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Structural Foundation and Foundation Types

Foundations must be designed to transmit forces
from the superstructure into the supporting soil
within acceptable deformations while providing
adequate safety against bearing or uplift failure,
Moehle (2014).
Foundation Types
❑ Shallow Foundations
❑ Deep Foundations
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Shallow Foundations
Shallow foundations include what we call spread
footings. Examples of spread footings are:
– Isolated spread footing
– Combined Footing
– Strap footing
– Wall footing

Deep Foundations
Common type of deep foundations:
– Pile foundation : precast or cast-in-place
• Driven Piles
• Bored piles
– End-bearing pile
– Friction pile
– Combination of end bearing and friction
– Batter pile

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Preliminary Analysis
For preliminary analysis, we may use presumptive
soil bearing capacities based on Chapter 3 of the
NSCP.

Preliminary Analysis
For preliminary analysis, we may use presumptive
soil bearing capacities based on Chapter 3 of the
NSCP, Table 304-1.

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Spread Footing Design (Isolated)

P M Sizing the foundation depends on the soil bearing capacity
and the value of eccentricity.

Define M
eccentricity:
e=
b P
h
P
e = 0; Uniform stress distribution; qmax = ;
bh
P e
0  e  h / 6; qmax = 1 + 6  ; q = P 1 − 6 e  ;
Trapezoidal stress distribution; bh  h  min bh  h

 
h / 6  e  h / 2; 2 P 1 
Triangular stress distribution; qmax =  
3 bh  1 − e 
2 h
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Spread Footing Design (Isolated)

The strength design of spread isolated footings depend on the following critical sections:

Critical section

d /2 d

Critical section Critical section

Two-way Shear One-way Shear Flexure

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Spread Footing Design (Isolated)

The footing capacities for Two-way Shear: NSCP Table 422.6.5.2
Critical section
The punching shear capacity is the least of the following:
d /2 1
1. Vc =  f ' cbo d
3
1 2
2. Vc = 1 +   f ' cbo d c2 + d
6   c1 + d

1 sd  40 Interior column

Two-way Shear
3. Vc = 2+   f ' cbo d  s = 30 Edge column
12  bo 
20 Corner column

Where: bo = 2(c1 + d ) + 2(c2 + d ) is the critical perimeter

 = c2 / c1 ratio of long to short column dimension

Spread Footing Design (Isolated)

The footing capacities for Two-way Shear: NSCP Table 422.6.5.2
Critical section
The design principle:
d /2 c2 + d
Vu  Vc c1 + d

The punching shear demand is calculated as

b
Vu = qu ( Afooting − Aat critical )

Vu = qu bh − (d + c1 )(d + c2 )
h
Two-way Shear
When the above condition is satisfied, then the thickness of the
footing is adequate, otherwise, increase the footing thickness.
Although providing shear reinforcement for footings failing in
shear is theoretical possible, it is seldom used in practice.

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Spread Footing Design (Isolated)

The footing capacity for One-way Shear: NSCP Section 422.5.5.1
The beam shear capacity is equal to:

1
d Vc =  f ' cbd c2
6 c1
The beam shear demand is calculated
as follows:
Critical section
h c  h
Vu = qu b  − 1 − d 
h 2 2 
One-way Shear The design principle:
Vu  Vc
When the above condition is satisfied, then the thickness of the
footing is adequate, otherwise, increase the footing thickness.
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Spread Footing Design (Isolated)

Flexural design of longitudinal reinforcements
The demand for flexure is calculated at the face of the column:
2
q h c 
Mu = u  − 1  c2
2 2 2 c1
The design for reinforcement will follow
the conventional flexural design.
Mu 0.85 f ' c  2 Ru  h
Critical section Ru = = 1 − 1 − 
 bd 2 fy  0.85 f ' c 
Flexure Ab Once the spacing of reinforcing bars is
S=
d determined, you can check if the initial
assumption that  = 0.9 will be check based on
the net tensile strain of concrete.

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Spread Footing Design (Isolated)

Detailing Requirements

NSCP 418.13.1 requires special detailing requirements for column and shearwall footings.

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Spread Footing Design (Isolated)

Presentation of Example Spreadsheet for Foundation Design
The required design forces from MIDAS/ETABS/STAAD/SAP200 are:
1. Service Load Combinations – needed for sizing the footing
2. Ultimate Load Combinations – thickness and reinforcement design

Description P (kN) Mx (kN-m) My (kN-m)

Max P Max P Corresponding MX Corresponding MY
Min P Min P Corresponding MX Corresponding MY
Max Mx Corresponding P Max Mx Corresponding MY
Min Mx Corresponding P Min Mx Corresponding MY
Max My Corresponding P Corresponding MX Max My
Min My Corresponding P Corresponding MX Min My

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Spread Footing Design (Isolated)

Presentation of Example Spreadsheet for Foundation Design

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Spread Footing Design (Isolated)

Presentation of Example Spreadsheet for Foundation Design

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Spread Footing Design using Plate Theory

Plate Theory: Designing foundation using plate elements
The Winkler Model
One very popular method for modeling the soil-interaction has its origins in the
work by Winkler in 1867. According to Winkler, the vertical translation of soil, w,
at a point is assumed to depend only upon the contact pressure, p, acting at
that point in the idealized elastic foundation and a proportionality constant, k.
Where k is the modulus of subgrade reaction.

p = kw
Application of the Winkler Model involves the solution of a fourth order
differential equation:
  
D 4 w + kw = q;  4 = + 4+ 4
x y z
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Spread Footing Design using Plate Theory

Plate Theory: Designing foundation using plate elements
The Winkler Model
The challenge in using the model lies in the determination of appropriate
subgrade modulus value.
Several approximation are used in practice such as the recommendation by
Joseph Bowles (1997):
ks = 40 SFqa In kN/m3
qa
p = kw; k = p = Settlement is limited to 25 mm
w 0.025 / SF
k = 40SFqa
Other models are those introduced by Biot (1937) and Vesic 1961.

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Spread Footing Design using Plate Theory

Understanding Plate Elements For plate under bending:
• Moment Mx refers to the
moment acting along the x
axis. It is produced by the
resultant force from  x
stresses.

Plate Bending (Cook et al., 2002)

• Moment My refers to the
moment acting along the y
• Mxy is the twisting moment also known as the
axis. It is produced by the
Wood-Armer moments.
resultant force from  y
M xtotal = M x + M xy stresses.
M ytotal = M y + M xy

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Spread Footing Design using Plate Theory

Understanding Plate Elements Plate Shear Stresses
• The shear stresses are
represented by  yz and
 zx . The stresses act
perpendicular to the
thickness of the plate.

Plate Bending (Cook et al., 2002)

• STAAD denotes these
values as SQX and SQY.
However, MIDAS provides a
better representation of
these stresses by presenting
them as Shear Resultant in
force per unit length.
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Spread Footing Design using Plate Theory

Procedures for Modeling Foundation using Plate Elements
• Size the footing dimension using conventional methods and assumed a
footing thickness.
• Select the mesh size, e.g., equal to column dimension or at least less than
or equal the effective depth.
• Select an analytical relationship for subgrade modulus.
• Extract the forces same way as for analytical procedure.
• Develop the model.
• Compare base pressure to allowable.
• Check shear using the same capacity equations for two-way and one-way
shear.
• Calculate demand. May vary depending on the selected FEM software.
• Design flexural reinforcements.

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Spread Footing Design using Plate Theory

It is important to understand the plate type adopted by the FEM Model.
STAAD uses

STAAD Internal Forces

MIDAS Internal Forces

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