Design of Shallow Foundation (Isolated Footings)
Aim:- To Design Shallow foundation by manual calculation.
Procedure:-
1. Calculate the Gross Soil Pressure or area of footing.
Formula:- (Unfactored load with surcharge + Self weight of footing)/Allowable Soil Pressure
((2000/1.5)*1.1)/150 = 9.77m2
Since, for self weight of footing, we can take the 10% of the unfactored load
Take, as Square footing = √ 9.77 = 3.2m
So, the dimension of the footing will be, L=3.2m, B=3.2m.
2. Net Soil Pressure or depth of footing
Formula:- Factored load/Actual area of footing
we get, = 2000/(3.2*3.2) = 195.3Kn/m2
Take, depth of footing as = 500mm
3. Checking of depth of footing
i) Check for bearing stress as per IS 456-200 Clause 34.4
= √ (Area of footing at base)/Area of column at base < 2
= √ (3.2*3.2)/(0.4*0.4) = 8 > 2
Therefore, area factor = 2
Permissible bearing stress = 0.45fck
= 0.45*25 = 11.25Mpa
= Permissible bearing stress* Area factor
= 11.25*2 = 22.5Mpa
Actual bearing stress at column base = Factored load/size of column
= 2000/(400*400) = 12.5Mpa
Since, Permissible bearing stress > Actual bearing stress ...Hence, O.K
4. Flexural Reinforcement or Calculation of Area of Steel(Ast)
W= net soil pressure * length of footing
W=195.3*3.2 = 625Kn
Bending Moment M= Wl2/2
M= 800knm
Mu= 0.87*fy*Ast*d((1- (Ast*fy/bd*fck))
Were, Ast= Area of Steel,
fy= Compressive Strength of steel = 500Mpa
d= Effective depth of footing = 450mm
b= Width of footing = 1000mm
fck= Compressive Strength of Concrete = 25Mpa
By, Substituting we get, Ast = 4350mm2
Provide, 16mm dia of bar with spacing as 125mm C/C.
5. One way shear stress check
i) Shear force in one way shaded area = a*l*net soil pressure
= 0.95*3.2*195.3 = 593.71Kn
ii) Design Shear stress
tau = factored load/cutted area
= (593.71*1000)/(3200*450) = 0.41N/mm2
iii) Shear stress capacity
Formula:- 100*As/bd where, As= Area of Steel
b= Width of footing = 1000mm
d= Effective depth of footing = 450mm
Shear stress capacity= 1.2
Since, Shear stress capacity > Design Shear Stress .... O.K
6. Two Way Shear Stress Check
i) Shear force = ((3.2*3.2)-(0.85*0.85))*195.3
= 1858.76Kn
ii) Design Shear Stress = Tau = Shear force/perimeter
Tau = 1858.76/(4*0.85)
= 0.546Mpa
iii) Shear Stress capacity = 0.25√ fck
= 1.25Mpa
Since, Shear stress capacity > Design Shear Stress .... O.K
Result:-
