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**Chapter 6 **

**Footings**

Isolated Footing Footings are structural elements that transfer loads from the building or individual columns to the earth. If these loads are to be properly transmitted, foundations must be and to provide adequate safety against sliding and overturning.

Theoretically speaking isolated footings must be designed for both axial load and moment but practically isolated footings are designed only for axial load.

Foundation may be broadly classfied under two heads: shallow foundation and deep foundation. According to Terzaghi, a foundation and deep foundation. According to Terzaghi, a foundation is shallow if its depth is equal to or less than it width. In the case of deep foundation, the depth is greater than the width. Apart from deep strip, rectangular or square foundations are; pier foundation, pile foundation and well foundation. The shallow foundation are of the following types: Spread footing, strap footing, combined footing and mat or raft footing.

**Spread footing: **A spread footing or simply footing, is a type of shallow foundation used to transmit the load of an isolated column, or that of a wall, on the subsoil. In the case of wall, the footing is continuous while in the case of column, is a isolated.

**Combined footings:** A spread footing which supports two or more columns is termed as a combined footing. Such a footing is provided when the individual footings are either very near to each other, or overlap. Combined footings may either be rectangular or trapezoidal.

**Strap or Cantilever footings:** A strap footing consists of spread footing of two columns connected by a strap beam. The strap beamdoes not remain in contact with soil, and thus does not transfer any pressure to the soil.

**Mat or Raft foundation:** A mat or raft is a combined footing that covers the entire area beneath a structure and supports all the walls and columns. When the available soil pressure is low or the building loads are heavy, the use of spread footing would cover more than one-half of the area and it may prove more economical to use mat or raft foundation.

**Pile foundation : **Pile foundation is a deep foundation used where the top soil is relatively weak. Piles transfer the load to a lower stratum of greater bearing capcity, by the way of end bearing, or to the intermediate soil through skin friction. This is more common type of deep foundation generally used for building where a group of piles transfer the load of the super-structure to the sub soil.

**Design of Isolated Footing**

**Rectangular footing**

Given values 1. Load = P or P_{u} 2. Bearing capacity of soil = q_{u} 3. Size of column 4. Grade of concrete and steel

**Design Steps** (i) Size of foundation Load from column = P Increase 10% of the total load Add weight of foundation (P_{F}) = 0.1 P Total load P_{T} = 1.1P (even for limit state method use unfactored load for calculation of area) Area of footing,

Choose L and B such taht A = L × B Net soil pressure

Net soil pressure over foundation

For LSM Net soil pressure (w_{u}) =

(ii) Check for bending moment Critical section for bending moment is at the face of the column

Consider 1 m strip of foundation Bending moment about X_{1} X_{1}

Maximum bending moment =

Similarly moment about Y_{1}Y_{1}

Maximum BM

Note: Use w = w m= 1.5 w for Limit State Method.

(iii) Depth required

where B = 1000 mm For LSM

(iv) Check for single shear (one-way shear) Critical section for one-way shear is at 'd' distance from the face of the column

Shear at X_{2}X_{2}

Overhang,

Shear force, V_{x} = w.1 × Oy

Similarly Shear force at Y_{2}Y_{2} overhang, Ox =

V_{y} = w.1 × Ox = w

Find out maximum of V_{x} and V_{y} Nominal shear stress

where, t_{c} is permissible design shear strength of concrete in N/mm2 as given in IS : 456 Footing should be always safe in shear. No shear reiforcement is provided.

**(v) Check for two-way (Punching Shear)**

Critical section for punching shear also called two-way shear is at (d/2) distance from face of the column all around.

P_{net} = P – w(a+d) (b+d)

Punching shear stress developed =

Cross section area = permiter × depth Now perimeter = 2[(a+d) + (b+d)] Depth = d

Punching shear stress

Above developed stress should be less than the permissible punching shear stress Permissible punching shear stress

ζcp = k_{s} × 0.16 (working stress method)

= k_{s} × 0.25 (Limit state method)

k_{s} = (0.5 + βc ) but not greater than 1, βc being the ratio of short side to long side of the column

(vi) Area of steel for the longer span The area of steel A_{st} of long bars parallel to direction L is calculated as under.

For My moment

(Working stress method)

(Limit state method) This reinforcement is equally distributed over entire width B.

Note: Area of steel calculated above is for 1 m, width, Calculate this area for width B and distribute uniformly over entire width For B m, total area of steel = B × A_{st}

(vii) Area of steel for shorter span The area of steel A_{st} of short bars parallel to direction B is calculated as under

for 1 m For L m, total area of steel = L × A_{st }This area is provided in two distinct band widths:

- the centre band B of width B, and the end bands A, each of width

The reinforcement in central band width

total reinforcement in short direction.

Where,β = ratio of long side to the short side of the footing The remainder or reinforcement shall be uniformly distributed in outer portions of the footing.

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