CRCP Reinforcement CRCP Source: WSDOT Pavement Guide Interactive - - PDF document

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CRCP Reinforcement CRCP

Source: WSDOT Pavement Guide Interactive CD-ROM

CRCP Reinforcement

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Design Variables

• Slab thickness, D (in)
• Slab width, Ws (in)
• Modulus of subgrade reaction, keff (psi/in)
• Design temperature drop, ΔTd (°F)
• Maximum wheel load magnitude, W (lb)
• Rebar diameter, φ (in)

Design Variables (cont.)

• Concrete thermal coefficient, αc (in/in/°F)
• Steel thermal coefficient, αs (in/in/°F)
• Concrete tensile strength, f′t (psi)
• Concrete shrinkage coefficient, Ζ (in/in)
• Allowable steel working stress, σs (psi)
• Tensile stress due to wheel loads, σw (psi)

Concrete thermal coefficient

3.8 Limestone 4.8 Basalt 5.3 Granite 6.0 Gravel 6.5 Sandstone 6.6 Quartz (10-6 in/in/°F) Aggregate Coefficient Type of Coarse Thermal

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Steel thermal coefficient

−

α = × °

6 s

5 10 in/in/ F Concrete Tensile Strength ′ =

t c

f 0.86 S Concrete shrinkage coefficient

0.0002 700 or more 0.0003 600 0.00045 500 0.0006 400 0.0008 300 or less (in/in) (psi) Coefficient Tensile Strength Shrinkage Indirect

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Allowable steel working stress

60,000 67,000 67,000 800 or more 59,000 65,000 67,000 700 58,000 63,000 67,000 600 56,000 61,000 67,000 500 55,000 60,000 67,000 400 54,000 57,000 65,000 300 or less

• No. 6
• No. 5
• No. 4

Indirect Tensile Strength (psi) Reinforcing Bar Size

Design Criteria

Minimum crack spacing = 3½‘

Minimize potential for punchouts

Maximum crack spacing = 8‘

Minimize potential for spalling

Maximum crack width = 0.04“

Minimize water infiltration and potential for spalling

Maximum allowable steel stress

Prevent failure of reinforcing steel

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Crack Spacing

( ) ( ) ( )

⎛ ⎞ ′ α ⎛ ⎞ + + + φ ⎜ ⎟ ⎜ ⎟ α ⎝ ⎠ ⎝ ⎠ = σ ⎛ ⎞ + + + ⎜ ⎟ ⎝ ⎠

1.15 6.70 2.19 t s c 5.20 4.60 1.79 w

f 1.32 1 1 1 1000 2 X 1 1 P 1 1000Z 1000

Minimum Crack Spacing

( ) ( ) ( )

⎛ ⎞ ′ α ⎛ ⎞ + + + φ ⎜ ⎟ ⎜ ⎟ α ⎝ ⎠ ⎝ ⎠ = − σ ⎛ ⎞ + + ⎜ ⎟ ⎝ ⎠

0.25 1.457 0.476 t s c max 1.13 0.217 0.389 w

3. f 1.062 1 1 1 1000 2 P 1 1 1 1000Z 1000 5 ft

Maximum Crack Spacing

( ) ( ) ( )

⎛ ⎞ ′ α ⎛ ⎞ + + + φ ⎜ ⎟ ⎜ ⎟ α ⎝ ⎠ ⎝ ⎠ = − σ ⎛ ⎞ + + ⎜ ⎟ ⎝ ⎠

0.25 1.457 0.476 t s c 1 min 1.13 0.217 0.389 w

8. f 1.062 1 1 1 1000 2 P 1 1 1 1000Z t 0 f 10

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Crack Width

( ) ( )

′ ⎛ ⎞ + + φ ⎜ ⎟ ⎝ ⎠ = σ ⎛ ⎞ + + ⎜ ⎟ ⎝ ⎠

6.53 2.20 t 4.91 4.55 w

f 0.00932 1 1 1000 CW 1 1 P 1000

Maximum Crack Width

( ) ( )

′ ⎛ ⎞ + + φ ⎜ ⎟ ⎝ ⎠ = − σ ⎛ ⎞ + ⎜ ⎟ ⎝ ⎠

1.435 0.484 t 2 min 1.079 0.220 w

f 0.04 .358 1 1 1000 P 1 1 1000 in

Steel Working Stress

( ) ( )

′ Δ ⎛ ⎞ ⎛ ⎞ + + ⎜ ⎟ ⎜ ⎟ ⎝ ⎠ ⎝ ⎠ σ = σ ⎛ ⎞ + + + ⎜ ⎟ ⎝ ⎠

4.09 0.425 t d s 3.14 2.74 0.494 w

f T 47,300 1 1 1000 100 1 1 P 1 1000Z 1000

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Maximum Steel Stress

( ) ( )

1.493 0.155 t d 3 min 1.146 0.365 0.180 w s c

f T 50.834 1 1 1000 100 P 1 1 1 1000 1000 ′ Δ ⎛ ⎞ ⎛ ⎞ + + ⎜ ⎟ ⎜ ⎟ ⎝ ⎠ ⎝ ⎠ = − σ ⎛ ⎞ + + δ ⎜ ⎟ ⎝ ⎠ σ

Required Steel

( )

1 2 3 min min min min

P max P ,P ,P =

( ) ( )

= π φ

min s min 2

P 100 W D N 4

( ) ( )

= π φ

max s max 2

P 100 W D N 4

Example

D = 9.5 in (from slab design) Ws = 144 in (from slab design) keff = 170 pci (from slab design) ΔTd = 60°F (from weather data) W = 20,000 lb (from loadometer data) f′t = 600 psi (from AASHTO T198) Limestone aggregate in concrete φ = 0.75 in (No. 6 bar assumed)

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Step 1

δc = αc = αs = σs = 0.003 in/in (Table 12.22) 3.8×10-6 in/in/°F (Table 12.23) 5×10-6 in/in/°F (default value) 58,000 psi (Table 12.24)

Step 2 – Steel Working Stress Step 3 – Min Crack Spacing

( ) ( ) ( ) ( ) ( ) ( )

+ + + = − = + +

1.457 0.25 0.476 max 1.13 0.217 0.389

3.5 f 1.062 1 0.6 1 0.66 1 0.75 P 1 0.70% 1 0.23 1 0.3 t

( ) ( ) ( )

0.25 1.457 0.476 t s b c max 1.13 0.217 0.389 w c

f 1.062 1 1 1 1000 2 P 1 1 1 1 3. 000 1000 5 ft ⎛ ⎞ ′ α ⎛ ⎞ + + + φ ⎜ ⎟ ⎜ ⎟ α ⎝ ⎠ ⎝ ⎠ = − σ ⎛ ⎞ + + δ ⎜ ⎟ ⎝ ⎠

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Step 4 – Max Crack Spacing

( ) ( ) ( ) ( ) ( ) ( )

+ + + = − = + +

1.457 0.25 0.476 1 min 1.13 0.217 0.389

8.0 1.062 1 0.6 1 0.66 1 0.75 P 1 0.42% 1 0.23 f 0.3 t 1

( ) ( ) ( )

0.25 1.457 0.476 t s b c 1 min 1.13 0.217 0.389 w c

f 1.062 1 1 1 1000 2 P 1 1 1 1 8. 000 1000 0 ft ⎛ ⎞ ′ α ⎛ ⎞ + + + φ ⎜ ⎟ ⎜ ⎟ α ⎝ ⎠ ⎝ ⎠ = − σ ⎛ ⎞ + + δ ⎜ ⎟ ⎝ ⎠

Step 5 – Max Crack Width

( ) ( )

1.435 0.484 t b 2 min 1.079 0.220 w

f 0.038 1 1 1000 P 1 0.04 i 1 1 00 n ′ ⎛ ⎞ + + φ ⎜ ⎟ ⎝ ⎠ = − σ ⎛ ⎞ + ⎜ ⎟ ⎝ ⎠ ( ) ( ) ( ) ( )

1.435 0.484 2 min 1.079 0.220

0.358 1 0.6 1 0.75 P 1 0.50% 1 0.2 0.04 in 3 + + = − = +

Step 6 – Max Steel Stress

( ) ( )

1.493 0.155 t d 3 min 1.146 0.365 0.180 w s c

f T 50.834 1 1 1000 100 P 1 1 1 1000 1000 ′ Δ ⎛ ⎞ ⎛ ⎞ + + ⎜ ⎟ ⎜ ⎟ ⎝ ⎠ ⎝ ⎠ = − σ ⎛ ⎞ + + δ ⎜ ⎟ ⎝ ⎠ σ ( ) ( ) ( ) ( ) ( )

1.493 0.155 3 min 1.146 0.365 0.180

50.834 1 0.6 1 0.6 P 1 0.52% 1 0.2 58,0 3 00 3 1 0. + + = − = + +

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Step 7 – Required Steel

( )

min

P max 0.39% , 0.50% , 0.52% 0.52% = =

( ) ( ) ( )( )( ) ( )( )

min s min 2 2 b

P 100 W D 0.52 100 144 9.5 N 16.1 4 4 0.75 = = = π φ π

( ) ( ) ( )( )( ) ( )( )

= = = π φ π

max s max 2 2 b

P 100 W D 0.70 100 144 9.5 N 21.7 4 4 0.75

Solution

< < 16.1 N 21.7 Choose N 18 bars = ( ) ( ) ( )( )( ) ( )( )( )

2 2 b s

N 4 18 4 0.75 P 0.58% 0.01 W D 0.01 144 9.5 π φ π = = =

Crack Spacing

( ) ( ) ( )

1.15 6.70 2.19 t s b c 5.20 4.60 1.79 w c

f 1.32 1 1 1 1000 2 X 1 1 P 1 1000 1000 ⎛ ⎞ ′ α ⎛ ⎞ + + + φ ⎜ ⎟ ⎜ ⎟ α ⎝ ⎠ ⎝ ⎠ = σ ⎛ ⎞ + + + δ ⎜ ⎟ ⎝ ⎠

( ) ( ) ( ) ( ) ( ) ( )

6.70 1.15 2.19 5.20 4.60 1.79

1.32 1 0.6 1 0.5 1 0.75 X 4.3 1 0.23 1 0.58 1 0.3 + + + ′ = = + + +

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Crack Width

( ) ( )

6.53 2.20 t b 4.91 4.55 w

f 0.00932 1 1 1000 CW 1 1 P 1000 ′ ⎛ ⎞ + + φ ⎜ ⎟ ⎝ ⎠ = σ ⎛ ⎞ + + ⎜ ⎟ ⎝ ⎠

( ) ( ) ( ) ( )

6.53 2.20 4.91 4.55

0.00932 1 0.6 1 0.75 CW 0.03 1 0.23 1 0.58 + + ′′ = = + +

Steel Working Stress

( ) ( )

4.09 0.425 t d s 3.14 2.74 0.494 w c

f T 47,300 1 1 1000 100 1 1 P 1 1000 1000 ′ Δ ⎛ ⎞ ⎛ ⎞ + + ⎜ ⎟ ⎜ ⎟ ⎝ ⎠ ⎝ ⎠ σ = σ ⎛ ⎞ + + + δ ⎜ ⎟ ⎝ ⎠

( ) ( ) ( ) ( ) ( )

4.09 0.425 s 3.14 2.74 0.494

47,300 1 0.6 1 0.6 51 ,707 psi 1 0.23 1 0.58 1 0.3 + + σ = = + + +