19 - Dowel Bars - Memphis - Dowel Bars.pdf · 0.45P Assumes 90% efficiency 15. Example Find the...

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

17

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.

23

Alternative Dowel Spacing

24

Alternative Dowel Spacing

25