Pile Cap Analysis

The axial and shear loads on each pile under the pile cap are calculated base d on the method described below with the following assumptions:

All piles are vertical.
Load from the supported column (and braces if applicable) is applied at centroid of pile cap.
The pile cap is thick enough to be considered rigid. Due to the shear requirements and minimum pile cap thicknesses used in the program this assumption is valid in the majority of cases.
Note: It is the engineer’s responsibility to confirm that this analysis assumption is valid for the final footing thickness.
Piles are assumed to resist both tension and compression axial loads.
Piles will be analyzed as if they can take tension loads larger than their maximum tension capacity.

Note: In all cases of shear and flexural design the pile cap self-weight and surcharge are removed from the pile reaction when calculating the moment and shear on the critical sections.

The calculated forces on each pile are based on its distance from the pile cap centroid as shown below.

\begin{matrix} P_{p \max} = \frac{P}{N} + \frac{M_{\min} x_{p}}{Σ x_{p}^{2}} + \frac{M_{maj} y_{p}}{Σ y_{p}^{2}} \\ P_{p \min} = \frac{P}{N} - \frac{M_{\min} x_{p}}{Σ x_{p}^{2}} - \frac{M_{maj} y_{p}}{Σ y_{p}^{2}} \end{matrix}

Equation 4-20

where

V_p

\sqrt{V_{maj}^{2} + V_{min}^{2}}

Equation 4-21

\begin{matrix} V_{p maj} = \frac{V_{maj}}{R} + \frac{T \sqrt{x_{p}^{2} + y_{p}^{2}}}{Σ x_{p}^{2} + Σ y_{p}^{2}} \sin (α) \\ V_{p min} = \frac{V_{min}}{R} + \frac{T \sqrt{x_{p}^{2} + y_{p}^{2}}}{Σ x_{p}^{2} + Σ y_{p}^{2}} \cos (α) \end{matrix}

Equation 4-22

where

P_p	=	Force on a single pile
P	=	Column axial load, pile cap self-weight, and surcharge
M_maj, M_min	=	Total moment on pile cap due to column moment and shear in major and minor direction, respectively
x_p, y_p	=	distance from each pile center to pile cap center parallel to major and minor direction, respectively.
α	=	angle between column center and pile center, calculated clockwise with an angle of zero being parallel to the local minor axis.
V_p, V_pmaj, V_pmin	=	Total shear in pile, pile shear in major direction and pile shear in minor direction, respectively.

If the total lateral force applied to the pile cap is larger than pile shear capacity, a warning message is given, indicating the total shear that will need to be transferred out of the pile cap through other means. For example, the additional shear can be resisted through a slab on grade or by soil bearing on the side of the pile cap.

Pile Capacity Check

For the pile capacity check the soil load combinations are used and the factored self-weight and surcharge on the pile are considered.

Concrete Capacity Check

For the concrete capacity check (flexure, beam shear and 2-way shear) the concrete load combinations are used without the factored self-weight and surcharge on the pile. When the option to design the pile cap based on the pile capacity is selected, the factored self-weight and surcharge are subtracted from the pile force to calculate the actual available pile capacity.

Note: When calculating the pile forces contributing to a critical area (for punching shear, beam shear and flexure) the pile is considered to contribute only when its center is inside the critical area.