Chapter three Design of Shallow Foundation.pdf

Design of shallow foundation with theories and calculated

1. CHAPTER THREE
Analysis and Design of Shallow Foundation

Out line
3.1 Introduction to Ethiopian and other standards in foundations area.
3.2 Bearing Capacity and Settlement of Shallow Foundation (review)
3.3 Design of Shallow Foundation Types
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2. 3.1 Introduction to Ethiopian and other standards in
Foundations Area
Ethiopian Building Code Standard-1995
(EBCS-7)
Compulsory Ethiopian Standard(CES), 2015

Geotechnical Design - Part 1: CES 158,2015. (General rules)

Geotechnical Design - Part 2: CES 159,2015. (Ground investigation and testing)

European Standard (EN).
EN 1997, Eurocode 7- Geotechnical design
American Concrete Institute (ACI )


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3. Conti..
•.
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Standard ( Code)
EBCS-1995 CES2015(ES EN 2015) ACI
Location of Critical section for
Punching Shear
At a distance of 1.5d From face of
the column
At a distance of2.0d From face
of the column
At a distance of 0.5d
From face of the column
Location of Critical section for Wide
beam Shear
at a distance of d From face of the
column
at a distance of d From face of
the column
at a distance of d From
face of the column
Location of Critical section for
Bending Moment at face of the RC column at face of the RC column at face of the RC column
Partial factor for Permanent Action 1.3 1.35 1.2
Partial factor for Variable Action 1.6 1.5 1.6

4. Imposed Loads On Buildings(CES 142)
Representation of actions
1. Imposed loads on buildings are those arising from
occupancy. Values given in this Section, include:
normal use by persons;
- furniture and moveable objects (e.g. moveable
partitions, storage, the contents of containers);
- vehicles;
- anticipating rare events, such as concentrations of
persons or of furniture, or the moving or stacking of
objects which may occur during reorganization or
redecoration.
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5. Conti..
(2) The imposed loads specified in this part are modeled by uniformly
distributed loads, line loads or concentrated loads or combinations of
these loads.
(3) For the determination of the imposed loads, floor and roof areas in
buildings should be sub-divided into categories according to their use.
(4) Heavy equipment (e.g. in communal kitchens, radiology rooms,
boiler rooms etc) are not included in the loads given in this Section.
Loads for heavy equipment should be agreed between the client and/or
the relevant Authority.
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6. Table: Categories
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7. Values of actions
The categories of loaded areas, as specified in Table (Categories) , shall be
designed by using characteristic values qk (uniformly distributed load) and
Qk (concentrated load).

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8. 3.2 Bearing capacity and settlement of shallow foundations
(review)

Bearing capacity of a soil is the resistance of soil to applied stress.

Modes of shear failure of soil:
I.General shear failure
II.Local shear failure
III.Punching shear failure


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9. Conti..







Figure : Modes of bearing failures

(a) General shear (b) Local shear and (c) Punching shear
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10. Conti..
Ultimate Bearing Capacity Equations:

1.Terzaghi’s Bearing Capacity equation
2.Meyerhof’s Bearing Capacity equation
3.Hansen’s Bearing Capacity Equation

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11. Conti..
Terzaghi’s Bearing Capacity equation

11/26/2021 Foundation Engineering by Estifanos B. 11 NBqNNcq
qcu 5.0' 
 Strip (or long) footing:
Square footing:
Circular footing:  NBDNNcq
qcu 5.0'   NBDNNcq
qcu 4.0'3.1   NBDNNcq
qcu 3.0'3.1 

12. Conti..
Meyerhof’s Bearing Capacity equation:


Hansen’s Bearing Capacity Equation


11/26/2021 Foundation Engineering by Estifanos B. 12  disNBdisDNdisNcq
qqqqccccu 5.0'   gbidsNBgbidsDNgbidsNcq
qqqqqqccccccu 5.0' 

13. Conti..
Where
q
u = Ultimate bearing capacity of footing,
C = Cohesion,
q =  D=Effective surcharge at the base level of
the footing.
 = effective unit weight of soil
N
c, N
q, N
 = Bearing capacity factors
S
c, S
q ,S
 = Shape factors
d
c ,d
q, d
 = Depth factors
i
c, i
q, i
 , = Inclination factors

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14. Conti..
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15. Conti..
•Table : Presumed Design Bearing resistance * under static loading(
EBCS 7)

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16. Conti..

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17. Conti..
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18. Settlement of shallow Foundation
Immediate Settlement (S
i)





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19. Conti..
Primary Settlement(S
c )


Where:
Cc = compression index from the e versus log P plot
eo = in situ void ratio in the stratum where Cc was obtained
H = stratum thickness..
??????'o = effective overburden pressure at mid-height of H
∆?????? = average increase in pressure from the foundation loads in layer at the
middle of the layer
mv = constrained modulus of elasticity determined from consolidation test
=1/Es





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S
T = S
i + S
C + S
sc

20. Limiting values of structural deformation and foundation movement (CES 158 pg
173)
•The components of foundation movement, which should be considered
include settlement, relative (or differential) settlement, rotation, tilt,
relative deflection, relative rotation, horizontal displacement and vibration
amplitude.
•The maximum acceptable relative rotations range from about 1/2000 to
about 1/300, to prevent the occurrence of a serviceability limit state in the
structure.
•A maximum relative rotation of 1/500 is acceptable for many structures.
The relative rotation likely to cause an ultimate limit state is about 1/150
•For normal structures with isolated foundations, total settlements up to 50
mm are often acceptable. Larger settlements may be acceptable provided
the relative rotations remain within acceptable limits.
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21. Allowable Settlement as per (EBCS-7)


Allowable settlement as per EBCS-7 pg70
When the supporting soil is
 For sandy soil – 50mm.
 For Clay soil -75mm.














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22. Conti..
•In 1956, Skempton and McDonald proposed the following
limiting values for maximum settlement and maximum angular
distortion, to be used for building purposes: Braja Das 8
th

edition pg348.

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23. Conti..
Table: Tolerable differential settlement of buildings in mm by Bowles,J.E (Note
recommended maximum values in parentheses.)

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Criterion Isolated Footing Mat Foundation
Angular Distortion (Cracking) 1/300
Greatest Differential Settlement
Clays 45(35)
Sands 32(25)
Maximun Settlement
Clays 75
75-125 (65-100)
Sands 20
50-75(35-65)

24. 3.3 Design of shallow Foundation
The requirements in design of foundations are:
1. The pressure on the soil should not exceed the bearing
capacity of the soil.
2.The settlement of the structure should be within
the permissible limits. Further there should be no
differential settlement.
In order to proportion shallow foundations one should
know either
1. the presumptive allowable soil pressure or
2.the appropriate strength parameters of the soil, i.e.,
the angle of internal friction,Ø , and cohesion, C.

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25. Factors To Consider In Foundation Design
The following factors should be considered
Footing depth and location:
Net and gross bearing capacity
Erosion problems for structures adjacent to
flowing water
Corrosion protection and sulfate attack
Water table fluctuation
Foundations in sand, silt and clays
Foundations on expansive soils
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26. Conti…
Footings must be designed to carry the column loads
and transmit them to the soil safely while satisfying
code limitations.
The area of the footing based on the allowable
bearing soil capacity
Two-way shear or punching shear.
One-way shear(wide beam shear)
Bending moment and steel reinforcement required

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27. Conti..
Footings should be carried below
1. The frost line
2. Zones of high volume change due to moisture fluctuations
3. Topsoil or organic material
4. Peat and muck
5. Unconsolidated material closed garbage dumps and similar filled in areas.

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28. Conti..
Conversely, Figure below indicates that if the new footing is lower
than the existing footing, there is a possibility that the soil may
flow laterally from beneath the existing footing results in
settlement cracks in the existing building

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29. 3.3 proportioning of Shallow Foundation
The area of footing can be determined from the
actual external loads such that the allowable soil
pressure is not exceeded.

11/26/2021 Foundation Engineering by Estifanos B. 29  
pressure soil allowable
weight-self including load Total
footing of Area 

30. Design Of Isolated Footings
Proportioning of Isolated footing

11/26/2021 Foundation Engineering by Estifanos B. 30  
pressure soil allowable
weight-self including load Total
footing of Area 

31. Structural Design of Footings
Before going in to the structural design, one should check if the
settlement of the selected footing is with in the prescribed safe
limits. If the settlement exceeds the safe limits, one should
increase the area of the footings until the danger of settlement is
eliminated.
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32. Conti..
One should design for the following modes of failures:

1.Shear failure
Punching shear
Wide beam shear (diagonal tension)
to avoid these provide adequate depth
2. Flexural failure
to avoid this provide adequate depth and reinforcement
3. Bond failure
column bar pullout
Flexural reinforcement bars failed in bond
to avoid these provide adequate development or anchorage length
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33. Conti..
•Location of Punching shear wide beam shear and bending
moment as per EBCS1995

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Critical section for punching
shear
Critical section for
wide beam shear
Critical section for
bending moment

34. Location of critical section as per ESEN2015
• Location of wide beam shear is at a distance d from face of
column which is similar to EBCS1995. But Location of punching
shear is at a distance of 2d from face of column.
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35. conti..
•Location of Punching shear wide beam shear anf bending
moment as per ES-EN2015

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36. Determination of Thickness

The thickness of a given footing is usually governed by punching
shear (for square and centrally loaded footings)
or wide beam shear (for rectangular footings with large L/B ratio
or eccentrically loaded footings)

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37. According to EBCS-2
I. Punching Shear Resistance
V
up = 0.25f
ctd k
1k
2 ud (MN)
where k
1 = ( 1+50e) ≤ 2.0
K
2 = 1.6 – d ≥ 1.0 ( d in meters)
For members where more than 50% of the bottom
reinforcement is c urtailed , k
2= 1

ex and 
ey correspond to the geometric ratios of longitudinal
reinforcement parallel to x and y
u = periphery of critical section

e =
ex + 
ey
d=
d
x + dy
2
d= the effective depth in x and y direction.


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38. II . Diagonal Tension (Wide beam ) shear resistance
V
ud = 0.25f
ctd k
1k
2 bw d (MN)
where k
1 = ( 1+50) ≤ 2.0
K
2 = 1.6 – d ≥ 1.0 ( d in meters)
For members where more than 50% of the
bottom reinforcement is curtailed , k
2= 1
Development length
I
d =
??????���
4���
(cm)

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39. material properties
.
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From EBCS-1, 1995 (table 3.1)
Safety factor for concrete work, γc =1.5
Safety factor for steel work, ᵧs =1.15
For footing column, Footing pad, C-30 is used
What is C-30?
For C-30
fck=0.85*30MPa =24Mpa
fctk=0.21*(fck)
2/3
=0.21*(24)
2/3
= 1.747Mpa
fcd=0.85*fck/ᵧs =0.85*24Mpa/1.5 =13.6Mpa
fctd=fctk/s =15.47/1.5 =1.16Mpa
ᵧc=25KN/m
3

Ec=4700(fck)
1/2
=4700*(24)
½
=23.025Mpa
Steel S-300
fyu=fyk=300Mpa
fyd =fyk/ ᵧs =300/1.15 =260.87Mpa ;
Steel S-400
fyu=fyk= 400Mpa
fyd = fyd/ ᵧs =400/1.15= 347.83Mpa ;

40. Conti…
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41. •Punching shear:- This factor generally controls
the depth of footings.

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42. From the figure it is apparent the concrete shear
resistance along the perimeter according to EBCS2

Where V
up = punching shear resistance
The net force on the perimeter due to the soil
pressure would be

From equilibrium consideration,
2( a’ +3d + b’+ 3d) dV
up =
The only unknown is d.

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43. •The selected depth using the punching shear criterion may not
be adequate to withstand the diagonal tension developed.
Hence one should also check the safety against diagonal
tension.


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44. .
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45. iii) Bending Moment
The critical sections for the bending moment vary
according to the type of columns.
According to EBCS 2-1995, the critical section for moment
shall be taken as follows:
- At the face of column, pedestal or wall for footings
supporting a concrete pedestal or wall
- Halfway between middle and edge of wall, for footings
supporting a masonry wall
- Halfway between face of column and edge of steel
base for footings supporting a column with base plates.

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46. Conti..
•Critical section for bending moment
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47. Flexural Reinforcement Distribution
In one-way footings and two-way square footings
reinforcement shall be distributed uniformly
across the entire width of footing
In two-way rectangular footings, reinforcement
shall be distributed as follows:
Reinforcement in longer direction shall be
distributed uniformly across the entire width of
footing

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48. Conti..
•For reinforcement in the short direction, a portion
of the total reinforcement given by equation below
shall be distributed uniformly over a band width
(centered on center line of column or pedestal)
equal to the length of the short side of footing .

Where: � is the ratio of long side to short side of the
footing
The remainder of the reinforcement required in the
short direction shall be distributed uniformly outside
the center band width of the footing

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49. Conti..
.
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50. Isolated Footing Design as per ES EN2015
Eurocode 7 has two parts:
Part 1: General Rules
Part 2: Ground Investigation and testing
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51. Conti…
Limit States
The following ultimate limit states apply to foundation
design:
EQU: Loss of equilibrium of the structure
STR: Internal failure or excessive deformation of the
structure or structural member
GEO: Failure due to excessive deformation of the
ground
UPL: Loss of equilibrium due to uplift by water
pressure
HYD: Failure caused by hydraulic gradients
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52. EQU
the loss of equilibrium of the structure or the supporting
ground when considered as a rigid body and where the internal
strengths of the structure and the ground do not provide
resistance.
This limit state is satisfied if the sum of the design values of the
effects of destabilising actions (Edst; d) is less than or equal to
the sum of the design values of the effects of the stabilising
actions (Estb; d) together with any contribution through the
resistance of the ground around the structure (Td).
Edst; d ≤ Estb; d + Td
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53. GEO
failure or excessive deformation of the ground, where the soil
or rock is significant in providing resistance .
This limit state is satisfied if the design effect of the actions (Ed)
is less than or equal to the design resistance (Rd).
Ed ≤ Rd
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54. STR
failure or excessive deformation of the structure, where the
strength of the structural material is significant in providing
resistance.
As with the GEO limit state, the STR is satisfied if the design
effect of the actions (Ed) is less than or equal to the design
resistance (Rd).
Ed ≤ Rd
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55. UPL
the loss of equilibrium of the structure or the supporting
ground by vertical uplift due to water pressures (buoyancy) or
other actions .
This limit state is verified by checking that the sum of the
design permanent and variable destabilising vertical actions
(Vdst; d) is less than or equal to the sum of the design
stabilising permanent vertical action (Gstb; d) and any
additional resistance to uplift (Rd) .
Vdst; d ≤ Gstb; d + Rd
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56. HYD
hydraulic heave, internal erosion and piping in the ground as
might be experienced, for example at the base of a braced
excavation.
This limit state is verified by checking that the design total pore
water pressure (udst; d) or seepage force (Sdst; d) at the base
of the soil column under investigation is less than or equal to
the total vertical stress (σstb; d) at the bottom of the column,
or the submerged unit weight ( G′stb; d) of the same column.
udst;d < σstb;d or Sdst;d < Gstb;d
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57. Conti…
The EQU, GEO and STR limit states are the most
likely ones to be considered for routine design.
Furthermore,in the design of retaining walls and
foundations it is likely that limit state GEO will be
the prevalent state for determining the size of the
structural elements.
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58. Conti…
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59. Partial Factors EQU,GEO,ST Limit states
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•.

60. Design approaches
the choice of partial factors to be used is dependent on the design
approach being followed (for the GEO and STR limit states).
When checking the GEO and STR limit state requirements, one of
three design approaches is used: Design Approach 1, Design
Approach 2 or Design Approach 3.

Europe-wide adoption of the Standard and offers designers in
different nations an approach most relevant to their needs. The
UK National Annex to EN 1997-1 states that Design Approach 1 is
to be used in the UK.
the choice of partial factors to be used is dependent on the design
approach being followed (for the GEO and STR limit states).
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61. Conti…
For each design approach, a different combination of partial factor sets
is used to verify the limit state.
For Design Approach 1: (for retaining walls and shallow footings),two
combinations are available and the designer would normally check the
limit state using each combination.

Design Approach 1: Combination 1: A1 + M1 + R1
Combination 2: A2 + M2 + R1

Design Approach 2: A1 + M1 + R2
Design Approach 3: A* + M2 + R3
(Note. A*: use set A1 on structural actions, set A2 on geotechnical
actions).
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62. Conti…
The sets for actions (denoted by A), material
properties (denoted by M) and ground resistance
(denoted by R),

Combination 1 – generally governs structural resistance
Combination 2 – generally governs sizing of foundations

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63. Spread Foundations as per ES EN2015
For the proportioning of shallow foundations,
CES-158: 2015 gives three methods;
a)Prescriptive method
b)Analytical method
c)Semi-empirical method


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64. Prescriptive Method
(Presumptive Allowable Bearing Capacity
If site investigation is not performed or is
unnecessary, it can be obtained based on the
basis of well-established local practice.
The new code (CES-158: 2015) does not provide
presumed allowable bearing capacity values for
soils (it only gives for rocks).

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65. Analytical method
•In this method calculations are carried out for each
limit state using a recognized analytical method.
•The bearing resistance of the soil should be
checked using a well-known method (e.g.
Meyerhof or Hansen bearing capacity equation).
•At the Serviceability Limit State (SLS), the
settlement of the foundations should be calculated
and checked against permissible limits.
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66. Conti…
When applying the bearing capacity equations one
should differentiate two states of loading conditions,
namely:
Initial or instantaneous or short-term loading condition
(Undrained condition) andFinal or long- term loading
condition (Drained condition).
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67. Flow chart for design of foundation
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68. STRUCTURAL DESIGN as per ESEN2015
The Structural design of foundations is covered in
CES 149: 2015.
The structural design for reinforced concrete
foundation includes:
Selecting an appropriate grade of concrete and
reinforcing steel.
Determining the required foundation thickness.
Determining the size, number & spacing of the
reinforcing bars.
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69. Conti…
NB: for the structural design of foundations, the
limit state that should be used is the Ultimate
Limit State (ULS) of collapse; that is verification
should be done for limit state STR.
•Therefore the load combination for the design
load will be:
Pd = 1.35 ⋅Gk + 1.5 ⋅Qk
•Where, Gk = the characteristic Dead Load
Qk = the characteristic Live Load

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70. SHEAR in FOOTINGS
Shear stresses usually govern the thickness of footings.
Note that, unlike beams and flat slabs, it is not a
common practice to provide shear reinforcement for
foundations.
•To avoid shear reinforcement, all of the applied shear
should be resisted by the concrete alone.
•To determine the thickness of footings two types of
shear are considered:
wide-beam shear and
punching shear.

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71. Wide-beam Shear
Wide-beam shear calculation
Wide-beam shear is the sum of the loads acting
outside the critical section,
It is the shear force at a distance d from the face of
the support (column).
For strip and isolated footings, the wide-beam
shear force, VEd, can be calculated by taking the
force due to the soil pressure at the critical
section.
For combined, strap and mat foundations, it can
be calculated from the shear force diagram.

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72. Conti…
Hence the applied wide-beam shear stress (in KPa) will
be;
&#3627408483;
??????&#3627408465;=
&#3627408457;
??????&#3627408465;
&#3627408463;
&#3627408484;&#3627408465;

VEd = the applied wide-beam shear force (in KN).
bw = the appropriate width of the cross-section.
d = effective depth.

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73. Wide-beam shear resistance

According to clause 6.2.2(1) of CES 149: 2015, the design
wide-beam shear resistance of a footing without shear
reinforcement, VRd,c, (in KN) is given by:
&#3627408483;
&#3627408453;&#3627408465;,&#3627408464;≥
&#3627408438;
&#3627408453;&#3627408465;,&#3627408464;??????(100??????
1&#3627408467;
&#3627408464;??????)
1/3
&#3627408463;
&#3627408484;&#3627408465;
&#3627408483;
&#3627408474;??????&#3627408475;&#3627408463;
&#3627408484;&#3627408465;

Hence the resisting wide-beam shear stress (in KPa) will be;
&#3627408483;
??????&#3627408465;=
&#3627408457;
&#3627408453;&#3627408465;,&#3627408464;
&#3627408463;
&#3627408484;∙&#3627408465;


&#3627408438;
&#3627408453;&#3627408465;,&#3627408464;=
0.18
&#3627409150;
&#3627408464;
=
0.18
1.5
=0.12
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74. Conti..
.
11/26/2021 Foundation Engineering by Estifanos B. 74
A
s = the area of tensile reinforcement anchored beyond the section
considered.
f
ck = characteristics cylindrical strength of concrete.
f
yk = characteristics yield strength of reinforcement.
f
ctm = the mean axial tensile strength of concrete
f ctm = 0.3⋅ f
ck
2 / 3
for concrete grade of ≤ C50/60.
v
min = 0.035 ⋅ k
1.5
f
ck
0.5


??????≤
1+
200
&#3627408465;
&#3627408458;ℎ&#3627408466;&#3627408479;&#3627408466; &#3627408465; ??????&#3627408480; ??????&#3627408475; &#3627408474;&#3627408474;.
2

??????
1≤
&#3627408436;??????
&#3627408463;&#3627408484;&#3627408465;
0.02
for design take ρ1=ρmin;

??????
&#3627408474;??????&#3627408475;≤
0.26&#3627408467;
&#3627408464;??????&#3627408474;
&#3627408467;
&#3627408486;??????
0.02

75. Conti..
To determine the footing effective depth (during
design), equate the applied wide-beam shear
with the resistance,
VEd = VRdc
•the value of k will not become greater than 2
unless d < 200mm, which is impractical.
•Therefore, expressing the effective depth in
meters, the value of k can be simply set as
•k = 1 + (0.4472/√??????)

11/26/2021 Foundation Engineering by Estifanos B. 75

76. Punching Shear as per ESEN2015
Punching shear calculation
•For footings, the punching shear should be
checked at the face of the column, at the basic
control perimeter u1 (at 2d from column face)
and additionally at control perimeters within a
distance less than 2d.
•For footings, the soil pressure within the
control perimeter should be subtracted when
determining the design punching shear force.

11/26/2021 Foundation Engineering by Estifanos B. 76

77. Conti..
Hence, the reduced applied punching shear force,
VEd,red, (in KN) is given by;
&#3627408457;
??????&#3627408465;,??????&#3627408466;&#3627408465;= &#3627408457;
??????&#3627408465;−∆&#3627408457;
??????&#3627408465;
V
Ed = the design axial column load, P
d.
ΔV
Ed = the upward force within the control perimeter
considered = σ
avg · A
i
A
i = area of the control perimeter considered.
σ
avg = the design soil pressure = P
d/(B`L`)
11/26/2021 Foundation Engineering by Estifanos B. 77

78. Conti..
In design, it is assumed that the distribution of shear
force around a certain perimeter is uniform.
But, the distribution of shear varies significantly
around the perimeter and accompanied by torsional
moments, which causes a reduction in the punching
shear strength.
A way of dealing with this in design is to increase the
design shear force by a factor which is a function of
the geometry of the perimeter and the moment
transferred.


11/26/2021 Foundation Engineering by Estifanos B. 78

79. Conti..
The provisions in CES 149: 2015 introduce a multiplier, β,
to increase the average shear stress around the perimeter.
Therefore, the design applied punching shear stress, νEd,
(in KPa) will be;
&#3627408483;
??????&#3627408465;=
&#3627409149;∙&#3627408457;
??????&#3627408465;,??????&#3627408466;&#3627408465;
&#3627408482;∙&#3627408465;

u = perimeter length of the control perimeter under consideration.
d = mean effective depth
β = shear multiplier, which can be taken as;
If the column does not support moment, β = 1.
If the column supports moment;
β = 1.15 for interior columns,
β = 1.4 for edge columns and
β = 1.5 for corner columns.

11/26/2021 Foundation Engineering by Estifanos B. 79

80. Punching Shear Resistance
According to clause 6.4.4(1) of CES 149: 2015, the design
punching shear resistance of a footing without punching shear
reinforcement, νRd,c, (in KPa) is given by;
&#3627408483;
&#3627408453;&#3627408465;,&#3627408464;≥
&#3627408438;
&#3627408453;&#3627408465;,&#3627408464;??????(100??????
1&#3627408467;
&#3627408464;??????)
1/3
∙
2&#3627408465;
&#3627408462;

&#3627408483;
&#3627408474;??????&#3627408475;∙
2&#3627408465;
&#3627408462;


Hence the resisting punching shear force (in KN) will be;
&#3627408457;
&#3627408453;&#3627408465;,&#3627408464;=&#3627408483;
&#3627408453;&#3627408465;,&#3627408464;∙&#3627408482;∙&#3627408465;
??????≤
1+
200
&#3627408465;
&#3627408458;ℎ&#3627408466;&#3627408479;&#3627408466; &#3627408465; ??????&#3627408480; ??????&#3627408475; &#3627408474;&#3627408474;.
2

⍴1≤
??????
1&#3627408485;∙??????
1&#3627408486;
0.02
for design take ??????
1&#3627408485;=??????
1&#3627408486;=ρmin
11/26/2021 Foundation Engineering by Estifanos B. 80

81. ?????? is the distance from the periphery of the
column to the control perimeter considered.
11/26/2021 Foundation Engineering by Estifanos B. 81

82. Conti..
The following is a summary of the design procedure:
Input: Typical input data includes; column data (loads,
sizes & column reinforcement), soil data
(bearing capacity or the soil strength parameters),
concrete and reinforcement grade.
Objective: The goal is to determine footing dimensions
(width, length, thickness), reinforcement, and relevant
details for construction.
Procedure: The following steps should be followed for
the design of an isolated footing.

11/26/2021 Foundation Engineering by Estifanos B. 82

83. Procedures
Step 1: Proportion the footing
Isolated footings are proportioned using un-factored
(service) loads. It is customary to include the self-weight
of the footing as an external dead load. But as the
dimensions of the footing are unknown, the self-weight
can be assumed to be 10% of the service loads.
Step 2: Depth from wide-beam shear
Calculate or check the depth of the footing based on
wide-beam shear. The critical sections that should be
considered are given in figure below. The applied shear
forces are calculated along the planes X-X and Y-Y.

11/26/2021 Foundation Engineering by Estifanos B. 83

84. Conti…
Step 3: Depth from punching shear
Calculate or check the depth of the footing based on punching shear at the
following locations;
i.At the column perimeter, uo (at the face of the column).
ii.At control perimeter within a distance less than 2d (usually at d
distance from column face).
iii.At the basic control perimeter u1 (at 2d from column face).
The perimeters at distances of d and 2d from the column face are shown in
figure

11/26/2021 Foundation Engineering by Estifanos B. 84

85. Conti..
Step 6: Flexural Reinforcement distribution
Step 7: Anchorage of reinforcements
Step 8: Working drawings

11/26/2021 Foundation Engineering by Estifanos B. 85

86. Combined Footing
A. Rectangular Combined Footing:
The following is a summary of the design procedure:
Input: Typical input data includes; column data (loads,
sizes, location, spacing & column reinforcement), soil
bearing capacity, concrete and reinforcement grade.
Objective: The goal is to determine footing dimensions
(width, length, thickness), steel reinforcement, and
relevant details for construction.
Procedure: The design is based on the assumption that
the footing is rigid and that the soil pressure under the
footing is uniform. The following explanation may
illustrate the procedure:

11/26/2021 Foundation Engineering by Estifanos B. 86

87. Conti…
•.
11/26/2021 Foundation Engineering by Estifanos B. 87
Figure: Rectangular Combined Footing

88. Conti…
Step 1: Design loads and net ultimate bearing capacity.
Step 2: Proportion the footing
Step 3: Draw the shear force and bending moment
diagrams
Step 4: Determine footing depth based on shear
Step 5: Determine the reinforcement in the long direction
Step 6: Determine the reinforcement in the short
direction
Step 7: Anchorage of reinforcements
Step 8: Working drawings

11/26/2021 Foundation Engineering by Estifanos B. 88

89. Conti…
B) Trapezoidal combined footing
Input: Typical input data includes; column data (loads,
sizes, location, spacing & column reinforcement), length
of footing (L), soil bearing capacity, concrete and
reinforcement grade.
Objective: The goal is to determine footing dimensions
(width & thickness), steel reinforcement, and relevant
details for construction.
Procedure: The design is based on the assumption that
the footing is rigid and that the soil pressure under the
footing is uniform. The following explanation may
illustrate the procedure:

11/26/2021 Foundation Engineering by Estifanos B. 89

90. Conti…
.
11/26/2021 Foundation Engineering by Estifanos B. 90
Figure: Trapezoidal Combined Footing

91. Conti…
Step 1: Design loads and net ultimate bearing capacity.
Step 2: Determine dimensions a and b
Step 3: Draw the shear force and bending moment
diagrams
Step 4: Determine footing depth based on shear
Step 5: Determine the reinforcement in the long direction
Step 6: Determine the reinforcement in the short
direction
Step 7: Anchorage of reinforcements
Step 8: Working drawings

11/26/2021 Foundation Engineering by Estifanos B. 91

92. Conti…
DESIGN OF STRAP FOOTINGS
A strap footing (cantilever footing) is a composite
of two spread (isolated) footings connected by
a rigid beam or strap, as shown in the figure
below.
The strap connects an eccentrically loaded
exterior footing (footing 1) with an interior
footing (footing 2), subsequently resulting in a
uniform soil pressure and minimum differential
settlement

11/26/2021 Foundation Engineering by Estifanos B. 92

93. Conti…
•Input: Typical input data includes; column data (loads, sizes,
location, spacing & column
reinforcement), soil bearing capacity, concrete and
reinforcement grade.
•Objective The goal is to determine the footing dimensions
(length, width, and thickness), steel
reinforcement, and relevant details for construction.
•Procedure: The design assumes no soil pressure under the
strap beam. (To confirm with this,
strap is constructed slightly above soil or soil under strap is
loosened). Additionally, the weight
of the strap is negated. The following steps summarize the
recommended approach for a strap
footing design.

11/26/2021 Foundation Engineering by Estifanos B. 93

94. Conti…
.
11/26/2021 Foundation Engineering by Estifanos B. 94
Figure: Strap Footing

95. Conti…
Step 1: Design loads and net ultimate bearing capacity.
Step 2: Assume a trial value for e
Step 3: Determine the values of R1 and R2
Step 4: Determine the dimensions, L and B of both
footings.
Step 5: Calculate the soil pressure distribution per meter
run (qu) under each footing.
Step 6: Draw the shear force and bending moment
diagrams
Step 7: Design the strap beam
Step 8: Design each footing (depth and reinforcement)
Step 9: Working drawings

11/26/2021 Foundation Engineering by Estifanos B. 95

96. Mat/ Raft Foundation

In most cases, since the dimensions of the mat (B &
L) are usually known, the main task in the
geotechnical design is to check if the total settlement
is less than the allowable settlement.
If the total settlement exceeds the allowable
settlement, increase the depth of the foundation (Df).
Next check whether the bearing capacity of the soil is
exceeded.
The ultimate bearing capacity of a mat foundation
can be determined by the same method used for
shallow foundations
11/26/2021 Foundation Engineering by Estifanos B. 96

97. Conti…
Mats may be designed and analyzed as either rigid bodies or as
flexible plates supported by an elastic foundation. An exact
theoretical design of a mat on elastic foundation can be made;
however a number of factors reduce the exactness to a
combination of approximations.
These include difficulty in predicting subgrade responses,
variations in soil properties, mat shape, variety of superstructure
loads and effect of superstructure stiffness on mat. The analysis
and design is carried out using any of the following methods

•Conventional Rigid Method,
• Approximate Flexible Method,
• Finite Difference Method and
• Finite Element Method
11/26/2021 Foundation Engineering by Estifanos B. 97

98. Conti…
Design of uniform mat foundation by rigid
method
•In this method the mat is assumed to be infinitely rigid and the
bearing pressure against the bottom of the mat follows a
planar distribution where the centroid of the bearing pressure
coincides with the line of action of the resultant force of all
loads acting on the mat.
11/26/2021 Foundation Engineering by Estifanos B. 98

99. Conti…
The design procedure is as follows
Step 1: Determine the line of action of the resultant of all the
loads acting on the mat
[ &#3627408448;
??????&#3627408466;&#3627408467;?????? ??????&#3627408465;&#3627408468;&#3627408466;=0] ⇒&#3627408459; =
&#3627408452;
??????&#3627408485;
??????
&#3627408452;
??????
∴ &#3627408466;
&#3627408485;=
&#3627408437;
2
−&#3627408459;
[ &#3627408448;
&#3627408437;&#3627408476;????????????&#3627408476;&#3627408474; ??????&#3627408465;&#3627408468;&#3627408466;=0] ⇒&#3627408460; =
??????
??????&#3627408486;
??????
??????
??????
∴ &#3627408466;
&#3627408486;=
&#3627408447;
2
−&#3627408460;

Where, X = Location of the resultant measured from the left edge of the mat.
Y = Location of the resultant measured from the bottom edge of the mat.
Q
i = Design load on each column.
x
i = Coordinates of each column measured from the left edge of the mat.
y
i = Coordinates of each column measured from the bottom edge of the mat








11/26/2021 Foundation Engineering by Estifanos B. 99

100. Conti…
11/26/2021 Foundation Engineering by Estifanos B. 100
Step 2: Determine the contact pressure distribution as;
If the resultant passes through the center of gravity of the mat, the contact pressure is given
by
σ=Q/A
If the resultant has an eccentricity of ex and ey in the x and y direction respectively;
??????=
??????
&#3627408436;
±
??????&#3627408466;
&#3627408485;&#3627408485;
??????
&#3627408486;&#3627408486;
±
??????&#3627408466;
&#3627408486;&#3627408486;
??????
&#3627408485;&#3627408485;

Where Q = Total design load (Resultant load) on the mat = ΣQi
Qi = Design load on each column.
A = Total area of the mat = B*L
x, y = Coordinates of any given point on the mat with respect to the x and y axes passing through the
centroid of the area of the mat.
ex, ey = Eccentricities of the resultant force.
Ixx, Iyy = Moments of Inertia of the mat with respect to the x and y axes respectively.
??????
&#3627408485;&#3627408485;=
&#3627408437;&#3627408447;
3
12
&#3627408462;&#3627408475;&#3627408465; ??????
&#3627408486;&#3627408486;=
&#3627408437;
3
&#3627408447;
12

The maximum contact pressure should be less than the bearing capacity of the soil.

101. Conti…
Step 3: Divide the slab mat into strips in x and y
directions. Each strip is assumed to act as
independent beam subjected to the contact
pressure and the columns loads.
Step 4: Determine the modified column loads
Let B
1 be the width of the strip and B is the length
of the strip. Let the average soil (contact)
pressure on the strip be σ
av.
11/26/2021 Foundation Engineering by Estifanos B. 101

102. Conti…
Average load on the strip is; ??????
&#3627408462;&#3627408483;=
1
2
(??????
1+??????
2+??????
3+??????
&#3627408462;&#3627408483;&#3627408437;
1&#3627408437;)
The modified average soil pressure is given by; ??????
&#3627408462;&#3627408483;=??????
&#3627408462;&#3627408483;
&#3627408452;
??????&#3627408483;
??????
??????&#3627408483;&#3627408437;
1&#3627408437;

The column load modification factor (F) is given by; ??????=
&#3627408452;
??????&#3627408483;
&#3627408452;
1+&#3627408452;
2+&#3627408452;
3

The columns loads in this strip are multiplied by F. The
modified column loads are FQ
1, FQ
2 and FQ
3.
Step 5: Draw the shear force and bending moment diagrams
for each strip using the modified
column loads and the modified average soil pressure.
Step 6: Calculate depth of mat from shear requirement.
Step 7: Calculate steel reinforcement from moment
requirement.

11/26/2021 Foundation Engineering by Estifanos B. 102

103. 11/26/2021 Foundation Engineering by Estifanos B. 103
.