Design of isolated or spread footing:
Spread footing is basically a pad used to spread out loads from columns over a sufficiently large area of the foundation soil. The design of isolated footing is the most economical types. And it is excessively used for the footing in residential building.
It is constructed as close to the ground surface as possible consistent with the design requirements. Isolated footing are used to support an individual point load such as that due to structural column. They may be circular or rectangular/ they usually consist of a block or the slab of uniform thickness but may be stepped or hunched if they have to resist heavy load from the column. Here we discuss about the design of isolated footing .
The design of isolated footing involves following procedure:
Step 1: Calculate factored loads and bending moment
The factored axial load and factored bending moment from the column is obtained from the structural software. Add 10% for self-weight of footing and soil above the footing.
The calculated factored bending moment is used for calculation of eccentricity. Either we can shift the position of footing equal to eccentricity or have to increase the thickness of footing. For simplicity in construction and supervision, it is better to increase the thickness of footing rather than shifting but it makes the structure little bit uneconomical. But here we discuss about both method: Shifting of footing and Non-shifting but increase in thickness of footing.
Step 2: Calculate an area of footings based on the factored axial load
Area of footing = factored axial load / safe bearing capacity of soil
The shape of the footing should be square or rectangular depending upon the shape of column. The area of footing should be taken greater than obtained from the formula.
Step 3: Calculate critical bending moment:
The critical section for the bending moment is taken at the edge the column in case of column footing.
Case I: Shifting
Ultimate soil pressure Pu = design load / area of footing
The ultimate upward soil pressure should be less than the bearing capacity of the soil.
Mux = ½ Pu * ( 0.5 B – 0.5b + ey)2
Muy = ½ Pu * ( 0.5 L – 0.5l + ex)2
Mu is max. of Mux and Muy
L and B is for footing and l and b for column
Case II: Non-Shifting
In this case, the ultimate soil pressure varies uniformly over the area of footing.
Ultimate soil pressure Pu = design load / area of footing * (1± 6e/(B or L))
For one edge, + sign is used and for other side – sign is used depending upon position of eccentricity. But for design it okey to take any one side of the footing because there may be case of moment reversal in the building.
Find the maximum soil pressure Pu,max and soil pressure at the edge of column Pux or y, then the moment should be calculated on both axis.
For moment calculation, first take average of Pu,max and Pux or y then
Mux = ½ Pux, avg * ( 0.5 B – 0.5b)2
Muy = ½ Puy,avg * ( 0.5 L – 0.5l)2
Mu is max. of Mux and Muy
L and B is for footing and l and b for column
Step 4. Thickness of Footing
The thickness of footing is calculated from the maximum critical bending moment.
Dreq. = √(Mu / 0.138 fck b)
Increase depth for 1.75 to 2 times more than calculated value for shear considerations [This is done just to decrease the possibility of shear failure of footing while checking]
i.e. d = (1.75-2) Dreq
The value of d is the effective thickness of footing. For overall thickness, clear cover and half of diameter of reinforcement should be added.
The thickness of isolated footing design is normally critical in shear case.
Step 5. Check for one way shear
The critical section is taken at a distance d away from the face of column.
Case I: Shifting
Shear force per meter, Vu = Pu * B *{0.5(L-l) – d+ex}
Case II: Non-shifting
Shear force per meter, Vu = Pu,avg * B *{0.5(L-l) – d}
Note: The shear force should also be checked on both axis both, but in most case the shear force is greater in lengthwise side.
Nominal shear stress Ʈu = Vu /Bd
The nominal shear stress should be less than shear strength of the footing, that is
Shear strength Ʈuc = k Ʈc
The value of k depend up on the thickness of footing which can be obtained from clause 40.2.1.1 of IS code 456:2000 and the value of Ʈu depend upon the grade of concrete and area of reinforcement which can be obtained from Table19 of IS code 456:2000.
Note: Since area of reinforcement of footing has not calculated before so assume suitable percentage of steel; better to take 0.25%
If the shear stress Ʈu of the footing is greater than shear strength Ʈuc , the depth of footing should be increase and revise the step.
Step 6: Check for two way action of shear – punching shear
The critical section for two-way shear is taken at a distance d/2 away from the face of column.
Case I: Shifting
Shear force per meter, Vu = Pu [ L*B – (l+d)*(b+d)]
Case II: Non-shifting
Shear force per meter, Vu = Pu,avg ([ L*B – (l+d)*(b+d)]
Nominal shear stress Ʈu = Vu /bo d
Where b0 = perimeter of critical section = 2( l+b+2d)
The nominal shear stress should be less than shear strength, that is
Ʈuc = 0.25 √fck
If the shear stress Ʈu of the footing is greater than shear strength Ʈuc , the depth of footing should be increase and revise the step.
Step 7: Calculation of reinforcement
The reinforcement is calculated from the critical maximum moment obtained in the step 4
Mu = 0.87 fy Ast [ d – fy* Ast / fck*b]
The area of reinforcement should be calculated on both axis or taken maximum one.
The area of reinforcement should not be less than 0.12% of Bd.
Step 8: Check for bearing stresses
The bearing strength of concrete of the footing can be checked from the clause 34.4 of IS code 456:2000.
Step 9: Check for development length
The development length can be calculated using the clause 26.2.1 of IS code 456:2000.
Development length Ld = Փ * 0.87 fy / 4τbd
Where, Փ = diameter of longitudinal bar of column
τbd = design bond stress given in clause 26.2.1.1.
The calculated development length should be less than the available development length in the shorter side.
Available development length = L/2 + l/2 – e – side clear cover.
The value of eccentricity e in non-shifting case is taken as zero. The value of side clear cover is normally taken as 50-75 mm
Step 10: Design Summary with arrangement of reinforcement.
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