Calculation of Stresses in Footings Subjected to Uniaxial or Biaxial Moments

When designing footings subjected to uniaxial or biaxial moments, the following steps can be followed:

Determine Applied Loads and Moments:

Identify the applied loads and moments acting on the footing, considering the superstructure configuration and loads from the structure above.
Determine the uniaxial or biaxial moments based on the magnitude and location of the loads.
Footing Geometry:

Determine the dimensions and shape of the footing, such as length (L) and width (B).
Calculate the centroid location (x-bar, y-bar) of the footing.
Design Approach:

Decide on the design approach based on the loading condition and available design methods (e.g., ultimate limit state, serviceability limit state).
Determine whether to use a bearing pressure approach or a structural analysis approach.
Bearing Pressure Design:

For uniaxial moments, calculate the maximum moment (M) and its eccentricity (e) relative to the footing centroid.
Determine the maximum soil pressure (qmax) at the footing base using the footing width (B) and length (L).
Distribute the soil pressure based on the eccentricity, resulting in a triangular pressure distribution under the footing.
Check the bearing capacity of the soil, ensuring it is not exceeded under the applied loads.
Structural Analysis Design:

For biaxial moments, perform a structural analysis of the footing to determine the bending moments and shear forces in both directions.
Calculate the bending stresses at critical sections of the footing using the moment distribution along the width and length of the footing.
Determine the maximum tensile and compressive stresses and compare them to the allowable limits.
Check the shear stresses and ensure they are within the allowable limits.
Reinforcement Design:

If required, design the reinforcement for the footing to resist the bending moments and shear forces.
Calculate the required area of reinforcement based on the maximum bending and shear stresses.
Determine the reinforcement layout and spacing to provide sufficient strength and ductility.
Check Stability and Settlement:

Verify the stability of the footing against overturning, sliding, and bearing capacity failure.
Perform settlement calculations to ensure that the footing settlements are within acceptable limits.
Construction Considerations:

Consider construction methods, such as formwork, reinforcement placement, and concrete pouring sequences.
Ensure proper compaction and curing of the concrete for structural integrity.