friberg analysis : distribution of dowel shear along joint
DESCRIPTION
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 - PowerPoint PPT PresentationTRANSCRIPT
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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
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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
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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
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. .
'
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
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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
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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
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Friberg Analysis: Distribution of Dowel Shear along Joint
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Friberg Analysis: Max Neg moment occurs where Distance = 1.8 l from
applied load (where shear = 0)
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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
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Dowel Looseness : space between dowel & concrete
Factors:01. Coatings 02. Shrinkage 03. Air Voids04. Bearing Press
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Keep Looseness to a minimum01. Vibrate Concrete02. Minimize bond breakers03. Design bar size & spacing
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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
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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.)
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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