Design Example 5: Pad base – axial load plus bending moment (small eccentricity).

A column pad base is subject to an axial load of 200 kN (dead) plus 300 kN (imposed), and a bending moment of  40 kNm. To suit site constraints, the base is limited to a length of L = 1.8 m.

Load eccentricity
When moments act on a foundation, it is normal to replace them by positioning the vertical load at an equivalent eccentricity. The resultant vertical superstructure load is

P = G + Q
   = 200 + 300
   = 500 kN

Q as a percentage of P is 100Q/P = (100 × 300)/500 = 60%.
From  "Fig. 11.22 Combined partial safety factor for dead + imposed loads",  the combined partial factor for superstructure loads is γP = 1.52.
The resultant eccentricity is given by

Bearing pressure check – design chart approach
A suitable base size can be checked or calculated using design chart H.1 in Appendix H. For the purpose of this example this is reproduced in Fig. 11.26 below. Assuming a superstructure bearing pressure of p = na = 300 kN/m2,

Assuming a base length of L = 1.8 m,

From Fig. 11.26, this gives a required base area of

A = BL = 2.1 m2

Thus

A width of B = 1.2 m will be adopted.

Bearing pressure check – calculation approach
The eccentricity eP = 0.08 m is less than L/6 = 1.8/6 = 0.3 m, and thus the formation is loaded in compression over the full plan area of the base. Assume a width of B = 1.2 m.

Thus pmax = 293 kN/m2 and pmin = 169 kN/m2. These are less than the allowable bearing pressure of na = 300 kN/m2 ; the width of B = 1.2 m is therefore satisfactory.

Resultant ultimate design pressures
Since the base is fully in compression, ultimate design pressures, pu, are obtained by simply factoring up these pressures using the combined partial safety factor γP.

This is shown in Fig. 11.27.

Effect of offsetting the base
Where the moment always acts in one direction, economies in the base size can be achieved by positioning the base eccentric to the vertical load. Thus if the centroid of the base is offset by eP = 0.08 m, the pressure becomes uniform, and is simply given by p = P/A. This would give

Compared to A = 1.8 × 1.2 = 2.16 m2, this would be a reduction of 23%. This approach is used in Design Example 8.

Fig. 11.26 Pad base (small eccentricity) design example – design chart H1 (Appendix H) for base size.

Fig. 11.27 Pad base (small eccentricity) design example
– loads and bearing pressures.

Pad Foundations with axial Loads and Bending Moments.

There are various ways of dealing with pad foundations which are subject to both axial loads and bending moments (and sometimes horizontal loads as well). The following design examples will explore the various merits of the  differing approaches to the design solutions. The designer should keep in mind at all times the various loading combinations which can apply to any one base. It is not always apparent which is the critical load case, and the base design often develops on an iterative basis.

In each of the following design examples the net allowable bearing pressure of the soil will be taken as  na = 300 kN/m2.

These examples concentrate on the analysis of foundation bases to limit bearing pressures arising from combinations of vertical loads, horizontal loads, and bending moments.

The design of these bases, to resist bending and shear, should be carried out in a similar manner to Design
Examples earlier in this blog. Calculations for bending moments and shear forces within the base will need to make due allowance for the variation in bearing stresses across the base.

Pad base –axial load plus bending moment (small eccentricity)   A column pad base is subject to an axial load of 200 kN (dead) plus 300 kN (imposed), and a bending moment of  40 kNm. To suit site constraints, the base is limited to a length of L = 1.8...

Design Example: Reinforced Pad Base.

The axially loaded pad base in Design Example 2 is to be redesigned as a reinforced base, founded in the weathered sandstone. Assuming settlements have been judged to be satisfactory, the base will have an allowable bearing pressure, na = 550 kN/m2.

Loadings

Since dead and imposed loads are approximately equal, a
combined partial load factor of γP = 1.5 will be used.

Area of base

Adopt a 3.0 m × 3.0 m square base, i.e. L = B = 3.0 m (see Fig. 11.25). Reactive design pressure on base for concrete design

Fig. 11.25 Reinforced pad base design example.

Depth of base
The base and its reinforcement must be capable of resisting bending, beam shear and punching shear. At first glance it is not always possible to judge which is critical. The process of selecting a suitable depth for the base is simplified by use of the charts for estimating effective depth. The effective depth will be checked for each case, assuming a typical reinforcement percentage
of between 0.25% and 0.50%. The results are shown in  Table 11.1.

 Table 11.1 Estimating effective depth for reinforced pad base design example

This indicates that bending is critical, i.e. it requires the greatest effective depth, for low percentages of reinforcement.


For this particular example an average effective depth in both directions of d = 600 mm will be selected.

Overall depth of base is, h = 600 + 25 (bar diameter) 
                                        + 50 (cover)
                                        = 675 mm
 
Bending
From Fig. 11.25, the cantilever moment at face of base  plate is

Shear
The base should be checked for both beam shear and punching shear, since either may be critical. Grade C40  concrete has been specified.


Local shear at column face
The shear at the face of the column should be checked.

Allowable concrete shear stress, vc = 0.57 N/mm2

From BS 8110: Part 1: 3.4.5.8, the critical location for beam shear is at a distance 2d = 2 × 600 = 1200 mm from the face  of the load (i.e. from the edge of the base plate in this  example). The shear force acting across this failure plane is

Vbeam = (design pressure) × (area of base beyondcritical location)

Punching shear
The critical location for punch- ing shear for a square load is a square perimeter a distance 1.5d = 1.5 × 600 = 900 mm from the face of the load.

The length of one side of this perimeter is

Area of base outside of perimeter

Comparison with vbeam = 0.12 N/mm2 indicates that, in this instance, punching shear is more critical than beam shear.

This is normally the case with square pad foundations. If however a foundation size of say 2 m × 4 m had been chosen in this example, beam shear may well become critical.

Local bond
Although not covered by BS 8110, local bond can be a problem in foundation design, and should therefore be checked at sections with high shear stress. Local bond is given by

where ∑ us is the sum of the bar perimeters at the section being considered.
Punching shear, Vu = 2979 kN

The length of the punching shear is u = 8800 mm.
T25 bars @ 175 centres each way are proposed. The total number of bars crossing the shear perimeter is u/175 = 50.
The local bond stress is

where la is the lever arm which CP 110 approximates to the effective depth d.

Design Decisions - Sizing up of the Design - Reinforced Concrete Pads and Strips..

Design decisions
The decision to reinforce a concrete foundation of this type usually follows the realization that the ground conditions are variable and/or deep trench fill is uneconomic.

Reference to (Table 10.2 Foundation selection to suit varying site conditions) on choice of foundation types will assist in this decision.

Sizing up of the design
The depth and width of the reinforced concrete strips are determined in a similar way to that adopted for unreinforced strips and trench fill. The depth to the underside of the footing is determined by the ground conditions and the level of suitable sub-strata, taking into account the need to be below the effect of any critical frost heave or swelling and shrinkage of sub-strata.

The fabric reinforced strip is used generally where there is both relatively poor ground and smallish loads or where some slight movements are expected from differential  settlement or subsidence.

More heavily reinforced strips, using bars and not fabric, are used where ground conditions are more critical and/or loading more excessive (see Fig. 11.21).

Fig. 11.21 Section through reinforced strip.

For particularly heavy loads and/or poor ground, beam strips are often used.

For axially loaded strip foundations, the breadth of the strip required is:

where P is the superstructure load/unit run and na is the net allowable bearing pressure.

The thickness of the foundation should be determined by designing for the cantilever action of the strip taking into account the bending, shear and bond stresses to be accommodated and allowing for the longitudinal moments and forces (see Fig. 11.20 Reinforced concrete strip design conditions.).

For strip footings a generous thickness for bending is  necessary in order to maintain the shear and bond stresses within permitted limits and in order to produce an economic balance for the ratio of concrete to reinforcement.

The detailed design of a reinforced concrete strip is covered in Design Example 3 which follows, but in general the  calculated foundation thickness required for shear and bending compression is rounded up to the nearest 50 mm as the economic thickness for the strip foundation.

Reinforced Concrete Pads and Strips.

Introduction
These pads are used in similar locations to those of the mass concrete pad, but where the reduction in cost of mass concrete exceeds the cost of the additional labour and materials.

These extras would include providing the reinforcement and any extra shuttering, blinding, or working space which may prove necessary for the reinforced solution.

The plan size and shape is determined from the vertical load and allowable bearing stress in conjunction with any physical requirements. The depth and amount of reinforcement is determined from the resulting bending moments and shear force considerations (see Fig. 11.20) or from  past experience. The experience basis is often used where reinforcement needs are related to variable ground for a familiar location and use or where there is a need to  cater for a number of time-related variations in differential settlement.


1 Design decisions and Sizing up of the design   Design decisions The decision to reinforce a concrete foundation of this type usually follows the realization that the ground conditions are variable and/or deep trench fill is...

2 Design Example 3: Reinforced strip foundation   The load-bearing wall of a single-storey building is to be supported on a wide reinforced strip foundation. A site investigation has revealed loose-to-medium granular soils...

3 Design Example 4: Reinforced pad base  The axially loaded pad base in Design Example 2 is to be redesigned as a reinforced base, founded in the weathered sandstone. Assuming settlements have been judged to be...

Fig. 11.20 Reinforced concrete strip design conditions.

Design Example: Deep Mass Concrete Pad Base.

A steel-framed building is to be built on a site adjoining previously, where variable fill extends down to the level of the bedrock. A heavily loaded stanchion, carrying axial load only, is to be supported on a pad foundation.

It has been decided to found the heavily loaded base in the sandstone bedrock, in order to minimize settlement. The base is to be constructed as a mass concrete pad.

Loadings
The superstructure working loads are as follows:

Allowable bearing pressure
From Design Example, the sandstone has a net allowable bearing pressure of na = 2000 kN/m2
.
Size of base
The foundation surcharge due to the groundbearing slab is small and can be neglected. Therefore,

Therefore a 1.5 m × 1.5 m pad foundation will be used, as shown in Fig. 11.15.

The stanchion bases are set at a common depth of 300 mm below slab level, and the remaining depth of excavation down to the sandstone rock is taken up by the mass concrete base.

The minimum depth of base required, before it becomes necessary for reinforcement to be introduced, is 500 mm (see depth to angle of load dispersion in Fig. 11.15). Clearly a mass concrete base is adequate in this instance.

Fig. 11.15 Mass concrete pad base design example.

The choice between the full sized mass concrete pad and the stub column solution is determined from economic  considerations.

The economic change-over point is where the cross-section required for groundbearing purposes becomes excessively wasteful in terms of the cost of concrete compared with the cost of introducing shuttering to form the smaller crosssection. Situations where this would apply are:

(1) Where the pads are very deep,
(2) Where the allowable groundbearing pressures are very low, or
(3) Where, due to the nature of the ground, a shuttered pad is required in any case.

The lower pad plan size is determined from the loading  and the allowable groundbearing capacity. If the section is reduced at higher level, the size at the point where it is reduced is generally based upon a 45° dispersion of load through the mass concrete (see Fig. 11.16).

Fig. 11.16 Stub column pad base.

The upper pedestal cross-section is determined from the load, the allowable bearing stress below the base plate and the allowable compressive stress on the mass concrete  in conjunction with a suitable practical and economic size for construction. For example, the size determined from stress considerations often needs to be rounded up to a larger practical mass concrete cross-section particularly where the mass pier is relatively tall (see Fig. 11.17).

Fig. 11.17 Mass pier criteria.

Unreinforced Concrete Pads and Strips.

In general, shallow pads and strips are the economic foundation for most structures where ground conditions allow this solution.

The suitability of shallow strips and pads should be one of the first considerations for the engineer and their use tends to form the  normal  foundation criteria against which the extra over cost of abnormal foundations tends to be judged.

This does not mean however, that strips and pads should be used wherever possible since as they become deeper or more heavily reinforced the alternatives of vibrocompaction and/or piles becomes competitive.

However, at shallow depth, they are the economic alternative.

1 Trench fill   A brief description of trench fill strips is given previously. The design of such strips is relatively simple, and it is true to say that there is more design involved in making the decision to

2 Trench fill design decisions   A typical trench fill foundation is shown in Fig. 11.7 where (a) indicates a typical section, (b) shows the typical design forces, and (c) illustrates the possible externally applied ground...

3 Sizing of the design   In the case of mass concrete trench fill the foundations can be sized using the assumptions that dispersion of load through the strip can be assumed to be at an angle of 45°. In the case...

4 Design Example 1: Trench fill strip footing   The internal load-bearing wall for a four-storey office block is to be supported on a strip foundation. Borehole investigations produced the consistent soil profiles shown in Fig. 11.13. Soil...

5 Design Example 2: Deep mass concrete pad base   A steel-framed building is to be built on a site adjoining previously, where variable fill extends down to the level of the bedrock. A heavily loaded stanchion, carrying axial load only, is to be supported on a...

6 Unreinforced concrete strips   The unreinforced strip footing requires slightly better ground conditions than trench fill to maintain trench stability during construction of the masonry over it. The adoption of a thin...

Cantilever Balanced Pad Foundations.

The cantilever balanced foundation consists of a ground beam picking up loading from the superstructure and
cantilevering out over a pad foundation with the pads designed, theoretically, to have uniform bearing stress (see Fig. 9.20).

The need for a cantilever arrangement can be produced by restrictions from adjacent buildings or existing services (see Fig. 9.21).

Fig. 9.20 Cantilever balanced foundation.

Fig. 9.21 Cantilever balanced foundation.

Holed Balanced Pad Foundations.

The holed balanced foundation is a pad type foundation supporting a number of loads and transferring the load  to the bearing strata in a relatively uniform fashion. The allowable variation in bearing pressure and differential settlement is again determined from the ground conditions and sensitivity of the superstructure.

The resultant load and its position are determined for the critical load case.

While with the rectangular base the balancing is done by varying the cantilever and with the trapezoidal base by varying the end dimensions, in this case the balancing is done by forming a hole in the base positioned so as to move the centroid of the base to coincide with that of the resultant load (see Fig. 9.19).

Fig. 9.19 Holed balanced pad foundation.

Trapezoidal Balanced Pad Foundations.

The trapezoidal balanced foundation is used in similar circumstances to the rectangular balanced foundation.

Adjusting the width of each end of the pad in relation to the load supported can produce a more economic solution.

This is particularly useful where two point loads of different sizes need to be supported and a relatively uniform bearing pressure is required (see Fig. 9.17). It is also useful where adjustments by cantilever action  are not possible, for example, where two different column loads on the edge of opposite building lines require support (see Fig. 9.18).

Fig. 9.17 Trapezoidal balanced pad foundation.

Fig. 9.18 Trapezoidal balanced pad foundation.

Rectangular Balanced Pad Foundations.

A typical rectangular balanced foundation supporting two point loads from a sensitive structure that has only a small tolerance to accommodate differential settlement is shown in Fig. 9.16. The problem has been overcome by adjusting the cantilevered ends of the base to produce a constant ground bearing pressure for the load conditions.

Fig. 9.16 Rectagular balanced pad foundation.

Balanced Pad Foundations.

Balanced pad foundations are used where a number of loads are required to be supported on a single pad and where excessive variations in pressure could produce unacceptable differential movement. They consist of reinforced concrete pad bases designed for the critical design loading with the aim of keeping the differential ground stresses  and hence settlements to an acceptable level. This requirement could be the result of a sensitive sub-strata and/or  a sensitive superstructure over. There are a number of  different types of balanced pad foundations which include rectangular, trapezoidal, holed and cantilever, and these are described in the following sections.

Deep Mass Concrete Pads.

Deep mass pads consist of mass concrete pads cast with their soffit at depths in excess of 1.5–2 m. They are generally used where a suitable ground bearing strata is relatively deep and where the piling alternative is more expensive, i.e. a small number of pads are required or access for piling is difficult and expensive. Deep mass pads tend to be of two types, one being constructed up to high level using a basic cross-section and the other using a reduced and shuttered cross-section for the upper levels (see Fig. 9.14).

An alternative to concrete for the upper reduced crosssection is to construct a brick pier off the mass concrete pad (see Fig. 9.15). This solution has the advantage of avoiding the need for expensive shuttering and can result in an overall saving. If brickwork is adopted it is necessary that the pad size provides the necessary working space for the bricklayers to build the pier.

Fig. 9.14 Deep mass concrete pad.

Fig. 9.15 Deep mass concrete pad with brick pier.

Deep Reinforced Concrete Pads.

Deep reinforced concrete pads are similar in cross-section to the shallow reinforced pad but are constructed at depth in situations where the suitable sub-strata is not available  at high level. Such pads are not often economic and more cost-effective mass concrete bases or piles and caps are often used. However in some situations they can prove  to be a suitable solution – see Fig. 9.13 which indicates a typical example of such a use.

Fig. 9.13 Deep reinforced concrete pad.

Shallow Reinforced Concrete Pads.

Reinforced concrete pads are similar to the mass concrete pads but for the same conditions can be thinner when reinforced with steel. The reduction in thickness is made possible by the introduction of reinforcement on the tensile face of the pad which increases the pad’s resistance to bending moment (see Fig. 9.12).

Fig. 9.12 Shallow reinforced concrete pad.

Shallow Mass Concrete Pads.

Shallow mass pads consist of mass concrete pads supporting point loads from columns, piers, etc. (see Fig. 9.10).

They are used for varying conditions of sub-strata where suitable load-bearing soils exist at shallow depths below the effects of frost and general weathering. They are particularly economic where the side of the excavation can be used as a shutter and where a suitable depth of mass can be accommodated to disperse the load without the need for reinforcement. The general assumption for load dispersion is as mentioned previously i.e. a 45° spread through the mass concrete (see the typical example shown in Fig. 9.11).

Fig. 9.10 Shallow mass concrete pad.

 

Fig. 9.11 Load spread on mass concrete pad.

Group One – Strip and Pad Foundations.

Strip footings and pad bases are used to deliver and spread superstructure loads over a suitable area at foundation  (formation) level. The foundation is required to be stiff enough to distribute the loadings onto the sub-strata in a uniform manner.

1 Strip footings  Strip footings are used under relatively uniform point loads or line loads. The main structural function of the strip is  to disperse the concentration of load sideways into an increased width of sub-strata in order to reduce the bearing stress and....

2 Masonry strips  Masonry strips are rarely used these days, however they can be adopted where good quality sub-strata exists and the raw materials for masonry construction are cheap and abundant. The wall is increased in width by corbelling out the masonry to...

3 Concrete strips – plain and reinforced
4 Concrete trench fill
5 Stone trench fill
6 Rectangular beam strips
7 Inverted T beam strips
8 Pad bases
9 Shallow mass concrete pads
10 Shallow reinforced concrete pads
11 Deep reinforced concrete pads
12 Deep mass concrete pads
13 Balanced pad foundations
14 Rectangular balanced pad foundations
15 Trapezoidal balanced pad foundations
16 Holed balanced pad foundations
17 Cantilever balanced pad foundations

Pad Foundations - Typical Types.

Pad foundations tend to be the simplest and cheapest foundation type and are used when the soil is relatively strong or when the column loads are relatively light. They are usually square or rectangular on plan, of uniform thickness and generally of reinforced concrete. They can be stepped or haunched, if material costs outweigh labour costs.

The reinforcement can vary from nothing at one extreme through to a heavy steel grillage at the other, with lightly reinforced sections being the most common. Typical types are shown in Fig. 1.5.

Fig. 1.5  Pad Foundations - Typical Types