What is the formula for determining the eccentricity "e" in footing design when given a moment and axial load?

In footing design, eccentricity "e" is a key factor in determining how forces are transmitted through the foundation to the ground. The correct formula for calculating eccentricity is derived from the relationship between the bending moment (Mu) caused by an external load and the axial load (Pu) acting on the footing.

The formula expressed as Mu/Pu shows how the moment causes a resultant force to act off the centroid of the footing, leading to an eccentric load condition. Essentially, the greater the moment (Mu) relative to the axial load (Pu), the larger the eccentricity will be, indicating that the load is not evenly distributed through the center of the footing. This relationship is crucial in assessing stability and designing footings that can accommodate both axial and lateral forces without failure.

Other options do not represent this relationship correctly: P/Mu contravenes the principle of moment distribution; Mu + Pu and Mu - Pu do not provide a clear representation of how moments cause eccentric forces relative to axial loads, failing to account for the moment-arm effect that results in bending of the footing.