Pile cap — preliminary sizing

What this page computes

The page preliminarily sizes a pile cap, in two stages:

1. the distribution of the column load over the pile group, assuming a rigid cap;
2. the reinforcement from a strut-and-tie model (EN 1992-1-1 §6.5).

Distribution: rigid cap

The assumption is that the cap is far stiffer than the piles, so it moves as a rigid body — it stays plane. From this follows the linear distribution:

\(N_i = \frac{N}{n} \pm \frac{M_x \, y_i}{\sum y^2} \pm \frac{M_y \, x_i}{\sum x^2}\)

One detail that matters for irregular groups: the second moments are taken about the centroid of the pile group, not about the geometric centre of the cap. If the group is asymmetric — a pile moved to avoid a service, say — the two do not coincide, and computing about the wrong centre gives wrong lever arms for every pile. The page detects this and flags it.

Piles in tension are not capped at zero

Under a large moment the formula gives negative reactions. I chose not to silently cap them.

A pile in tension is perfectly possible — a bored pile reinforced over its full length can take it. But it means three distinct things:

• continuity reinforcement over the whole pile length, not just at the head;
• anchorage into the cap, designed for the tensile force;
• uplift capacity, which is an entirely different calculation from compression — the base does not work, and shaft friction has a different value in tension.

If the result were capped at zero, none of this would be visible. The page shows the negative value and adds a note.

Reinforcement: why strut-and-tie

A pile cap is usually a short member: the distance from the column face to the pile is comparable with the depth of the cap. The plane-sections assumption — on which all bending design rests — no longer holds. Strain no longer varies linearly over the depth, and classical moment design underestimates the required reinforcement.

The transition criterion is:

\(a_v \le 2d\)

where a_v is the distance from the column face to the pile centre. Below it the member is "deep" and the strut-and-tie model applies; above it, design returns to bending. The page checks the criterion and reports it explicitly — if the cap comes out slender, the model applied is no longer the right one and the values shown remain indicative.

The node convention is worth ~10%

The compression strut starts at the point where the load is applied and runs down to the pile centre. Exactly where it starts is a convention, not a certainty:

• at the quarter point of the column side towards the pile — used here, usual for a uniformly compressed column;
• at the centre of the column — more conservative, since it gives a longer lever;
• at the face of the column — the least conservative.

The choice changes the tie force by about 10%. It is stated explicitly in a note, so you know what you compared against if you recalculate from another source.

The tie force follows from node equilibrium:

\(T = \sum N_i \cdot \frac{a_i}{d}\)

where a_i is the horizontal lever from the application point to the pile centre, and d the vertical lever. Only compressed piles contribute: one in tension does not compress the strut, so it produces no tie in its direction. Otherwise the reinforcement would be overestimated through a mechanism that does not exist.

Pile spacing

The usual spacing is 2.5…3 diameters. Below it, the stress bulbs of the piles overlap and the group capacity falls below the sum of the individual capacities — the group effect. Above it, the cap becomes large and expensive, and a_v grows, pushing the member towards the slender range where strut-and-tie no longer applies.

What it does not cover

• Punching around the column and around each pile. It rarely governs for thick caps, but the control perimeters of a pile cap have their own rules (§6.4.4), different from an ordinary slab.
• Design of the piles themselves — the bearing capacity of each. The single-pile page covers that, with the caveat that it does not treat group effects.
• Anchorage of the reinforcement into the cap, which for a deep member is precisely where the strut-and-tie model becomes real or does not: the tie must be anchored beyond the node above the pile.
• Node verification to §6.5.4 — strut stress against the compression-tension node limit. The exact geometry depends on the bearing width.
• Suspension reinforcement and side-face reinforcement.

The rigid distribution is classical mechanics, verifiable by equilibrium — and the page does check internally that the reactions sum to N_Ed. The strut-and-tie model follows §6.5, but with a node convention chosen by us. The result is a starting point, not a complete design.