22 - CRCP Reinforcement - CRCP Reinforcement.pdf · 700 or more 0.0002 Average 0.0005 AASHTO Pavement Design Guide. Concrete Thermal Coefficient Aggregate Type Coefficient (10-6 in/in/oF)

CRCP Reinforcement

JPCP

Source: WSDOT Pavement Guide Interactive CD-ROM

JRCP


CRCP


CRCP

Source: CRCP Performance and Best Practices, ACPT Tech Brief, FHWA-HIF-12-039

CRCP Reinforcement

CRCP Reinforcement

Design of CRCP Reinforcement

Goal: provide sufficient reinforcement to

– Produce a desirable crack pattern

• Crack spacing between 3.5 and 8 ft

– Keep transverse cracks tightly closed

• Maximum crack width less than 0.4 in

– Keep steel stresses within allowable levels

Design of CRCP Reinforcement

Source: FHWA/CRSI Continuously Reinforced Concrete Pavement Design & Construction Guidelines

Design Variables

• Concrete tensile strength, ft (psi)• Concrete shrinkage strain, c (in/in)• Concrete thermal coefficient, c (in/in/°F)• Rebar diameter, b (in)• Allowable steel working stress, s (psi)• Steel thermal coefficient, s (in/in/°F)• Design temperature drop, Td (°F)• Tensile stress due to wheel loads, w (psi)

Concrete 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

Concrete Thermal Coefficient

AggregateType

Coefficient(10-6 in/in/oF)

Quartz 6.6Sandstone 6.5

Gravel 6.0Granite 5.3Basalt 4.8

Limestone 3.8Average 5.0

Allowable Steel Working Stress

Indirect TensileStrength of Concrete Reinforcing Bar Size

at 28 days (psi) No. 4 No. 5 No. 6300 or less 65,000 57,000 54,000

400 67,000 60,000 55,000500 67,000 61,000 56,000600 67,000 63,000 58,000700 67,000 65,000 59,000

800 or more 67,000 67,000 60,000

Steel Thermal Coefficient

s = 510-6 in/in/oF

Tensile stress due to wheel loads

w

Crack Spacing

1.156.702.19t s

bc

5.204.60 1.79w

c

f1.32 1 1 11000 2

1 1 1 1000X

P1000

average crack spacing (ft) percentage steel ne

XP eded

Crack Spacing

0.251.4570.476t s

bc

1.130.217 0.389w

c

PX

f1.062 1 1 11000 2

11 1 1000

1000

average crack spacing (ft) percentage steel ne

XP eded

Minimum Crack Spacing

0.251.4570.476t s

bc

max 1.130.217 0.389w

c

f1.062 1 1 11000 2

P 11 1 13. 000

10005 ft

Maximum Crack Spacing

0.251.4570.476t s

bc1

min 1.130.217 0.389w

c

f1.062 1 1 11000 2

P 11 1 18. 000

10000 ft

Crack Width

6.532.20t

b

4.914.55w

f0.00932 1 11000

1 11000

CWP

Crack Width

1.4350.484t

b

1.0790.220w

f0.358 1 11000 1

100

PCW

10

Maximum Crack Width

1.4350.484t

b2min 1.079

0.220w

f0.358 1 11000P 1

0.04 i11 00

n0

Steel Working Stress

4.09 0

s

.425t d

3.142.74 0.494w

c

f T47,300 1 11000 100

1 1 1 1000P1000

Maximum Steel Stress

1.493 0.155t d

3min 1.146

0.365 0.180ws c

f T50.834 1 11000 100P 1

1 1 10001000

Required Steel

1 2 3min min min minP max P , P , P

min smin 2

b

P 100 W DN

4

max smax 2

b

P 100 W DN

4

Example

D = 9.5 in (from design equation)Ws = 144 in (12-ft slab)Td = 60°F (from weather data)f‘t = 600 psi (from AASHTO T198)keff = 170 pci (from Figure 3.6)b = 0.75 in (No. 6 bar assumed)

Step 1

c =c =s =s =

Concrete Shrinkage Coefficient

Indirect TensileStrength at

28 days (psi)

ShrinkageCoefficient

(in/in)300 or less 0.0008

400 0.0006500 0.00045600 0.0003

700 or more 0.0002

Concrete Thermal Coefficient

c = 510-6 in/in/oF

Allowable Steel Working Stress

Indirect TensileStrength of Concrete Reinforcing Bar Size

at 28 days (psi) No. 4 No. 5 No. 6300 or less 65,000 57,000 54,000

400 67,000 60,000 55,000500 67,000 61,000 56,000600 67,000 63,000 58,000700 67,000 65,000 59,000

800 or more 67,000 67,000 60,000

Steel Thermal Coefficient

s = 510-6 in/in/oF

Step 1

c = 0.0003 in/inc = 5×10-6 in/in/°Fs = 5×10-6 in/in/°Fs = 58,000 psi

Step 2 – Tensile Stress

Step 3 – Min Crack Spacing

1.457 0.25 0.476

max 1.13 0.217 0.389

1.062 1 0.6 1 0.5 1 0.75P 1 0.66%

1 0.23 1 03. .35 ft

0.251.4570.476t s

bc

max 1.130.217 0.389w

c

f1.062 1 1 11000 2

P 11 1 13. 000

10005 ft

Step 4 – Max Crack Spacing

1.457 0.25 0.4761min 1.13 0.217 0.389

1.062 1 0.6 1 0.5 1 0.75P 1 0.39%

1 0.23 8.0 1 .ft 0 3

0.251.4570.476t s

bc1

min 1.130.217 0.389w

c

f1.062 1 1 11000 2

P 11 1 18. 000

10000 ft

Step 5 – Max Crack Width

1.4350.484t

b2min 1.079

0.220w

f0.038 1 11000P 1

0.04 i11 00

n0

1.435 0.4842min 1.079 0.220

0.358 1 0.6 1 0.75P 1 0.50%

1 0.2 0.04 in3

Step 6 – Max Steel Stress

1.493 0.155t d

3min 1.146

0.365 0.180ws c

f T50.834 1 11000 100P 1

1 1 10001000

1.493 0.1553min 1.146 0.365 0.180

50.834 1 0.6 1 0.6P 1 0.52%

1 0.2 58,0 3003 1 0.

Step 7 – Required Steel

minP max 0.39% , 0.50% , 0.52% 0.52%

min s2min 2

b

0.52 100 144 9.P 10 50 W DN 16.1

4 04 .75

max s2max 2

b

0.66 100 144 9.P 10 50 W DN 20.4

4 04 .75

min smin 22

b

P 100 W D 0.52 100 144 9.5N 16.1

4 4 0.75

max smax 22

b

P 100 W D 0.66 100 144 9.5N 20.4

4 4 0.75

Solution

16.1 N 20.4

Choose N 18 bars

22b

s

N 4 18 4 0.75P 0.58%

0.01 W D 0.01 144 9.5

Crack Spacing

1.156.702.19t s

bc

5.204.60 1.79w

c

f1.32 1 1 11000 2

X1 1 P 1 1000

1000

6.70 1.15 2.19

5.20 4.60 1.79

1.32 1 0.6 1 0.5 1 0.75X 4.3

1 0.23 1 0.58 1 0.3

Crack Width

6.532.20t

b

4.914.55w

f0.00932 1 11000CW

1 1 P1000

6.53 2.20

4.91 4.55

0.00932 1 0.6 1 0.75CW 0.03

1 0.23 1 0.58

Steel Working Stress

4.09 0.425t d

s 3.142.74 0.494w

c

f T47,300 1 11000 100

1 1 P 1 10001000

4.09 0.425

s 3.14 2.74 0.494

47,300 1 0.6 1 0.651,707 psi

1 0.23 1 0.58 1 0.3

Reinforcement Spacing


Bar Size #5 #6 #7 #8

Spacing(in) 5 6 7 5 6 7 8 9 6 7 8 9 6 7 8 9

Slab

Thickne

ss (in)

8 0.77% 0.64% 0.55% 0.92% 0.79% 0.69% 0.61% 0.94% 0.84%

9 0.68% 0.57% 0.98% 0.82% 0.70% 0.61% 0.95% 0.84% 0.74% 0.97%

10 0.61% 0.51% 0.88% 0.74% 0.63% 1.00% 0.86% 0.75% 0.67% 0.98% 0.87%

11 0.56% 0.80% 0.67% 0.57% 0.91% 0.78% 0.68% 0.89% 0.79%

11.5 0.53% 0.77% 0.64% 0.87% 0.75% 0.65% 0.98% 0.85% 0.76%

12 0.51% 0.74% 0.61% 0.84% 0.72% 0.93% 0.82%

13 0.68% 0.57% 0.77% 0.66% 1.01% 0.86% 0.76%

Skewed Lap Splices


Staggered Lap Splices

Source: Caltrans Continuously Reinforced Concrete Pavement (CRCP) Design & Construction Guide

Tie Bars

TieBar

Tie Bars

TieBar

Tie Bar Spacing

c avgbar

sbar s

L f hAAs f

23 yf

fy = 40,000 or 60,000 psi

Steel Reinforcing Bar

55

Tie Bar Spacing

c avgbar

sbar s

L f hAAs f

56

2

4

s bar s

barc avg c avg

f A d fsL f h L f h

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

57

Tie Bar Spacing

L'

L'

L distance to nearest free edge58

Tie Bar Spacing

L'

L'

L distance to nearest free edge59

Tie Bar Spacing

L distance to nearest free edge

L'

L'

60

Tie Bar Length

allowable bond stress (assume 350 psi)allowable bar stress (2/3 of yield stress)bar diameter (in)additional length for misalignment (3 in)

s

a

fd

12

sa

f dt

61

Transverse Reinforcement

TransverseSteel

Transverse Reinforcement

TransverseSteel

Percent Transverse Steel

2 c avgbar

sbar s

s f hA WA

s f

64

100%2

c s avgss

s

W fAPh f

Transverse Steel Spacing

22

4 2 s

bars c s avg

d fdsP h W f h

65

bar diameterslab thickness (in)slab width (in)

s

dh

W

Documents

22 - CRCP Reinforcement - CRCP Reinforcement.pdf · 700 or more 0.0002 Average 0.0005 AASHTO Pavement Design Guide. Concrete Thermal Coefficient Aggregate Type Coefficient (10-6 in/in/oF)