Design of Shallow Foundation (Isolated Footings)
Aim :-
Design a square footing for a column size of 400x400 by using given data and conditions.
Procedure :-
Steps involved in the Footing design :-
1) Calculation of gross soil pressure and footing area
2) Calculation of Net soil pressure for flexure and shear design
3) Initial depth of footing calculation
4) Flexural reinforcement calculation
5) One way shear check
6) Two way shear check
Calculation of gross soil pressure and footing area :-
* Unfactored load with surcharge + self weight of footing / allowable soil pressure
= (2000/1.5x1.1)/150
= 9.78m2
Assuming we have squre footing
Square root of 9.78 = 3.12 meter side footing
Consider, 3.2meter sided isolated footing
Net soil pressure and initial footing depth :-
* Factored load/actual area of footing
= 2000x1000/(3.2x3.2)
= 195300N/m2
Pn= 195.3kN/m2
* Assume depth of footing 500mm and checking it for bearing stress as per IS:456-2000 clause 34.4
Square root of (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 permissible 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.
Flexural reinforcement :-
* Conversion of net pressure into Uniformly distributed load = 195.3x3.2 = 625kN/m
* Bending moment due to UDL over a cantilever section= (wL^2)/2 =625x1.6x1.6/2
M = 800kNm
* Reinforcement calculation as per IS:456-2000 Annex - G
Assume Fy = 500N/mm2, In result Ast required = 4350mm2'
If we provide 16mm dia rebar at 125mm spacing, the actual rebar provided= (3200/125)x201
Ast provided = 5146mm2
One way shear stress check :-
* shear force in the one way shaded area = 0.95x3.2x195.3 = 593.7 kN
* Design shear stress at One way cut face = (593.7x1000)/(3200x450)
= 0.412N/mm2
* Shaer stress 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.
Two way shear stress check :-
* Shear force in the two way shaded area = (3.2x3.2)-(0.85x0.85)x195.3 = 1859kN
* Design shear stress at Two way cut free = (1859x1000)/(3400x450) = 1.215N/mm2
* Shear stress capacity of section as per IS:456-2000 clause 31.6.3.1 = 0.25xsquare root of Fck = 1.25N/mm2
* Design shear stress is less than shear capacity. Hence OK.
Result :-
Successfully complete the design of square footing for a column size of 400x400 by using given data and conditions.
