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Introduction to Spread Footing Design Flow Charts
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Strunet.com: Spread Footing Design V1.01 - Page 1
Spread Footing Charts in Bullets:
• All code provisions are listed, where applicable, on the charts for quick
reference.
• Analysis assume rigid footing condition, resulting in a uniform soilpressure for concentric load, and a triangular or trapezoidal soil
pressure for eccentric loading (combined axial and bending)
• Establish preliminary size under service loads, and proportionrectangular footing dimensions, if required, around a rectangular column.
• Calculate in one single equation one -way shear, two-way shear, and
design moment, under factored loads, respectively.
• Deal separately with two eccentricity conditions, while e<L/6 flexural
equations are used, and for e>L/6 equilibrium equations are used.
• Drive the nominal shear strength of the concrete for bo th beam shear
(one way) and punching shear (two way, or slab shear). Alternatively,provide reference to the code provisions where shear reinforcement
may be used in case of factored shear force exceeded nominalconcrete shear strength with restricted foot ing depth.
• Calculate required flexural reinforcement ratio and compared with the
minimum and maximum permitted by code, and provide requiredtensile reinforcement, and calculate rebar development length.
• Address axial force transfer at the column base (f or compression only),and fully detailing the dowels design and development length requiredinto footing and column.
• Include sketches illustrating the subject under investigation.
Include notations sheet explaining in details all symbols used in the char s.
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As = area or reinforcement.
b = column width dimension.
bo = perimeter of critical shear section for footing.
B = footing width dimension.
d = distance from extreme compression fiber to centroid of tensionreinforcement.
d b = nominal diameter of bar.
f’ c = specified compressive strength of concrete.
f y = specified tensile strength of reinforcement.
h = overall member thickness.
l = column length dimension.
l ava = available length for bar development.
l d = development length of bar in tension.
l s = compression lap splice length.
l db = basic development length of bar in compression.
L = footing length dimension.
P o = axial load, service.
P u = axial load, ultimate.
qact = actual soil pressure based on service loads condition.
qall = allowable soil bearing pressure.
qs = factored actual soil pressure.
R u = coefficient of resistance.
V u = factored shear force at section considered.
V c = nominal shear strength of concrete.
β c = ratio of long side to short side of column dimensions.
ρ = ratio of tension reinforcement.
ρ b = ratio of tension reinforcement at balanced strain condition.
ρ max = maximum ratio permissible by code.
ρ min = minimum ratio permissible by code.
ρ req’d = required ratio of tension reinforcement.
ρ prov’d = provided ratio of tension reinforcement.
φ = strength reduction factor.
Notations for Spread Footing Design Flow Charts
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Force transfer atcolumn/footing
for compressionforce only
Reinforcement
One Way Shear (Beam Action)
Two Way Shear (Slab Action)
Ultimate DesignForces V u & M u
Rebar Development
EquilibriumEquations
Ultimate DesignForces V u & M u
Ultimate SoilsPressure
FlexuralEquations
Ultimate DesignForces V u & M u
Ultimate SoilsPressure
Shear Check
Footing subjectedto vertical load only
Preliminary Size Preliminary Size
Main Input &Notation
Footing Subjectedto vertical loadand moment
Strunet.com: Spread Footing Design V1.01- Page 3
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Spread Footing Analysis & DesignMain Chart
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footing sizeis given?
=o
F
all
P A
q
square or
rect. footing?
≅ = F B L A
Roundup B,L
F
A = BL
us
F
P q =
A
YES
SquareRect.
NO
PreliminarySize
ultimate bearingpressure
oact all
F
P q = < q
A
l= column longer dimensionb= column shorter dimension
Proceed toultimate Design
forces
Footingsubjected to
vertical load only
proportion of footing w/ column
′ = 4a
′ = +2b (l b)
′ = − F c lb A
′ ′ ′ ′+′ =
′
2 4
2
-b b - a c k
a
= +2L l k'
F AB =
L
Strunet.com: Spread Footing Design V1.01- Page 4
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Preliminary Size of Footing Subjected to Vertical Loads only.
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one way shear (beam action)
( )u sV = q B 0.5L-0.5l - d
( )u sV = q L 0.5B -0.5b- d
two way shear (slab action)
( ) ( ) ob = 2 l + d + b+ d use w/ V c
calculation
( ) ( ) u s F V = q A - l + d b+ d
finding M u
TransverseDirection
LongitudinalDirection
( )2
u sM = 0.125q L B - b
( )2
u sM = 0.125q B L - l
ShortDirection
long.Direction
L
l
b B
L
qs
d
d/2 Pud/2
l
qs
finding V u
L
B
l+d
b + d
e: the following footing forcesculations are based on:column dimension parallel to L
= column dimension parallel to B
Ultimate Design
Forces V u & M u
Strunet.com: Spread Footing Design V1.01- Page 5
STRUNETCONCRETE DESIGN AIDS Ultimate Forces for Footing Subjected to Vertical Loads only
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L>6e
o o
2
all
P 6M 1B = +
q L L
max all q < q
o omin
F F
P M q = -
A S
oe
o
3M L =1.5L-
P
o
all e
2P B =
q L
B & L
omax
e
2P q =
BL
max all q > q
STOP.Increase B or L
Proceed to UltimateSoils BearingPressure, use
flexural equations
minq >0.0
Proceed to UltimateSoils BearingPressure, use
equilibrium equations
Lmax = maximum
permissible footinglength .
o
o
M
e = P
L=Lmax
NO
YESYES
YES
NO NO
NO
oceed to Ultimate
ring Pressure, useuilibrium equations
L
qmax
Mo
Po
qmin
e
Soils Pressure distribution if
L
qmax
Mo
Poe
Soils Pressure distribution if
Le
PreliminarySize
YES
Strunet.com: Spread Footing Design V1.01- Page 6
=F A BL
=2
6
F
BLS
= +o omax
F F
P M q
A S
6
Le <
6
Le >
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Preliminary Size of Footing Subjected to Vertical Load and Moment
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ShortDirection
long.Direction
u umax
F F
P M q = +
A S
u umin
F F
P M q = - A S
minq >0.0
mine
min max
q LL =L -
q +q
STOP.
go to equilibrium for
continuation
max minq = q -qδ
( )
( )
( )
( )
( )
1 min
2 min
3 min
4 min
5 min
0.5 L - l - d q = q + q
L0.5 L- l
q = q + qL
0.5 L+l q = q + q
L
0.5 L+l+d q = q + q
L
0.5 L+ l + d q = q + q
L
δ
δ
δ
δ
δ
L
qmax
q5
d
d/2
Mu
Pud/2
q2q1
l
qmin
q3q4
Ultimate DesignForces V u & M u
one way shear (Beam Action)
( )( )u max 5 V =0.5B q +q 0.5L-0.5l -d
( )( )u max minV =0.5L q +q 0.5B-0.5b-d
two way shear (Slab Action)
finding V u
finding M u
( )( )2
u 3 max M =0.0625B q +q L- l
( )( )2
u min max M =0.0625L q +q B -bTransverseDirection
LongitudinalDirection
YESNO
( )( )
( )( ) ( )
( )( )
u min 1
1 4
4 max
V =0.25B q +q L - l -d
+0.5 q +q B - b - d l +d
+0.25B q +q L - l - d
Strunet.com: Spread Footing Design V1.01- Page 7
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Ultimate Forces with Flexural Equations for FootingSubjected to Vertical Load and Moment
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Ultimate BearingPressure using
Equilibrium Equations
one way shear (Beam Action)
ShortDirection
long.Direction
two way shear (Slab Action)
STOP.ncrease L
YESNO
Ultimate DesignForces V u & M u
TransverseDirection
LongitudinalDirection
finding M u
NO
Strunet.com: Spread Footing Design V1.01- Page 8
2 u
max e
P
q BL=
31 5 u
e
u
M L . L
P = −
( )
( )
( )
( )
( )
1
2
3
4
5
0 52
0 52
0 52
0 5 2
0 52 2
max e
e
max e
e
max e
e
max e
e
max e
e
. qq L L l d
L
. qq L L l
L
. qq L L l
L
. qq L L l d L
. qq L L l d
L
= − − −
= − −
= − +
= − + +
= − + +
( ) ( )50 5 0 5 0 5u max V . B q q . L . l d = + − −
( )0 5 0 5 0 5u max eV . q L . B . b d = − −
( )0 5eL . L l d > + +
( )( )
( )( )
4
4
0 25
0 25 2
u max
e
V . B q q L l d
. q L L l d B b d
= + − −
+ − + + − −
( )
( )( )( )
( )( )
1
1 4
4
0 25 2
0 5
0 25
u e
max
V . q B L L l d
. q q B b d l d
. B q q L l d
= − − −
+ + − − +
+ + − −
0 5 0 5eL . L . l > +
( )2
0 0625u e max M . L q B b= −
( )( )2
30 0625u max M . B q q L l = + −
YES
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L
qmax
q5
d
d/2
Mu
Pu d/2
q2q1
l
q3q4
Le
Ultimate Forces with Equilibrium Equations for Footing Subjected to Vertical Load and Moment
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is f ct given?
use ACI11.3.2.1
repeat check
one wayshear o.k.
NO
YESNO
NO
ACI 15.5.1 ACI 11.12
ACI 11.3.1.1
'
100c f psi≤
ACI 11.1.2
ACI 11.2.1.2 ACI 11.2.1.1
YESNO
see V ucalculations
ACI 9.3.2.3
As = provided
flexural reinf.
YES
can increase f c '
or footing depth?
Req'd increase
V u=φ V c
find d or f' c
One way Shear
Normal or LightWt Concrete
finding V c
LIGHT
ACI 11.12.1.1
ACI 11.2.1
YES
NORMAL
,
,
w
w
b = B
b = Ld = h-3.5 , h=
footing width short direction
footing length long directionfooting depth
Strunet.com: Spread Footing Design V1.01- Page 9
( )′=all-Light wt 0 75 2c c w :V . f b d
( )′=
Sand Light wt 0 85 2c c w :V . f b d
=
≤
26 7
6 7
ct c w
' ct c
f V b d
.
f f .
= 2 '
c c w V f b d
c V
uV φ = 0 85.
φ >u c V V
ρ = sw
w
A
b d
ρ
= + ≤ 1 9 2500 3 5' ' u
c c w w c w
u
V d V . f b d . f b d
M
φ >u c V V
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One-Way Shear Check for Spread Footing
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Two wayShear
option to useshear
reinforcement?
N.G., increase footingdepth d or f' c
Repeat
Check
two wayshear is o.k.
Proceed toreinforcement
NO YES
YES
ACI 11.12.1.2
( ) ( )2 +o
b b d l d = + +
b & l are columnwidth and lenght
ACI 9.3.2.3
ACI 11.12.3
ACI 11.12.3.1 ACI 11.12.3.2
YESNO
ACI 11.5.6.2
ACI 11.1.2
N.G. increase footingdepth d or f' c
YESNORepeatCheck
NO
L
B
l+d
b + d
≤100'
c
f psi
c V
β =c
l
b
β
α
= +
= +
=
42
2
4
'
c c o
c
' sc c o
o
'
c c o
V f b d
d V f b d
b
V f b d
uV
φ = 0 85.
φ >u c V V
> 2 '
c c oV f b d
= v y
s
A f d V
s
s u c V =V - V φ φ
6 '
u c oV f b d >
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Two-Way Shear Check for Spread Footing
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YES
use deeper section or higher
strength
NO
NO ACI 10.5.2
YES
YES
NO
NO YES
NO YES
ACI 10.2.7.3
ACI 8.4.3
ACI 10.3.3
YES
proceed to rebar development
ACI 7.12.2
ACI 10.3.3
ACI 10.2.7.3
see M ucalculations
ACI 9.3.2.1
NO
Strunet.com: Spread Footing Design V1.01- Page 11
uM
φ =
2u
Mu
R bd φ = 0 9.
ρ ′
= − − ′
0 85 21 1
0 85c u
req' d
y c
. f R
f . f
ρ ρ ≥req' d min
ρ ρ ≤req' d max
ρ ρ =1 33 req' d .
ρ ρ < Min
ρ ρ =1 33 req' d .e Min ρ ρ =
ρ ρ = ≥ =mins s min A bd A bh
ρ finding min
> 60 ksi ?y f
> 60 ksi ?y f 60,000
0.0018min
y f ρ
=
0.002min ρ =0.0018min ρ =
ρ min
MAX b=0.75 ρ ρ
1
0 85 87 000
87 000
c b
y y
. f ,
f , f
ρ β ′
= +
′ ≤ 4000c f psi
ρ finding max
β =1 0 85.c 1
f -4000 = 0.85 - 0.05 0.65
1000 β
′ ≥
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Area of Reinforcementfor Spread Footing
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c=one-half bar spacing , or
center of bar to the nearestconcrete surface, which is smaller
ACI 12.2.4
ACI 12.2.3
ACI 318-9512.2.3
ACI 12.2.3
Rebar Development
k tr =0.0 for footing
+≤ 2 5tr
b
c k .
d
αβ ≤1 7.
′ ≤ 100c f psi
αβγλ =
+′
3
40
y
d btr c
b
f l d
c k f d
γ
γ
=
=
0 8 for bar size 6 or smaller.
1 0 for bar size 7 or larger.
.
.
=
=
′= ≥
1 0 , normal weight concrete.1 3 , light weight concrete, if is not s pecified.
6 71 0 , light weight concrete, if is speci fied
ct
c ct
ct
.
. f
.f . f
f
β β
β
= 1.5 Epoxy coated w/ cover < 3db and cl ear spacing < 6db= 1.5 all other epoxy coated
= 1.5 uncoated
α
α
=1.3 fresh concrete below bars is more t han 12"
=1.0 fresh concrete below bars is 12" or less
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Rebar Development
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ACI 15.8
Bearing strengthof column
Bearing strengthof footing
select dowelsreinforcement
the largest
ACI 15.8.1.1
ACI 15.8.2.1 ACI 15.8.1.2YESNO
for compression
force only
Proceed todowels
development
ACI 10.17.1
the least
ACI 10.17.1
φ
=
=
1
0 7 ACI 9.3.2.4
A bl
.
′ ′> 2cc cf f f
′ ′=
′ ′=
footing
column
cf c
cc c
f f
f f
[ ]φ φ ′=2
1
1
0 85nb cf
AP ( . f A )
A
φ φ ′= 10 85nb cc P ( . f A )
φ ′= 11 19nb cf P . f Aφ ′= 10 595nb cc P . f A
φ nbP
φ
φ
−=
u nbs
y
P P A
f = 10 005
mins A . A
prov' d s A
=req' d
prov' d
s
r
s
Ak
A
≤2
12 0
A. A
( )= maxreq' d mins s s A A ,A
u nbP P φ >
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Forces Transfer at Column/Footing Interface
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col. bars are #14or #18 and in
compression only?
dowel comp. lapsplice l s
use larger number of smaller size dowels, or increase footing depth
STOP. dowels arefully developed.
development isthe largest of
RepeatCheck
ACI 15.8.2.3
col. bar (d b 14 &
18) develop. length
ACI 15.8.2.3
ACI 12.3.2
ACI 12.16.1
CI 12.3.2
ACI 12.3.3.1
dowelsdevelopment
into footingl 1
into columnl 2
NOYES
NO YES
NO YES
the largest
NOYES
l 2
l 1
= column rebar
& dowels
yc y f f
= ≥′
0 02
0 0003b yc
db b yc
cc
. d f
l . d f f
= ≥′
0 020 0003
b yc
db b yc
cf
. d f . d f
f ≤ 60y f ksi
= >0 0005 12s b yc l . d f " ( )= − >0 0009 24 12s yc bl . f d " =d r dbl k l
= ≥′
0 020 0003
b yc
db b yc
cc
. d f l . d f
f
′ < 3000c f psi
= 1 33s sl . l =s sl l
sl
>d aval l
= − 6aval h
( )2 max s dbl l ,l =
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Column Dowels Development