## Numerical on footings

**Q.** Design an isolated footing for a square column, 450 mm × 450 mm, reinforced with 8–25 φ bars, and carrying a service load of 2300 kN. Assume soil with a safe bearing capacity of 300 kN/m^{2} at a depth of 1.5 m below ground. Assume M 20 grade concrete and Fe 415 grade steel for the footing, and M 25 concrete and Fe 415 steel for the column

**Sol.
**

Size of footing

• Given: P = 2300 kN, q_{a} = 300 kN/m^{2} at h = 1.5 m

Assuming the weight of the footing backfill to be 10 % of the load

Assume a 3 m × 3 m footing base

Thickness of footing slab based on shear

• Net soil pressure at ultimate loads (assuming a load factor of 1.5)

**(a) One-way shear**

• The critical section is at a distance d from the column face

Assuming ζ_{c}= 0.36 MPa (for M 20 concrete with, say, p_{t} = 0.25) [refer Table 6.1 or Table 13 of the Code],

**= (1080d) N**

(b) Two-way shear

• The critical section is at d/2 from the periphery of the column

Assuming **d = 658 mm** (obtained earlier)

Solving, d ≥ 621 mm

Evidently, in this problem, one-way shear governs the thickness. Assuming a clear cover of 75 mm and 16 φ bars in both directions, with an average d = 658 mm,

thickness **D****≥ 658 75 16 = 749 mm**

Provide D = 750 mm. The effective depths in the two directions will differ by one bar diameter, which is not significant in relatively deep square footings. For the purpose of flexural reinforcement calculations, an average value of d may be assumed: