Design of Shallow Foundation (Isolated Footings)

Obkectives of challange: To know general design procedure of spread footing with hand calculations.

To practice how inputs can be collobrateda and arrrived as data for calculations.

How assumptions are helpful when certain inputs are not available.

Procedure :StepsInvolved inFooting Design:

• Calculation of Gross Soil Pressure for Footing Area.
• Calculation of Net Soil Pressure for Flexural AND Shear Design.
• Initial depth of Footing calculation.
• Flexural Reinforcement Calculation.
• One way Shear check.
• Two way shear check.

Step :1

Calculation of Gross Soil Pressure for Footing Area.

Unfactored load with surcahrge + self weight of footing/allowable soil pressure.

=(20000/1.5 x 1.1)/150 =9.78m2.

Assuming we have square footing.

`square root`9.78 = 3.12 metre side footing.

consider 3.2 metre sided isolated footing.

Step:2

Calculation of Net Soil Pressure for Flexural & Shear Design.

Factored load / actual area of Footing.

2000 x 1000/(3.2x3.2)

Pn=195.3Kn/m2

Assuming depth of footing 500mm and checking it for bearing stress as per IS-456-2000 Clause 34.4

`square root`(Footing base bearing area / Loaded area )`le`2

STEP:3

Net Soil Pressure & initial footing depth:

Permissible bearing stress 0.45 Fck=11.25 N/mm2.

Permissible bearing stress multiplied with area factor 11.25x2=22.5 N/mm2.

Actual bearing stress at column base.

(2000x1000)/(400x400)=12.5 n/mm2.

12.5N/mm2 actual stress is less than the permisssible stress 22.5 N/mm2 . Hence okay.

we can proceed with depth 500mm footing for durther design checks.

If we can assumue 50mm cover for footing, the effective depth (D) shall be taken as 450mm.

Flexural Reinforceement:

conversion of net pressure into uniformly distributed load =195.3x3.2 =625KN/m.

Bending Movement due to UDL over a cantilever section =wL2/2=625X1.6/2.

M=800kNm.

Reinforcement calcualtion as per IS456-2000 annex-g

Mu=0.87fy.Ast .d(1-Ast/bdxfy/fck).

Assume Fy=500 N/mm2 . in result Ast required is =4350 mm2..

If we provide 16mm dia rebat at 125mm spacing the actual rebar provided =3200/125x201=5146mm2.

Ast provided =5146mm2

One way shear stress check:

shear force in one way shaded area

=0.95x3.2x195.3=593.7 kN.

Design shear stress at one way cut face

`tau`v=593.7x1000/(3200x450)=0.412N/mm2.

shear stress capacity of section as pe ris 456-2000 tablee 19(include rebar)=0.425n/mm2.

Design shear stress is less than capacity. hence okay

TWO WAY SHEAR STRESS CHECK:

shear force in two way shaded area

=(3.2x3.2)-(0.85x0.85)x195.3=1859kN.

Design shear stress at two way cut face

`tau`v=1859x1000/(3400x450)=1.215N/mm2.

shear stress capacity of section as pe ris 456-2000clase 31.6.3.1

=0.25x`square root`Fck=1.25N/mm2.

Design shear stress is less than shear capacity. hence okay