Footings

FootingsFootings

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Acknowledgement

This Powerpoint presentation was prepared by Dr. Terry Weigel, University of Louisville. This work and other contributions to the text by Dr. Weigel are gratefully acknowledged.

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FootingsFootings

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Design for load transfer to soil uses unfactored loads

Support structural members and transfer loads to the soil

Structural members are usually columns or walls

Structural design of footing is done with factored loads

FootingsFootings

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Typically, bottom of footing must be located below frost line

Footings must be designed to prevent bearing failure, sliding and overturning

Footings must be designed to prevent excessive settlement or tilting

Excavation may be required to reach a depth where satisfactory bearing material is located

Wall FootingWall Footing

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Wall footings – enlargement of the bottom of the wall

Isolated Square FootingIsolated Square Footing

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Isolated or single column square footing – loads relatively light and columns not closely spaced

Combined FootingCombined Footing

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Combined footings – support two or more columns – heavily loaded columns; closely spaced columns; columns near property line

Mat FootingMat Footing

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Mat or raft foundation – continuous concrete slab supporting many columns; soil strength relatively low; large column loads; isolated spread footings would cover more than 50 percent of area; reduce differential settlement

Pile CapPile Cap

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Pile caps – distribute column loads to groups of piles

Soil PressureSoil Pressure

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Soil pressure is assumed to be uniformly distributed beneath footing if column load is applied at the center of gravity of the footing

Footings supported by sandy soils

Footings supported by clayey soils

Footings supported eccentric loads

Assumed Soil PressureAssumed Soil Pressure

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Soil Pressure - Sandy SoilSoil Pressure - Sandy Soil

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Soil Pressure - Clayey SoilSoil Pressure - Clayey Soil

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Allowable Soil PressureAllowable Soil Pressure

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Actual soil pressure is based on unfactored loads

Allowable soil pressure may be determined by a geotechnical engineer

When soil exploration is not feasible, values provided by building codes may be used

Factor of safety is typically 3

Allowable Soil Pressure (Table Allowable Soil Pressure (Table 12.1)12.1)

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Maximum Allowable Soil PressureMaterial Allowable Pressure, ksf

Rock 20% of ultimate strength

Compact coarse or fine sand, hard clay or sand clay

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Medium stiff clay or sandy clay 6

Compact inorganic sand and silt mixtures

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Loose sand 3

Soft sand clay or clay 2

Loose inorganic sand-silt mixtures 1

Loose organic sand-silt mixtures, muck or bay mud

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Design of Wall FootingsDesign of Wall Footings

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Generally, beam design theory is used

Shear strength almost always controls footing depth

Compute moment at the face of the wall (concrete wall) or halfway between wall face and its centerline (masonry walls)


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Shear may be calculated at distance d from face of the wall

Use of stirrups is not economical – set d so that 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 stripSection 15.7 of ACI Code:

Depth of footing above bottom reinforcement not less than 6 in for footings on soil and not less than 12 in for footings on piles

Minimum practical depth of footing is 10 in and 16 in for pile caps

Wall Footing Design Wall Footing Design ExamplesExamples

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Example 12.1Example 12.1

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Design a wall footing to support a 12-in. wide reinforced concrete wall with a dead load of 20 k/ft and a live load of 15 k/ft. The bottom of the footing is to be 4 foot below final grade, the soil weighs 100 lb/ft3 the allowable soil pressure is 4 ksf. The concrete strength is 3,000 psi and the steel is Grade 60.


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Assume a footing thickness of 12 in. With a minimum cover of 3 in., this gives a d value of about 8.5 in. Compute the footing weight and

soil weight:

Footing weight12 in 150 150 psf

12 in/ftSoil weight

36 in 100 300 psf12 in/ft


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Effective soil pressure and required width of footing:

4000 psf 150 psf 300 psf 3550 psfWidth of footing required20 k/ft 15 k/ft 9.86 ft

3.55 ksfUse 10 ft

eq


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Factored bearing pressure for design of concrete:

1.2 20 k/ft 1.6 15 k/ft4.80 ksf

10 ftuq


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Compute design shear (at distance d from face of wall):

10 ft 6 in 8.5 in 4.80 ksf 18.2 k2 12 in/ft 12 in/ft

18, 200 lb 18.46 in0.75(1.0) 2 3000 ksi 12 in

Much larger than orginal assumptionTry a thicker footing - say 20 in thick

16.5 in

uV

d

d


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20 in4000 psf 150 psf12 in/ft

28 in 100 psf 3517 psf12 in/ft

Width of footing required20 k/ft 15 k/ft 9.95 ft

3.517 ksfUse 10 ft

eq


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10 ft 6 in 16.5 in 4.80 ksf 15.0 k2 12 in/ft 12 in/ft

15,000 lb 15.21 in0.75 2 3000 ksi 12 in/ft

15.21 in 3.5 in 18.71 inUse a 20 in thick footing

uV

d

h


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22

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10 ft 6 in 4.5 ft2 12 in/ft

Compute moment on a one-foot-long strip

4.80 k/ft 4.5 ft48.6 k-ft/ft

2 212 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, = 0.00345 < 0.0136, section is tension controlled; = 0.9

2in0.00345 12 in 16.5 in 0.68

ftsA

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 cover0.875c 3 3 3.4375 3.5

2 210 in 5 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

cd use c in

c

c Kd


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'

2,

2,

340

3 60,000 psi 1 32.86 diameters40 2.53000 psi

0.68 in /ft32.86 31.03 diameters0.72 in /ft

31.03 0.875 in 27.15 in

yd t e s

b trb c

b

s requiredd

b s provided

d

fc Kd f

d

Ad 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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20.0018 12 in 20 in 0.432 in / ftsA

Temperature and shrinkage steel

Use No 5 at 8 in (As = 0.465 in2 / ft)

Design of Isolated Square Design of Isolated Square FootingsFootings

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Most isolated square footings have a constant thickness

For very thick footings, it may be economical to 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

One-way ShearOne-way Shear

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'2u

c w

Vd

f bSame as for wall footings

One-way ShearOne-way Shear

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Two-way ShearTwo-way Shear

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ACI Code Section 11.11.1.2 states that critical section is at a distance d/2 from face of support


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46


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'

'

'

4

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ratio of the length of the long side of the column to the length of the short side of the column bearing on the footing

2

c c o

c c oc

c

sc c o

o

V f b d

V f b d

dV f b db

<- ACI Code Equation 11-33




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s = 40 for interior columns

s = 30 for exterior columns

s = 20 for corner columns

Flexural Design – Isolated Flexural Design – Isolated Square FootingsSquare Footings

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Flexural reinforcement is required in two directions

The values of d for the layers of steel in the two directions will be different

For square footings, design using the value of d for the upper layer is typical

For square footings supporting non-square columns, moments are larger in the shorter direction of the column


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Reinforcing steel areas required to resist moment are often less than minimum required steel:

Code Section 10.5.4 states that minimum area and maximum spacing need only be equal to values required for temperature and shrinkage steel

,min

'

,min

200

3

s wy

cs w

y

A b df

fA b d

f


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Maximum steel spacing may not exceed three times the footing thickness or 18 in.

Load Transfer from Column Load Transfer from Column to Footingto Footing

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All forces at the base of the column must be transferred to the footing

Compressive forces must be transferred by bearing

Tensile forces may be transferred by reinforcement or mechanical connectors


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Columns transfer loads directly over the area of the column

Load transfer into the footing may by assumed to occur over an effective area which may be larger than the column area

For the same strength of concrete, the footing can support more bearing load than can the column


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Bearing strength permitted at the base of the column ->

Bearing strength permitted on the footing is the same value multiplied by ->

See ACI Code Section 10.14.1

'10.85 cf A

2

1

2AA

Definition of ADefinition of A11 and A and A22

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A2 is the area of footing geometrically similar to and concentric with the column

A1 is the area of the column

Column DowelsColumn Dowels

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Excess Bearing LoadExcess Bearing Load

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Excess bearing load can be carried by dowels or column bars extended into footing

ACI Code Section 15.8.2 requires that the dowel area not be less than 0.005 times the gross cross-sectional area of the column

Development Length for Development Length for DowelsDowels

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Development length of dowels must be sufficient to transfer column force to footing

Development length of dowels may not be less than the length required if bearing stress was not exceeded

Splice Length for DowelsSplice Length for Dowels

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ACI Code does not permit splicing of No 14 or No 18 bars

ACI Code Section 15.8.2.3 does permit No 14 or No 18 bars to be spliced to No 11 (or larger) dowels in footings

These dowels must extend into the column not less than the development length for the No 14 or No 18 bar, or the compression lap splice length for the dowels, whichever is larger

Splice Length for DowelsSplice Length for Dowels

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These dowels must extend into the footing for a distance not less than the development length for dowels

Insufficient Development or Insufficient Development or Splice LengthSplice Length

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Use a larger number of smaller dowels

Use a deeper footing

Add a cap or pedestal to the footing

Column UpliftColumn Uplift

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Development length must be those for tension

Splice requirements are those found in ACI Code Section 12.17

Isolated Rectangular Isolated Rectangular FootingsFootings

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Square footings are more econonical than rectangular footings

Long direction steel is uniformly distributed along short direction

Short direction steel is non uniformly distributed along long direction


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ACI Code Section 15.4.4.2Reinforcement in band width 2

Reinforcement in short direction 1

is the ratio of the length of the footing in the long direction to the length in the short direction

Remaining steel is distributed uniformly throughout the two portions of the footing outside the band


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Footing Design ExamplesFooting Design Examples

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Design a square column footing for a 16-in. square tied interior column that supports loads 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 below final grade, the soil weighs 100 lb/ft3 the allowable soil pressure is 5 ksf. The concrete strength is 3,000 psi and the steel is Grade 60.


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Assume a footing thickness of 24 in. with a minimum cover of 3 in., this gives a d value of about 19.5 in. Compute the footing weight and

soil weight:


12 in/ftSoil weight

36 in 100 300 psf12 in/ft


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Effective soil pressure and required area of footing:

2

5000 psf 300 psf 300 psf 4400 psf200 k 160 k 81.82 ft

4.40 ksfUse 9 ft x 9 ft

eq

A


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Factored bearing pressure for design of concrete:

2

1.2 200 k 1.6 160 k6.12 ksf

81 ftuq


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Depth required to resist punching shear:

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4(16 19.5) 142 in

81.0 ft 2.96 ft 6.12 442.09 k

442,090 lb 18.95 in 19.5 in Ok0.75 4 3000 psi 142 in

442,090 lb40 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 lb 13.71 in 19.5 in Ok0.75 2 3000 psi 108 in

uV

d


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22

22

6.12 ksf 9 ft 3.83 ft404 k-ft

2 212 in/ft 404,000 lb-ft

131.2 psi0.9 108 in 19.5 in

u

u

wLM

Mbd

Flexural design


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Appendix Table 4.12, = 0.00225 < min

2

200 0.003360,000 psi

3 3000 psi0.00274

60,000 psi0.0033 108 in 19.5 in 6.95 insA

Use nine No 8 (As = 7.07 in2)


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Development length:

1 bottom cover 3.5 in one-half center-to-center bar spacing 6 in

3.5 in 0 3.5 Use 2.51.0 in

t e s

b

b

b tr

b

ccc K

d


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'

2,

2,

340

3 60,000 1 32.86 diameters40 2.53000

6.95 in32.86 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

fc Kd f

d

Ad 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 and footing in Example 12.2. The strength of the 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 Okcf A


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Design bearing force in the footing 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 psi16.74 in

0.85 4000 psib 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 psib 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 in8.0 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. square column to a 13 ft square footing if Pu = 800 k. Normal weight concrete is used in both the column and the footing. The concrete in the column is 5 ksi and in the footing is 3 ksi. The column is reinforced with eight No 8 bars.


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Bearing force at the column base = 800 k

Design bearing force at the column base:

2'10.85 0.65 0.85 5 ksi 14 in

541.5 k 800 k No goodcf A


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Design bearing force in the footing concrete:

2

22

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

AA

Af AA


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Design dowels to resist excess bearing force:

2

2 2

800 k 541.5 k 258.5 k258.5 k 4.79 in

0.9 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 psi14.85 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 f

f

d f

Dowel development length into the column


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'

0.02 0.02 0.875 in 60,000 psi19.42 in

1.0 3000 psi

0.0003 0.0003 0.875 in 60,000 ksi

15.75 in8.0 in

b yd

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 and L = 150 k. The long side of the footing should be twice the length of the short side. The normal weight concrete strength for both the column and the footing is 4 ksi. The allowable soil pressure is 4000 psf and the bottom of the footing is 5 ft below grade.


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Assume a footing thickness of 24 in. with a minimum cover of 3 in., this gives a d value of about 19.5 in. Compute the footing weight and

soil weight:


12 in/ftSoil weight

60-24 in 100 300 psf12 in/ft


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Effective soil pressure and required area of footing:

2

2

2

4000 psf 300 psf 300 psf 3400 psf185 k 150 k 98.5 ft

3.40 ksfUse a footing 7'-0" x 14'-0" 98.0 ft

1.2 185 k 1.6 150 k4.71 ksf

98.0 ft

e

u

q

A

A

q


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Depth required to resist one-way shear. Take b = 7 ft.

1 7 ft 4.625 ft 4.71 ksf 152.49 k

152,490 lb 19.14 in0.75 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:

222

4 18 19.5 in 150 in

98.0 ft 3.125 ft 4.71 ksf 415.58 k

415,580 lb 14.60 in 19.5 in Ok0.75 1 4 4000 psi 150 in

415,580 lb40 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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97

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14 ft 9 in 6.25 ft2 12 in/ft

6.25 ft6.25 ft 7 ft 4.71 ksf 643.9 k-ft2

12 in/ft 643,900 lb-ft268.8 psi

0.9 84 in 19.5 in

u

u

M

Mbd

Flexural design (steel in long direction)


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Appendix Table 4.13, = 0.00467

20.00467 84 in 19.5 in 7.65 insA

Use ten No 8 (As = 7.85 in2)


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7 ft 9 in 2.75 ft2 12 in/ft

2.75 ft2.75 ft 14 ft 4.71 ksf 249.3 k-ft2

12 in/ft 249,300 lb-ft52.0 psi

0.9 168 in 19.5 in

u

u

M

Mbd

Flexural design (steel in short direction)

Too low for Table A.13


100

2

200 0.003360,000 psi

3 4000 psi0.00316

60,000 psi0.0033 168 in 19.5 in 10.81 insA

Use 18 No 7 (As = 10.82 in2)


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Reinforcement in band width 2 2 2Reinforcement in short direction 1 2 1 3

Use 2/3 x 18 = 12 bars in band width


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