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This Powerpoint presentation was prepared byDr. Terry Weigel, University of Louisville.This work and other contributions to the
text by Dr. Weigel are gratefullyacknowledged.
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Design for load transfer to soil uses
unfactored loads
Support structural members and transferloads to the soil
Structural members are usually columns orwalls
Structural design of footing is done withfactoredloads
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Typically, bottom of footing must be locatedbelow frost line
Footings must be designed to prevent bearingfailure, sliding and overturning
Footings must be designed to preventexcessive settlement or tilting
Excavation may be required to reach a depthwhere satisfactory bearing material islocated
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Wall footings enlargement of the bottom ofthe wall
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Isolated or single column square footing loads relatively light and columns notclosely spaced
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Combined footings support two or morecolumns heavily loaded columns; closelyspaced columns; columns near property line
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Mat or raft foundation continuous concreteslab supporting many columns; soil strengthrelatively low; large column loads; isolated
spread footings would cover more than 50percent of area; reduce differentialsettlement
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Pile caps distribute column loads to groupsof piles
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Soil pressure is assumed to be uniformlydistributed beneath footing if column loadis applied at the center of gravity of thefooting
Footings supported by sandy soils
Footings supported by clayey soils
Footings supported eccentric loads
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Actual soil pressure is based on unfactoredloads
Allowable soil pressure may be determined bya geotechnical engineer
When soil exploration is not feasible, values
provided by building codes may be usedFactor of safety is typically 3
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Maximum Allowable Soil Pressure
Material Allowable Pressure,ksf
Rock 20% of ultimate
strengthCompact coarse or fine sand,hard clay or sand clay
8
Medium stiff clay or sandy clay 6
Compact inorganic sand and siltmixtures
4
Loose sand 3
Soft sand clay or clay 2
Loose inorganic sand-siltmixtures
1
Loose organic sand-silt mixtures,muck or bay mud 0
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Generally, beam design theory is used
Shear strength almost always controlsfooting depth
Compute moment at the face of the wall
(concrete wall) or halfway between wallface and its centerline (masonry walls)
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Shear may be calculated at distance d fromface of the wall
Use of stirrups is not economical set d sothat concrete carries all the shear
'
'
2
2
c c w
u
c w
V f b d
Vdf b
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Design a 12-in wide strip
Section 15.7 of ACI Code:
Depth of footing above bottomreinforcement not less than 6 infor footings on soil and not lessthan 12 in for footings on piles
Minimum practical depth of footing is 10 inand 16 in for pile caps
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Design a wall footing to support a 12-in. widereinforced concrete wall with a dead loadof 20 k/ft and a live load of 15 k/ft. The
bottom of the footing is to be 4 footbelow final grade, the soil weighs 100lb/ft3the allowable soil pressure is 4 ksf.The concrete strength is 3,000 psi and thesteel is Grade 60.
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Assume a footing thickness of 12 in. With aminimum cover of 3 in., this gives a d valueof about 8.5 in. Compute the footing
weight andsoil weight:
Footing weight
12 in150 150 psf
12 in/ft
Soil weight
36 in100 300 psf
12 in/ft
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Effective soil pressure and required width offooting:
4000 psf 150 psf 300 psf 3550 psf
Width of footing required
20 k/ft 15 k/ft9.86 ft
3.55 ksf
Use 10 ft
eq
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Factored bearing pressure for design ofconcrete:
1.2 20 k/ft 1.6 15 k/ft4.80 ksf
10 ftuq
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Compute design shear (at distance d fromface of wall):
10 ft 6 in 8.5 in
4.80 ksf 18.2 k 2 12 in/ft 12 in/ft
18,200 lb18.46 in
0.75(1.0) 2 3000 ksi 12 in
Much larger than orginal assumption
Try a thicker footing - say 20 in thick
16.5 in
uV
d
d
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20 in4000 psf 150 psf
12 in/ft
28 in 100 psf 3517 psf 12 in/ft
Width of footing required
20 k/ft 15 k/ft
9.95 ft3.517 ksf
Use 10 ft
eq
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10 ft 6 in 16.5 in4.80 ksf 15.0 k
2 12 in/ft 12 in/ft15,000 lb
15.21 in0.75 2 3000 ksi 12 in/ft
15.21 in 3.5 in 18.71 in
Use a 20 in thick footing
uV
d
h
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22
22
10 ft 6 in4.5 ft
2 12 in/ft
Compute moment on a one-foot-long strip
4.80 k/ft 4.5 ft48.6 k-ft/ft
2 2
12 in/ft 48,600 lb-ft/ft 198.3 psi0.9 12 in 16.5 in
u
u
wLM
Mbd
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Appendix Table 4.12,r = 0.00345 < 0.0136,section is tension controlled; = 0.9
2
in0.00345 12 in 16.5 in 0.68ft
sA
Use No 7 at 10 in (As = 0.72 in2 / ft from
Table A.6)
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Development length:
1
5 in side cover
0.875c 3 3 3.4375 3.5
2 2
10 in5 in one-half c-c spacing of bars
23.5 in 0
4.0 Use 2.50.875 in
t e s
b
bb b
b
b tr
b
c
duse c in
c
c K
d
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'
2,
2
,
3
40
3 60,000 psi 1 32.86 diameters
40 2.53000 psi
0.68 in /ft32.86 31.03 diameters
0.72 in /ft
31.03 0.875 in 27.15 in
yd t e s
b trb c
b
s requiredd
b s provided
d
f
c Kd fd
A
d A
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10 ft 12 in/ft6 in 3 in 51 in 27.15 in
2
Available length for development
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2
0.0018 12 in 20 in 0.432 in / ftsA
Temperature and shrinkage steel
Use No 5 at 8 in (As = 0.465 in2 / ft)
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Most isolated square footings have a constantthickness
For very thick footings, it may be economicalto step or taper footing
Two types of shear must be considered one-
way shear and two-way shear
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Constant thickness
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Stepped
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Tapered
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'2
u
c w
Vd
f b
Same as for wall footings
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ACI Code Section 11.11.1.2 states that criticalsection is at a distance d/2 from face ofsupport
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s= 40 for interior columns
s= 30 for exterior columns
s= 20 for corner columns
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Flexural reinforcement is required in twodirections
The values of d for the layers of steel in
the two directions will be different
For square footings, design using the value ofd for the upper layer is typical
For square footings supporting non-squarecolumns, moments are larger in theshorter direction of the column
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Reinforcing steel areas required to resistmoment are often less than minimumrequired steel:
Code Section 10.5.4 states that minimumarea and maximum spacing need only beequal to values required for temperatureand shrinkage steel
,min
'
,min
200
3
s w
y
c
s w
y
A b d
f
fA b d
f
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Maximum steel spacing may not exceed threetimes the footing thickness or 18 in.
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All forces at the base of the column must betransferred to the footing
Compressive forces must be transferred bybearing
Tensile forces may be transferred byreinforcement or mechanical connectors
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Columns transfer loads directly over the areaof the column
Load transfer into the footing may byassumed to occur over an effective areawhich may be larger than the column area
For the same strength of concrete, thefooting can support more bearing loadthan can the column
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Bearing strength permitted at the base ofthe column ->
Bearing strength permitted on the footing isthe same value multiplied by ->
See ACI Code Section 10.14.1
'
10.85 cf A
2
1
2A
A
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A2 is the area of footing geometrically similarto and concentric with the column
A1 is the area of the column
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Development length of dowels must besufficient to transfer column force tofooting
Development length of dowels may not be lessthan the length required if bearing stresswas not exceeded
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ACI Code does not permit splicing of No 14 orNo 18 bars
ACI Code Section 15.8.2.3 does permit No 14
or No 18 bars to be spliced to No 11 (orlarger) dowels in footings
These dowels must extend into the columnnot less than the development length forthe No 14 or No 18 bar, or thecompression lap splice length for thedowels, whichever is larger
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These dowels must extend into the footingfor a distance not less than thedevelopment length for dowels
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Use a larger number of smaller dowels
Use a deeper footing
Add a cap or pedestal to the footing
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Development length must be those fortension
Splice requirements are those found in ACICode Section 12.17
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Square footings are more econonical thanrectangular footings
Long direction steel is uniformly distributedalong short direction
Short direction steel is non uniformlydistributed along long direction
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ACI Code Section 15.4.4.2
Reinforcement in band width 2
Reinforcement in short direction 1
is the ratio of the length of the footing inthe long direction to the length in theshort direction
Remaining steel is distributed uniformlythroughout the two portions of thefooting outside the band
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Design a square column footing for a 16-in.square tied interior column that supportsloads of D = 200 k and L = 160 k. The
column is reinforced with eight No 8 bars,the bottom of the footing is 5 foot belowfinal grade, the soil weighs 100 lb/ft3theallowable soil pressure is 5 ksf. The
concrete strength is 3,000 psi and thesteel is Grade 60.
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Assume a footing thickness of 24in. with aminimum cover of 3 in., this gives a d valueof about 19.5 in. Compute the footing
weight andsoil weight:
Footing weight
24 in150 300 psf
12 in/ft
Soil weight36 in
100 300 psf 12 in/ft
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Effective soil pressure and required area offooting:
2
5000 psf 300 psf 300 psf 4400 psf 200 k 160 k
81.82 ft4.40 ksf
Use 9 ft x 9 ft
eq
A
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Factored bearing pressure for design ofconcrete:
2
1.2 200 k 1.6 160 k 6.12 ksf
81 ftuq
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Depth required to resist punching shear:
22
2
4(16 19.5) 142 in
81.0 ft 2.96 ft 6.12 442.09 k
442,090 lb18.95 in 19.5 in Ok
0.75 4 3000 psi 142 in
442,090 lb
40 19.5 in0.75 2 3000 psi 142 in
142 in
10.12 in 19.5 in Ok
o
u
b
V
d
d
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Depth required to resist one-way shear:
1 9 ft 2.208 ft 6.12 ksf 121.62 k
121,620 lb13.71 in 19.5 in Ok
0.75 2 3000 psi 108 in
uV
d
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Appendix Table 4.12,r = 0.00225
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Development length:
1
bottom cover 3.5 inone-half center-to-center bar spacing 6 in
3.5 in 03.5 Use 2.5
1.0 in
t e s
b
b
b tr
b
cc
c K
d
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'
2,
2,
3
40
3 60,000 1 32.86 diameters
40 2.53000
6.95 in
32.86 32.30 diameters7.07 in
32.30 1.0 in 32.30 in
yd t e s
b trb c
b
s requiredd
b s provided
d
f
c Kd fd
A
d A
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9 ft 12 in/ft 16 in
3 in 43 in 32.30 in2 2
Available length for development
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Design for load transfer for the column andfooting in Example 12.2. The strength ofthe sand-lightweight concrete (different
from Example 12.2) in the column is 4 ksi.
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Bearing force at the column base:
1.2 200 k 1.6 160 k 496 k
Design bearing force at the column base:
2'
10.85 0.65 0.85 4 ksi 16 in
566 k 496 k Ok
cf A
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Design bearingforce in thefooting
concrete:
2
2
' 21
1
2
108 in6.75 Use 2
16 in
0.85
0.65 0.85 3 ksi 16 in 2
848.6 k 496 k Ok
cAf AA
Minimum dowel area:
2 20.005 16 in 1.28 in
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'0.02 0.02 0.75 in 60,000 psi
16.74 in0.85 4000 psi
b y
d
c
d f
f
Dowel development length into the column
'
0.02 0.02 0.75 in 60,000 psi16.43 in
1.0 3000 psi
b y
d
c
d f
f
Dowel development length into the footing
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0.0003 0.0003 0.75 in 60,000 ksi
13.50 in
8.0 in
d b y
d
d f
Development length must not be less than:
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Design for load transfer for a 14-in. squarecolumn to a 13 ft square footing if Pu =800 k. Normal weight concrete is used in
both the column and the footing. Theconcrete in the column is 5 ksi and in thefooting is 3 ksi. The column is reinforcedwith eight No 8 bars.
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Design bearing force in the footing concrete:
2
2
2
1
' 21
1
2
156 in11.14 Use 2
14 in
0.85
0.65 0.85 3 ksi 14 in 2
649.7 k 800 k No good
c
A
A
Af A
A
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Design dowels to resist excess bearing force:
2
2 2
800 k 541.5 k 258.5 k
258.5 k 4.79 in0.9 60 k
0.005 14 in 0.98 in
sA
Use eight No 7 bars (As = 4.80 in2)
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'0.02 0.02 0.875 in 60,000 psi 14.85 in
1 5000 psi
0.0003 0.0003 0.875 in 60,000 ksi
15.75 in8.0 in
b yd
c
d b y
d
d ff
d f
Dowel development length into the column
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'
0.02 0.02 0.875 in 60,000 psi
19.42 in1.0 3000 psi
0.0003 0.0003 0.875 in 60,000 ksi
15.75 in
8.0 in
b y
d
c
d b y
d
d f
f
d f
Dowel development length into the footing
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Design a rectangular footing for an 18-in.interior square column for D = 185 k andL = 150 k. The long side of the footing
should be twice the length of the shortside. The normal weight concretestrength for both the column and thefooting is 4 ksi. The allowable soil
pressure is 4000 psf and the bottom ofthe footing is 5 ft below grade.
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Effective soil pressure and required area offooting:
2
2
2
4000 psf 300 psf 300 psf 3400 psf
185 k 150 k 98.5 ft
3.40 ksf
Use a footing 7'-0" x 14'-0" 98.0 ft
1.2 185 k 1.6 150 k 4.71 ksf
98.0 ft
e
u
q
A
A
q
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Depth required to resist one-way shear. Takeb = 7 ft.
1 7 ft 4.625 ft 4.71 ksf 152.49 k
152,490 lb19.14 in
0.75 1 2 4000 psi 84 in
19.14 4.5 in 23.64 in
uV
d
h
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Depth required to resist punching shear:
22
2
4 18 19.5 in 150 in
98.0 ft 3.125 ft 4.71 ksf 415.58 k
415,580 lb14.60 in 19.5 in Ok
0.75 1 4 4000 psi 150 in
415,580 lb
40 19.5 in0.75 2 4000 psi 150 in
150 in
8.11 in 19.5 in Ok
o
u
b
V
d
d
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22
14 ft 9 in
6.25 ft2 12 in/ft
6.25 ft6.25 ft 7 ft 4.71 ksf 643.9 k-ft
2
12 in/ft 643,900 lb-ft 268.8 psi0.9 84 in 19.5 in
u
u
M
Mbd
Flexural design (steel in long direction)
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Appendix Table 4.13,r = 0.00467
20.00467 84 in 19.5 in 7.65 insA
Use ten No 8 (As = 7.85 in2)
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2
2000.0033
60,000 psi
3 4000 psi
0.0031660,000 psi
0.0033 168 in 19.5 in 10.81 insA
r
r
Use 18 No 7 (As = 10.82 in2)
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Reinforcement in band width 2 2 2
Reinforcement in short direction 1 2 1 3
Use 2/3 x 18 = 12 bars in band width
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