Design of Shallow Foundation (Isolated Footings)

Objectives of the challenge:

• To know the general design procedure of Spread footing with hand calculations.
• To participate in how the inputs can be collaborated and arrived as data for calculations.

Steps involved in Footing design:

• Calculation of gross soil pressure for footing area
• Calculation of Net soil pressure for flexure and shear design
• Initial depth of footing calculation
• Flexural reinforcement calculation
• One-way shear check
• Two-way shear check

Gross soil pressure & Footing area:

• Unfactored load with surcharge + self-weight of footing/ allowable soil pressure
  =(2000/1.5x1.1)=9.78 m2
  Assuming we have square footing
  
  √9.75=3.12 meter side footing
  
  Consider, 3.2 meter-sided isolated footing

Net soil pressure and initial footing depth:

• Factored load/ actual area of the footing
  
  2000x1000/(3.2x3.2)
  
  Pn=195.3 kN/m2
  
• Assume the depth of footing is 500 mm and check it for bearing stress as per IS-456-2000 clause 34.4
  
  √(footing base bearing are/loaded area)≤2
  
• Permissible bearing stress 0.45 x Fck = 0.45 x 25 = 11.25 N/mm2
  
  Permissible bearing stress multiplied with area factor 11.25x2=22.5 N/mm2
  
  
• Actual bearing stress at the column base
  
  (2000x1000)/(400x400)=12.5 N/mm2
  
  12.5 N/mm2 actual stress is less than the permissible 22.5 N/mm2. Hence Okay.
  
  We can proceed with 500 mm depth footing for further design checks.
  
  If we assume a 50mm cover for footing, the effective depth (d) shall be taken as 450mm.

Flexural reinforcement:

• Conversion of net pressure into Uniformly distributed load = 195.3 x 3.2 = 625 kN/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 IS-456-2000 Annex-G
  
  Assume Fy= 500 N/mm2, In result Ast required = 4350 mm2
  
  If we provide 16mm dia rebar at 125mm spacing, the actual rebar provided = 3200/125 x 201
  Ast provided = 5146 mm2

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
  Tv= 593.7 x 1000 / (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

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 Tv=1858x1000/(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