Design of Shallow Foundation (Isolated Footings)

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.

Please do go through the solved examples in the document provided with the challenge.

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

INTRODUCTION :

Footings are an important part of foundation construction. They are typically made of concrete with rebar reinforcement that has been poured into an excavated trench. The purpose of footings is to support the foundation and prevent settling. Footings are especially important in areas with troublesome soils.

• Individual footing or isolated footing. Combined footing. Strip foundation. Raft or mat foundation

PROCEDURE :

• Steps involved in Footing Design,

1. Calculation of gross soil pressure for footing area
2. Calculation of net soil pressure for flexure and shear design
3. Initial depth of footing Calculation
4. Flexural Reinforcement Calculation
5. One way shear check
6. Two way Shear check.

GROSS SOIL FOOTING AREA:

• Un factored load with surcharge + (self weight of footing / allowable soil pressure)

= (2000/1.5*1.1)/150 = 9.78m^2

• Assumimg we have square footing,
• `root`9.78 = 3.12 meter side footing
• Consider 3.2 meter sided isolated footing

NET SOIL PRESSURE & INITIAL FOOTING DEPTH:

• Factored load / actual area of footing
• 2000*1000 / (3.2*3.2)
• `underset(n)(P)` = 195.3 KN/m^2
• Assume depth of footing 500mm and checking it for bearing stress as per IS456-2000 Clause 34.4
• `root`(footing base bearing area / loaded area) `le`2

• Permissible bearing stress 0.45 * fck = 11.25N/mm^2
• Permissible bearing stress multiplied with afrea factor 11.25 * 2 = 22N/mm^2
• Actual bearing stress @ column base
• (2000*1000) / (400*400) = 12.5N/mm^2
• 12.5N/mm^2 actual stress is less than permiisible 22.5 N/mm^2. Hence okay,
• we can proceed with 500mm depth footing for further design check,
• If we assume 50mm for cover footing the effective depth (d) shall be taken as 450mm.

FLEXURAL REINFORCEMENT:

• Conversation of net pressure into uniformly distributed load = 1953 * 3.2 = 625 KN/m
• Bending moment due to udl over a cantilever section = WL^2 / 2 = 625 *1.6*1.6 / 2 = 800KN/m
• Reinforcement calculation as per IS456-2000 ,
• 
• Assume Fy = 500N/mm^2 ,
• In result as required = 4350mm^2
• If we provide 16mm dia rebar at 125mm spacing , the actual rebar provided = 3200/125*201
• Ast provided = 5146 mm^2

ONE WAY SHEAR STRESS CHECK:

• Shear force in the one way shaded area = 0.95*3.2*195.3 = 593.7 KN
• Desiogn shear stress at one way cut face
• `underset(v)(tau)` = 593.7 *1000 / (3200 *450) = 0.412 N/mm^2
• Shear stress capacity of section as per IS456-2000 Table-19(include rebar) = 0.425N/mm^2
• Design shear stress is less than shear capacity , Hence okay.

TWO WAY SHEAR STRESS CHECK:

• Shear force in two way shaded area = (3.2*3.2) - (0.85*0.85) *195.3 = 1859KN
• Design shear stress at two way cut face
• `underset(v)(tau)` = 1859 *1000 / (3400*450) = 1.215N/mm^2
• Shear stress capacity of section as per IS456-2000 clause 31.6.3.1 = 0.25 * `root`fck = 1.25N/mm^2
• Design shear stress is less than shear capacity,
• Hence okay.

ISOLATED SPREAD FOOTING:

RESULT :

Thus, we required spread footing is designed and detailed as per the given inputs , All the required limit state criteria are verified and found to Ok.