Design of Shallow Foundation (Isolated Footings)

Design a square footing for a column size of 400x400. The compression axial load for the load combination of (1.5 DL + 1.5 LL) is 2000 KN. The safe soil bearing capacity is 150 KN/m2 at a depth of 2 metres below E.G.L. Participants are free to go for either a tapered or stepped footing. Besides the total axial load, also account for the self-weight of the footing and soil above it. Assume M25 concrete grade. Do the following checks:

• If the gross bearing pressure under the footing is within safe bearing capacity
• Provide sufficient depth and longitudinal steel for resisting bending and shear
• Sufficient anchorage for column steel into the footing
• If the bearing pressure at column-footing joint is within 0.45 times the maximum concrete compressive strength

Provide a simple sketch showing the size of the footing, maximum and minimum depth of the section, flexural reinforcement in both directions and anchorage of column steel.

Please do go through the solved examples in the document provided with the challenge.

ANS:

Column Size = 400 x400

The compression axial load for the load combination of (1.5 DL + 1.5 LL) is 2000 KN

The safe soil bearing capacity is 150 KN/m2 at Foundation depth below E.G.L = 2metres

Grade of concrete for footing = M25

• Area of footing

Unfactored load with surcharge + self weight of footing/allowable soil pressure

=(2000/1.5x1.1)/150=9.78m2

assuming we have square footing

Ѵ9.78=3.12m

consider,3.2 m sided isolated footing

• Net soil pressure & initial footing depth

Factored load / sctual area of footing

2000x1000/(3.2x3.2)

Pn=195.3kn/m2

Assume deoth of footing 500mm and checking it for bearing stress as per IS 456-2000 clause34.4

Ѵ(footing base bearing area/loaded area)<=2

Permissible bearing stress 0.45xFck=11.25N/mm2

permissible bearing stress multiplied with area factor 11.25x2=22.5N/mm2

Actual bearing stress at column base

(2000x1000)/(400x400)=12.5N/mm2

12.5N/mm2 actual stress is less than permisible 22.5N/mm2.hence ok

we can proceed with 500mm depth footing for further design checks.

if we assume 50mm cover for footing, the effective depth (d) shall be taken as 450mm.

• Flectural reiforcement:

Conversion of net pressure into uniformly distributed load=195.3x3.2=625kn/m

Bending moment due to UDL over a contiliver section =wL2/2=625x1.6x1.6/2

M=800knm

Reinfocement calculation as per IS456 2000 Annex-G

Assume Fy=500N/mm2, In result as required=4350mm2

if we provide 16mm dia rebar at 125mm spacing the actual rebar provided=3200/125x201

As provided mm2

• Check for one way shear stress

Shear force in the one way shaded area=0.95x3.2x195.3=593.7kn

Design shear stress at one way cut face

Tv = 593.7x1000/(3200x450)=0.412N/mm2

Shear stree capacity of section as per IS 456-2000 table-19(include rebar)=0.425N/mm2

Design shear stress is less than shear capacity.hence ok

• Check for Two way shear stress

Shear force in the two way shaded area=(3.2x3.2)-(0.85x0.85)x195.3=1859kn

Design shear stress at two way cut face

Tv = 1859x1000/(3400x450)=1.215/mm2

Shear stree capacity of section as per IS 456-2000 clause31.6.3.1=0.25xѴFck=1.25N/mm2

Design shear stress is less than shear capacity.hence ok