# Bearing Capacity Equations for Square, Rectangular and Circular Strip Footings

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:

quÂ = CNcÂ + Î³1DfNqÂ + 0.5BÎ³2NÎ³

Â

• qu= Ultimate Bearing Capacity of the soil
• C= Cohesion
• Î³1,Î³2= Unit weight of the soil above and below the footing levelÂ
• Nc,Nq,NÎ³= 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

### 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

quÂ = 1.3CNcÂ + Î³DfNqÂ + 0.4BÎ³NÎ³

#### 2. Circular Foundations

quÂ = 1.3CNcÂ + Î³DfNqÂ + 0.3BÎ³NÎ³

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

The above equations were derived from the assumptions of general shear failure. When local shear failure comes into play, the shear parameters in the equations i.e. the c and Ñ„ are reduced to a lower limit. Hen e, here instead of c we use Äˆ = 0.67c; and instead of Ð¤, we use á‰” = 0.67tan
Ð¤;Â

The values ofÂ Nc,Â Nq, andÂ NÎ³, 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.Â

Then the bearing capacity for:

### Ultimate Bearing Capacity for Cohesionless and Cohesive Soils

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.