Structural Design of Footings

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Structural Design of Footings

• Prof. Jie Han, Ph.D., PE
• The University of Kansas

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Outline of Presentation

• Introduction
• Design for Square Footings
• Design for Continuous Footings
• Design for Rectangular Footings
• Connections with Superstructures

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Factored Normal Load (ACI)
Pu 1.2 D 1.6 L
D dead load
L live load
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Minimal Requirements
d
T
db
3in.
3in.
Flexural steel
Effective depth
Minimal thickness
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Common Selection of Materials
Concrete
Compressive strength
Steel
Grade 40 steel Grade 60 steel
fy 40,000psi (300MPa)
fy 60,000psi (420MPa)
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Design Criterion for Shear
Design Criterion
Vuc factored shear force on critical surface
? resistance factor for shear 0.75
Vnc nominal shear capacity on critical surface
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Nominal Shear Capacity
Vnc nominal shear capacity on critical surface
Vc nominal shear capacity of concrete
Vs nominal shear capacity of steel (ignored)
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Design for Square Footings
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Design of Square Footings for One-Way Shear
Pu
c
B
d
T
d
Factored shear force on one critical surface
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Design of Square Footings for One-Way Shear
Pu
Mu
c
Vu
d
d
Most critical face
Factored shear force on one critical surface
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Design of Square Footings for Two-Way Shearing
Pu
c
B
d/2
Mu
d/2
T
d
c d
Most critical face
Factored shear force on one critical surface
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Design of Square Footings for Two-Way Shearing
Pu
Vu
Most critical faces
Most critical faces
cd
Factored shear force on one critical surface
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Nominal One-Way Shear Capacity
English Units
SI Units
Vnc nominal shear capacity on one critical
surface (lb or N)
Vnc nominal shear capacity of concrete (lb or N)
bw length of one critical surface B (in or mm)
d effective depth (in or mm)
fc 28-day compressive strength of concrete
(psi or MPa)
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Nominal Two-Way Shear Capacity English Units
Smallest of
Vnc nominal shear capacity on one critical
surface (lb)
?c long side length cl/short side length cs of
columns
?s 40, 30, and 20 for interior, edge, and
corner columns
b0 length of one critical surface c d (in)
c column width (in or mm)
d effective depth (in)
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Nominal Two-Way Shear Capacity SI Units
Smallest of
Vnc nominal shear capacity on one critical
surface (N)
?c long side length cl/short side length cs of
columns
?s 40, 30, and 20 for interior, edge, and
corner columns
b0 length of one critical surface c d (mm)
c column width (mm)
d effective depth (mm)
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Critical Locations for Flexure
Critical sections
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Flexural Design Principles
Neutral axis
b
0.85fc
a/2
c
C
a
d
d-a/2
fs
T
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Nominal Moment Capacity

• As cross-sectional area of reinforcing steel
• steel ratio
• b width of flexural member

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Required Cross-Sectional Area of Reinforcing Steel
Design Criterion
Required Area of Reinforcing Steel

• Muc factored bending moment
• ? 0.9 for flexure in reinforced concrete
• b width of flexural member

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Factored Bending Moment at Critical Section
Pu
Mu
c
l
B
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Location of Critical Section for Bending
c
c
c
c/4
cp
l
l
l
B
B
B
Concrete
Masonry
Steel
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Development Length
- Develop proper anchorage
c
ld
l
B
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Development of Bars in Tension
English
SI
ld minimum required development length (in or
mm)
db nominal bar diameter (in or mm)
c half-spacing or cover dimension (in or mm)
s max. c-c spacing of transverse reinf. within
ld (in or mm)
n number of bars
Atr total cross-sectional area of all
transverse reinf. (in2 or mm2)
fyt yield strength of transverse reinforcement
(psi or MPa)
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Definition of Transverse Reinforcement Atr
Atr 2Ab
Atr 4Ab
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Modifiers for Development Length
Factor
Modifier
Condition
1.3
?
Top reinf. (bars w/ 12in. Concrete below)
Bottom bars
1.0
?
Epoxy-coated bars w/ cover lt 3db or Clear
spacing lt 6db
1.5
All other epoxy-coated bars
1.2
Uncoated reinforcement
1.0
?
No. 6 and smaller bars deformed wire
0.8
No. 7 and larger bars
1.0
?
Lightweight-aggregate concrete
1.3
Normal weight concrete
1.0
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Development of Bars in Compression
English
ld minimum required development length (in)
lab basic development length (in)
db nominal bar diameter (in)
?s modifying multiplier
Excess reinforcement ?s required As/provided As
Spirally enclosed reinforcement ?s 0.75
fc compressive strength of concrete (psi)
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Design for Continuous Footings
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Continuous Footings
c
T
d
d
B
d
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Transverse Reinforcement - One-Way Shear
c
d
d
d
English
B
SI
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Transverse Reinforcement - Flexure
450
Zone of compression
No transverse steel is needed if the entire base
is within a 450 frustum
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Transverse Reinforcement - Flexure
c
l
d
Required Area of Reinforcing Steel
B
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Design for Rectangular Footings
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Design Philosophy

• Similar to those for square footings
• Check one-way and two-way to determine minimal d
  T
• Design long steel bars and evenly distribute
  them
• Design short steel bars distribute the portion
  (E) of the
• total short steel area within the inner zone

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Critical Shear Surfaces
One-way shear surface
Two-way shear surface
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Long Steel and Short Steel
Long steel
Short steel
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Distribution of Short Steel
B
B
Inner zone
Outer zone
Outer zone
L
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Connections with Superstructures
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Use of Dowels for Connection
Wall steel
Concrete or masonry column
Lap joint
Dowel
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Design for Compressive Loads
Nominal column bearing capacity
Design criterion
Pu factored column load
A1 cross-sectional area of the column c2
s (A2/A1)0.5 lt 2 if c 4d lt B otherwise, s 1
A2 (c 4d)2
? 0.7