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
GIVEN :
- 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 = 2 m.
PROCEDURE :
STEP 1. GROSS SOIL PRESSURE & FOOTING AREA
IO% INCREASE IN UNFACTORED LOAD =1333.33X10%=133.33
TOTAL UNFACTORED LOAD
=1333.33 + 133.33
= 1466.63 KN
AREA OF FOOTING (A)
= UNFACTORED LOAD/SBC
= 1466.63/150
= 9.77 m2 -----------Taking root of this value
= 3.15 m
lets consider 3.2 m X 3.2 m Isolated Footing.
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STEP 2. NET SOIL PRESSURE
NET UPWARD PRESSURE BY SOIL (Pn)
= FACTORED AXIAL LOAD/ AREA OF FOOTING
= 2000/3.2X3.2
= 195.3125 KN/m2
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STEP 3. DEPTH OF FOOTING
ASSSUME DEPTH OF FOOTING IS 500 MM
AS PER IS 456 34.4, SLOPE 1:2
PERMISSIBLE BEARING STRESS
= 0.45 X fck
=0.45 X 25
= 11.25 N/mm2.
PERMISSIBLE BEARING STRESS MULTIPLY BY AREA FACTOR OF 2.
AS PER IS CODE 456 34.4, 11.25 X 2 = 22.5 N/mm2
ACTUAL BEARING STRESS UNDER THE LOADED COLUMN
= 2000X1000/400X400 = 12.5 N/mm2
WHICH IS LESS THAN PERMISSIBLE STRESS, HENCE OK.
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STEP 4. FLEXURAL REINFORCEMENT CALCULATION
CONVERSION OF NET PRESSURE INTO UDL
=195.3 X 3.2
= 624.96 = 625 KN/m.
BENDING MOMENT DUE TO UDL OVER A CANTILEVER SECTION OR CRITCAL SECTION (MU)
= wL^2/2
= 625 X 1.6^2/2 = 800 KN.m
MU = 800 KN.m
CALCULATION OF REINFORCEMEN
AS PER IS CODE 456 , ANNEX G
MU = 0.87.Fy.AST.d (1- AST.Fy/bd.fck) ----------------ASSUME Fy=500
800 = 0.87 X 500 X Ast X 450 [1- (Ast X 500/3.3 X 450 X 25)]
Ast required = 4350 mm^2
BUT, IF WE PROVIDE 16mm DIA REBAR AT SPACING OF 125 mm THE ACTUAL REBAR PROVIDED
= 3200/125 X 201
= 5146 mm^2 = Ast provided.
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STEP 5. ONE WAY SHEAR STRESS CHECK
SHEAR FORCE IN ONE WAY SHADED AREA
= 0.95 X 3.2 X 195.3
= 593.7 KN
DESIGN SHEAR STRESS AT ONE WAY CUT FACE `tau`v
`tau`v = 593.7 X 1000/(3200X450)
`tau`v = 0.412 N/mm^2
SHEAR STRESS CAPACITY OF SECTION AS PER IS 456 TABLE 19
= 100 X Ast/bd
= 100 X 5146/3200X450
= 0.425 N/mm^2
DESIGN SHEAR STRESS IS LESS THAN SHEAR CAPACITY, HENCE OKAY
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STEP 6. TWO WAY SHEAR STRESS CHECK
AREA OF HIGHLIGHTED PORTION
= (3.2 X 3.2) - (0.85 X 0.850)
= 9.5175 m^2
SHEAR FORCE AT HIGHLIGHTED AREA
= upward force x area highlighted
= 195.3 x 9.5175
= 1859 KN
DESIGN SHEAR STRESS AT TWO WAY CUT FACE `tau`v
`tau`v = 1859 X 1000/ (850+850+850+850) X 450
`tau`v = 1.215 N/mm^2
SHEAR STRESS CAPACITY AS PER IS 456-2000 AS PER CLAUSE 31.6.3.1
= 0.25 X `sqrt Fck`
= 0.25 X `sqrt 25`
= 1.25 N/mm^2
DESIGN SHEAR STRESS IS LESS THAN SHEAR CAPACITY, HENCE OKAY
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REINFORCEMENT SKETCH
