2010-11.1 LRFD Effect DOTs and RCP

The Use of AASHTO LRFD The Use of AASHTO LRFD Bridge Design Specifications with Bridge Design Specifications with CulvertsCulvertsCulvertsCulverts

Josh BeakleyJosh BeakleyNovember, 2010November, 2010

2

LRFD is Required

June 28th, 2000 FHWA Memo

AASHTO AASHTO DesignDesignSpecificationsSpecificationsSpecificationsSpecifications

AASHTO Standard SpecificationsAASHTO Standard Specifications for Highway Bridges Section 3 Section 3 –– LoadsLoads Section 6Section 6 –– CulvertsCulverts Section 6 Section 6 CulvertsCulverts Section 8 Section 8 –– Reinforced ConcreteReinforced Concrete

S ti 12S ti 12 S ilS il C t d M t lC t d M t l Section 12 Section 12 –– SoilSoil--Corrugated Metal Corrugated Metal Structure Interaction SystemsStructure Interaction Systems

Section 16 Section 16 –– SoilSoil--Reinforced Concrete Reinforced Concrete Structure Interaction SystemsStructure Interaction Systems

Section 17 Section 17 –– SoilSoil--Thermoplastic Pipe Thermoplastic Pipe Interaction SystemsInteraction Systems

AASHTO LRFD Bridge DesignAASHTO LRFD Bridge Design Specifications Section 3 Section 3 –– Loads and Load FactorsLoads and Load Factors Section 4Section 4 –– Structural Analysis andStructural Analysis and Section 4 Section 4 Structural Analysis and Structural Analysis and

EvaluationEvaluation Section 5Section 5 Concrete StructuresConcrete Structures Section 5 Section 5 –– Concrete StructuresConcrete Structures Section 12 Section 12 –– Buried Structures and Tunnel Buried Structures and Tunnel

LiLiLinersLiners

Structures Designed Per Section 12

Section 12.7 Section 12.7 -- Metal Pipe, Pipe Arch, and Metal Pipe, Pipe Arch, and Arch StructuresArch Structures

Section 12.8 Section 12.8 -- LongLong--Span Structural Plate Span Structural Plate StructuresStructuresStructuresStructures

Section 12.9 Section 12.9 -- Structural Plate Box Structural Plate Box StructuresStructuresStructuresStructures

Section 12.12 Section 12.12 –– Thermoplastic PipesThermoplastic Pipes Section 12.13 Section 12.13 –– Steel Tunnel Liner PlateSteel Tunnel Liner Plate

Concrete Structures Designed PerConcrete Structures Designed Per Section 12 Section 12.10 Section 12.10 –– Reinforced Concrete PipeReinforced Concrete Pipe Section 12.11Section 12.11 -- Precast Box Culverts, CastPrecast Box Culverts, Cast-- Section 12.11 Section 12.11 Precast Box Culverts, CastPrecast Box Culverts, Cast

inin--place Box Culverts, Castplace Box Culverts, Cast--inin--place Archesplace Arches Section 12 14Section 12 14 Precast ThreePrecast Three SidedSided Section 12.14 Section 12.14 -- Precast ThreePrecast Three--Sided Sided

StructuresStructures

What We Will Discuss

LoadsLoads Load FactorsLoad Factors Load FactorsLoad Factors Load ModifiersLoad Modifiers

C it C l l tiC it C l l ti Capacity CalculationsCapacity Calculations

Live LoadLive Load

Live Load

3.6.1.2 Design Vehicular Live Load3.6.1.2 Design Vehicular Live Load3.6.1.2.1 General3.6.1.2.1 General3.6.1.2.1 General3.6.1.2.1 General“Vehicular live loading on the roadways “Vehicular live loading on the roadways

of bridges or incidental structuresof bridges or incidental structuresof bridges or incidental structures, of bridges or incidental structures, designated HLdesignated HL--93, shall consist of a 93, shall consist of a combination of:combination of:combination of:combination of:Design truck or design tandem, andDesign truck or design tandem, andDesign lane loadDesign lane load

Live Load Spacing – HL-934000 lb.

14 f6 f

12,500 lb. 12,500 lb.

14 ft.6 ft.

12,500 lb. 12,500 lb.

16000 lb. 16000 lb.

AASHTO AASHTO (12,00 lb per STD)

HS 20 LOAD ALTERNATE LOAD

Applied Live loads – No Lane Load 3 6 1 3 3 Design Loads for Decks Deck3 6 1 3 3 Design Loads for Decks Deck 3.6.1.3.3 Design Loads for Decks, Deck 3.6.1.3.3 Design Loads for Decks, Deck

Systems, and the Top Slabs of Box CulvertsSystems, and the Top Slabs of Box Culverts Where the slab spans primarily in the Where the slab spans primarily in the

longitudinal direction:longitudinal direction:longitudinal direction:longitudinal direction: For top slabs of box culverts of all spans and For top slabs of box culverts of all spans and

for all other cases, including slabfor all other cases, including slab--type type bridges where the span does not exceed 15 0bridges where the span does not exceed 15 0bridges where the span does not exceed 15.0 bridges where the span does not exceed 15.0 ft, only the axle loads of the design truck or ft, only the axle loads of the design truck or design tandem of Articles 3.6.1.2.2 and design tandem of Articles 3.6.1.2.2 and 3 6 1 2 3 respectively shall be applied3 6 1 2 3 respectively shall be applied3.6.1.2.3, respectively, shall be applied.3.6.1.2.3, respectively, shall be applied.

Applied Live loads – No Lane Load

3 6 1 3 3 D i L d f D k D k3 6 1 3 3 D i L d f D k D k 3.6.1.3.3 Design Loads for Decks, Deck 3.6.1.3.3 Design Loads for Decks, Deck Systems, and the Top Slabs of Box Systems, and the Top Slabs of Box CulvertsCulvertsCulvertsCulvertsWhere the slab spans primarily in the Where the slab spans primarily in the

transverse direction, only the axles of transverse direction, only the axles of the design truck of Article 3.6.1.2.2 or the design truck of Article 3.6.1.2.2 or design tandem of Article 3.6.1.2.3 design tandem of Article 3.6.1.2.3 shall be applied to the deck slab or theshall be applied to the deck slab or theshall be applied to the deck slab or the shall be applied to the deck slab or the top of box culverts.top of box culverts.

Lane Load – 3.6.1.3 LRFDLRFD –– 20042004 –– Truck and Lane LoadTruck and Lane Load LRFD LRFD 2004 2004 Truck and Lane LoadTruck and Lane Load

64 lbs across a 10 ft width64 lbs across a 10 ft widthDLA not appliedDLA not appliedDLA not appliedDLA not applied

LRFD LRFD –– 2005 2005 –– Truck onlyTruck onlySt d d S ifi tiSt d d S ifi ti 3 7 1 13 7 1 1 Standard Specification Standard Specification –– 3.7.1.13.7.1.1Either truck or Lane LoadEither truck or Lane LoadTruck governs for shorter spansTruck governs for shorter spans

Pipe Culverts

Lane Loads not applied to pipeLane Loads not applied to pipe For top slabs of box culverts of all spans and For top slabs of box culverts of all spans and for all for all

other cases, including slabother cases, including slab--type bridges where the span type bridges where the span does not exceed 15.0 ft,does not exceed 15.0 ft, only the axle loads of the only the axle loads of the design truck or design tandem of Articles 3.6.1.2.2 anddesign truck or design tandem of Articles 3.6.1.2.2 anddesign truck or design tandem of Articles 3.6.1.2.2 and design truck or design tandem of Articles 3.6.1.2.2 and 3.6.1.2.3, respectively, shall be applied.3.6.1.2.3, respectively, shall be applied.

HistoryHistoryyy

Tire Footprint

LRFD LRFD –– 3.6.1.2.63.6.1.2.6w = 20 in.w = 20 in.w 20 in.w 20 in. l = 10 in.l = 10 in.

St d d S ifi tiSt d d S ifi ti 6 4 16 4 1 Standard Specification Standard Specification –– 6.4.16.4.1“Concentrated Load” “Concentrated Load”

Box Under Shallow FillBox Under Shallow Fill Distribution Width

Distribution Width

LRFD (4.6.2.10)LRFD (4.6.2.10)E = 96 + 1.44S (for axle)E = 96 + 1.44S (for axle)E 96 + 1.44S (for axle)E 96 + 1.44S (for axle)E in inches and S in feetE in inches and S in feet

St d d (3 24 3 2)St d d (3 24 3 2) Standard (3.24.3.2)Standard (3.24.3.2)E = 4 + 0.06S (for wheel)E = 4 + 0.06S (for wheel)E in feet and S in feetE in feet and S in feet

Distribution Steel

Live Load Distribution Parallel to Box Culvert Span under Shallow FillFill

Live Load Distribution

STD Spread a = a + 1 75*H STD Spread b = b + 1 75*HSTD – Spread a = a + 1.75*HLRFD – Spread a = a + 1.15*H

STD – Spread b = b + 1.75*HLRFD – Spread b = b +1.15*H

Pipe Under Shallow Fill

Live Load Area for Depths ≥ 2 ft.

LRFD (3.6.1.2.6) LRFD (3.6.1.2.6) AALL = (20/12 + 1.15D= (20/12 + 1.15DEE)(10/12 + 1.15D)(10/12 + 1.15DEE))AALL (20/12 + 1.15D (20/12 + 1.15DEE)(10/12 + 1.15D)(10/12 + 1.15DEE))

1.15 above should be replaced with 1.0 1.15 above should be replaced with 1.0 if select granular backfill is not usedif select granular backfill is not usedif select granular backfill is not usedif select granular backfill is not used

Standard (6.4.1)Standard (6.4.1)AALL = (1.75D= (1.75DEE))22

Live Load Spread

Dynamic Load Allowance

LRFD LRFD –– Dynamic Load Allowance (3.6.2.2)Dynamic Load Allowance (3.6.2.2)DLA = 0.33(1.0DLA = 0.33(1.0 -- 0.125D0.125DEE))DLA 0.33(1.0 DLA 0.33(1.0 0.125D0.125DEE))

Standard Standard –– Impact Factor (3.8.2.3)Impact Factor (3.8.2.3)IM 0 3IM 0 3 0’0’ 0” t 1’0” t 1’ 0” INCL0” INCL IM = 0.3 IM = 0.3 –– 0’0’--0” to 1’0” to 1’--0” INCL.0” INCL.

IM = 0.2 IM = 0.2 –– 1’1’--1” to 2’1” to 2’--0” INCL.0” INCL. IM = 0.1 IM = 0.1 –– 2’2’--1” to 2’1” to 2’--11” INCL.11” INCL.

Two Trucks Passing

Live Load Distribution throughLive Load Distribution through Pipe and Soil

Multiple Presence FactorMultiple Presence Factor

Design CodeDesign Code

Lanes AASHTO AASHTO CHBDCSTD LRFD

1 1.0 1.2 1.0

2 1.0 1.0 0.90

3 0.90 0.85 0.80

4 0 75 0 65 0 704 0.75 0.65 0.70

Box Culverts – Shallow Fill

Design Using Single Lane

Soil Load

FrictionalSoil P i

FrictionalSoil P i

ForcesPrism

ForcesPrism

N t l G d N t l G dNatural Ground Natural Ground

Soil Load

WWEE = = FFeessBBccHHBoxes Boxes –– Section 12.11.2.2.1Section 12.11.2.2.1Pipe Pipe –– Section 12.10.2.1Section 12.10.2.1

Soil-Structure Interaction FactorSoil Structure Interaction FactorBoxes WWEE = = FFeessBBccHH

FFee = 1 + 0.20(H/= 1 + 0.20(H/BBcc))ee (( cc))FFee shall not exceed 1.15 for installations shall not exceed 1.15 for installations

with compacted fill along the sides of with compacted fill along the sides of p gp gthe box section, or 1.40 for installations the box section, or 1.40 for installations with with uncompacteduncompacted fillfill

Soil-Structure Interaction FactorSoil Structure Interaction FactorPipe “Standard installations for both “Standard installations for both

embankments and trenches shall be embankments and trenches shall be designed for positive projection, designed for positive projection, embankment loading conditions where Fembankment loading conditions where Feegg eeshall be taken as the vertical arching factor, shall be taken as the vertical arching factor, VAF, specified in Table 12.10.2.1VAF, specified in Table 12.10.2.1--3 for 3 for ppeach type of standard installation.”each type of standard installation.”

www.concrete-pipe.org

AASHTO LRFD 12 10 2 1AASHTO LRFD 12.10.2.1

Vertical Pressures and Reactions

Vertical Soil Load

0.81.21.6

2

VAFi

1 2 3 4 5 6 7 80

0.4

li

“Bedding and Fill Heights for Concrete Roadway PipeAnd Box Culverts” – C. Yoo, F. Parker, and J. Kang,Auburn University, June 2005

Bottom Reaction to VerticalBottom Reaction to Vertical Loads

LRFD (C12.11.2.3)

“While typical designs assume a uniform “While typical designs assume a uniform pressure distribution across the bottom slab, pressure distribution across the bottom slab, p ,p ,a refined analysis that considers the actual a refined analysis that considers the actual soil stiffness under box sections will result soil stiffness under box sections will result in pressure distributions that reduce bottom in pressure distributions that reduce bottom slab shear and moment forces (McGrath et slab shear and moment forces (McGrath et ((al. 2004.”al. 2004.”

LRFD C12.11.2.3

“Such an analysis requires knowledge of in“Such an analysis requires knowledge of in--situ soil properties to select the appropriate situ soil properties to select the appropriate p p pp pp p pp pstiffness for the supporting soil. A refined stiffness for the supporting soil. A refined analysis taking this into account may be analysis taking this into account may be y g yy g ybeneficial when analyzing existing beneficial when analyzing existing culverts.”culverts.”

Pipe Pressure Distribution

Lateral Live Load

LRFD (3.11.6.2)LRFD (3.11.6.2)“The horizontal pressure“The horizontal pressure hh in ksf, on ain ksf, on a The horizontal pressure The horizontal pressure phph in ksf, on a in ksf, on a

wall resulting from a point load may be wall resulting from a point load may be taken as:”taken as:”taken as:taken as:

P 3ZX2 R (1 2)[ ]ph =PR2

3ZX2

R3

R (1 - 2)R + Z[ ]

B i Di t ib tiBoussinesq Distribution

Live Load Lateral Uniform Pressure

LRFD LRFD –– 3.11.6.4 3.11.6.4 ΔΔpp = K = K γγss hheqeqpp γγss eqeq

H H << 5 ft 5 ft –– hheqeq = 4 ft= 4 ftHH << 10 ft10 ft –– hh = 3 ft= 3 ftH H 10 ft 10 ft hheqeq 3 ft 3 ftH H << 20 ft 20 ft –– hheqeq = 2 ft= 2 ft

Lateral Uniform Live Load

“In general, LRFD produces greater live load surchargepressures than Standard for depths of fill of 5 ft or less and less pressure for greater depths In addition live loadless pressure for greater depths. In addition, live load surcharge pressures from AASHTO M 259 and M 273 are much greater than those from LRFD for depths of fill from 0 1 f d l h LRFD f fill h i h I0 to 1 ft and less than LRFD for greater fill heights. Inspite of the significant differences in live load surchargepressures, their impact on reinforcement areas is relatively p p yminor”

“Comparison of AASHTO Standard and LRFD Code Provisions for Buried Concrete Box C l t ” R R d & T M G th STP 1368Culverts” – R. Rund & T. McGrath, STP 1368, 2000, Concrete Pipe for the New Millenium

Lateral Earth Pressure

Lateral Earth Load - LRFD

3.11.5.5 3.11.5.5 –– Equivalent Fluid MethodEquivalent Fluid MethodLoose Sand or Gravel = 55 pcfLoose Sand or Gravel = 55 pcfLoose Sand or Gravel 55 pcfLoose Sand or Gravel 55 pcfDense Sand or Gravel = 45 pcfDense Sand or Gravel = 45 pcf

3 11 5 23 11 5 2 At R t PAt R t P 3.11.5.2 3.11.5.2 –– At Rest PressureAt Rest Pressurekkoo = 1= 1--sinsin

= 30= 30°°, k, koo = 0.5, press = 60 pcf= 0.5, press = 60 pcf

Other Loads

Always ConsideredAlways ConsideredSelf WeightSelf WeightSelf WeightSelf Weight Internal Fluid LoadInternal Fluid Load

S ti C id dS ti C id d Sometimes ConsideredSometimes ConsideredConstruction LoadsConstruction LoadsExternal Hydrostatic LoadsExternal Hydrostatic Loads Internal Fluid PressureInternal Fluid Pressure Internal Fluid PressureInternal Fluid Pressure

Load FactorsLoad Factors

Load FactorsLoad Load Factor

Standard LRFDMinimum MaximumMinimum Maximum

Dead 1.3 0.90 1.25Water 1.3 1.0 1.0E h V i l 1 3 0 90 1 30Earth – Vertical 1.3 0.90 1.30Earth - Horizontal 1.3 0.90* 1.35Live 1.3 x 1.67 = 2.17 0.0 1.75**

*Per 3.11.7, a 50% reduction in load may be used in lieu of the minimum load factorthe minimum load factor.**A multiple presence factor is included in the total load.

LRFD Design

Phi Factors

Strength Reduction FactorsStrength Reduction Factorsff = 1.0= 1.0ff 1.0 1.0vv = 0.9= 0.9

LRFDLRFD 12 5 512 5 5 11LRFD LRFD –– 12.5.512.5.5--11Standard Standard –– 16.7.4.616.7.4.6

“Basis of LRFD Methodology”

ηηiiiiQQii << RRnn

i = a statistically based load factor = a statistically based resistance factorQi = force effectRn = nominal resistancenηi = load modifier relating to ductility,

redundancy, and operational importancey, p p

Load Modifier - Culverts

LRFD 12.5.4LRFD 12.5.4“Load modifiers shall be applied to“Load modifiers shall be applied to Load modifiers shall be applied to Load modifiers shall be applied to

buried structures and tunnel liners as buried structures and tunnel liners as specified in Article 1.3, except that thespecified in Article 1.3, except that thespecified in Article 1.3, except that the specified in Article 1.3, except that the load modifiers for construction loads load modifiers for construction loads shall be taken as 1.0”shall be taken as 1.0”shall be taken as 1.0shall be taken as 1.0

Load Modifiers

LRFD C 1.3.2.1LRFD C 1.3.2.1“Ductility, redundancy, and operational“Ductility, redundancy, and operational Ductility, redundancy, and operational Ductility, redundancy, and operational

importance are significant aspects importance are significant aspects affecting the margin of safety of bridges.”affecting the margin of safety of bridges.”affecting the margin of safety of bridges.affecting the margin of safety of bridges.

Load Modifiers (LRFD)Load Modifiers (LRFD)For Culverts Standard = N/AStandard = N/A LRFD (1.3.2)LRFD (1.3.2) LRFD (1.3.2)LRFD (1.3.2)

Ductility = Ductility = ηηDD = 1.0= 1.0R d dR d d 1 05 1 01 05 1 0Redundancy = Redundancy = ηηRR = 1.05 or 1.0= 1.05 or 1.0

Importance = Importance = ηηII = 1.0 or 1.05= 1.0 or 1.05

Load Modifier Culverts

LRFD 1.3.3 LRFD 1.3.3 –– DuctilityDuctility“The structural system of a bridge shall“The structural system of a bridge shall The structural system of a bridge shall The structural system of a bridge shall

be proportioned and detailed to ensure the be proportioned and detailed to ensure the development of significant and visibledevelopment of significant and visibledevelopment of significant and visible development of significant and visible inelastic deformations at the strength and inelastic deformations at the strength and extreme event limit states before failure.”extreme event limit states before failure.”extreme event limit states before failure.extreme event limit states before failure.


LRFD 12.5.4 LRFD 12.5.4 -- RedundancyRedundancy“For strength limit states, buried“For strength limit states, buried For strength limit states, buried For strength limit states, buried

structures shall be considered structures shall be considered nonredundantnonredundant (1.05)(1.05) under earth fill andunder earth fill andnonredundantnonredundant (1.05) (1.05) under earth fill and under earth fill and redundant redundant (1.0) (1.0) under live load and under live load and dynamic load allowance.”dynamic load allowance.”dynamic load allowance.dynamic load allowance.


LRFD 12.5.4 LRFD 12.5.4 -- ImportanceImportance“Operational importance shall be“Operational importance shall be Operational importance shall be Operational importance shall be

determined on the basis of continued determined on the basis of continued function and/or safety of the roadway.”function and/or safety of the roadway.”function and/or safety of the roadway.function and/or safety of the roadway.

Design CapacityDesign Capacity

Design for: FlexureFlexure

Steel ReinforcementSteel ReinforcementConcrete CompressionConcrete Compression

Crack ControlCrack Control Crack ControlCrack Control ShearShear Radial Tension (for pipe only)Radial Tension (for pipe only) Fatigue (not required for box culverts or Fatigue (not required for box culverts or

pipe per LRFD)pipe per LRFD)

Box Culverts and Pipe

Section 12.10 Section 12.10 –– Reinforced Concrete PipeReinforced Concrete Pipe Section 12.10.4.2 Section 12.10.4.2 –– Direct Design Direct Design –– AAss = ?= ?gg ss

Section 12.10.4.3 Section 12.10.4.3 –– Indirect Design Indirect Design –– Class = ?Class = ? Section 12 11Section 12 11 -- Precast Box CulvertsPrecast Box Culverts Section 12.11 Section 12.11 -- Precast Box CulvertsPrecast Box Culverts

Flexure

Asig f d Nu g g f d 2 Nu 2 f d t 2 Mu

f

fy

E ti 12 10 4 2 4 1 F Di t D i f PiEquation 12.10.4.2.4a-1 – For Direct Design of Pipe

Section 5.7.2 – Assumptions for Strength and Extreme EventLimit States takes a broader view of flexural design

Flexure (Minimum Steel)Flexure (Minimum Steel)LRFD - 12.11.4.3.2: STD - 16.7.4.8

AsAsminmin = 0.002 b h= 0.002 b hb = 12 inch unit widthb = 12 inch unit widthb 12 inch unit widthb 12 inch unit widthh = thickness of member in inchesh = thickness of member in inches

LRFD (12 11 4 3 2)LRFD (12 11 4 3 2) LRFD (12.11.4.3.2)LRFD (12.11.4.3.2) Standard (16.7.4.8)Standard (16.7.4.8)

ACI 318-08ACI 318 08

Flexure (maximum steel)

Box culvert walls and slabs are designed as Box culvert walls and slabs are designed as tension controlled members, with a tension controlled members, with a ,,maximum steel area of 75% of the balanced maximum steel area of 75% of the balanced condition (steel will always yield before condition (steel will always yield before ( y y( y yconcrete crushes)concrete crushes)

Compression controlled design is allowedCompression controlled design is allowed Compression controlled design is allowed Compression controlled design is allowed with other concrete structures as long as a with other concrete structures as long as a modified phi factor is applied.modified phi factor is applied.modified phi factor is applied.modified phi factor is applied.

Tension Controlled - Ductile

Crack Control (LRFD – 5.7.3.4)

s700 e

f2 dc

s fs

LRFD Concerns itself with steel spacingLRFD Concerns itself with steel spacing Standard Specification concerns itself withStandard Specification concerns itself with Standard Specification concerns itself with Standard Specification concerns itself with

stress in the steel (maximum of 0.6 fy?)stress in the steel (maximum of 0.6 fy?)

Service Load Stress

M N dh

fs

Ms Ns d2

s As j i d

Equation C12 11 3 1Equation C12.11.3-1

Factors affecting crack control

Exposure Conditions

SHEARSHEAR

ShearLRFD – 5.14.5.3: STD – 8.16.6.7LRFD 5.14.5.3: STD 8.16.6.7

Slabs under 2 feet or more of fill

V 0 0676 f'c 4 6As

Vu de

b d

Slabs under 2 feet or more of fill

Vc 0.0676 f c 4.6b de Mu

b de

Need not be taken less thanNeed not be taken less than

Vc 0.0948 f'c b d e

Equivalent to = 3

ShearLRFD 5 8 3 3 STD 8 16 6 2 1LRFD – 5.8.3.3: STD – 8.16.6.2.1Slabs with less than two feet of cover, and sidewalls

V 0 0316 f'c b d

and sidewalls

Vc 0.0316 f c bv dv

is based on the dimensions of the element and the strain in the steel

ShearLRFD 5 8 3 3 STD 8 16 6 2 1LRFD – 5.8.3.3: STD – 8.16.6.2.1Slabs with less than two feet of cover, and sidewalls

F ti ith ll d th l th 16 i hFor sections with an overall depth less than 16 inches, and no tension, can be assumed equal to 2

Top Slab

12X12 @20’12X12 @20’

Side Wall

12X12 @ 20’@

Distribution Steel

Distribution Steel

In bottom of top slab (LRFD 9.7.3.2)In bottom of top slab (LRFD 9.7.3.2)Percentage of main positive momentPercentage of main positive momentPercentage of main positive moment Percentage of main positive moment

reinforcement = 100/Sreinforcement = 100/S1/21/2

S = span in feetS = span in feetS = span in feetS = span in feetNeed not be more than 50 percentNeed not be more than 50 percent

In top of top slabIn top of top slabAsAs66 = 0.002 x Ag= 0.002 x Ag66 gg

CONCRETE PIPE DESIGNCONCRETE PIPE DESIGN

Concrete Pipe Indirect Design – 12.10.4.3D-Load Equation


E th L d B ddi F tEarth Load Bedding Factor

Extra Safety Factor for Type 1 InstallationsInstallations


Live Load Bedding Factor

Pipe Indirect DesignD-Load Equation


Class V Pipe (C76/M 170)

Concrete Pipe Special Design/Direct DesignSpecial Design/Direct Design –12.10.4.2 Flexure Flexure –– 12.10.4.2.4.a & b12.10.4.2.4.a & b Radial TensionRadial Tension –– 12.10.4.2.4c12.10.4.2.4c Radial Tension Radial Tension 12.10.4.2.4c12.10.4.2.4c Crack Control Crack Control –– 12.10.4.2.4d12.10.4.2.4d

ShSh 12 10 4 2 512 10 4 2 5 Shear Shear –– 12.10.4.2.512.10.4.2.5

FLEXURE CRACK CONTROL

RADIAL TENSIONSHEAR

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2010-11.1 LRFD Effect DOTs and RCP

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