Design of Shallow Foundation (Isolated Footings)

* DESIGN OF SHALLOW FOUNDATION ISOLATED FOOTING *

Aim :-

To design a square footing for a column of size 400x400 using some of the informations such as

• The compression axial load for the load combination of (1.5 DL + 1.5 LL) = 2000 KN.
• The safe soil bearing capacity = 150 KN/m^2 at a depth of 2 metres below E.G.L.
• Grade of concrete = M25

Then to perform 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 and other foundation units transfer loads from the structure to the soil or rock supporting the structure.
• The distribution of soil pressure under a footing is a function of the type of soil and the relative rigidity of the soil and the foundation pad.
• Most common types of footings used are :-
  • Strip or wall footing
  • Spread footing
  • Stepped footing
  • Tapered footing
  • Pile cap
  • Combined footing
  • Mat or raft footing.

• This project is dealing with isolated footing for a column or spread footing.

Procedure :-

- Given datas include :-

• Column size = 400mmx400mm
• Compression axial load (1.5DL+1.5LL) = 2000kN - factored load
• Safe bearing capacity of soil at a depth of 2m below EGL = 150kN/m^2
• Assuming the self weight of footing and soil above it as 10% load.
• Grade of concrete = 25N/m^2
• Assuming fy = 500N/mm^2

- Here a sloped footing is designed and the steps involved in the design are as follows :-

1) Size of footing :

Unfactored or service load = 2000/1.5=1333.33kN

Safe bearing capacity of soil , q_c = 150kN/m^2

Hence, the required base area = 1333.33⋅1.1/150=9.78m

Hence, provide 3200mmx3200mm which gives 10.24m^2 base area for footing. (This area later proves to be insufficient).

2) Thickness of footing slab based on one way shear.

Factored bearing pressure(Net soil pressure) = 2000/3.2⋅3.2=195.31N/m^2

Now, assuming 0.15% reinforcement in footing slab.

From table 19 of IS456:2000, design shear strength of concrete, τ_c= 0.29N/mm^2 for M25 grade concrete.

From the condition, One way shear resistance≥One way shear force -->

0.29d x 3200 x d≥0.195x(1400-d)x3200

d≥562.88mm ≈600mm

So, provide d = 600mm

Assuming 20mm dia bars and 70mm cover , total depth of the footing = 600+70+20+10 =700mm

3) Check for two way shear

Here, the critical section is ABCD, so shear resistance at critical depth = area of critical section x permissible shear stress

i.e, shear resistance = (400 + 600) x 4 x 600 x K_sτ_c =

K_sτ_c = 0.25√fck= 1.25N/mm^2

Hence, shear resistance = 1000 x 4 x 600 x 1.25 = 3000kN

Now, the shear force = [3.2 x 3.2 - (0.4+0.6)^2] x 0.195 = 2944.5kN < 3000kN

Hence, safe.

4) Gross bearing capacity

Assuming unit weight of concrete and soil as 25kN/m^3 and 18kN/m^3, we have,

Load on footing = 1333.3kN

Weight of footing = 3.2x3.2x0.7x25=179.2kN

Weight of soil = 3.2x3.2x(2-0.7)x18=239.61kN

Total load = 1751.81kN

Hence, gross bearing capacity = 1751.81/3.2⋅3.2=171.07kN/m^2 > 150kN/m^2. Hence, we need to increase the size of footing to 3600mmx3600mm.

So, now the weight of footing = 226.8kN

Weight of soil = 303.26kN

Total load = 1863.06kN

Now, gross bearing capacity = 1863.06/3.6⋅3.6=143.75kN/m^2<150kN/m^2. Hence safe.

So, the corrected net soil pressure = 2000/3.6⋅3.6=154.32kN/m^2

5) Bending moment

We need to determine the area of steel in one direction as it is a square footing.

Consider effective depth = 600mm.

Bending moment at critical section is obtained as , Mu= 3600x16000.154x1600/2= 709.63kNm

Mu/bd^2 =709.63⋅10^6/3600⋅600⋅600 =0.5475N/mm^2

Now, from table 3 of SP16 for fck = 25N/mm^2 and fy = 500N/mm^2, % of reinforcement = 0.1294%

Hence, area of steel = 0.1294/100⋅3600⋅600 =2795.04mm^2

So, no. of bars required is given by, 2795.04/314 =8.9 ≈10bars

Hence, provide 10 nos of 20mm dia bars both ways.

6) Development Length

For 20mm dia bars, Ld = 0.87fyϕ/4τbd =970.98mm ≈1000mm

7) Providing slope in footing slab

Since the three critical sections are within a distance of 600mm from the face of the column , the full depth of footing slab is to be atleast 700mm, which is the provided depth of footing.

Hence, the one way shear force = 0.154(1600-600)3600=554400N=554.4kN

One way shear resistance is given by 0.29 x 3600 x 600= 626.4kN which is greater than the shear force. Hence safe.

So, we need to provide a depth of 700mm near the column and the depth can be reduced to about 400mm at the edges of the footing.

Result :-

• Sloped isolated footing for a square column has been designed with the given specification.