# Pile Caps – Structural Design Overview

February 18, 2020

ASDIP FOUNDATION is a structural engineering software for footing design. It includes the design of concrete pile caps based on the latest ACI 318 provisions and CRSI Design Guide. This article provides an engineering background of the design of pile caps when subject to a combination of vertical and horizontal loads, and biaxial bending.

Pile caps are structural elements designed to transfer the loads from the structure to the pile foundation. They are almost invariably made of reinforced concrete, and designed to resist all the applied loads above the cap, including the self-weight and the soil on top. The pile cap is considered a perfectly rigid structure that transfers these loads to the supporting piles. The piles are considered pinned at the top, since a true fixed connection is very difficult to achieve at the field. The soil under the pile cap is not assumed to offer any support.

The images below show the general case of a rectangular pile cap with an offset column subject to a vertical load, two horizontal loads, and two bending moments around the orthogonal axes.

## What is the typical layout of a pile group?

Wherever the conditions permit, the piles should be arranged in the most compact geometric form in order to keep the stresses in the pile cap to the minimum. The minimum pile spacing is the largest of 2-ft + dp, 3-ft, and 3 * dp, where dp is the pile diameter, otherwise the capacity of the piles would be affected by adverse group effects. The minimum edge distance varies from 15" for 60-Ton piles to 36" for >280-Ton piles.

The pile group configuration plays an important role in the calculation of the pile reactions. Since the pile cap is assumed perfectly rigid and all piles have the same area, the pile reactions can be calculated based on the moment of inertia of the pile group as follows, where Xi and Zi are the coordinates of a pile from the C.G. of the pile group:

For a simple pile cap with a vertical concentric compression load, the resulting pile reactions are of the same magnitude for all piles. If the column is subject to biaxial moments, then these moments will be transferred to the foundation as well. Additional moments are produced if the column is placed eccentrically on the pile cap, or due to the horizontal loads applied at the top of a pedestal. As a result, the axial forces on the piles will vary accordingly as shown in the expression above.

The image below shows typical layouts of pile groups, which have given good results in actual structures, as recommended by the CRSI.

## What are the design provisions for shear in pile caps?

A number of limit states must be checked for shear, including both traditional and special investigations. The following checks apply to the column:

1. Punching shear at d/2 from the column face - Traditional punching shear check in ACI 318.
2. One-way shear at d from the column face - Traditional one-way shear check in ACI 318 in X and Z directions, at each side of the column.
3. Punching shear at the column face - Special investigation applicable when at least one pile is located at less than d/2 from the column face. A larger value of φVc is used for this check, as derived in the CRSI Design Guide.
4. One-way shear at the column face - Special investigation applicable when at least one pile is located at less than d from the column face in X and Z directions, at each side of the column. A larger value of φVc is used for this check, as derived in the CRSI Design Guide.

The following shear limit states adjacent to individual piles must also be checked:

1. Punching shear at d/2 from the pile face - Traditional punching shear check in ACI 318.
2. Punching shear at d/2 from face of a pair of piles - Traditional punching shear check in ACI 318 applicable to a pair of closely spaced piles.
3. Punching shear at d/2 from a corner pile face - Traditional punching shear check in ACI 318 applied to a corner pile, where a shorter overall failure length may be obtained by extending the line to the edges of the pile cap.
4. One-way shear at d < 13" from the corner pile face - Traditional one-way shear check at a corner pile, measured diagonally.

Piles may be driven accidentally offset during the driving operations. To account for this, an accidental offset of at least 3" should be considered in the calculations. This is important when a pile is close to the limits where the special investigations apply, and it may determine if a pile is included or excluded in the investigation.

Shear limit states at column

Shear limit states at piles

## How do you calculate the moments in pile caps?

The compression piles will try to push the pile cap up, creating a moment at the effective section located at the column face. The total positive bending moment is equal to the sum of the pile reaction times its distance to the column face. Note that the accidental pile offset should also be considered in the bending moment calculations.

Once the moments are calculated, the rebars are designed per the ACI Ultimate Strength Design theory. Most pile caps will need steel reinforcement for bending at the bottom only. However, since pile caps are usually very thick, top steel may be required to comply with the minimum shrinkage and temperature reinforcement.

The images below show the bending moments about X and Z at the column face, as generated by ASDIP FOUNDATION. Note that only the piles inside the blue shaded area are included in the calculation.

## Takeaway

The design of pile caps subject to vertical and horizontal loads, and biaxial bending may be cumbersome and time-consuming, particularly for heavy loading conditions. The calculation of pile axial forces, pile cap shears and moments, and reinforcement design implies the check of multiple limit states. ASDIP FOUNDATION includes the design of pile caps, with multiple options to optimize the design easily.

For our collection of blog posts about foundation design please visit Structural Footing Design.