19 - dowel bars - memphis - dowel bars.pdf · 0.45p assumes 90% efficiency 15. example find the...
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Rigid Pavement Mechanics
Dowel Bars
Allowable Bearing Stress
43b c
df f
allowable bearing stressconcrete compressive strengthdowel bar diameter (in)
b
c
ffd
ACI Empirical Equation
4
Bar Deformation Under Load
5
Bar Deformation Under LoadFreberg (1940)
3
24c
od d
P zy
E I
load on the critical dowel barrelative dowel concrete stiffnessmaximum joint opening (0.25 in)
cP
z
6
Actual Bearing Stress
44
d d
KdE I
Freberg (1940)
4
64d
dI
elastic modulus of the dowelmoment of inertia of the dowelbar diameter
d
d
EId
7
Bearing Stress Under LoadFreberg (1940)
3
24c t
b od d
KP zKy
E I
modulus of dowel support
300 1500 ksi/in
K
8
Modulus of Dowel SupportFreberg (1940)
43
33
4
44
4
bd d
KK EI dE I Kd
EI
4
1
44 3
44
4
KKEIEIK
EI
4b K
9
Dowel Spacing
Pt
Pc
1.8
10
P
P/2 P/2
Load Transfer
P
Assumes 100% efficiency
12
P
P/2
Load Transfer
P/2
Assumes 100% efficiency
13
P
0.55P 0.45P
Load Transfer
P
Assumes 90% efficiency
14
P
0.45P
Load Transfer
0.45P
Assumes 90% efficiency
15
Example
Find the required dowel bar size for contractionjoints in a 10" concrete slab resting on a subgradematerial with a 200 psi/in modulus of subgradereaction. The design load is a 9,000-lb dual wheelload centered 6" from the slab edge. Assume a 12"dowel spacing.
16
Example
33
44 2
3,000,000 100033.6
12 0.9775 200 /12 1C
psi inE h inpsi ink
1.8 60 in
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Example
4050 lb
60"
1.0Pt0.8Pt
0.6Pt0.4Pt
0.2Pt
3.0Pt = 4050 lb
18
Example
Assumptions
d = 1 in (Trial 1)K = 1500 ksi/inE = 30,000 ksi
z = 0.25 in
19
Multiple Wheel Loads
4050#
84"
4050#
20
Dowel Spacing (Updated)
Pt
Pc
1.0
21
Dowel Spacing (Updated)
4050#
84"
4050#
22
PCA HeuristicsOften, dowel bars are sized and spaced using heuristics.
AASHO originally recommended dowel diameters 1/8th theslab thickness, which is 1" for an 8" slab, 1.25" for a 10"slab, and 1.5" for a 12" slab.
PCA recommends using 1.25″ dowel bars for slabs up to10″ thick and 1.5″ bars for slabs over 10″ thick. A commonsize is 1.5″ by 18″ or 20″ long. The most common spacingis 12″ center-to-center, but alternatives exist.
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Alternative Dowel Spacing
24
Alternative Dowel Spacing
25