Design of Shallow Foundation (Isolated Footings)

AIM ; TO Design a square footing for a column size of 400x400. The compression axial load for the load combination of (1.5 DL + 1.5 LL) is 2000 KN. The safe soil bearing capacity is 150 KN/m2 at a depth of 2 metres below E.G.L. Participants are free to go for either a tapered or stepped footing. Besides the total axial load, also account for the self-weight of the footing and soil above it. Assume M25 concrete grade. Do the following checks:

• If the gross bearing pressure under the footing is within safe bearing capacity
• Provide sufficient depth and longitudinal steel for resisting bending and shear
• Sufficient anchorage for column steel into the footing
• If the bearing pressure at column-footing joint is within 0.45 times the maximum concrete compressive strength

Provide a simple sketch showing the size of the footing, maximum and minimum depth of the section, flexural reinforcement in both directions and anchorage of column steel.

GIVEN DATA;

COLUMN SIZE: 400X400

FACTOURED AXIAL LOAD: 2000KN

UNFACTORED AXIAL LOAD: 2000/1.5=1333.33 KN

SAFE SOIL BEARING CAPACITY: 150KN/M2

HEIGHT OF SURCHARGE: 2M

STEP 1

IO% INCREASE IN UNFACTORED LOAD =1333.33X10%=133.33

TOTAL UNFAACTORED LOAD =1333.33+133.33

= 1466.63 KN

AREA OF FOOTING: = UNFACTORED LOAD/SBC

1466.63/150= 9.77 M2

A=3.15X3.15

step 2

NET UPWARD PRESSURE BY SOIL= FACTORED AXIAL LOAD/ AREA OF FOOTING

Pn = 2000/3.15X3.15 = 201.56 KN/M2

STEP3

DEPTH OF FOOTING

ASSSUME DEPTH OF FOOTING IS 500 MM

AS PER IS 456 34.4

SLOPE 1:2

PERMISSIBLE BEARING STRESS= 0.45Xfck

=0.45x25= 11.25N/mm

PERMISSIBLE BEARING STRESS MULTIPLY BY AREA FACTOR OF 2 . AS PRE IS CODE 456 34.4

11.25X2 =22.5N/MM2

ACTUAL BEARING STRESS UNDER THE LOADED COLUMN IS 2000X1000/400X400

12.5 N/MM2 WHICH IS LESS THAN PERMISSIBLE STRESS , HENCE OK

STEP 4

CONVERSION OF NET PRESSURE INTO UDL

201.56X3.15= 635 KN/M

BENDING MOMENT DUE TO UDL OVER A CANTILEVER SECTION OR CRITCAL SECTION =

MU= WL2/2

635X1.375X1.375/2 = 600 KN-M

MU=600 KN-M

STEP 5

Mu=0.133xfckxbxd2

d=235mm

take 2 times

d= 470 (EFFECTIVE DEPTH)

D=470+50+20+10 = 550MM ( OVER ALL DEPTH )

REVISED THE NET UPWARD PRESSURE BY SOIL ,TAKING INTO ACCOUNT OF SELF WEIGHT OF FOOTING AND SOIL SURCHARGE

Pu= factored load+ wt of footing + wt of soil upto 2 meter/area of footing

2000+3.15x3.13x0.55x25+2x3.15x3.15x16/3.15x3.15

= 247 kn

Mu= 247x3.13x1.375.1.375/2= 735kn-m

CALCULATION OF REINFORCEMEN=

AS PER IS CODE 456 , ANNEX G

MU = 0.87 .FY. AST.d(1-AST.FY/bdfck)

438.34= 0.87x415xAstx 450( 1-Astx415/3.15x450x25)

Pt = 50fck/fy(1- `sqrt`1-4.6`div`fckxbxd2`d^2`)

Pt=1.686%

Ast= Pt`div`100`ast`bd

1.686`div`100`ast`3150x470

= 22040mm2

take 20mm , 314mm2

no of steel= 2240/314 =7bar

take 16mm,201mm2

no of steel = 2240/201 =11 bar

take 12mm , 113mm2

no of steel ,2240/113= 19.82= 20 bar

spacing of bar= length/no of bar -1

3150-50-5-/7-1 = 508 mm which is not correct as per is code should be less than 180 mm

spacing for 16mm= 305 >180

spacing for 12mm= 160.5 take 160mm< 180 so ok

provide 20 no 12mm @160mm c/c

step 6

check for one way shear

create relation betweenand `tav`c

at a effective distance d form face of column

length of highlighted section =3150/2-400/2 -470=900mm

Vu = upward force at the cricitical section for one way shear xarea of highlighted or critical section

= 247x 3.15x.9= 700kn

`tau`v= Vu/b`

700x1000/3150x470= 0.472n/mm2

now cal culate `tau`c from is 456 and compare `

step 7

check for two way shear or punching shear

area of highlighted portion= 3.15x3.15-.87x.87

9m2

shear force at the highlighted area= upward force x area highlighted

= 247x 9=2223kn

`tau`v = Vu/bd

2223000/3150x470 = 1.50

compare this with tau c it should be less.

reinforcement arrangement