Design of Shallow Foundation (Isolated Footings)

Aim 

      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 

Procedure

      Calculation of gross soil pressure for footing area 

      Calculation of Net soil pressure for flexture and shear design 

      Initial depth of footing calculation 

      Flextural 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 

                 = (2000/1.5*1.1)/150 =9.78 m^2

      Assuming we have square footing 

      √9.78 = 3.12 m side footing 

     Consider 3.2 m sided isolated footing 

Net soil pressure & Initial footing depth 

       Factored load / actual area of footing 

       2000*1000 / (3.2*3.2)

      Pn = 195.3 kN/m^2 

Asuume depth of footing 500 mm and checking it for bearing stress as per IS-456-2000 clause 34.4 

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

Net soil pressure & Intial footing depth 

     Permissible bearing stress 0.45 *Fck = 11.25 N/mm^2 

     Permissible bearing stress multiplied with area factor 11.25 * 2 = 22.5 N/mm^2    

     Actual bearing stress at coloumn base 

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

          12.5 N/mm^2 actual stress is less than permissible 22.5 N/mm^2 .Hence ok 

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

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

Flextural reinforcement 

         Conversion of net pressure into uniformly distributed load 

              = 195.3 * 3.2 = 625 kN/m 

         Bending moment due to UDL over a cantilever section 

             = wL^2/2 = 625*1.6*1.6/2  =  800 kNm 

          Reinforcement calculation as per IS-456-2000 Annex G

            Mu = 0.87 fy Ast d (1- Ast fy/bd fck)

 Assume Fy = 500 N/ mm^2 In result Ast req = 4350 mm^2 

 If we provide 16 mm dia rebar at 125 mm spacing the actual rebar provided = 3200/125*201 

    Ast provided = 5146 mm^2 

One way shear stress check 

 

Shear force in the one way shaded area                              Shear stress capacity of section as per IS-456-2000 Table-19 

    = 0.95 * 3.2 * 195.3 = 593.7 kN                                       (include rebar)  = 0.425 N/mm^2 

Design shear stress at One way cut face                              Design shear stress is less than shear capacity 

Tv = 593.7 * 1000 / (3200*450)= 0.412 N/mm^2                  Hence ok 

Two way shear stress check 

Shear force in the two way shaded area                              Shear stress capacity of section as per IS-456-2000 clause 

    =(3.2 * 3.2) - (0.85 * 0.85) * 195.3 = 1859 kN               31.6.3.1                        (include rebar)  = 0.425 N/mm^2 

Design shear stress at Two way cut face                              Design shear stress is less than shear capacity 

Tv =1859 * 1000 / (3400*450)=1.215 N/mm^2                  Hence ok