Strip Foundation Design Greek Lecture

7/23/2019 Strip Foundation Design Greek Lecture

1/21

77

77.. --.. -- .. 20052005 -- 0606

20.12.2006

:

1. ,

( )

2. (..

,

)

3. (..

)

4. ,

:

(.. > 50%),

(

)

,


2/21

,


3/21

1.

:

:

(q)

:

1. 1.1

1. :

( ) VLBLo =+21

( ) ooLo MLBLL

BL =

+

3

2

2

1

2

= V

L

M

LB

o

L

32

=

L

MV

LB

oo

32

2

( )dxxqVVL

i

i +=0

:

(x=0) :

( ) dxxxqxVMML

i

ii

i

io ++=0

=


4/21

1.

1.1

2.

() (L, o)

:

. ,

.

: (), (L),

=

= V

L

M

LB

oL

32

=

L

MV

LB

oo

32

2

:

:

: = 1.20m

: L = 12m

:

V1 = V2 = 400 kN , V3 = 640 kN :


5/21

=i

iVV :

x=0 := i

iio xVM

= 1440 kN

= 9600 kNm

= 133 kN/m2

= 67 kN/m2

x=0

= V

L

M

LB

o32max

=

L

MV

LB

o322

min

:

-150

-100

-50

0

50

100

150

200

250

300

350

0 2 4 6 8 10 12

length (m)

bendingmoment(kNm)

-400

-300

-200

-100

0

100

200

300

400

0 2 4 6 8 10 12

length (m)

shearforce(kN).

400 kN400 kN 640 kN400 kN400 kN 640 kN

:


6/21

1.

1.2 Winkler

Winkler :

ykp=

p = (kPa)

y = (m)

k = Winkler (kN/m3)

(y)

(p)

(p)

(y),

: p = k y

,

.

Winkler

1. 1.2 Winkler

(y)

(p)

: k

.

(

, Poisson )

( )

( )

Winkler : ykp=


7/21

k ks ( Winkler)

1. (ks) :

-

pks =

A

Ppks ==

ks =

k ( Winkler)2. k :

k ( / m3) Terzaghi

( = 0.305m) :

8 MN/m3

13 MN/m3

6.4 19.2

< 50 %

96 MN/m326 MN/m3 k

160 MN/m342 MN/m3 k

96 - 32019.2 - 96 k (MN/m3)

> 75%50-75% (Dr)

:

2.1 - () :


8/21

k ks ( Winkler)

2.2 () :

(D=0 D=1)

( ) BEIqk Sis 21

1 ==

Steinbrenner :

: s = 0.79

: s 1

(L/B=) : s

2 :

Si IE

Bq21

=

() (=0.5, = u),

= 0.305m (1 ), ks :

150

200

300

350

400

400

Eu / cu

> 200> 35> 200

165 22030 40100 200

100 - 16517.5 3050 -100

50 10010 17.525 50

25 505 1012.5 25

< 25< 5< 12.5

ks (MN/m3)Eu (MPa)cu (kPa)

ks =

()

k ks ( Winkler)

( Bo) ks = ko = qo / (

qo = , = ) ,

:

B

Bkk oo=

:

(

).

, k

.

0

0.2

0.4

0.6

0.8

1

0 1 2 3 4 5 6 7 8 9 10

(m)

k/ko

ko =

= 0.305m

(L= > ):

+=

L

B

B

Bkk oo

3

1

3

2 (L=) :

B

Bkk oo

3

2=

3. k , k :

3.1 () :


9/21

k ( Winkler)

:

qB

B

B

Loi

239.0

305.0

20254.0

+

=

2

305.03.0

+=

B

B

N

qi

2.1 Alpan :

: ks= q / i

2.2

Terzaghi & Peck :

:

( )

2

39.0

305.084.9

+=

B

mB

BLk

o

2305.0

3.0

+=

B

mBNk :

3.2 - () :

k ( Winkler)

222305.0

14305.0

305.0

+=

+

+

=

B

mk

mB

mB

B

Bkk o

o

oo

: ,

( Bo = 0.305m)

ko = qo / (qo = , = ) ,

> Bo

:

k :

k L > B :

+

+=

+

+

+

=

L

B

B

mk

L

B

mB

mB

B

Bkk o

o

oo

3

1

3

2305.01

43

1

3

2

305.0

305.0 222

k (L=):

222305.0

16305.0

305.0

3

2

+=

+

+

=

B

mk

mB

mB

B

Bkk o

o

oo

:

3.2 - () () :


10/21

0

0.2

0.4

0.6

0.8

1

0 1 2 3 4 5 6 7 8 9 10

(m)

k/ko

Terzaghi

k ( Winkler)

(k) :

ko = = 0.305m

B

Bkk oo=

22

305.0

305.0

+

+

=

mB

mB

B

Bkk

o

oo

:

:

k ( Winkler)4. - :

Es, = Poisson

b, , I= ,

Vesic :

B

E

IE

BEk s

b

s

121

4

21

65.0

=

:

: = 1.20m, H=0.60m, Eb = 25 GPa

: u = 15 MPa (u = 0.5)

= 3 / 12 = 0.0216 m4

312

14

2 /

2.1

15

0216.025000

2.115

5.01

65.0mMNk

= = 8.5 MN/m3

: (L/B= Is 2) :

( ) ( ) 2.115

25.01

1

1

122

=

==B

E

I

qk

Si = 8.3 MN/m3


11/21

k ( Winkler)

(k)

( Bowles) :

5 12

12 18

18 24

24 48

> 48

:

(qu = 25-50 kPa)

(qu = 50-100 kPa)

(qu = 100-200 kPa)

(qu = 200-400 kPa)

(qu > 800 kPa)

24 48

32 80

4.8 16

9.6 80

64 128

:

(Dr< 50%)

(Dr= 50-75%)

(Dr> 75%)

k (MN/m3)

: 10 MN/m3 = 1 kg/cm3 : (k)

(L, B, I,

b). , .

1. 1.2 Winkler

Winkler :

ykp=

p = (kPa)

y = (m)

k = Winkler (kN/m3)

:

Bpqdx

ydIEb =4

4

q = (kN/m)

= (m)

b , = (kN/m2) (m4)

qyBkdx

ydIEb =+4

4

(V, M,

q), (b ,, ,L) (k)

(.. )


12/21

1.

1.2 Winkler

qyBkdx

ydIEb =+4

4

Eb =

= . :

y = (m)

k = Winkler (kN/m3)

= (m)

q = (kN/m)

p = (kPa) : p = k y

:

12

3HBI=

(

) : LIE

Bk

b

41

4

=

, (Hetenyi, 1946) :

: < (/2)

: (/2) < < Winkler

: >

1. 1.2 Winkler

Eb =

= s =

= (m)

L = (m)

,

Meyerhof :

LBEIE

s

b3=

: > 0.5

( > 0.5),

. < 0.5,

Winkler


13/21

:

Winkler - ( )

:

= 1.20m, H=0.60m, L = 12m

: Eb = 25 GPa

: = 3 / 12 = 0.0216 m4

:

,u = 15 MPa (u = 0.5)

V1 = V2 = 400 kN , V3 = 640 kN :

Winkler

312

14

2 /

2.1

15

0216.025000

2.115

5.01

65.0mMNk

= = 8.5 MN/m3

Vesic :

LIE

Bk

b

41

4

=

:

= 3.146

B

E

IE

BEk

b

121

4

21

65.0

=

()

Winkler ( )

(y)

:

Winkler ( )


14/21

-400

-300

-200

-100

0

100

200

300

400

0 2 4 6 8 10 12

length (m)

shea

rforce(kN).

-150

-100

-50

0

50

100

150

200

250

300

350

0 2 4 6 8 10 12

length (m)

bendingmoment(kNm).

400 kN400 kN 640 kN

400 kN400 kN 640 kN

:

Winkler - ( )

( )

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0 2 4 6 8 10 12

length (m)

vertic

alsettlement(

0

20

40

60

80

100

120

140

0 2 4 6 8 10 12

length (m)

reactionsoilpressure(kPa)

400 kN400 kN 640 kN

400 kN400 kN 640 kN

67 kPa

133 kPa

:

Winkler - ( )

( )


15/21

-150

-100

-50

0

50

100

150

200

250

300

0 2 4 6 8 10 12

length (m)

bendingmoment(kNm)

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0.018

0 2 4 6 8 10 12

length (m)

verticalsettlement(m).

:

Winkler

400 kN400 kN 640 kN

400 kN400 kN 640 kN

=0.25m ( =0.60m) LIE

Bk

b

41

4

= = 6.066 2

:

( ) ( )

1. 1.2 Winkler

( : L )

>

= L

IE

Bk

b

41

4

:(Hetenyi, 1946)

1. x=0 :

:

:

:

12

kLB

Py=

24

LPM=

32

PQ =

1 , 2 , 3 = ( )


16/21

()

2. x=0 :

:

:

:

( )4

3/

kB

LMy o=

32

oM

M =

1 , 3 , 4 = ( )

41

4/

=

IE

BkL

b

( ) 1/2

LM

Q o=

3. :

, x=0

() : 1 , 2 , 3 , 4 x :

xIE

Bk

L

x

b

41

4

=


17/21

2. (k) :

1. :

LIE

Bk

b

41

4

=

LBE

IE

s

b

3= ( )

(Winkler)

> 0.5

< 0.5Meyerhof

( )

(Winkler) (Winkler L=)

< (/2)

(/2) < < >

Hetenyi

/

( ) ( ) ko (k)

Vesic

3. :

:

: Winkler :

(k) () (B x L) (V) () :

V

Me=

LB

V= : :

e < B/61. : 0 e B / 6

+=

B

e61max 061min

=

B

e

Winkler : ymax = max / k , ymin = min / k

: ( )

=B

yy minmaxtan

:

kLB

M

K

3

12

1

== (kNm / rad)

kLB

M3

12=

:

==k

V

y

VKV

(kN / m)LBkKV =

B =


18/21

e > /6

(k)

() (B x L) (V) () :

V

Me=

LB

V= : :

2. : / 6 e B / 2

Winkler : ymax = max / k

:

=B

ymaxtan

:

( ) keLBM

K 2

2

1==

(kNm / rad)

( ) kLBV2

2

=

:

(kN / m)

= eBB2

3B

B

= 2max

==k

V

y

VKV

LBkKV =

B =

(k)

( b ,

) V

.

( ).

(k=), ,

(V)

V (e=0).

S

M = V e, :

S = V e / H

(

k), V

e (0 < e < e).

, S

M = V (e e) :

S = V(e-e) / H

:EbI


19/21

(k)

()

= V (e e) ,

:

( )IE

HeeV

IE

HM

bb 33

==

( )

e :

3

361

BLHk

IE

ee

b+

= :

k = e = e

:EbI

()

(k) = V e :

kLB

eV

kLB

M

K

M

33 1212 ===

(e) :

:EbI

: : B = 2m L = 4m

: V = 2000 kN

: k = 10 MN/m3

Eb = 25 GPa ()

: b = 0.4m d = 0.6m

: = 4.5m

= b d3

/12 = 0.4 x 0.63

/ 12 = 0.0072 m4

e = B/2 d/2 = 1 0.3 = 0.7m

3

361

BLHk

IE

ee

b+

=

e = 0.13m < B/6

312

V e

K B L k = =

( ) :

S = V(e-e) / H = 253.3 kN

: = S H = 1140 kN

= 0.00975 rad = 0.56o


20/21

2.

(c ) (Westergaard, 1939) :

Eb , b = Poisson

t =

k = Bc .

.

,

.

( ).

.

,

Winkler. (k)

Bc.

( )

4/1

2

3

1125.2

=

b

bc

k

tEB

: Bc

= /2 Hetenyi (1946)

2.

1 : (Eb = 25 GPa, b =

0.30) t = 0.80m ko = 75 MN/m3 (

= 0.305m)

B

Bkk oo= ( )

4/1

2

3

1125.2

=

b

bc

k

tEB

: :

: 10m

, 10 m .

:

2.3 MN/m3 = 0.23 kg/cm3

=

=

=3/1

2

33/1

2

3

)3.01(305.07512

)8.0(2500040.3

)1(1240.3

boo

bc

Bk

tEB

===10

305.075

B

Bkk oo


21/21

2.

2 : (Eb = 25 GPa, b =

0.30) t = 0.80m ko = 50 MN/m3 (

= 0.305m)

2

1

4

+=

B

Bkk oo

)1(325.6)(

2

3

bo

bo

k

tEBBB

=+

4/1

2

3

)1(125.2

=

b

b

k

tEB

:

:

: (+) = 60.5m B = 7.63 7.6 m

, 7.6 m .

:

= 1.35 kg/cm33

22

/5.136.7

305.01

4

501

4mMN

B

Bkk oo =

+=

+=

Documents

Strip Foundation Design Greek Lecture