Part 1: Calculation of bearing pressures for checking against allowable bearing pressures
(1) Determine the relevant load cases to be considered using engineering judgement and guidance from the limit-state code appropriate to the foundation material.
The load factors to be used can be taken from Table 10.4 which can be of further help in assessing critical load cases.
For each of the load cases the following procedures should be adopted.
(2) Calculate the superstructure characteristic (unfactored) load in terms of
If the base is subject to biaxial bending calculate H and M about both x and y axes to give Hx and Mx and Hy and My.
(3) Estimate the foundation size using the middle third rule where applicable, and calculate the foundation load
F = FG + FQ
where FG = dead load from foundation
FQ = imposed load from foundation.
(4) Calculate the total vertical load at the underside of the foundation
T = P + F
(5) Calculate the eccentricity of the total load
Consider if economy could be gained by offsetting the base to cancel out or reduce this eccentricity, and recalculate as necessary.
(6) Assess which bearing pressure distribution is appropriate and calculate the total bearing pressure, t, in accordance previously and Figs 10.21–10.23.
(a) Axial loading: i.e. uniform pressure eT ~ 0
(c) Axial plus bending with zero pressure under part of the base:
(i) For single axis bending, use the shortened base theory to establish the pressure diagram under the base such that the resultant is under the line of the total load T. From this calculate the maximum total bearing pressure. For a rectangular base, this becomes
(ii) For biaxial bending, it is recommended that this situation should not be allowed to develop.
Consider increasing the size of base or adjust itsposition relative to the column, to reduce eTx and/or eTy as appropriate.
(7) Check t against the total allowable bearing pressure, ta (note: the total allowable bearing pressure can be increased by 25% when resisting wind loads), or calculate the net bearing pressure from
n = t − s
where s is the existing soil pressure.
(8) If the base is of plain concrete, calculate the minimum depth where hmin = maximum distance from edge of column to edge of base (see Fig. 10.19).
(9) If the base is of reinforced concrete proceed to Part 2 below.
Fig. 10.21 Design of axially loaded foundation.
Fig. 10.22 Design of foundation in bending – base fully in compression.
Fig. 10.23 Design of foundation in bending – zero pressure under part of base.
Part 2: Calculation of bearing pressures for design of reinforced concrete or steel foundation elements
Before progressing with the design of the reinforced concrete elements of the foundation the engineer must make an assessment as to whether it is necessary to make a full reanalysis of the bearing pressures in the manner described above but using factored loads, or whether sufﬁcient accuracy can be achieved by taking the short cut of multiplying the bearing pressures by an overall factor γP, γF or γT as appropriate. In the vast majority of cases the short cut method is perfectly satisfactory but there are cases when it is not and the engineer must be careful! If in doubt he should use the full method. Typical cases where the short cut method does not apply include the following:
(1) Where wind loading forms a signiﬁcant part of the foundation loading particularly where generating uplift.
(2) Where a live load applied to the structure will increase the horizontal load, H, and/or moment, M, without a proportional increase in the vertical load, P.
(3) Where there is partial zero pressure under the foundation (T is outside the middle third rule for rectangular foundations).
(1) Determine the ultimate total pressure distribution, tu, under the base from
where γT = combined total load factor assessed with the aid of Fig. 10.20
t = unfactored total stress distribution from
(2) Determine the ultimate foundation pressure distribution, fu, under the base from
fu =γF f
where γF = combined foundation load factor assessed with the aid of Fig. 10.20 (usually 1.4 unless there is an imposed load element or uplift is being considered).
(3) Determine the resultant ultimate design pressure causing bending, pu, from
pu = tu − fu
(see Figs 10.21–10.23).
Note that in the case of axially loaded foundations this calculation can be reduced further by calculating pu directly from the superstructure pressure
where γP = combined superstructure load factor assessed with the aid of Fig. 10.20
p = bearing pressure due to the superstructure.
(see Figs 10.21 and 10.22).
(4) Having determined the resultant ultimate design pressure, pu, this is used to determine the ultimate shear,
bending moments and axial forces using accepted structural theory and to design those elements in accor- dance with the appropriate British Standards.
(1) Calculate the ultimate superstructure loading in terms of
(2) Calculate the ultimate foundation loading in terms of:
Fu =γGFG +γQFQ
(3) Calculate the total ultimate load
Tu = Pu + Fu
(4) Calculate the total ultimate load eccentricity
(5) Calculate the ultimate bearing pressure distribution using the procedure in section 10.10 but with ultimate loads:
(a) Axial loading: i.e. uniform pressure eTu ~ 0
(b) Axial plus bending with base pressure wholly compressive:
(c) Axial plus bending with zero pressure under part of the base, i.e. eTu > L/6:
pu = tu − fu
where fu is the factored pressure due to the foundation construction and backﬁll deﬁned by
(7) Having determined the resultant ultimate design pressure, pu, this is used to determine the ultimate shear,
bending moments and axial forces using accepted structural theory and to design those elements in accord-
ance with the appropriate British Standards.
Foundation design complete.
Figures 10.21–10.23 show the various stress distributions graphically and clearly show the difference between working and ultimate loads and stresses, and the resultant ultimate pressure for foundation element design using both the full and the short cut methods.