Design of Shallow Foundation (Isolated Footings)

Aim & Introduction :

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.

Procedure :

1. Steps involved in Footing Designs

• 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 Chech

Calculation of Gross Soil Pressure for footing area

(Unfactored Load with Surcharge x Self weight of footing)/Allowable Soil Pressure

=(2000/1.5 x 1.11)/150

=9.78mm2

Assume we have square footing

=√ (9.78)

=3.12m WIDE footing

=3.2 m Isolated Footing

Calculation of net soil pressure for flexural and Shear Design

= Factored Load/Actual Area of footing

= 2000x1000 / (3.2 x 3.2)

Pn = 195.3 Kn/m2

Assume depth of footing 500mm and check it for bearing Stress as per IS 456-2000

√(Footing base area/Loaded area)<= 2

Permissible Bearing Stress = .45 x fck = 11.25KN/m2

Permissible bearing Stress x Area of factor = 11.25 x 2 = 22.5N/mm2

Actual bearing Stress at Column BAse = 2000 x 2000 /(400 x 400) = 12.5N/mm2

Therefore, 12.5N/mm2 Actual Bearing Stress is less than Permissible bearing Stress

hence it's Okay

WE CAN proceed with Cover of 50mm and effective Cover depth is 450mm

Flexural Reinforcement

Conversion of Net Pressure into uniformly Distributed Load

= 195.3 x 3.2 = 625KN/m

Bending Moment due to UDL over cantilever Section

=wl2/2

=.626 x 1.6 x 1.6 / 2

M = 800KNm

Reinforcement Calculation as per IS 456-2000

Mu = .87fy Ast d (1-(Ast fy/bd fck)

Assume Fy = 500N/mm2 and Ast required = 4350mm2

Place 16mm dia of rebar at spacing of 125mm

Actual Rebar Provided =(3200/125 x 201)

Ast Provided = 5146mm2

Hence Ast Provided is greater than ast required hence it is okay

One Way Shear Check

Shear Force in One Way

=.95 x 3.2 x 195.3 = 593.7KN

Design Shear Stress at one way

=593.7 x 1000 / (3200 x 450)

=.412N/mm2

Shear Stress Capacity of Section as Per IS 456-2000

= .425n/mm2

design Shear stress is less than Shear capacity

Hence it is okay

Two way Shear Stress

Shear force in two way

=(3.2 x 3.2) - (.85 x .85) x 195.3 = 1859 KN

Design Shear Stress at two way

= 1895 x 1000 / (3400 x450) = 1.215 N/mm2

Shear Stress Capacity of Section as Per IS 456-2000

=.25 x √fck = 1.25N/mm2

design Shear Stress is less than the Shear Capacity

hence okay

Diagram

Result :

From the above procedure we come to know how design and Check for footing