Design of Shallow Foundation (Isolated Footings)
Q1). 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.
ANSWER :
AIM :
To design a square footing for the column size of 400x400 mm2. And to check whether the gross bearing pressure of the footing is within the safe bearing capacity. And to provide sufficient depth and the longitudinal steel for the resisting bending and shear and to also check the sufficient anchorage for the column steel into the footing.
INTRODUCTION :
Footing are designed to transmit the loads to the soil evenley without exceeding the safe bearing capacity.Isolated footing is the simpliest form of foundation used to depending upon the soil type.Isolated footing are independent footing designed to support single column.
PROCEDURE:
Given That :
Size of column = 400mm x 400 mm2
Factored load due to the column = 2000kN
SBC at the site = 150kN/m2
Concrete grade = M25
Steel grade = Fe415
Steps involved in the Footing design :-
1) Calculation of gross soil pressure and 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
Calculation of gross soil pressure and footing area :
P = F/A
Where:
P: soil pressure
F: unfactored load of column + self-weight of footing and surcharge pressure
A: Area of footing
* Unfactored load with surcharge + self weight of footing / allowable soil pressure
= (2000/1.5x1.1)/150
= 9.78m2
Assuming we have squre footing
Square root of 9.78 = 3.12 meter side footing
Consider, 3.2meter sided isolated footing
Net soil pressure and initial footing depth :
- Factored load/actual area of footing
= 2000x1000/(3.2x3.2)
= 195300N/m2
Pn= 195.3kN/m2
- Assume depth of footing 500mm and checking it for bearing stress as per IS:456-2000 clause 34.4
Square root of (footing base bearing area/loaded area)</= 2
- Permissible bearing stress 0.45xFck = 11.25N/mm2
- Permissible bearing stress multiplied with area factor 11.25x2
= 22.5N/mm2
- Actual bearing stress at column base
= (2000x1000)/(400x400)
= 12.5N/mm2
12.5N/mm2 actual stress is less than permissible 22.5N/mm2. Hence OK.
We can proceed with 500mm depth footing for further design checks.
If we assume 50mm cover for footing, the effective depth(d) shall be taken as 450mm.
Flexural reinforcement :
- Conversion of net pressure into Uniformly distributed load = 195.3x3.2 = 625kN/m
- Bending moment due to UDL over a cantilever section= (wL^2)/2 =625x1.6x1.6/2
M = 800kNm
- Reinforcement calculation as per IS:456-2000 Annex - G
Assume Fy = 500N/mm2, In result Ast required = 4350mm2'
If we provide 16mm dia rebar at 125mm spacing, the actual rebar provided= (3200/125)x201
Ast provided = 5146mm2
One way shear stress check :
- shear force in the one way shaded area = 0.95x3.2x195.3 = 593.7 kN
- Design shear stress at One way cut face = (593.7x1000)/(3200x450)
= 0.412N/mm2
- Shaer stress capacity of section as per IS:456-2000 Table 19 (include rebar)
= 0.425N/mm2
- Design shear stress is less than shear capacity. Hence OK.
Two way shear stress check :
- Shear force in the two way shaded area = (3.2x3.2)-(0.85x0.85)x195.3 = 1859kN
- Design shear stress at Two way cut free = (1859x1000)/(3400x450) = 1.215N/mm2
- Shear stress capacity of section as per IS:456-2000 clause 31.6.3.1 = 0.25xsquare root of Fck = 1.25N/mm2
- Design shear stress is less than shear capacity. Hence OK.
Result :-
Successfully complete the design of square footing for a column size of 400x400 by using given data and conditions.
