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.

AIM:

Design of shallow foundation (isolated footing).

Procedure:

Steps Involved in Footing Design :

1. Calculations of gross soil pressure for footing area.

2. Calculations of net soil pressure for flexure and shear design.

3. Initial depth of footing calculations.

4. Flexural reinforcement calculations .

5. One way shear check.

6. Two way shear check.

1. Gross soil pressure & Footing area:

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

= (2000/1.5x 1.1)/150=9.78 m2

Assuming we have square footing

√9.78 = 3.12 meter side footing

Consider. 3.2 meter sided isolated footing.

2. Net soil pressure and initial footing depth:

Net soil pressure = factored load / actual area of footing

= 2000/(3.2^2)

= 195.31 kn/m.sq,

= 0.195n/mm.sq

3. Assume depth of footing 500mm and checking it for bearing stress as per IS 456-2000, clause 34.4

√(footing base bearing area/ loaded area)<2

Permissible bearing stress 0.45 x Fok

= 11.25 N/mm2

Permissible bearing stress multiplied with area factor 11.25 x 2 = 22.5 mm.

Actual bearing stress at column base.

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

12.5N/mm2 actual stress is less than permissible 22.5 N/mm2. Hence Okay.

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

If we assume 50mm cover for tooting, the effective depth idj shall be taken as 450mm.

4. Flexural reinforcement:

Come of net pressure into Uniformly distributed load.

= 195.3 x 3.2 = 625KN/m

Bending moment due to UDL over a cantilever section.

wL^2/2 = 625 x 1.6 x 1.6 / 2

M= 800 kNm

Reinforcement calculation as per 16-450-2000 Annex-G.

M-087, A4

Assume fy = 500 N/mm2, In result Ast required = 4350 mm2

If we provide 16mm dia rebar at 125 mm spacing, the actual rebor provided

= 3200/125 x 201

Ast provided = 5146mm2.

5. One way shear stress check:

Shear force in the one way shaded area

= 0.95 x 3.2 x 195.3 = 593.7 kN

Design shear stress at One way cut face

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

Shear stress capacity of section as per IS-456-2000 Table-19 (include rebar)

= 0.425 N/mm2

Design shear stress is less than shear capacity.

Hence Okay.

6. Two way shear stress check:

Shear force in the two way shaded area

= (3.2x3.2) (0.85x0.85) x 195.3 = 1859 kN

Design shear stress at Two way cut face

T = 1859x1000/(3400x450) = 1.215 N/mm2

Shear stress capacity of section as per IS-456-2000 clause 31.6.3.1 = 0.25 x √Fck = 1.25 N/mm2.

Design shear stress is less than shear capacity.

Hence Okay.

Result:-

Provide a 3.2x3.2m footing with a depth of 500 mm.

Provide reinforcement of 20mm dia bars in both directions.

Provide anchorage for column and footing at 750mm.