### Example: Pile cap design.

**Fig. 14.30**.

Pile caps can be designed either by the truss analogy or by bending theory (see BS 8110: Part 1: 3.11.4.1(5)). In this example bending theory will be used.

For a pile cap with closely spaced piles, in addition to bending and bond stress checks, a check should be made on the local shear stress at the face of the column, and a beam shear check for shear across the width of the pile cap. For more widely spaced piles (spacing > 3 × diameter), a punching shear check should also be carried out.

**Local shear check**

The ultimate column load is Pu = 6400 kN.

Length of column perimeter is u = 2(400 + 400) = 1600 mm.

The shear stress at the face of the column is

**Bending shear check**

In accordance with BS 8110: Part 1: 3.11.4.3, shear is checked

__across a section 20% of the diameter of the pile (i.e. D/5) inside the face of the pile. This is section A–A in__

**Fig. 14.30**.

The shear force across this section – ignoring the self-weight of the pile cap, which is small in comparison – is given by

The corresponding shear stress is given by vu = Vu/bvd, where bv is the breadth of section for reinforcement design.

In accordance with BS 8110: Part 1: 3.11.4.4, this must not exceed (2d/av)vc where av is deļ¬ned in

**Fig. 14.30**and vc is the design concrete shear stress from BS 8110: Part 1: Table 3.8. Thus

For grade C35 concrete, from BS 8110: Part 1: Table 3.8, assuming six T25 bars, the minimum value of vc is 0.4 N/mm2, giving

Thus, provided the average effective depth exceeds d = 846 mm (the local shear check), minimum reinforcement to satisfy bond and bending tension requirements will be adequate in this instance.

The necessary depth for the pile cap is

h = d + 25(diameter bar) + 75(cover)

= 846 + 100

= 946 mm ⇒use h = 950 mm

Fig. 14.30 Pile cap design example. |

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