Direct Design and IndirectDirect Design and IndirectDirect Design and Indirect Direct Design and Indirect Design of Concrete PipeDesign of Concrete Pipe

Part 1Part 1

Josh BeakleyJosh BeakleyJosh BeakleyJosh BeakleyMarch 2011March 2011

Why are We Here?Why are We Here?Why are We Here?Why are We Here?

AASHTO LRFD Bridge DesignAASHTO LRFD Bridge DesignAASHTO LRFD Bridge Design AASHTO LRFD Bridge Design SpecificationsSpecifications

Metal PipeMetal Pipe Section 12 7Section 12 7–– Metal Pipe Metal Pipe –– Section 12.7Section 12.7–– Concrete Pipe Concrete Pipe –– Section 12.10Section 12.10

Plastic PipePlastic Pipe Section 12 12Section 12 12–– Plastic Pipe Plastic Pipe –– Section 12.12Section 12.12

AASHTO Section 12.10.1 AASHTO Section 12.10.1 GGGeneralGeneral

“The structural design of the types of pipes“The structural design of the types of pipesThe structural design of the types of pipes The structural design of the types of pipes indicated above may proceed by either of indicated above may proceed by either of two methods:two methods:two methods:two methods:–– The direct design method at the strength limit The direct design method at the strength limit

state as specified in Article 12 10 4 2 orstate as specified in Article 12 10 4 2 orstate as specified in Article 12.10.4.2, orstate as specified in Article 12.10.4.2, or–– The indirect design method at the service limit The indirect design method at the service limit

state as specified in Article 12.10.4.3.”state as specified in Article 12.10.4.3.”state as specified in Article 12.10.4.3.state as specified in Article 12.10.4.3.

Indirect Design MethodIndirect Design MethodIndirect Design MethodIndirect Design Method

For Special Cases, use the For Special Cases, use the Direct Design MethodDirect Design Method

Fill HeightsFill Heights –– Type 2 InstallationType 2 InstallationFill Heights Fill Heights Type 2 InstallationType 2 InstallationPipe Pipe SiSi

Class IIIClass III Class IVClass IV Class VClass VSize Size (in)(in) II DD II DD II DD

2424 1616 88 2525 2424 3939 30302424 1616 88 2525 2424 3939 3030

3636 1616 1414 2525 2222 3939 3030

4848 1616 1414 2525 2020 3939 2929

7272 1515 1414 2424 2020 3838 2626

I = Indirect Design in Accordance with AASHTO Section 12D = Direct Design in Accordance with AASHTO Section 12

Benefits of the Indirect Design Benefits of the Indirect Design MethodMethod

Its validity has been proven over timeIts validity has been proven over timeIts validity has been proven over timeIts validity has been proven over timeIt is a simple method to useIt is a simple method to useIt i fIt i f ff f th df th dIt is a proofIt is a proof--ofof--performance methodperformance method

Benefits of the Current Direct Benefits of the Current Direct Design MethodDesign Method

It is simple (relatively speaking)It is simple (relatively speaking)It is simple (relatively speaking)It is simple (relatively speaking)It is safeIt is safeIt iIt iIt is provenIt is proven

Intention for Direct DesignIntention for Direct DesignIntention for Direct DesignIntention for Direct Design

Used for higher strength pipe that can notUsed for higher strength pipe that can notUsed for higher strength pipe that can not Used for higher strength pipe that can not be found in ASTM C 76 Tablesbe found in ASTM C 76 TablesUsed for larger diameter pipesUsed for larger diameter pipesUsed for larger diameter pipesUsed for larger diameter pipesUsed for specific loads and load casesUsed for specific loads and load casesUsed when stirrup reinforcement is Used when stirrup reinforcement is requiredrequired

Some Factors for DifferenceSome Factors for DifferenceSome Factors for DifferenceSome Factors for Difference

Reinforcement ProportionsReinforcement ProportionsReinforcement ProportionsReinforcement ProportionsSize FactorSize FactorSt l R i f t P tiSt l R i f t P tiSteel Reinforcement PropertiesSteel Reinforcement PropertiesDouble ReinforcementDouble Reinforcement

Conservative DesignsConservative DesignsConservative DesignsConservative Designs

The simplification of the direct designThe simplification of the direct designThe simplification of the direct design The simplification of the direct design process for concrete pipe results in process for concrete pipe results in conservative designsconservative designsconservative designs.conservative designs.The designs are most conservative for The designs are most conservative for smaller diameter pipesmaller diameter pipesmaller diameter pipe.smaller diameter pipe.

0.60Asi

1 0 Asi

0.60Asi

1.0 Asi

≤ 36” ≤ 36” ≤ 66” > 66”

Reinforcement ProportionsReinforcement Proportions

R i f t P tiReinforcement Proportions

Aso = 0.6 Asi

Previously 0 75 APreviously - 0.75 Asi

Asi

Correction for Larger Springline Correction for Larger Springline ffReinforcingReinforcing

“A Theory for Structural Behavior of Reinforced Concrete Pipe”, Frank Heger, 1962

0.60Asi

1 0 Asi

0.60Asi

1.0 Asi

≤ 36” ≤ 36” ≤ 66” > 66”

Size FactorSize Factor

Mc = 0.318 Mc = 0.249 Mc = 0.324 Mc = 0.254

ThreeThree--Edge Bearing TestEdge Bearing TestThreeThree Edge Bearing TestEdge Bearing Test

M = 0.318 P r

Experimental vs FEM Results Pipe# 18SP

(72.73 psi)

(75 psi) (75 psi)(75 psi) ( p )

Location of First and Second CrackLocation of First and Second CrackLocation of First and Second CrackLocation of First and Second Crack

2nd Crack

1st Crack

2nd Crack

Small Diameter

Large Di t

1st Crack

Diameter Diameter

Mc = 0.318 Mc = 0.249 Mc = 0.324 Mc = 0.254

First Crack vs Second CrackFirst Crack vs Second CrackFirst Crack vs. Second CrackFirst Crack vs. Second Crack5000

D-load Required for Second Crack Versus Pipe Diameter

4000

4500

3000

3500

econ

d C

rack

Dcracki

Dl d

2000

2500

D-lo

ad a

t S

2000

Dloadi

500

1000

1500

12 15 18 21 24 27 30 33 36

Pipe Inside Diameter (inches)

Di

Nonreinforced Size FactorNonreinforced Size FactorNonreinforced Size FactorNonreinforced Size Factor

ASCE 27-00, “Standard Practice for Direct Design of Precast Concrete Pipe forJacking in Trenchless Construction”

“However, the author has also made experimental calculations based on the theory of plasticity and foundcalculations based on the theory of plasticity and found reasonably good correspondence with the test results although it seems unlikely that an unreinforced concrete pipe might be calculated in accordance with a theory of this kind.”

“After the occurrence of the first crack the pipe will not collapse however becausecollapse, however, becausea hinge is created at the crown.”

“Calculation of Unreinforced Concrete Pipes Based on a New Theory for the Rupture” John B Ingwersen Danish Concrete Industry AssociationRupture , John B. Ingwersen, Danish Concrete Industry, Association

We calculate the We calculate the moment at a specific moment at a specific location without any location without any

consideration of consideration of moment distribution moment distribution

as a result of the as a result of the pipe size or pipe size or

reinforcement reinforcement proportionsproportions

0.5 * P * rm = Msum

0.5*(DLu * Di/12) * Dm/2 = Msum( u i ) m sum

DLu = [48/(Di * Dm)] * Msum

“Experimental Evaluation of SIDD Design Procedures for Shear, RadialTension and Crack Width Control with Emphasis on Small Diameter ConcretePipe”, SG&H, 1993

Steel PropertiesSteel Properties

StressStress--Strain CurvesStrain CurvesStressStress Strain CurvesStrain Curves

Actual StressActual Stress--Strain CurvesStrain CurvesActual StressActual Stress Strain CurvesStrain Curves1 105

Stress vs. Strain

9.643 1040.005

7.5 104

8.75 104

75000

5 104

6.25 104St

ress

(psi

)65000

1i

2i

3i

2.5 104

3.75 104

0 0.002 0.004 0.006 0.008 0.010

1.25 104

0

0 010 1 2 3

Strain

0.010 1i 2i 3i

University of Nebraska ProposalUniversity of Nebraska ProposalPower Formula (Smooth Wire)

100

120

Power Formula (Smooth Wire)

60

80

ress

(ksi

)

20

40

St

00 0.5 1 1.5 2 2.5 3 3.5

Strain %

Q 1 puRR

pyss

sss fKfEQQEf

/1)/((1

1

fpu fpy Q Es R Kfpu fpy Q Es R K80 65 0 28310.54 2.2680 1.23847

Compression/Tension in BendingCompression/Tension in Bending

0 85*f` *b*a 0 85*f` *b*a

Stresses

0.85 f c b a 0.85 f c b a

N.A.

Asfs Asfs

Strains

N Ac = 0.003

N.A.

s = εy fs = fy

Neutral Axis IterationNeutral Axis IterationNeutral Axis IterationNeutral Axis Iteration

c = 0.003

C = 0.5” C = 0.6”C = 0.7”

c = 0.003

s = 0.007 s = 0.005s = 0.006

Mild Steel T = Asfy T = AsfyT = Asfy

Wire T = AsfsT = AsfsT = Asfs

Rebar versus WireRebar versus WireRebar versus WireRebar versus Wire1 105

Stress-Strain Curves

8 104

1 10

9.376 104

6 104

Stre

ss 1i

MSi

2 104

4 104

0 0.002 0.004 0.006 0.0080

0

9.6 10 30 1i 1i

Strain

We Force Ourselves to be We Force Ourselves to be Beyond the Yield PointBeyond the Yield Point

Rebar versus WireRebar versus WireRebar versus WireRebar versus Wire1 105

Stress-Strain Curves

9.376 104

“When tested the yield strength

4

8 104

When tested, the yield strength shall be determined at an extensionunder load of 0.0035 mm/mm (0.0035 in./in.)”

4 104

6 104

Stre

ss 1i

MSi “The material shall not exhibita definite yield point as evidenced

2 104

y pby a distinct drop of the beam orhalt in the gage of the testing machine prior to reaching ultimatetensile load ”

0 0.002 0.004 0.006 0.0080

Strain

0

9.6 10 30 1i 1i

tensile load.

ASTM A82. “Standard SpecificationF St l Wi Pl i f C tFor Steel Wire, Plain, for ConcreteReinforcement”

Crack ControlCrack Control

1 105Stress-Strain Curves

Work with Stresses Below Yield

8 104

1 10

9.376 104

6 104

Stre

ss 1i

MSi

2 104

4 104

0 0.002 0.004 0.006 0.0080

0

9.6 10 30 1i 1i

Strain

When Does Crack Control Kick When Does Crack Control Kick In?In?

University of Nebraska ProposalUniversity of Nebraska ProposalPower Formula (Smooth Wire)

100

120

Power Formula (Smooth Wire)

60

80

ress

(ksi

)

20

40

St

00 0.5 1 1.5 2 2.5 3 3.5

Strain %

Q 1 puRR

pyss

sss fKfEQQEf

/1)/((1

1

fpu fpy Q Es R Kfpu fpy Q Es R K80 65 0 28310.54 2.2680 1.23847

Double ReinforcementDouble Reinforcement

LRFD 5 7 3 2 Flexural ResistanceLRFD 5 7 3 2 Flexural ResistanceLRFD 5.7.3.2 Flexural ResistanceLRFD 5.7.3.2 Flexural Resistance

Concrete Design per AASHTO Concrete Design per AASHTO S 12S 12Section 12Section 12

0 85*f` *b*a *C0.85 f c b a a = 1*C

MuNu

AsfyAsfy

A Weakness of Equation 12.10.4.2.4aA Weakness of Equation 12.10.4.2.4a--qq1 1 –– One Layer of SteelOne Layer of Steel

UNO – Behavior and Design of Buried Concrete Pipe– 48 inch pipe

Strain DistributionStrain DistributionStrain DistributionStrain Distribution

Two CagesTwo CagesTwo CagesTwo Cagescu = 0.003

0 003

C

cu

yo C

cu = 0.003

oiyo

doi

d

ii ii

Small Diameter Pipe Large Diameter Pipe

36 inch Class III Pipe36 inch Class III Pipe36 inch Class III Pipe36 inch Class III PipeSecond Cage Flexure

1 105Stress-Strain Curves

9.376 104Neutral Axis C = 0.56 in

g

6 104

8 104

Stre

ss 1i

MSi

2 104

4 104

S

0

i

0 0.002 0.004 0.006 0.0080

Strain

0

9.6 10 30 1i 1i

72 inch Class III Pipe72 inch Class III Pipe72 inch Class III Pipe72 inch Class III PipeSecond Cage Crack Control

1 105Stress-Strain Curves

9.376 104Neutral Axis C = 1.15 in

g

6 104

8 104

Stre

ss 1i

MSi

2 104

4 104

S

0

i

0 0.002 0.004 0.006 0.0080

Strain

0

9.6 10 30 1i 1i

To Be Continued…..To Be Continued…..