Rigid Pavement Mechanics

Friction Stresses

Unrestrained Slab

L/2L/2

max 2

L t

c t

c

h

x

max

(x)

0

4

Coefficient of Thermal Expansion

AggregateType

Coefficient(10-6 in/in/oF)

Quartz 6.6Sandstone 6.5

Gravel 6.0Granite 5.3Basalt 4.8

Limestone 3.8Average 5.5

5

Fully Restrained Slab

L/2L/2

c c c cE E t

c

c = 0

xc (x)

0

6

Partially Restrained Slab

L/2L/2

c t

c

c

L/2

0.06"

L/2

ultff (x)

h

x

max

x

ultf

(x)

0

0

8

Friction Stresses

cx h f x

const cx h

x x f x

9

Friction Stresses

F1

f(x)

1

2

1 L

cx

F h f x dx

xx1 L/2

fult

h

0

10

Friction Stresses

Fmax

f(x)

x0 L/2

2

max0

L

cF h f x dx

fult

h

11

Friction Stresses

Fmax

f(x)

x0 L/2

favg

max 2 c avg

LF h fh

12

Friction Coefficient

Type of Material Beneath Slab favg

Lime stabilized soil 1.8Asphalt stabilized soil 1.8Cement stabilized soil 1.8

River gravel 1.5Crushed stone 1.5

Sandstone 1.2Natural subgrade 0.9

standard

13

Friction Stresses

c

f(x)

x0 L/2

favg

2c c avg

Lh h f h

14

Friction Stresses

c

f(x)

x0 L/2

favg

h2

c c avgL f

15

Example

Calculate the longitudinal tensile stress that will develop in a concrete slab 50′ long due to a drop in temperature.

19

Slab Length & Joint Opening

Aggregate Interlock

Source: WSDOT Pavement Guide Interactive CD-ROM 21

Joint Opening

L – L

c cL L t

c = 510-4 in/in

Unrestrained Slab22

Shrinkage Strain

TensileStrength

(psi)

ShrinkageStrain(in/in)

300 or less 0.0008400 0.0006500 0.00045600 0.0003

700 or more 0.0002

Average 0.0005

AASHTO Pavement Design Guide

23

Joint Opening

L – L

c cL CL t Partially Restrained Slab

24

Joint Opening

L – L

0.650.8

c c

C for stabilized baseL CL t

C for unstabilized base25

Maximum Slab Length

Lmax

max 0.04" c cCL t Aggregate Interlock

26

Example

Find the maximum allowable slab length for a design temperature drop of 60F for a slab on a stabilized base.

27

Dowel Bars

Source: WSDOT Pavement Guide Interactive CD-ROM 28

Maximum Slab Length

max 0.25" c cCL t Doweled Joints

Lmax

29

Temperature Steel

Wire Reinforcement

Source: http://rebar.ecn.purdue.edu/wwr/ 31

JRCP

Source: WSDOT Pavement Guide Interactive CD-ROM 32

Tie Bars

Tie Bars

Source: WSDOT Pavement Guide Interactive CD-ROM 40

Tie Bar Baskets

Source: http://www.daytonsuperior.com/ 41

Tie Bars

Source: http://www.dot.state.oh.us/ 42

Tie Bar Steel Area

s s cA f h

cs

s

hAf

43

Friction Stresses

c

f(x)

x0

favg

c c avgh h fL h

L

L

44

Tie Bar Spacing

c avgbar

sbar s

L f hAAs f

23 yf

fy = 40,000 or 60,000 psi

Steel Reinforcing Bar

45

Tie Bar Spacing

L'

L'

L distance to nearest free edge46

Tie Bar Spacing

L'

L'

L distance to nearest free edge47

Tie Bar Spacing

L distance to nearest free edge

L'

L'

48

Example

Determine the amount of steel required for a highway consisting of two 12' driving lanes with 10' shoulders on each side. Assume a 10" concrete slab resting on a gravel base and a 60-ksi yield stress for the rebar.

49

Tie Bar Spacing

c avgbar

sbar s

L f hAAs f

bar bar sbar

s c avg

A A fsA L f h

50

Standard Rebar Sizes

BarSize

Weight(lb/ft)

NominalDiameter

(in)

NominalArea(in²)

#3 0.376 3/8 0.11

#4 0.668 1/2 0.20

#5 1.043 5/8 0.31

#6 1.502 3/4 0.44

#7 2.044 7/8 0.60

#8 2.670 1.000 0.79

#9 3.400 1.128 1.00

#10 4.303 1.270 1.27

#11 5.313 1.410 1.56

#14 7.650 1.693 2.25

#18 13.60 2.257 4.00

51

Tie Bar Spacing

Source: FHWA Technical Advisory T 5040.30 52

Tie Bar Length

22 s

bond steelstrength strength

r f r

allowable bond stress (assume 350 psi)embedment length (half the bar length)allowable bar stressbar radius (half the bar diameter)

sfr

54

Tie Bar Length

allowable bond stress (assume 350 psi)embedment length (half the bar length)allowable bar stressbar radius (half the bar diameter)

sfr

122

sf dt

55