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2. 1- Introduction
A foundation is the structural element that is
generally embedded underground and connects the
superstructure to the ground. Its function is to
transmit the load from the superstructure to the
underlying soil or rock such that the superstructure
can be safely supported by the soil or rock.

3. 2- Foundation Safety
Foundations should be safe against:
 Shear failure in soil.
 Excessive total or differential settlements.
 Depression settlement due to excessive dewatering.
 Uplift during construction due to high G.W.T.
 Sliding or overturning due to large horizontal loads.

4. 3- Foundation Types
Foundations are divided into two major
categories: shallow foundations and deep foundations,
depending on the depth of embedment of the
foundation.
Generally, if the ratio of the embedment to the width
of a foundation (D/B) is larger than 4, then the
foundation is considered a deep foundation; otherwise,
the foundation is considered a shallow foundation.

5. 4- Requirements For Foundation Design
The following information is needed for this purpose
 A lay out plan of the project.
 A plan of the load – bearing elements such as
columns, walls, etc. with estimated dead and live
loads.
 The strength and settlement characteristics of the
subsoil.
 The hydraulic conditions of the site.

6. 5- Concept for Foundation selection
Choosing a shallow foundation or a deep foundation
depends on many factors, including:
• Loads (or actions) acting on the superstructure, such as
horizontal, vertical, and seismic loads.
• Subsurface conditions.
• Performance (serviceability) requirements, such as
required bearing capacity and settlement.
• Available materials and contractor’s capabilities.

7. 6- Foundation Design Requirements
The design of foundations mainly includes three
primary aspects:
a- Bearing capacity (ultimate limit state).
b- Settlement (serviceability limit state).
c- Structural design (ultimate and serviceability limit states).
The following parameters are required as input values in a
foundation design:
1- Loads from superstructure.
2- Factor of safety for bearing capacity (or partial factors of
safety for geotechnical properties and structural loads).

8. 3- Required total settlement and differential settlement.
4- Subsoil conditions, such as density, cohesion, internal
friction angle, and depth to groundwater table.
A foundation design should determine the following:
1- Foundation type: deep or shallow foundation.
2- Material: steel, timber, concrete, or masonry.
3- Embedment depth.
4- Dimensions.
5- Bearing capacity and factor of safety (or limit state
verification if partial factors of safety are used for design).

9. 6- Total and differential settlements.
7- Reinforcement, if using reinforced concrete, and structural
stability.
To perform satisfactorily, shallow foundations must have two
main characteristics:
1. They have to be safe against overall shear failure in the soil
that supports them.
2. They cannot undergo excessive displacement, or settlement.
(The term excessive is relative, because the degree of
settlement allowed for a structure depends on several
considerations).

10. 7- Design of Shallow Foundation
Shallow foundation can be classified into:-
• Spread footing (support one column).
• Combined footing (support more than one column).
• Raft or mat footing.
Spread Footing
1- with concentric load only
The applied axial load acts at the center of gravity of footing
the pressure under footing is uniform
𝑞𝑎𝑐𝑡 = Q/A ≤ 𝑞𝑎𝑙𝑙

17. Combined Footings
The footing must be combined due to one or two the following
reasons:
- Two columns so closely spaced, if using spread footing the overlap
between them occur.
- The limitation of column located at property lead to
unsymmetrical loading, so to prevent eccentricity, using the
combined footing.
Types of combined footings
Rectangular combined footing
Trapezoidal combined footing
Strap beam combined footing

18. X )

22. If there is no limited value of L use it as the distance as out to
out of columns.
Solve above equations to find B1 & B2 values which give a
uniform pressure under footing:
B1 = (2A/L) * ((3Xc/L) -1, B2 = (2A/L) – B1
Example:- Find B1 & B2
for footing shown.
Design for uniform pressure, qall = 180 kPa
Col. Dimensions (mm) Load(kN)
A 500*500 1000
B 400*400 900

23. Solution: - x = (900*3.2)/1900= 1.52 m
Xc = 1.52 + 0.25 = 1.77 m
A = 1900/180 = 10.56 m2
B1 = (2*10.56)/[4.45 (3*1.77/4.45 -1)] = 0.92 m
B2 = (2*10.56/4.45) – 0.92 = 3.83 m

25. Usually the interior footing is square footing.
The eccentricity value is assumed as (1/6 -1/7) S.
Find the distance between the resultants R1 & R2
𝑺
= S-e
Compute the resultants of force on the footing as:-
R2 = Q2 * S/𝑺
R1 = Q1 + Q2 – R2
Exterior footing:-
L = 2(c + e)
A1 = R2 /qall B1 = A1 / L
Interior footing:-
A2 = R1/ qall B2 = 𝑨𝟐

27. Solution: - take moment about col. B
R1 * (7.2 – 1.5) = 1000 * 7,
R1 = 1228 kN
∑Fy = 0, R2 = 2200 -1228 = 972 kN
External footing:
A1 = 1228/200 = 6.14 m, B1 = 6.14/3 = 2.05 m
Internal footing:
A2 = 972/200 = 4.86, B2 = 4.86/2 = 2.43 m

28. Rafted or Mat foundation: - consists of one footing usually
placed under the entire building area. They are used, when soil
bearing capacity is low, and/or the column loads are so large
that more than 50% of the area covered by conventional
spread, differential settlement must be reduced

30. To design a mat we:-
L = L1 + L2 + 2C
Find location of the resultant R = Pu (total) = 𝑖=1
𝑛
𝑃𝑢𝑖 as:-
∑M @ 1-1= 0
𝑥 =
𝑃𝑢2+𝑃𝑢5+𝑃𝑢8 𝐿1+ 𝑃𝑢3+𝑃𝑢6+𝑃𝑢9 𝐿1+𝐿2
𝑃𝑢𝑇 = 𝑅
= 𝑖=1
𝑛
𝑃𝑢𝑖𝑥𝑖
𝑅
and ex =
eL = 𝑥 − 𝐿2
∑M @ a-a = 0
𝑦 =
𝑃𝑢4+𝑃𝑢5+𝑃𝑢6 𝐵1+ 𝑃𝑢7+𝑃𝑢8+𝑃𝑢9 𝐵1+𝐵2
𝑃𝑢𝑇= 𝑅
= 𝑖=1
𝑛
𝑃𝑢𝑖𝑦𝑖
𝑅
and ey
= eB = 𝑦 − 𝐵1
Find B from
𝑞𝑚𝑎𝑥 =
𝑅
𝐿𝐵
1 +
6𝑒𝐿
𝐿
+
6𝑒𝐵
𝐵
≤ qall
and no tension zone
𝑞𝑚𝑖𝑛 =
𝑅
𝐿𝐵
1 −
6𝑒𝐿
𝐿
−
6𝑒𝐵
𝐵
≥ 0

31. L
B

32. The pressure under any point of mat is computed as:-
Iy Ix
Pu = total load on columns.
B, L: dimensions of mat.
X, y: coordinates of the point, where the pressure is
computed.

33. Example:-

37. Point x y Sign for x Sign for y qu applied, kPa
A 8 10.5 - + 41.622
B 0 10.5 + + 49.062
C 8 10.5 + + 56.502
J 8 10.5 - - 39.018
K 0 10.5 + - 46.458
L 8 10.5 + - 53.898

38. 𝒒𝒎𝒂𝒙 =
𝟏𝟏𝟎𝟎𝟎
𝟐𝟏.𝟓∗𝟏𝟔.𝟓
𝟏 +
𝟔∗𝟎.𝟏
𝟐𝟏.𝟓
+
𝟔∗𝟎.𝟒𝟒
𝟏𝟔.𝟓
= 𝟑𝟔. 𝟖𝟑𝒌𝑷𝒂 < 𝒒𝒂𝒍𝒍
𝒒𝒎𝒊𝒏 =
𝟏𝟏𝟎𝟎𝟎
𝟐𝟏.𝟓∗𝟏𝟔.𝟓
𝟏 −
𝟔∗𝟎.𝟏
𝟐𝟏.𝟓
−
𝟔∗𝟎.𝟒𝟒
𝟏𝟔.𝟓
= 𝟐𝟓. 𝟏𝟖 𝒌𝑷𝒂 > 𝟎,
𝒐. 𝒌
Therefore, the dimensions are adequate.
8- Structural Design of Spread Footings:
To design a spread footing, use the ultimate
strength design method, and the reduction factors are:-
Design consideration Ø
Moment, without axial load (flexural) 0.90
Shear: Two-way action 0.85
Unreinforced footings (plain concrete) 0.65
Bearings on concrete 0.70

39. Design Steps.
Step 1. Compute the footing area via B x L, for a
square footing BxB = A = (Q / qall) for a rectangular
footing BxL= Q / qall
Step 2. Find the soil reaction under ultimate structural
loads to check bearing capacity.
Find the ultimate load and pressure is
Qult = 1.2 D.L + 1.6 L.L
qult = Qult / A = qall *(Qult / Qall)

40. Step 3. Compute the shear in the concrete vc.to find depth of footing
Case (a) wide beam shear: - the critical section is located at a distance (d)
from the face of the column as shown in Fig. below The resisting shear
force
𝒗𝒄 =
∅
𝟔
𝒇𝒄 𝑩 𝒅 , ∅ = 𝟎. 𝟖𝟓 B- Direction
And the ultimate shearing force at critical section is:-
𝒗𝒖 = 𝒒𝒖 𝑩 (
𝑳
𝟐
−
𝒄
𝟐
− 𝒅) to determine d assuming 𝒗𝒄 = 𝒗𝒖 , then
𝒅 =
(
𝒒𝒖𝒍𝒕
𝟐
) 𝑳−𝒄
∅
𝟔
𝒇𝒄+𝒒𝒖𝒍𝒕
B- Direction
or 𝒅 =
(
𝒒𝒖𝒍𝒕
𝟐
) 𝑩−𝒃
∅
𝟔
𝒇𝒄+𝒒𝒖𝒍𝒕
L-Direction
Use larger (d).

42. Case (a) Two - way shear (punching): - inclined cracks
may occur in the footing at distance (d/2) from the face of
the column on all the face sides.
The analysis of a square or rectangular footing may first
be performed by assuming there is no steel in the
member. The depth (d) from the top of the footing to the
tension axis is:-
𝒗𝒄 =
∅
𝟑
𝟏
𝟐
+
𝟏
𝜷𝒄
𝒇𝒄 ≤
∅
𝟑
𝒇𝒄 (∅ = 𝟎. 𝟖𝟓)
(Shear strength of concrete)

43. 𝜷𝒄 =
𝒄𝒐𝒍
.
𝒍𝒆𝒏𝒈𝒕𝒉
𝒄𝒐𝒍
.
𝒘𝒊𝒅𝒕𝒉
∑ Fy = 0
Qu = 2d vc (b + d) + 2d vc (c + d) + (c+d)(b+d) qult
(shear on 4 faces) (bottom face)
Set Qu = BL qult
d2(4 vc + qult) + d (2 vc + qult)(b + c) - (BL - cb) qult = 0
For the special case of a square column, where c = b = w,
d2 (vc + qult/4) + d (vc + qult/2)w - (BL - w2) qult/4 = 0
For the case of a round column, with a = diameter,
d2 (vc + qult/4) + d (vc + qult /2) a - (BL - Acol) qult /π= 0
Effective depth is the largest value of (d) computed from two - way and
one - way shear

46. Step 4. Compute the required area of steel As (each
way) for bending (flexure).
l l
l
l
L
B - direction
l
L
L - direction
B

47. Moments
MuL = qult Bl2 / 2
MuB = qult Ll2 / 2
Where l: critical length as sho
Steel ratios 𝜌 :-
𝜌𝐿 =
0.85𝑓𝑐
𝑓𝑦
1 − 1 −
2𝑅𝑢𝐿
0.85∅𝑓𝑐
, 𝑤ℎ𝑒𝑟𝑒 𝑅𝑢𝐿 =
𝑀𝑢𝐿
𝐵𝑑2
𝜌𝐵 =
0.85𝑓𝑐
𝑓𝑦
1 − 1 −
2𝑅𝑢𝐵
0.85∅𝑓𝑐
, 𝑤ℎ𝑒𝑟𝑒 𝑅𝑢𝐵 =
𝑀𝑢𝐵
𝐿𝑑2
Check minimum area of steel:
𝜌𝐿 & 𝜌𝐵 ≥ 𝜌𝑚𝑖𝑛 =
1.4
𝑓𝑦
𝐴𝑆𝐿 = 𝜌𝐿 𝐵 𝑑 ,& 𝐴𝑆𝐵 = 𝜌𝐵 𝐿𝑑

48. Select bar diameter and compute No. of bars in both
directions.
Step 5. Distribution of reinforcement:-
In L – direction, use uniform distribution of bars.
ASL
D
L - Direction
B

49. ASB1
D
B - Direction
B
ASB - ASB1
In B – direction, place a ratio of reinforcement (AsB1) in a
region of width equal to (B). The rest steel used in equal
parts in both sides.
𝑨𝒔𝑩𝟏 =
𝟐
𝜷+𝟏
𝑨𝑺𝑩, 𝒘𝒉𝒆𝒓𝒆 𝜷 =
𝑳
𝑩

50. Step 6. Compute bond length, column bearing, and the
steel area required for dowels.
Bearing strength is :-
𝑁 = 0.85∅𝑓𝑐 𝐴1
𝐴2
𝐴1
,
∅ = 0.7
Where: - A1 = column area, A2 = (c + 4d)*(b + 4d)
And
𝐴2
𝐴1
≤ 2
Hence, area of dowels is: -
Ad =
𝑄𝑢𝑙𝑡−𝑁
𝑓𝑦
≥ 0.005 𝐴1, and use least 4 equal bars one
at each corner.
Step 7. Draft the above information into a complete
drawing showing all the details.

51. 9- Structural Design of Rectangle Combined Footings
To compute the depth of a rectangular combined footing as
follow:-
Find pressure per unit length under footing as
Pult = 1.2 D.L + 1.6 L.L
qult = Pult/L
Find the pressure due to column load on column width as:-
q1=Pu1/w1 & q2 = Pu2/w2
Where:- w1: width of column 1, w2: width of column 2
Draw shear force diagram and choose the column of max.
shear force (vmax).
Use one – way shear (wide beam) to find the depth of footing
as:-
vu = vmax – qult *d
vc =
∅
6
𝑓𝑐 ∗ 𝐵 ∗ 𝑑
Draw bending moment diagram and choose the column of
max. B.M (Mmax).

53. 10- Structural DESIGN OF MAT FOUNDATIONS
There are several methods to design a mat (or
plate) foundation.
a- An approximate method. The mat is divided into strips
loaded by a line of columns and resisted
by soil pressure. This strip is then analyzed as a combined
footing. This method can
be used where the mat is very rigid and the column
pattern is fairly uniform in both spacing
and loads. This method is not recommended at present
because of the substantial amount
of approximations and the wide availability of computer
programs that are relatively easy
to use—the finite grid method

54. b- Approximate flexible method. This method was
suggested by ACI Committee 336 (2008) and is briefly
described here, and the essential design aids are provided.
c- Discrete element methods. In these the mat is divided
into elements by gridding. These
methods include the following:
1. Finite-difference method (FDM)
2. Finite-element method (FEM)
3. Finite-grid method (FGM)