Ground beam design

The beam between the pads · one worked example

In a framed building the load arrives at the ground in a handful of isolated pad footings. The walls between those columns have nothing underneath them. The ground beam is what they sit on.

It is the member most often built without being designed, because everybody knows the answer is 225 × 450 with four T16. This page works out why that is right, which is the part that tells you when it stops being right.

What it is for — three separate jobs

  1. It carries the ground floor blockwork. Walls laid on filled ground crack, because fill settles and blockwork does not bend. The beam takes the wall to the footings.
  2. It ties the footings together. Pads under different loads settle by different amounts. Joined by beams, the substructure settles more nearly as one thing, and the differential the frame above has to absorb is smaller.
  3. It is part of the tie system. BS 8110's robustness requirements ask for horizontal ties at each floor level, and the ground beams are the ones at the bottom. That is a regulatory requirement in its own right, not a by-product of the bending calculation.

It is not a foundation. A ground beam is supported by the footings at its ends; a strip footing is supported by the soil along its whole length. They look similar in a trench and are designed for opposite things. Casting a beam on fill and calling the fill a support is how a ground beam ends up spanning further than its steel was sized for.

The example

A framed two-storey house. Ground beams span 4.0 m between column bases, and carry a 225 mm rendered blockwork wall 3.0 m to the first floor. Section 225 × 450, fcu 25, fy 460, T8 links, T16 main bars. Ground floor slab is cast on compacted fill and does not bear on the beam.

Step 1 — Load

Wall 225 rendered blockwork, 3.9 kN/m2 x 3.0 m = 11.70 kN/m
Self weight 0.225 x 0.450 x 24 = 2.43 kN/m
Gk = 14.13 kN/m
Qk = 0 the slab is on fill; nothing imposed reaches this beam

w = 1.4 Gk + 1.6 Qk = 1.4 x 14.13 = 19.8 kN/m

Qk = 0 is the whole character of this member. A ground beam carrying only walls has no imposed load at all, so 1.4Gk is the entire ultimate load, and the design is dominated by something that does not vary. It is also what makes Table 3.5 available — that table needs Qk ≤ Gk, and zero satisfies it with room to spare.

If the ground floor slab is suspended, stop and start again

A suspended ground floor — over a void, over a basement, or because the fill is too deep to trust — puts slab dead load and 1.5 to 2.0 kN/m² of imposed load onto this beam as well. That can triple w. Everything below changes, and the 225 × 450 stops being the automatic answer.

Step 2 — Moments, treating it as continuous

Ground beams run through the column stubs from one end of the building to the other. They are continuous, and continuity puts hogging moment over the columns — tension in the top face, where a simply supported design has no steel at all.

F = wL = 19.8 x 4.0 = 79.2 kN total ultimate load on one span

Mid, end span 0.09 FL = 0.09 x 79.2 x 4.0 = 28.5 kNm sagging
1st int. support 0.11 FL = 0.11 x 79.2 x 4.0 = 34.8 kNm hogging
Shear there 0.60 F = 0.60 x 79.2 = 47.5 kN

Design a continuous ground beam as simply supported and you get no top steel. The beam then cracks over every column, in the top face, where it is buried in the ground and nobody will ever see it. The crack does not fail the building; it opens a path straight to the steel in the wettest part of the structure.

Step 3 — Cover, and the effective depth it leaves

This member is in the ground. Cover is not the 25 mm of a first floor beam — see cover, grades and mixes:

d = h - cover - link - bar/2
= 450 - 50 - 8 - 8 = 384 mm

At 75 mm cover it would be 359 mm, and every steel area below rises about 7%. Cover is not a detail on this member; it is an input.

Step 4 — Steel

Top, over the column

K = M / (b d² fcu) = 34.8 x 10&sup6; / (225 x 384² x 25) = 0.042
K <= K' = 0.156 PASS — singly reinforced

z = d[0.5 + sqrt(0.25 - K/0.9)] = 365 mm, capped at 0.95d = 364.8 mm

As = M / (0.87 fy z) = 34.8 x 10&sup6; / (0.87 x 460 x 364.8) = 238 mm²

Bottom, at mid-span

K = 28.5 x 10&sup6; / 829.4 x 10&sup6; = 0.034
z = 0.95d = 364.8 mm the cap governs again
As = 28.5 x 10&sup6; / (0.87 x 460 x 364.8) = 195 mm²

As,min = 0.13% bh = 0.0013 x 225 x 450 = 132 mm²

Provide 2T16 top and 2T16 bottom = 402 mm² each face

2T12 (226 mm²) satisfies both numbers on paper. Ground beams are detailed with equal top and bottom steel carried right through anyway, and it is worth knowing why rather than copying it:

Step 5 — Shear

v = V / (b d) = 47.5 x 10³ / (225 x 384) = 0.550 N/mm²

100As/bd = 100 x 402 / 86 400 = 0.465
vc = (0.79/1.25)(0.465)1/3(400/384)1/4 = 0.495 N/mm²

v > vc links needed
v < vc + 0.4 = 0.895 minimum links govern

Asv/sv = 0.4b / (0.87 fyv) = 0.4 x 225 / (0.87 x 250) = 0.414
sv = 100.5 / 0.414 = 243 mm (max 0.75d = 288 mm)
Provide T8 links @ 225 c/c

Step 6 — Deflection, for form's sake

span/d = 4000 / 384 = 10.4
fs = (2/3)(460)(195/402) = 149 N/mm²
M/bd² = 0.86
MF = 0.55 + (477 - 149)/[120(0.9 + 0.86)] = 2.10, capped at 2.0
allowable = 26 x 2.0 = 52

10.4 <= 52  PASS, by a factor of five

Which is the honest summary of this member: nothing in the structural calculation is close. What sizes a ground beam is geometry and durability — the depth needed to get below the oversite and sit on the pad, the width of the wall it carries, and the cover the ground demands.

The answer

ItemProvided
Section225 × 450 mm
Top steel2T16, continuous through the columns
Bottom steel2T16, continuous
LinksT8 @ 225 c/c
Cover50 mm on blinding, 75 mm against earth

The reaction has to go somewhere

Every ground beam delivers its load into the column bases at its ends, and that load lands on the footing underneath.

At an interior column 0.60F + 0.55F = 1.15 x 79.2 = 91 kN ultimate

Ninety-one kilonewtons is not a rounding error on a small building — on the three-storey column in the load takedown it is about a sixth of the column load again. It is also the load most commonly left out, because the ground beams are drawn after the foundations have been sized.

Size the footings after the ground beams are known, or allow for them and check. A load takedown that stops at the column base and never adds the substructure is an under-estimate of the one number the foundation depends on.

Detailing, and the three things that go wrong

Run the ground beam, and the column it lands on

Structura designs beams to BS 8110 — flexure, shear links and deflection, with the calc sheet, the bar bending schedule and a dimensioned detail sheet — and checks Table 3.5's own validity before using its coefficients. Beams are free to run, as many as you like. The whole-building load takedown, which carries every reaction down to the foundation for you, is the paid part.

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