Footing Design | Worked Example

Footing design can be done simple manner when it is on an isolated footing. It is sometimes, raft foundations, strip footings, and combined footings are also considered footings.

In this worked example, we are concertation on footing design and its process.

The following procedure can be followed in the design of footings.

Footing Desing Process

1. Calculate the column axial load in Serviceability Limit Stage (SLS) and Ultimate Limit State (ULS)
2. Get the soil’s allowable bearing capacity. This could be obtained by a geotechnical investigation report.
3. Calculate the area of the footing using SLS load and allowable bearing capacity. [ A = N / σ ]
4. From the area calculate the dimension of the footings
5. Since the dimension are known, now calculate the ultimate pressure under the foundation.
6. Calculate the bending moment at the face of the column and then calculate the reinforcement.
7. Calculate the shear at the face of the column. This is also called the vertical line shear. Check whether this shear stress is less than the maximum allowable shear for the footing. According to BS 8110, the value is less of 5 N/mm² or 0.8√fcu.
8. Check the footing for punching shear. This is one of most important check in the footing design. Consider punching shear perimeter based on your standard used for the design. According to the BS 8110, the punching shear perimeter is considered as 1.5d from the face of the column. Calculate the shear stress at the critical perimeter and check whether it is less than the shear capacity (Vc). If V<Vc section need not provide shear links. In general, isolated footing are provided with shear links. To avoid that we may increase the section depth or reinforcement area.

Footing Desing Work Example

Column Load SLS = 250 kN

Column Load ULS = 375kN

Allowable bearing capacity = 150 kN/m²

Size of column = 250mm

Assume, weight of the footing as 7% of column load.

Therefore, total weight = 1.07 x 250 = 267.5 kN

Area of footing = 267.5 / 150 = 1.78 m²

Consider square footing

Width of the footing = √1.78 = 1.33 m, say 1.4m

Ultimate pressure under the footing = 375 / (1.4 x 1.4) = 191.3 kN/m²

Calculate the Bending Moment at the face of the column

Consider 1m width strip

M = 191.3 x 1 x (1.4/2 – 0.25/2) x (1.4/2 – 0.25/2) / 2 = 31.62 kNm

From this we can calculate the reinforcement area. This shall be done based on the relevant standard.

According to the BS 8110, when cover to the reinforcement 50mm, concrete grade 25, thickness of footing 250mm consider, rebar area can be calculated as

As = 366 mm²

Check the Vertical Line Shear

Effective depth = 250 – 40- 10/2 = 205mm

Shear stress  = 375 x 1000 / (4 x 250 x 205) = 1.83 N/mm²

Allowable shear stress = 5 N/mm² or 0.8√25 = 4 N/mm²

Shear stress < 4 N/mm²

Hence Ok.

Check Punching Shear

Pouching shear perimeter = (1.5 x 205 + 250) x 4 = 2230mm

Outside area of the punching shear perimeter

A out = 1.4 x 1.4 – (1.5 x 0.205 + 0.250)² = 1.65 m²

Shear force at punching shear perimeter = 191.3 x 1.65 = 315.65 kN

Shear stress at the punching shear perimeter = v /bd = 315.65 x 1000 / (4 x 2230 x 205) = 0.17 N/mm²

From standard, we can calculate the shear capacity. This could be checked with relevant standards.

Vc = 0.42 N/mm²

Hence footing ok for punching shear and no shear links are required.