Terzaghi (1943) developed a rational bearing capacity equation for strip footing, by assuming the bearing capacity failure of the foundation in general shear mode. Terzaghi's bearing equation is given by:
qu = CNc + γ1DfNq + 0.5Bγ2Nγ
Â
- qu= Ultimate Bearing Capacity of the soil
- C= Cohesion
- γ1,γ2= Unit weight of the soil above and below the footing levelÂ
- Nc,Nq,Nγ= Bearing capacity factors that are a function of friction angle
- Df= Depth of the foundation below the ground levelÂ
- B = Width or diameter of the footing
- L= length of the footing
Square, Rectangular, and Circular Strip Footings |
Bearing Capacity Equation for Square, Rectangular, and Circular Foundations - General Shear Failure
Terzaghi modified the above bearing capacity equation by introducing shape factors for different shapes of the foundation. Then forÂ
1. Square Foundations
qu = 1.3CNc + γDfNq + 0.4BγNγ
2. Circular Foundations
qu = 1.3CNc + γDfNq + 0.3BγNγ
3. Rectangular Foundations
Bearing Capacity Equation for Square, Rectangular, and Circular Foundations - Local Shear Failure
The values of Nc, Nq, and Nγ, also change to reduced values that are obtained from Terzaghi's bearing capacity factors for the general shear failure graph, where the bearing capacity factors corresponding to reduced Ф i.e, 0.67tanФ, must be determined.Â
Then the bearing capacity for:
1. Strip FoundationÂ
2. Square Foundation
3. Circular Foundation
4. Rectangular Foundation
When the soil is cohesionless, the cohesion factor c = 0; If c =0; the bearing capacity factor Nc = 0; Then the equations for qu can be modified accordingly.
If the soil is cohesive, then the angle of frictional resistance, Ф = 0; then the bearing capacity factors from the graph above, Nγ = 0; Nq= 1; and Nc = 5.7; Based on which the qu equation is determined.
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