Terzaghi (1943) developed a rational bearing capacity equation for strip footing, by assuming the bearing capacity failure of the foundation inÂ general shear mode.Â Terzaghi's bearing equation isÂ given by:

q_{u}Â = CN_{c}Â + Î³_{1}D_{f}N_{q}Â + 0.5BÎ³_{2}N_{Î³}

Â

- q
_{u}= Ultimate Bearing Capacity of the soil - C= Cohesion
- Î³
_{1},Î³_{2}= Unit weight of the soil above and below the footing levelÂ - N
_{c},N_{q},N_{Î³}= 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

q_{u}Â = 1.3CN_{c}Â + Î³D_{f}N_{q}Â + 0.4BÎ³N_{Î³}

#### 2. Circular Foundations

q_{u}Â = 1.3CN_{c}Â + Î³D_{f}N_{q}Â + 0.3BÎ³N_{Î³}

#### 3. Rectangular Foundations

_{}

### Bearing Capacity Equation for Square, Rectangular, and Circular Foundations - Local Shear Failure

The values ofÂ

**N**,Â_{c}**N**, andÂ_{q}**N**_{Î³}, also change to reduced values that are obtained fromÂ Terzaghi's bearing capacity factors for the general shear failure graph, where the bearing capacity factors corresponding to reducedÂ Ð¤ i.e,Â 0.67tanÐ¤, must be determined.ÂThen 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, Ð¤ = 0; then the bearing capacity factors from the graph above, NÎ³ = 0; Nq= 1; and Nc = 5.7; Based on which the qu equation is determined.