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The Use of AASHTO LRFD The Use of AASHTO LRFD Bridge Design Specifications with Bridge Design Specifications with CulvertsCulvertsCulvertsCulverts
Josh BeakleyJosh BeakleyNovember, 2010November, 2010
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 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”
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
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
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
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.
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
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
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
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.”
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[ ]
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
“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 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 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.
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.
Load Modifier - Culverts
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.
Load Modifier - Culverts
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 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)
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.
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?)
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
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 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