Flexural Design

Beam Theory

When a pile cap on top of a group of 5 or more piles is designed, beam theory is used to calculate the flexural moment and required reinforcement. The design of the flexural reinforcement used to resist the moments in the pile cap is outlined in Section 5.12.3. The pile axial forces replace the soil stress when calculating the force inducing the moment at the column face. The centroid of the force is calculated based on the effective centroid of the pile axial loads. The moment is taken as the distance from the pile force centroid to the column face + the maximum construction tolerance. This helps account for construction tolerances in the location of the piles or the column.

Top reinforcement is only provided if at least one pile is in tension.

Note:

Reinforcement is considered hooked and therefore development length is not considered.
3.11.3.2 of BS 8110: Part 1: 1997 - Distribution of Reinforcement is not implemented for pile caps.

Truss Theory

In the case of pile caps on 3, 4 and 5 pile groups it has been found that the pile cap behaves more like a truss than a beam. This truss behavior produces a tension force at the bottom of the pile cap that must be resisted by the reinforcement. Using the equations outlined in By A.H. Allen:

Piles in Group	Tension force across pile cap with column size taken into account
3	$T_{maj} = 2 \frac{P_{u}}{18 l d} (2 l^{2} - b^{2})$ $T_{min} = \frac{P_{u}}{36 l d} (4 l^{2} + b^{2} - 3 a^{2})$
4	$T_{maj} = 2 \frac{P_{u}}{24 l d} (3 l^{2} - b^{2})$ $T_{min} = 2 \frac{P_{u}}{24 l d} (3 l^{2} - a^{2})$
5	$T_{maj} = 2 \frac{P_{u}}{30 l d} (3 l^{2} - b^{2})$ $T_{min} = 2 \frac{P_{u}}{30 l d} (3 l^{2} - a^{2})$

The required tension reinforcement is calculated as $A_{s} = \frac{T}{0.95 f_{y}}$

In the case where there is moment and shear in addition to the column axial load, the value for P_u is calculated as the largest axial load in a pile multiplied by the total number of piles under the pile cap.

Bar spacing for the truss method are similar to flexural reinforcement as outlined in the Technical Notes section 5.5.4.

Note: Reinforcement is considered hooked and therefore development length is not considered.

Side Reinforcement

Side reinforcement is provided as 25% of the main tension reinforcement area based on the larger area of the bottom length and width directions during the optimization process. However, the provided side reinforcement is not checked during the design check because guidelines for side reinforcement are not provided in BS8110. Rather, the guidelines are adopted from page 191 of Reinforced Concrete Design to BS 8110 Simply Explained by A.H. Allen.