Design of Shallow Foundation (Isolated Footings)

DESIGN SHALLOW FOUNDATION ISOLATED FOOTING

Que.

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.

Ans.

Aim :-

To design footing for a column of size 400X400 using some information such as

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

Then perform following checks:

• If the gross bearing pressure under the footing is within safe bearing capacity
• Provide sufficient depth and longitudnal steel for resisting bending and shear
• Sufficient anchorage for column steel into footing
• If the bearing pressure at column-footing joint is within 0.45 times maximum concrete compressive strength.

Introduction :-

• Footing and other foundation units transfer loads from the structure to the soil or rock supporting the structure.
• The soil pressure distribution under footing id a function of type of soil and relavtive rigidity of soil and foundation pad.
• Most common types of footing are

1. Strip or wall footing
2. spread footing
3. Stepped footing
4. Tapered footing
5. Pile cap
6. Combined footing
7. Mat or Raft footing

Procedure :-

Given data

• Column size 400X400 mm
• Compression axial load (1.5D.L +1.5L.L) = 2000KN.........Factored load
• Safe bearing capacity of soil at the depth of 2m below EGL = 150KN/sq.m
• Assume self wt. of footing and soil above it at 10% load
• Grade oc concrete = 25KN/ sq.m
• Assume fy = 500N/sq.mm

Slope is designed for footing for which following steps are to be followed:-

1) Size of footing:

• Unfactored or service load = 2000/1.5 = 1333.33KN
• Safe bearing capacity of soil, qc = 150KN/sq.m
• Hence, required base area = (1333.33X1.1) /150 = 9.78 sq.m
• Thus, provide 3200X3200mm which gives 10.24sq.m base area for footing (The area later proved to be insufficient )

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

• Factored bearing pressure (Net soil pressure) =(2000/3.2X3.2) = 195.31KN/sq.m
• Now, assume 0.15% reinforcement in footing slab

From the table 19 of IS 456-2000, design shear strength of concrete, Ƭc =0.29N/sq.mm for 25 grade of concrete.

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

0.29d x3200 X d ≥ 0.195X (1400-d) X3200

d ≥562.88mm ≈ 600mm

So, provide d=600mm

3) Check forr two way shear:

Here, critical section is ABCD, so shear resistance at critical depth= area of critical section X permissble shear stress

i.e. shear resistance = (400+600) X 4 X 600 X K_{s .} Ʈc =

K_{s .} Ʈc = 0.25 √fck =125N/sq.mm

Hence, shear reistance =1000 X 4 X 600 X 1.25 = 3000 KN

Now, shear force = [3.2 X 3.2 - (0.4+0.6)²] X 0.195 = 2944.5KN < 3000KN....................Hence, safe.

4) Gross bearing capacity :

Assume unit wt of concrte and soil =25KN/sq.m and 180KN/sq.m ........we have

a. Load of footing =1333.33 KN

b. Wt of footing = 3.2 X 3.2 X 0.7 X 25 = 179.2KN

c. Wt of soil = 3.2 X 3.2 X (2-0.7) X 18 = 239.61KN

Thus, Total load = a+b+c = 1751.81KN

Hence, gross bearing capacity = 1751.81/(3.2X3.2) = 171.07KN/sq.m.........Hence need to increase footing size.

Lets say 3600X3600

So, now

a. wt. of footing = 226.8KN

b. wt of soil =303.26KN

Total a+ a +b = 1863.06KN

Now, gross bearing capacity = 1863.06/(3.6X3.6) = 143.75KN/sq.m. < 150KN/sq.m.............Hence,safe

So, corrected net soil pressure = 2000/(3.6X3.6) = 154.32KN/sq.m

5) Bending moment :

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

Consider depth =600 mm

Bending moment at critical section is obtained as Mu =3600X16000.154X1600/2 =709.63KN-m

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

6) Development length :

7) Providing slope in footing slab :

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

Hence, one way shear force = 0.154 (1600-600) X3600 = 554400N = 554.4KN

One way shear resistance is given by 0.29X 3600X600 =626.4KN > 554.4KN..............Hence,safe

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

Result :-

Sloped isolated footing of square column has been designed with given specification.