Eccentrically loaded footing design example

Footing the structural member which transfers the load of the structure to the soil. Footing is the most important and critical section of the structure. The success behind the whole structure is depended on the footing.

The failure of footing may cause the failure of the whole structure. It may cause greater loss of properties as well as lives. Failure of footing is caused due to over shear stress and moment on the footing than the required capacity of shear and moment.

So, it is very important to design the footing very carefully with full accurate detail of the bearing capacity of the soil, the area covered, etc.

Footing may be of different shapes like square, rectangular, trapezoidal, etc. Different shapes of footing may be required according to the soil bearing capacity and area of land available to us. According to the position of the column on footing, it may be divided into two types eccentric footing and centric footing.

Types of isolated footing

There are different types of footing according to different criteria like shape, loading, depth, etc. According to loading footing can be divided into two types i.e centric footing and eccentric footing which are described below.

Further eccentric flooding is uni-axial and bi-axial eccentric footing. All of the footings are designed according to spacing available, load capacity required, soil bearing capacity, etc.

What is eccentric footing?

The footing in which the position of the column on it is not exactly at the center of footing is known as eccentric footing. In any case, we do not have an area of the land enough for placing the column at the center of the footing, In that case, we have to provide the column beside the center or at the edge of the footing.

Further eccentrical footing can be designed as uniaxial and biaxial footing. In uniaxial eccentric footing, the axial load is acted on one of the center lines of the footing ie. either on the x-axis or y-axis.

But, in bi-axial footing, the axial load is acted beside the both center line i.e x-axis and y-axis.

Difference between the centric footing and eccentric footing

S.N	Centric Footing	Eccentric Footing
1.	Load is applied exactly at the center of the footing.	Load is applied at other areas than the center of the footing.
2.	Eccentricity is unavoidable while designing centric footing.	Eccentricity is un avoidable considered while designing.
3.	This type of footing is provided if we have sufficient plot area beside the column.	This type of footing is provided if we do not have sufficient plot area beside the column.
4.	It takes short time to design.	It takes a long time to Design as uniaxial and biaxial eccentric loading should be considered.
5.	Stress distribution at the base of footing is uniform.	Stress distribution at the base of the footing is linear and non-uniform.

How to design eccentric footing?

• First of all the required area of footing is determined by using formula (Area = Load/Safe bearing capacity of Soil).
• After that, we should calculate the net earth pressure due to soil acting upward to footing (BCS) is calculated by using the formula BCS =Factored Load/Area of Footing.
• The factored load can be calculated by multiplying the safe value (Generally taken 1.5) with a load of column and self-load of footing.
• After that maximum bending moment in footing at different critical sections should be calculated according to the plot country code.
• Now, the depth of flooding is calculated with the help of the maximum moment calculated. The depth of footing should be increased 1.5 to 2 times for shear consideration.
• After that, the detail of reinforcement should be prepared according to the moment calculated and the formula provided by Country Code.
• Finally, the designed footing should be checked for one-way shear, two-way shear, and development length.
• If all the checks are passed, then a summary of footing materials with reinforcement should be prepared with a suitable diagram.

Eccentrically loaded footing design example – Numerical

Design a rectangle footing to carry a column load of 1150 KN and B.M. of 250 KN-m from 600 x 600 mm square column with 20 mm diameter longitudinal steel. The bearing capacity of soil is 200 KN/m². Consider depth of foundation as 1.5 m. Take unit weight of earth is 17 KN/m3. Use M20 concrete and Fe 415 steel. 

Solution:

Given, Service load on footing = 1150 KN

Service BM on footing (M) = 250 KM-m

Size of column = 600mm x 600mm

Depth of foundation (Df) = 1.5 m

Safe bearing capacity of soil (SBCS) = 200 KN/m²

Unit weight of earth (γs) = 17 KN/m³

Diameter of longitudinal bar of column (∅1) = 20 mm

Grade of Concrete = M20 

Steel Used = Fe 415

Here, Total Service load (P) = Service load + Self weight of footing

[*NOTE: IF DEPTH OF FOOTING IS NOT GIVEN, ASSUME SELF WEIGHT OF FOOTING AS 10% OF GIVEN SERVICE LOAD, OTHERWISE, ASSUME SELF WEIGHT OF FOOTING EQUIVALENT TO THE WEIGHT OF BACKFILL SOIL]

Assuming Length (L) to Breadth (B) ratio of footing to be 1.5, we get

I.e, L/B = 1.5

or, L = 1.5 B

Thus,

Area of Footing = L X B

Or, 6.48 = 1.5 B x B

Or, B2 = 4.32

Or, B = 2.08 m

Provide B = 2.2 m

L = 1.5 x 2.2 m

= 3.3 m 

[NOTE: IF RECTANGULAR FOOTING IS TO BE DESIGNED FOR RECTANGULAR COLUMN, IT IS MORE EFFECTIVE TO PROVIDE L/B RATIO OF FOOTING IN THE SAME PROPORTION AS THAT OF THE COLUMN]

To compensate the effect of moment, we shift the axis of column from the axis of footing at a distance e = (217 mm) as shown in figure below:

Calculation of Maximum Bending Moment:

From Clause 34.2.3.1 and 34.2.3.2 of IS code 456: 2000, the maximum bending moment occurs at the face of column.

Design of Isolated Footing: Chapter 4 | 227 From the geometry of above figure, maximum BM occurs at section YY or Section XX

Thus,

Calculation of depth of footing:

The depth of footing is calculated for maximum BM.

For Fe 415, 

Mmax = 0.138 fck.b.d2min

Or, 723.61 x 106 = 0.138 x 20 x 2200 x d2 min

Or, d2min = 1191171.61

Or, dmin = 345.21mm

To resist shear, we increase d by two times

Thus, d = 2 x 345.21 mm = 690.42mm

Let’s provide, d = 700 mm 

Providing cover d = 65 mm

Overall depth of footing (D) = 700 + 65mm (Cover) = 765 mm

Calculation of reinforcement:

For longer direction,

Or, 723.61 x 106 = 252735 Ast – 3.41 Ast²

Or, 3.41 Ast2 – 252735 Ast + 723.61 x 106 = 0

Solving using calculator, we get,

Ast = 2983.49 mm2 

Providing 12 mm ∅ bar,

Or, 282.9 x 106 = 252735 Ast – 2.27 Ast2 

Or, 2.27 Ast2 – 252735 Ast + 282.9 x 106 = 0

Solving using calculator, we get,

Ast = 1130.84 mm2 

Providing 12 mm ∅ bar,

Area of 1 bar (At1) =  113.04 mm²

Check for spacing (S) 300 mm ≯ 300mm

≯ 3d(=3 x 700 = 2100mm)

Hence Provide 12 mm ∅ bar@ 300 mm c/c

Providing 12 mm ∅ bars, Area of 1 bar (At1) = 113.04 mm2

.’. Provide 12 mm & bars @ 250 mm c/c. over a central Band of width B = 2200 mm

Check:

1. Check for one-way shear

From clause 34.2.4.1(a) of IS code 456:2000, critical section for one-way shear lies at a distance d from the face of column as shown in figure below:

From the geometry of figure; critical shear forces are:

Hence safe in one-way shear.

1. Check for two-way ‘shear: 

Critical section for two-way shear lies at distance d/2 from each face of the column as shown in figure below:

Here, Vu = BCS x [L x B – (l+d)(b+d)]

= 267.9 x [3.3 x 2.2 – (0.6+0.8) x (0.6+0.8)]

= 267.9 x (7.26 – 1.96) = 1419.9 KN

Hence, the slab is safe in two- way shear. 

1. Check for development length 

From clause 26.2.1 of IS code 456:2000, development length (Ld) is given by:

Where, ∅= Nominal diameter of longitudinal bar of column

= 20 mm

σs = Stress in bar at section considered at design load

= 0.87 fy

= 0.87 x 415 = τbd

= Design bond stress given in clause 26.2.1.1 of IS code 456:2000

= 1.2 x 1.6

Ld (available) in shortest side is calculated from figure below:

Since Ld (required) <Ld (available), the footing has safe development length.

Design Summary: 

Length of footing = 3.3m

Breadth of footing = 2.2m

Effective depth of footing = 800 mm

Cover = 65 mm 

Overall depth of footing = 865 mm

Reinforcement along longer side = 12 mm ∅ bar @ 80mm c/c

Reinforcement along shorter side= 12 mm ∅ bar @ 300mm c/c

Reinforcement in central band = 12 mm ∅ bar @ 250 mm c/c

The design details are shown in figure below:  

Different Footing size for columns

The size of footing i.e length, width, and height of footing depend upon the load acting on the footing. By the way, we can use the size of footing according to experience and previously used data for different construction. We do not recommend you to put the same value as i have mentioned below.

Proper design of footing is required including different factors. It may depend upon the load-bearing capacity of the soil. By the way, in contact of India, we have constructed different buildings and we have provided the size of footing like below.

S.N	No. of Storey	Size of Column	Length of footing	Width of footing	Thickness of footing	Depth of footing
1.	1	(300×400) mm	4′ (Four feet)	4′ (Four feet)	1.5′ (1.5 feet)	5′ (Five feet)
2.	2	(300×400) mm	5′ (Five feet)	5′ (Five feet)	1.5′ (1.5 feet)	5′ (Five feet)
3.	3	(300×460) mm	5′ (Five feet)	5′ (Five feet)	2′ (Two feet)	6′ (Six feet)
4.	4	(300×460) mm	6′ (Six feet)	6′ (Six feet)	2′ (Two feet)	6′ (Six feet)
5.	5	(460×460) mm	6′ (Six feet)	6′ (Six feet)	2.5′ (2.5 feet)	7′ (Seven feet)

Courtesy: https://www.civilconcept.com/eccentrically-loaded-footing-design-example/