Introduction

Pad foundations are one of the simplest and most straightforward type of foundations that is used to distribute the load from a structural column to the supporting soil. They are generally designed for columns that are centrally or eccentrically loaded. This type of foundation is designed to transfer the column loads to the soil below and must ensure that the soil pressure does not exceed the bearing capacity of the soil. The goal is to ensure that the foundation is both structurally adequate and cost-effective, meeting the safety and serviceability requirements specified in the Eurocode 2.

Principle of Pad Foundation Design

Pad foundations are designed to ensure that the applied load is spread evenly across the soil. To prevent excessive settlement or failure, the foundation must be stiff enough so that the pressure applied to the soil does not exceed its permissible bearing capacity. For single-column supports, a square pad is generally the most efficient solution. However, if a significant bending moment acts in one direction, a rectangular footing is preferred, with the longer dimension aligned with the direction of the moment.

Bearing Pressure Distribution

The bearing pressure distribution under a pad foundation depends on the applied load:

• Axial Load Only: The pressure distribution is uniform, calculated as \( p = \frac{N}{B \times D} \), where \( N \) is the axial load, \( B \) is the width, and \( D \) is the length.
• Axial Load with Bending Moment: The bearing pressure is non-uniform, with the formula \( p = \frac{N}{B \times D} \pm \frac{6Ne}{B \times D^2} \), where \( e = \frac{M}{N} \) is the eccentricity.
• Moments in Both Directions: The bearing pressure formula becomes more complex: \[ p = \frac{N}{B \times D} \pm \frac{6N e_y}{B \times D^2} \pm \frac{6N e_x}{B^2 \times D} \] where \( e_x \) and \( e_y \) are the eccentricities in the \( x \) and \( y \) directions.

Shear Design and Punching Shear Checks

Punching shear must be checked at the column face and the basic control perimeter (2d from the column face). The design axial load, \( N_{ED} \), should not exceed the punching shear resistance, \( V_{RD,max} \), calculated as:

\[ V_{RD,max} = 0.2 \left[1 - \frac{f_{ck}}{250}\right] f_{ck} p d \] where \( f_{ck} \) is the characteristic concrete strength, \( p \) is the column perimeter, and \( d \) is the effective depth.

A secondary check for punching shear is performed at a perimeter \( 2d \) away from the column face. The applied shear stress \( v_{ED} \) must be less than the concrete’s shear resistance \( v_{RD,c} \).

Flexural Design

The pad foundation is treated like an inverted slab, subjected to soil pressure. The design moment at the column face is calculated as \( M_{ED} = \frac{p l^2}{2} \), where \( p \) is the soil pressure, and \( l \) is the distance from the column face to the pad’s edge.

The required reinforcement area is determined using \( A_s = \frac{M_{ED}}{0.87 f_{yk} z} \), where \( f_{yk} \) is the yield strength of the reinforcement, and \( z \) is the lever arm (typically \( 0.95d \)).