded area at the column base
A2= 0.6×0.6
=0.36 mm²
√ A1 /A2 =√6.25/0.36
=4.16 restricted to 2
Permissible bearing stress
= 0.45 fck ×2
=22.5 N/mm²
Actual bearing stress on the loaded area
=6.02 N/mm²  < 18 N/mm²
Hence ok

CHECK FOR  SAFE BEARING CAPACITY OF SOIL: