22 - crcp reinforcement - crcp reinforcement.pdf · 700 or more 0.0002 average 0.0005 aashto...
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CRCP Reinforcement
JPCP
Source: WSDOT Pavement Guide Interactive CD-ROM
JRCP
Source: WSDOT Pavement Guide Interactive CD-ROM
CRCP
Source: WSDOT Pavement Guide Interactive CD-ROM
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
Source: FHWA/CRSI Continuously Reinforced Concrete Pavement Design & Construction Guidelines
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
Source: FHWA/CRSI Continuously Reinforced Concrete Pavement Design & Construction Guidelines
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