**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 P_{u} = design load / area of footing

The ultimate upward soil pressure should be less than the bearing capacity of the soil.

M_{ux }= ½ P_{u} * ( 0.5 B – 0.5b + e_{y})^{2}^{}

M_{uy }= ½ P_{u} * ( 0.5 L – 0.5l + e_{x})^{2 }

M_{u }is max. of M_{ux } and M_{uy}

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 P_{u} = 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 P_{u,max} and soil pressure at the edge of column P_{ux or y}, then the moment should be calculated on both axis.

For moment calculation, first take average of P_{u,max } and P_{ux or y} then

M_{ux }= ½ P_{ux, avg} * ( 0.5 B – 0.5b)^{2}^{}

M_{uy }= ½ P_{uy,avg} * ( 0.5 L – 0.5l)^{2 }

M_{u }is max. of M_{ux } and M_{uy}

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.**

D_{req. }= √(M_{u} / 0.138 f_{ck} 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) D_{req}

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, V_{u} = P_{u} * B *{0.5(L-l) – d+e_{x}}

**Case II: Non-shifting**

Shear force per meter, V_{u} = P_{u,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 Ʈ_{u }= V_{u }/Bd

The nominal shear stress should be less than shear strength of the footing, that is

Shear strength Ʈ_{uc} = k Ʈ_{c}

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 Ʈ_{u }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 **Ʈ _{u }of the footing is greater than shear strength *

*Ʈ*

_{uc }, 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, V_{u }= P_{u }[ L*B – (l+d)*(b+d)]

**Case II: Non-shifting**

Shear force per meter, V_{u} = P_{u,avg }([ L*B – (l+d)*(b+d)]

Nominal shear stress Ʈ_{u }= V_{u }/b_{o }d

Where b_{0} = perimeter of critical section = 2( l+b+2d)

The nominal shear stress should be less than shear strength, that is

Ʈ_{uc} = 0.25 √f_{ck}

*If the shear stress **Ʈ _{u }of the footing is greater than shear strength *

*Ʈ*

_{uc }, 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

M_{u} = 0.87 f_{y} A_{st} [ d – f_{y}* A_{st} / f_{ck}*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 L_{d }= Փ * 0.87 f_{y} / 4τ_{bd}

Where, Փ = diameter of longitudinal bar of column

τ_{bd }= 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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