1 2

3

Crack Width

1

0.80

0.65 .

shr

shr ave

CW CL T

L slab length

CTE

T T T

h

C granular

stab base

20.039

'. .

1.453

Shear Capacity

=

=

0.0312

ccap

A I

hS ae

P

Vertical Shear Stress

h Slab Thickness

a h

AI

D

AggJ =

k

1log( ) 0.214 0.183 1.18 log 1

DJ =

Sk1

1 112

dowel spacing

Total joint/crack stiffness

J AI D

aJ

LTE

D

DCI CS

J J

f

es

c

bsJ

f

es

c

bsJ

eeeecki egedeaeJLog

00

)(

J c k i = ( A g g / k l ) c = j o i n t s t i f f n e s s o n t h e t r a n s v e r s e c r a c k c o m p u t e d o n s e a s o n a l b a s i s f o r e a c h t i m e i n c r e m e n t i ( t y p i c a l v a l u e s 0 . 1 t o 1 5 , 0 0 0 ) a = - 4 . 0 0 b = - 1 1 . 2 6 c = 7 . 5 6 d = - 2 8 . 8 5 e = 0 . 3 5 f = 0 . 3 8 g = 5 6 . 2 5 s 0 = s 0 k i = 1 = D i m e n s i o n l e s s s h e a r c a p a c i t y ( t h e r a n g e i s 0 t o . 9 ) . N O T E : S t a r t i n g f r o m s e c o n d t i m e i n c r e m e n t ( i = 2 ) , u s e s k i i n p l a c e f o r s 0 . V a l u e o f

s k i i s a d j u s t e d o n s e a s o n a l b a s i s f o r e a c h t i m e i n c r e m e n t i J s = ( A g g / k l ) S = L o a d t r a n s f e r o n t h e s h o u l d e r / l o n g i t u d i n a l j o i n t . T y p i c a l v a l u e s a r e g i v e n i n

t h e f o l l o w i n g t a b l e :

S h o u l d e r t y p e ( A g g / k l ) s G r a n u l a r 0 . 0 4 A s p h a l t 0 . 0 4 T i e d P C C 4 T i e d P C C M o n o l i t h i c 4 0 0

. .

'

3 2

1 ; =

(LTE )ln %

LTE

4.3262; 8.413; 0.7444

1dowel shear stiffness

1 112

12; Beam τ sti

1

A I

DLT d LT LT

Dd LT

D

d d d d

d z

JP P P P P Total Load Transferred P TLE

J

Ln aTLE d b c

l

d b c

JP P

J

J

DCI CE I E I

Cw G A w

4

2

3

4

d

ff

; ; 0.964 2 1

opening of joint

4DCI= ; ; eff. mod.of dowel support

2 4E

dd d z d

d

d d

d d

d

EdI G A A

A r w

E I KdK

I

1

LT d agg

Dd

D

c

c

1LTE

0.214 0.183 log( )1 log

1.18

P =P +P

JP =

JJ

1J

P =

Critical dowel load (P )

AI LT d

d dc

aJ

l

P

P P P P

P f

1 1 1 1

edge load

2corner load

1

1 1 1 1 1 1 1 1tan tan tan . tan

2 2 2 2

0.180 0.1033

57.38259 0.17798

14.

dc

dc

LD

sf

es

efs

e

x b y e x b y es a d ge c f c f

ax J y

ea e

b f

c

bc

40811 13.0777

12.084

Bearing Stress

c

g

d

KP

DCI

Friberg Analysis: Distribution of Dowel Shear along Joint

Friberg Analysis: Max Neg moment occurs where Distance = 1.8 l from

applied load (where shear = 0)

JOINTS: Doweled

To transfer load First used 1917–18 1930 wide spread use

Dia, spacing & length varied widely

Factors Load transfer Spacing of dowel Size & spacing dowel Joint type Dowel bar bearing

3(4 " ) 20'width4

'4 bar dia3 cbf f

Dowel Looseness : space between dowel & concrete

Factors:01. Coatings 02. Shrinkage 03. Air Voids04. Bearing Press

Keep Looseness to a minimum01. Vibrate Concrete02. Minimize bond breakers03. Design bar size & spacing

Timoshenko : dowel encased in Concrete

4

4

03

4

: modulus of support, b: bar , y: deflection

cos cos sin2

;4

K: rate concrete reacts against defl = 1,500,000 pci?

tends to vary:

concrete properties,

slab

x

t

d yEI Kby K

dx

ey P x M x x

EI

KbKy

EI

thickness,

bar

length

looseness

Type Joint Recommended Type JointLongitudinal Longitudinal Joints

1 and 5 Tied - # 11 DeformedNo load Transfer – No Ties or Nominal Ties Bars at 2 in. on Ctrs

2, 3 and 4Tied - #11 Deformed Bars at 12 in Ctrs.

Transverse TransverseDowelled Between Longitudinal Joints Dowelled with 11” at 2 in. Ctrs

1 and 5 with 2” at 12 in. Ctrs.Undowelled Outside Joints 1 and 5

DESIGN AIRCRAFTWide Bodied Aircraft(DC – 10, 747, etc.)

Type Joint Recommended Type JointLongitudinal Longitudinal Joints

1 and 5 Tied - # 8 DeformedNo load Transfer – No Ties or Nominal Ties Bars at 12 in. on Ctrs

2, 3 and 4Tied - #11 Deformed Bars at 12 in Ctrs.

Transverse TransverseDowelled Between Longitudinal Joints Dowelled with 1-1/4” at 12 in. Ctrs

1 and 5 with 1-1/4” at 12 in. Ctrs.Undowelled Outside Joints 1 and 5

DESIGN AIRCRAFT727 Class