Two Way Eccentricity

7/22/2019 Two Way Eccentricity

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ECGD 4122ECGD 4122 Foundation EngineeringFoundation Engineering

Lecture 6

Lecture 6

Faculty of Applied Engineering and Urban PlanningFaculty of Applied Engineering and Urban Planning

Civil Engineering DepartmentCivil Engineering Department

2

2ndnd

Semester 2008/2009Semester 2008/2009


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ContentContent

Eccentrically Loaded FoundationsEccentrically Loaded Foundations

Foundations with twoFoundations with two--way eccentricityway eccentricity

Field Load TestField Load Test


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Stress ConceptStress Concept


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Stress DistributionStress Distribution Rigid FootingsRigid Footings


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Effect of EccentricityEffect of Eccentricity


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+

=

B

e

BL

Qq

6

1max

Q = total vertical load on the foundationQ = total vertical load on the foundationM = moment on the foundationM = moment on the foundation

ee = M/Q= M/Q


-

=

B

e

BL

Qq 6

1min


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MeyerhofMeyerhofs Principles Principle

OfOf

Effective Area MethodEffective Area Method



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Step 1:

Step 1:

Ultimate Load with EccentricityUltimate Load with Eccentricity

Find Eccentricity,Find Eccentricity,Q

Me=

If e B/6

+=

Be

BLQq

6

1max

-=B

e

BL

Qq

6

1min

If e > B/6

( )eBLQ

q

2

3

4

max+

=


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Step 2:

Step 2:

B

= B

2e

L

= L

If eccentricity is in the direction of B

If eccentricity is in the direction of L

B

= BL

= L

2e


Determine the Effective DimensionsDetermine the Effective Dimensions


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Step 3:

Step 3: Use general equation to calculate the soilUse general equation to calculate the soil

ultimate bearing capacityultimate bearing capacity

q'u= c

Nc Fcs Fcd Fci + q Nq Fqs Fqd Fqi

+ 0.5 B

Fs Fd Fi

DONT use B

to calculate:

Fcd , Fqd , Fd

USE B

to calculate:Fcs , Fqs , Fs



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Step 4:

Step 4: Determine the total ultimate load:Determine the total ultimate load:

Qult = qult A

= qult B

L

Step 5:

Step 5: Factor of safety against bearing failure:Factor of safety against bearing failure:

Q

QFS ult=



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Example 1

Example 1

For the footing shown below, determine theFor the footing shown below, determine the

ultimate vertical loading with an 0.15 multimate vertical loading with an 0.15 m

eccentricity using the general formula. Take Neccentricity using the general formula. Take Nqq

==

18.4, N

18.4, Ngg

= 22.4

= 22.4..


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Example 1Example 1 -- SolutionSolution

462.

1

30tan

5.

1

2.

1

1

tan

1

/

6.

12)

18)(

7.

0(

5.

0'

5.

1

2.

1)

15.

0)(

2(

5.

1

2

'

'

'

2

1

''

'

'

=

+=

+=

==

=++=

==

=-=

-=

f

g

g gggg

L

B

F

mkN

Dq

FFFNBFFFqNFFFNcq

mLL

m

eBB

qs

idsqiqdqsqcicdcscult


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68.

0

5.

1

2.

1

4.

0

1

4.

0

1

1

90

1

135.

1

30tan)

30sin

1(

5.

1

7.

0

2

1

tan)sin

1(

2

1

'

'

2

2

'

2'

=

-=

-=

=

-=

=-

+=

-

+=

L

B

F

F

B

DF

s

qi

f

qd

g

b

ff


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2

''''

2

'

2

'

/

59.

988)

5.

1)(

2.

1)(

21.

549(

/

21.

549

)

1)(

1)(

68.

0)(

4.

22)(

2.

1)(

18)(

5.

0(

)

1)(

135.

1)(

462.

1)(

4.

18)(

6.

12(

0

1

1

1

mkN

LBqQ

mkN

q

F

F

ultult

ult

i

d

==

=

=

+

+=

=

-=

=

f

bg

g


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Two Way EccentricityTwo Way Eccentricity


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ult

xL

ult

y

B

Q

Me

Q

Me

=

=

'' AqQ ultult =



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DONT use B

and L

to calculate:Fcd , Fqd , Fd

USE B

and L

to calculate:

Fcs , Fqs , Fs



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'

''

3

5.

1

3

5.

1

2

1

'

1

1

1

1

L

AB

L

eLL

B

eBB

LBA

L

B

=

-=

-=

=

Case I: eCase I: eLL/L/L 1/6 and e

1/6 and eBB/B/B 1/61/6



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Case II: eCase II: eLL

/L < 0.5 and 0 < e

/L < 0.5 and 0 < eBB

/B < 1/6/B < 1/6

( )

larger)(the'

larger)(the

''

2

1

'

2

1

2

1

2

1

LorLL

LorL

AB

LLBA

=

=

+=



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0

10

20

30

40

50

60

70

80

90

1st

Qtr

2nd

Qtr

3rd

Qtr

4th

Qtr

East

WestNorth


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Case III:Case III: eeLL

/L < 1/6 and 0


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Case IV: eCase IV: eLL

/L < 1/6 and e

/L < 1/6 and eBB

/B < 1/6/B < 1/6

( )( )

LL

L

AB

BBLLBLA

=

=

+-+=

'

''

2

1

'

2

2

2



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Example 2

Example 2

Refer to Example 1 and the figure shown belowRefer to Example 1 and the figure shown below

to determine the ultimate vertical loading usingto determine the ultimate vertical loading using

the general formula.the general formula.


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mL

m

LLBA

mL

LL

mLLL

chartFrom

IICaseBe

Le

B

L

28.

1

20.

1)

32.

0

28.

1)(

5.

1)(

5.

0(

)(

5.

0

32.

0)

5.

1)(

21.

0(

21.

0/

28.

1)

5.

1)(

85.

0(

85.

0/

:

1.

0

5.

1/

15.

0/

2.

0

5.

1/

3.

0/

'

2

2

1'

2

2

1

1

=

=+=

+=

==

@

==@

==

==


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424.

1

30tan

28.

1

94.

0

1

tan

1

/

6.

12)

18)(

7.

0(

5.

0'

94.

0)

28.

1/()

20.

1(

/

'

'

'

2

1

''

1

''

=

+=

+=

==

=

++=

==

=

f

g

g gggg

L

BF

mkN

Dq

FFFNBFFFqNFFFNcq

m

LAB

qs

idsqiqdqsqcicdcscult


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706.

0

28.

1

94.

0

4.

0

1

4.

0

1

1

90

1

135.

1

30tan)

30sin

1(

5.

1

7.

0

2

1

tan)sin

1(

2

1

'

'

2

2

'

2'

=

-=

-=

=

-=

=-

+=

-

+=

L

B

F

F

B

DF

s

qi

f

qd

g

b

ff


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2

'''

2

'

2

'

/

20.

610)

20.

1)(

50.

508(

/

50.

508

)

1)(

1)(

706.

0)(

4.

22)(

94.

0)(

18)(

5.

0(

)

1)(

135.

1)(

424.

1)(

4.

18)(

6.

12(

0

1

1

1

mkN

AqQ

mkN

q

F

F

ultult

ult

i

d

===

=

+

+=

=

-=

=

f

bg

g


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33/37



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Clayey SoilClayey Soil

)(u)(u PF qq =

Sandy SoilSandy Soil

P

F

PFB

Bqq

)(u)(u=

qqu(F)u(F) Ultimate capacity for proposed foundationUltimate capacity for proposed foundation

qqu(P)u(P) Ultimate bearing capacity for test plateUltimate bearing capacity for test plateBB FF Width of foundationWidth of foundation

BB PP Width of test plateWidth of test plate

P

FPFB

BSS )()( =

2

)()(

2

+

=PF

FPF

BB

BSS



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Example 3

Example 3

Refer to the accompanied figure for the resultsRefer to the accompanied figure for the results

of a plate load test on a sandy soil. Define theof a plate load test on a sandy soil. Define the

dimensions of a square footing to carry a load ofdimensions of a square footing to carry a load of

2500 kN with a permissible settlement of 25 mm.2500 kN with a permissible settlement of 25 mm.

The test plate is 1

The test plate is 1 in diameter.in diameter.


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Example 3

Example 3


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Two Way Eccentricity