Design of Shallow Foundation (Isolated Footings)

AIM

Designing a footing for a column size of 400*400

INTRODUCTION

• The footing is a structural member that safely transmits the load of the upper building to the ground, and is the first construction member of the building.
• Loads from the structure are transferred to the soil or rock under the structure via footings and other foundation elements
• The kind of soil and the foundation pad , affect how much pressure the soil exrts on a footing
• The most typical forms of footing are
  • Strip or wall footing
  • Spread footing
  • Stepped footing
  • Tapered footing
  • Pile cap
  • Combined footing
  • Mat or raft footing

GIVEN DATA

• Column size = 400mm*400mm
• Compression axial load (1.5DL+1.5LL) = 200kN-factored load
• Safe bearing capacity of soil at a depth of 2m below EGL = 150kN/m2
• Assuming the self -weight of footing and soil above it as 10% load
• Grade of concrete= 25kN/m
• Assuming Fy =500N/mm2

STEPS TO DESIGN FOOTING

• Gross soil pressure for footing area
• Net soil pressure for flexure and shear design
• Depth of footing
• Flexural reinforcement
• One way shear
• Two way shear

PROCEDURE

Step:1

• GROSS SOIL PRESSURE AND FOOTING AREA
  • Unfactured load with surcharge+self weight of footing/allowable soil pressure

=(2000/1.5*1.1)/150

= 9.82m^2

Assuming we have square footing =3.12 side footing

consider 3.2m sided isolated footing

Step:2

• NET SOIL PRESSURE AND INITIAL FOOTING DEPTH
  • Factored load/ actual area of footing

= 2000/(3.2*3.2)

=Pn= 195.3kN/m2

Assume the depth of the footing 500mm

check it for bearing stress as per IS 456-2000,clause 34.4

Therefore,

Permissible bearing stress 0,45*fck=0.45*25=11.25 N/mm^2

Permissible bearing stress multiplied by the area factor of 2 = 11.25*2 =22.5 N/mm^2

Actual bearing stresses at the column base of the footing

2000*1000/400*400 = 12.5N/mm^2

Actual bearing stress

12.5<22.5

Hence 500mm depth is okay and provide 50mm for cover

D=500mm

d'=50mm

d = D-d'

Effective depth (d)= 450mm

Step:3

• FLEXURAL REINFORCEMENT

Conversion of netpressure into UDL

= 195.3*3.2 = 625kN/m

Bending moment due to UDL over cantilever section

= WL^2/2

M= 625*1.6*1.6/2

M = 800 kN-m

Reinforcement calculation as per IS -456:200 , Annuex G

Mu = 800 kN-m

D= 450mm

fy = 500N/mm^2

b = 400 mm

fck = 20 N/mm^2

Ast = 4350mm^2

If we provide 16mm dia rebar at 125mm spacing actual rebar provided = 3200/125*202

Ast provided = 5146 mm^2

Step:4

• ONE WAY SHEAR STRESS CHECK

Shear force in one way shaded area

= 0.95*3.2*195.3 = 593.7kN

Design shear stress at one way cut face

T = 593.7*1000/(3200*450) = 0.412N/mm^2

Design shear stress is less than shear capacity

Hence okay

Step:5

• TWO WAY SHEAR STRESS CHECK

Shear force in two way shaded area

V = (3.2*3.2)-(0.85*0.85)*195.6

= 1859kN

Design shear stress at any two cut face

T = 1859*1000/(3400*450)=1.215 N/mm^2

Shear stress capacity of section as per IS -456

-2000 clause 31.6.3.1 = 0,25 * fck = 1.25 N/mm^2

Design shear stress is less than shear capacity

Hence okay.

RESULT

• Provide a 3.2m*3.2m footing with a depth of 500mm
• Provide reinforcement pf 20 mm dia bars in both directions
• Provide anchorage for column and footing at 750mm

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