Course · lesson 6 of 7

Pile caps: strut and tie

Where the ground is too weak for spread footings, piles carry the load down, and a pile cap joins the column to the piles. This lesson finds the pile loads, designs the cap as a truss of concrete struts and steel ties, and checks shear, punching and the layout with the STATIX pile cap calculator. The pile capacity is taken as given.

1. Learning outcomes

After this lesson you can:

share a column's load and moment between the piles of a rigid cap;
draw the strut-and-tie model of a 2-, 3- or 4-pile cap and find the tie force;
size and anchor the tie steel;
check beam shear with enhancement, punching at the column and at a corner pile, and the pile layout;
design a cap in the STATIX pile cap calculator.

2. Before you start

RC Design 1, lesson 7 (shear and punching) and lesson 2 of this course (load with moment).
The free pile cap calculator; the pile cap Learn page as background. The pile capacity comes from the pile designer or lesson 5.
About 55 minutes.

3. The cap and its piles

A pile cap gathers a column's load and shares it between a group of piles. The STATIX pile cap calculator offers preset caps of two to six piles (a line, a triangle, a square, a square with a centre pile, a 2 × 3 grid) and general layouts by grid or coordinates.

Pile loads. The cap is taken as rigid, so the piles share N equally and a moment adds to the piles on one side and takes from the other, in proportion to their distance from the centre. N includes the cap's own weight (factored at ULS). The SLS reactions are checked against the pile capacity.

rigid cap: R_i = N/n + M_x y_i/Σy² + M_y x_i/Σx² (N with the cap weight) SLS reactions ≤ R_all (the pile capacity); ULS reactions for the cap design

4. Strut and tie

The strut-and-tie (truss) model. Concrete struts run from under the column down to each pile, and the bottom steel ties the pile heads together. Taking moments about the strut's top gives the tie force. SANS 10100-1 4.10.4 allows a cap to be designed this way or by bending; the calculator uses the truss and cross-checks bending.

A four-pile cap in plan. Struts fan out from the column to the four piles; the ties run between the piles along both sides, as bands of bars over the piles. With N shared equally, each tie carries N s / 8d. A triangle and larger groups follow the same idea.

The tie steel. A_s = T / 0.87 f_y, placed in bands over the piles (or spread uniformly, as the calculator also allows), with at least the minimum steel across the whole cap. The bars must be anchored past the pile centre; there is seldom room for a straight length, so they are bobbed up at the ends. The calculator sizes the bend radius and the leg.

2 piles: T = R (s/2) / d (= N s / 4d for equal piles) 4 piles: T = N s / 8d in each tie; A_s = T / 0.87 f_y

5. Shear and punching

Shear across the cap. The critical section is taken a fifth of a pile diameter inside the pile face (SANS 10100-1 4.10.4.3); because the piles sit close to the column, the shear strength is enhanced by 2d/a_v, with a_v the distance from the column face. The calculator cuts both sides in both directions.

Punching. The shear at the column face must stay below the crushing limit v_max. A corner pile can punch up through the cap, checked on the part of a perimeter that lies inside the cap. A full perimeter round the column is checked only when piles lie outside it.

6. Layout and the rest of the cage

Layout. Piles are normally at least three diameters apart (so they work as separate piles), and the cap reaches at least about 150 mm past the face of each pile so the ties can be anchored and the edge does not split. The calculator flags both as advisory checks.

The rest of the cage. A nominal top mat (and a designed one when a pile is in tension or the cap hogs), side links round the cap, and the column starters. The calculator lists them and schedules the bars to SANS 282.

Which loads check what. The pile capacity R_all is a working value (from the pile designer, or lesson 5), so it is compared with the service reactions; the cap's concrete and steel use the ultimate ones. Give both N_ULS and N_SLS.

7. In STATIX

In STATIX: the column loads at ULS and SLS, the piles (number, diameter, spacing and capacity), and the cap (column size, depth, overhang). The calculator draws the truss, lists every check with its clause and schedules the bars.

On the SANS route the calculator follows SANS 10100-1 4.10: the truss for the ties, a bending cross-check, beam shear with enhancement and punching. It does not check strut and node stresses separately; the crushing limit at the column face covers the column end.